%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT126+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : 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 05:06:03 PM UTC 2026
% Result : Theorem 3.19s 5.73s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_609)
% Comments :
%------------------------------------------------------------------------------
fof(fact_RangeE,axiom,
! [X23,X19,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X12),c_Relation_ORange(X19,X7,X23)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X3),X12)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).
fof(fact_converse__rtranclE2,axiom,
! [X23,X48,X49,X50,X51,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X51),X50)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X49),X48))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X19),X23)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X7,X19),X51),X50) != hAPP(hAPP(c_Product__Type_OPair(X7,X19),X49),X48)
=> ~ ! [X21,X22] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X51),X50)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X21),X22))),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X21),X22)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X49),X48))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X19),X23))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
fof(fact_RangeP__Range__eq,axiom,
! [X4,X23,X19,X7] :
( c_Predicate_ORangeP(X7,X19,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),X7,c_COMBC(X19,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_prod(X7,X19)),tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X19),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool),X19,c_member(tc_prod(X7,X19)))),c_Product__Type_OPair(X7,X19)))),X23),X4)
<=> hBOOL(hAPP(hAPP(c_member(X19),X4),c_Relation_ORange(X7,X19,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_Range__def,axiom,
! [X23,X7,X19] : c_Relation_ORange(X19,X7,X23) = c_Relation_ODomain(X7,X19,c_Relation_Oconverse(X19,X7,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__def) ).
fof(fact_ImageE,axiom,
! [X9,X23,X19,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X12),hAPP(c_Relation_OImage(X19,X7,X23),X9)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X3),X12)),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(X19),X3),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ImageE) ).
fof(fact_compose__assoc,axiom,
! [X35,X36,X37,X38,X1,X39,X8,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X8))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X39)),X1),c_FuncSet_OPi(X19,X39,X8,c_COMBK(tc_fun(X39,tc_HOL_Obool),X19,X38))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X39,X37)),X36),c_FuncSet_OPi(X39,X37,X38,c_COMBK(tc_fun(X37,tc_HOL_Obool),X39,X35))))
=> c_FuncSet_Ocompose(X7,X39,X37,X9,X36,c_FuncSet_Ocompose(X7,X19,X39,X9,X1,X2)) = c_FuncSet_Ocompose(X7,X19,X37,X9,c_FuncSet_Ocompose(X19,X39,X37,X8,X36,X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__assoc) ).
fof(fact_compose__def,axiom,
! [X2,X1,X9,X19,X39,X7] : c_FuncSet_Ocompose(X7,X39,X19,X9,X1,X2) = c_FuncSet_Orestrict(X7,X19,hAPP(c_COMBB(X39,X19,X7,X1),X2),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__def) ).
fof(fact_funcset__compose,axiom,
! [X38,X1,X39,X8,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X8))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X39)),X1),c_FuncSet_OPi(X19,X39,X8,c_COMBK(tc_fun(X39,tc_HOL_Obool),X19,X38))))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X39)),c_FuncSet_Ocompose(X7,X19,X39,X9,X1,X2)),c_FuncSet_OPi(X7,X39,X9,c_COMBK(tc_fun(X39,tc_HOL_Obool),X7,X38)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__compose) ).
fof(fact_extensional__funcset__restrict__domain,axiom,
! [X52,X2,X19,X17,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X17))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional__funcset(X7,X19,hAPP(hAPP(c_Set_Oinsert(X7),X4),X17),X52)))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),c_Fun_Ofun__upd(X7,X19,X2,X4,c_HOL_Oundefined(X19))),c_FuncSet_Oextensional__funcset(X7,X19,X17,X52))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__restrict__domain) ).
fof(fact_converseE,axiom,
! [X23,X25,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),X25),c_Relation_Oconverse(X19,X7,X23)))
=> ~ ! [X3,X26] :
( X25 = hAPP(hAPP(c_Product__Type_OPair(X7,X19),X26),X3)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X3),X26)),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseE) ).
fof(fact_converse__tranclE,axiom,
! [X23,X20,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X20)),c_Transitive__Closure_Otrancl(X7,X23)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X20)),X23))
=> ~ ! [X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X26)),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X20)),c_Transitive__Closure_Otrancl(X7,X23))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__tranclE) ).
fof(fact_tranclE,axiom,
! [X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Otrancl(X7,X23)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23))
=> ~ ! [X62] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X62)),c_Transitive__Closure_Otrancl(X7,X23)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X62),X12)),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclE) ).
fof(fact_converse__rtranclE,axiom,
! [X23,X20,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X20)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( X4 != X20
=> ~ ! [X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X26)),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X20)),c_Transitive__Closure_Ortrancl(X7,X23))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE) ).
fof(fact_rtranclE,axiom,
! [X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( X13 != X12
=> ~ ! [X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X26)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X12)),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclE) ).
fof(fact_compose__extensional,axiom,
! [X1,X2,X9,X39,X19,X7] : hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),c_FuncSet_Ocompose(X7,X39,X19,X9,X2,X1)),c_FuncSet_Oextensional(X7,X19,X9))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__extensional) ).
fof(fact_Range__iff,axiom,
! [X23,X19,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),c_Relation_ORange(X19,X7,X23)))
<=> ? [X26] : hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X26),X13)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).
fof(fact_Id__compose,axiom,
! [X8,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X8))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional(X7,X19,X9)))
=> c_FuncSet_Ocompose(X7,X19,X19,X9,c_FuncSet_Orestrict(X19,X19,c_COMBI(X19),X8),X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__compose) ).
fof(fact_compose__Id,axiom,
! [X8,X9,X1,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X1),c_FuncSet_OPi(X7,X19,X9,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X8))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X1),c_FuncSet_Oextensional(X7,X19,X9)))
=> c_FuncSet_Ocompose(X7,X7,X19,X9,X1,c_FuncSet_Orestrict(X7,X7,c_COMBI(X7),X9)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__Id) ).
fof(fact_inj__on__insert,axiom,
! [X9,X13,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,hAPP(hAPP(c_Set_Oinsert(X7),X13),X9))
<=> ( c_Fun_Oinj__on(X7,X19,X2,X9)
& ~ hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X13)),c_Set_Oimage(X7,X19,X2,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__insert) ).
fof(fact_DomainE,axiom,
! [X23,X19,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),c_Relation_ODomain(X7,X19,X23)))
=> ~ ! [X26] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X26)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).
fof(fact_compose__id__inv__into,axiom,
! [X8,X9,X2,X7,X19] :
( c_Set_Oimage(X19,X7,X2,X9) = X8
=> c_FuncSet_Ocompose(X7,X19,X7,X8,X2,c_FuncSet_Orestrict(X7,X19,c_Hilbert__Choice_Oinv__into(X19,X7,X9,X2),X8)) = c_FuncSet_Orestrict(X7,X7,c_COMBI(X7),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__id__inv__into) ).
fof(fact_fun__upd__image,axiom,
! [X10,X2,X19,X9,X4,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Set_Oimage(X7,X19,c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X9) = hAPP(hAPP(c_Set_Oinsert(X19),X10),c_Set_Oimage(X7,X19,X2,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Set_Oimage(X7,X19,c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X9) = c_Set_Oimage(X7,X19,X2,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__image) ).
fof(fact_inj__on__fun__updI,axiom,
! [X4,X10,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X19),X10),c_Set_Oimage(X7,X19,X2,X9)))
=> c_Fun_Oinj__on(X7,X19,c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).
fof(fact_notin__Lin__iff,axiom,
! [X10,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))
=> ( X4 != 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),X4),X10)),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),X10),X4)),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X12,X13,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))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X13),X12)),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),X12),X13)),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_surj__compose,axiom,
! [X38,X1,X39,X8,X9,X2,X7,X19] :
( c_Set_Oimage(X19,X7,X2,X9) = X8
=> ( c_Set_Oimage(X7,X39,X1,X8) = X38
=> c_Set_Oimage(X19,X39,c_FuncSet_Ocompose(X19,X7,X39,X9,X1,X2),X9) = X38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__compose) ).
fof(fact_acyclic__insert,axiom,
! [X23,X4,X10,X7] :
( c_Wellfounded_Oacyclic(X7,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X4)),X23))
<=> ( c_Wellfounded_Oacyclic(X7,X23)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Ortrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__insert) ).
fof(fact_quotientE,axiom,
! [X23,X9,X64,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X64),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23)))
=> ~ ! [X3] :
( X64 = hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X3),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotientE) ).
fof(fact_not__acc__down,axiom,
! [X18,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),c_Wellfounded_Oacc(X7,X18)))
=> ~ ! [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X40),X4)),X18))
=> hBOOL(hAPP(hAPP(c_member(X7),X40),c_Wellfounded_Oacc(X7,X18))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).
fof(fact_Range__Diff__subset,axiom,
! [X8,X9,X19,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Relation_ORange(X19,X7,X9),c_Relation_ORange(X19,X7,X8)),c_Relation_ORange(X19,X7,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X19,X7),tc_HOL_Obool),X9,X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).
fof(fact_Range__Int__subset,axiom,
! [X8,X9,X19,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Relation_ORange(X19,X7,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X19,X7),tc_HOL_Obool),X9,X8)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),c_Relation_ORange(X19,X7,X9),c_Relation_ORange(X19,X7,X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
fof(fact_compose__eq,axiom,
! [X2,X1,X19,X39,X9,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_FuncSet_Ocompose(X7,X39,X19,X9,X1,X2),X4) = hAPP(X1,hAPP(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__eq) ).
fof(fact_Range__insert,axiom,
! [X23,X12,X13,X7,X19] : c_Relation_ORange(X19,X7,hAPP(hAPP(c_Set_Oinsert(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X13),X12)),X23)) = hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Relation_ORange(X19,X7,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__insert) ).
fof(fact_PiE,axiom,
! [X4,X8,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,X8)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X4)),hAPP(X8,X4)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
fof(fact_RangeI,axiom,
! [X23,X12,X13,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X12)),X23))
=> hBOOL(hAPP(hAPP(c_member(X19),X12),c_Relation_ORange(X7,X19,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).
fof(fact_irrefl__tranclI,axiom,
! [X4,X23,X7] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),c_Relation_Oconverse(X7,X7,X23),c_Transitive__Closure_Ortrancl(X7,X23)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X4)),c_Transitive__Closure_Otrancl(X7,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).
fof(fact_flat__lub__def,axiom,
! [X12,X9,X7] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> c_Partial__Function_Oflat__lub(X7,X12,X9) = X12 )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> c_Partial__Function_Oflat__lub(X7,X12,X9) = c_HOL_OThe(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_flat__lub__def) ).
fof(fact_extensional__funcset__arb,axiom,
! [X4,X52,X17,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional__funcset(X7,X19,X17,X52)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X17))
=> hAPP(X2,X4) = c_HOL_Oundefined(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__arb) ).
fof(fact_cut__def,axiom,
! [X2,X19,X23,X4,X10,X7] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X4)),X23))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X7,X19),X2),X23),X4),X10) = hAPP(X2,X10) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X4)),X23))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X7,X19),X2),X23),X4),X10) = c_HOL_Oundefined(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__def) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [X10,X18,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),c_Relation_ODomain(X7,X7,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Ortrancl(X7,X18)))
<=> X4 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_inf2E,axiom,
! [X10,X4,X8,X9,X19,X7] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),X9,X8),X4),X10))
=> ~ ( hBOOL(hAPP(hAPP(X9,X4),X10))
=> ~ hBOOL(hAPP(hAPP(X8,X4),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).
fof(fact_acyclic__def,axiom,
! [X23,X7] :
( c_Wellfounded_Oacyclic(X7,X23)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),c_Transitive__Closure_Otrancl(X7,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__def) ).
fof(fact_acyclicI,axiom,
! [X23,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),c_Transitive__Closure_Otrancl(X7,X23)))
=> c_Wellfounded_Oacyclic(X7,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicI) ).
fof(fact_irrefl__def,axiom,
! [X23,X7] :
( c_Relation_Oirrefl(X7,X23)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(fact_subset__insert__iff,axiom,
! [X8,X4,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),X8))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X8) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert__iff) ).
fof(fact_bot2E,axiom,
! [X10,X4,X19,X7] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_fun(X19,tc_HOL_Obool))),X4),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot2E) ).
fof(fact_extensional__arb,axiom,
! [X4,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional(X7,X19,X9)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(X2,X4) = c_HOL_Oundefined(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__arb) ).
fof(fact_Diff__iff,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
& ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__iff) ).
fof(fact_DiffD2,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD2) ).
fof(fact_IntE,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).
fof(fact_restrict__def,axiom,
! [X2,X19,X9,X4,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_FuncSet_Orestrict(X7,X19,X2,X9),X4) = hAPP(X2,X4) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_FuncSet_Orestrict(X7,X19,X2,X9),X4) = c_HOL_Oundefined(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__def) ).
fof(fact_restrict__apply,axiom,
! [X2,X19,X9,X4,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_FuncSet_Orestrict(X7,X19,X2,X9),X4) = hAPP(X2,X4) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_FuncSet_Orestrict(X7,X19,X2,X9),X4) = c_HOL_Oundefined(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__apply) ).
fof(fact_DiffI,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X8))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffI) ).
fof(fact_inf1E,axiom,
! [X4,X8,X9,X7] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),X4))
=> ~ ( hBOOL(hAPP(X9,X4))
=> ~ hBOOL(hAPP(X8,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).
fof(fact_Int__insert__left,axiom,
! [X8,X38,X13,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X13),X38))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X13),X8),X38) = hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X38))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X13),X8),X38) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left) ).
fof(fact_Int__insert__right,axiom,
! [X8,X9,X13,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right) ).
fof(fact_Range__empty,axiom,
! [X7,X19] : c_Relation_ORange(X19,X7,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X19,X7),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty) ).
fof(fact_Diff__insert__absorb,axiom,
! [X9,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9),hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).
fof(fact_insert__Diff__if,axiom,
! [X9,X8,X4,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X8))
=> c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9),X8) = c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X8))
=> c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9),X8) = hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__if) ).
fof(fact_insertCI,axiom,
! [X12,X8,X13,X7] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X8))
=> X13 = X12 )
=> hBOOL(hAPP(hAPP(c_member(X7),X13),hAPP(hAPP(c_Set_Oinsert(X7),X12),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
fof(fact_subset__insert,axiom,
! [X8,X9,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),X8))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert) ).
fof(fact_Range__converse,axiom,
! [X23,X7,X19] : c_Relation_ORange(X19,X7,c_Relation_Oconverse(X7,X19,X23)) = c_Relation_ODomain(X7,X19,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__converse) ).
fof(fact_insert__ident,axiom,
! [X8,X9,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X8))
=> ( hAPP(hAPP(c_Set_Oinsert(X7),X4),X9) = hAPP(hAPP(c_Set_Oinsert(X7),X4),X8)
<=> X9 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(fact_Range__empty__iff,axiom,
! [X23,X7,X19] :
( c_Relation_ORange(X19,X7,X23) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> X23 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X19,X7),tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
fof(fact_trancl__range,axiom,
! [X23,X7] : c_Relation_ORange(X7,X7,c_Transitive__Closure_Otrancl(X7,X23)) = c_Relation_ORange(X7,X7,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__range) ).
fof(fact_Int__insert__left__if0,axiom,
! [X8,X38,X13,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X38))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X13),X8),X38) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
fof(fact_Int__insert__right__if0,axiom,
! [X8,X9,X13,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
fof(fact_empty__iff,axiom,
! [X6,X7] : ~ hBOOL(hAPP(hAPP(c_member(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__iff) ).
fof(fact_emptyE,axiom,
! [X13,X7] : ~ hBOOL(hAPP(hAPP(c_member(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_emptyE) ).
fof(fact_le__infE,axiom,
! [X60,X61,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X7,X58,X61)
=> ~ c_Orderings_Oord__class_Oless__eq(X7,X58,X60) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infE) ).
fof(fact_all__not__in__conv,axiom,
! [X9,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
<=> X9 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_Range__Id__on,axiom,
! [X9,X7] : c_Relation_ORange(X7,X7,c_Relation_OId__on(X7,X9)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).
fof(fact_equals0D,axiom,
! [X13,X7,X9] :
( X9 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equals0D) ).
fof(help_c__fconj__2,axiom,
! [X75,X28] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X28),X75))
| hBOOL(X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [X75,X28] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X28),X75))
| hBOOL(X75) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
fof(help_c__fequal__1,axiom,
! [X10,X4] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X4),X10))
| X4 = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_linorder__le__cases,axiom,
! [X57,X58,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X7,X58,X57)
=> c_Orderings_Oord__class_Oless__eq(X7,X57,X58) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(help_c__fconj__1,axiom,
! [X75,X28] :
( ~ hBOOL(X28)
| ~ hBOOL(X75)
| hBOOL(hAPP(hAPP(c_fconj,X28),X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(fact_equalityE,axiom,
! [X7,X8,X9] :
( X9 = X8
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
fof(help_c__fNot__1,axiom,
! [X28] :
( ~ hBOOL(hAPP(c_fNot,X28))
| ~ hBOOL(X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(help_c__fNot__2,axiom,
! [X28] :
( ~ ~ hBOOL(X28)
| hBOOL(hAPP(c_fNot,X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(fact_rtrancl__induct2,axiom,
! [X28,X23,X42,X43,X44,X45,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X45),X44)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X43),X42))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X19),X23)))
=> ( hBOOL(hAPP(hAPP(X28,X45),X44))
=> ( ! [X21,X22] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X45),X44)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X21),X22))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X19),X23)))
=> ! [X46,X47] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X21),X22)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X46),X47))),X23))
=> ( hBOOL(hAPP(hAPP(X28,X21),X22))
=> hBOOL(hAPP(hAPP(X28,X46),X47)) ) ) )
=> hBOOL(hAPP(hAPP(X28,X43),X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
fof(fact_converse__rtrancl__induct2,axiom,
! [X28,X23,X42,X43,X44,X45,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X45),X44)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X43),X42))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X19),X23)))
=> ( hBOOL(hAPP(hAPP(X28,X43),X42))
=> ( ! [X21,X22,X46,X47] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X21),X22)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X46),X47))),X23))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X46),X47)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X43),X42))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X19),X23)))
=> ( hBOOL(hAPP(hAPP(X28,X46),X47))
=> hBOOL(hAPP(hAPP(X28,X21),X22)) ) ) )
=> hBOOL(hAPP(hAPP(X28,X45),X44)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
fof(fact_inf__Int__eq2,axiom,
! [X10,X4,X17,X18,X19,X7] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),X7,c_COMBC(X19,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_prod(X7,X19)),tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X19),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool),X19,c_member(tc_prod(X7,X19)))),c_Product__Type_OPair(X7,X19)))),X18),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),X7,c_COMBC(X19,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_prod(X7,X19)),tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X19),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool),X19,c_member(tc_prod(X7,X19)))),c_Product__Type_OPair(X7,X19)))),X17)),X4),X10))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X4),X10)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),X18,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_adm__wf__def,axiom,
! [X15,X18,X19,X7] :
( c_Recdef_Oadm__wf(X7,X19,X18,X15)
<=> ! [X53,X55,X3] :
( ! [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X40),X3)),X18))
=> hAPP(X53,X40) = hAPP(X55,X40) )
=> hAPP(hAPP(X15,X53),X3) = hAPP(hAPP(X15,X55),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__wf__def) ).
fof(fact_conversep__converse__eq,axiom,
! [X10,X4,X23,X19,X7] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X7,X19,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),X7,c_COMBC(X19,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_prod(X7,X19)),tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X19),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool),X19,c_member(tc_prod(X7,X19)))),c_Product__Type_OPair(X7,X19)))),X23)),X4),X10))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X4),X10)),c_Relation_Oconverse(X7,X19,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__converse__eq) ).
fof(fact_fold__graph_H_Oequations_I2_J,axiom,
! [X66,X33,X32,X67,X68,X19,X7] :
( c_Nitpick_Ofold__graph_H(X7,X19,X68,X67,X32,hAPP(hAPP(X68,X33),X66))
<=> ( ( X32 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
& hAPP(hAPP(X68,X33),X66) = X67 )
| ? [X3,X26] :
( hAPP(hAPP(X68,X33),X66) = hAPP(hAPP(X68,X3),X26)
& hBOOL(hAPP(hAPP(c_member(X7),X3),X32))
& c_Nitpick_Ofold__graph_H(X7,X19,X68,X67,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X32,hAPP(hAPP(c_Set_Oinsert(X7),X3),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
fof(fact_accp__acc__eq,axiom,
! [X4,X23,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7,c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X7,c_member(tc_prod(X7,X7)))),c_Product__Type_OPair(X7,X7)))),X23)),X4))
<=> hBOOL(hAPP(hAPP(c_member(X7),X4),c_Wellfounded_Oacc(X7,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_pred__subset__eq2,axiom,
! [X17,X18,X19,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),X7,c_COMBC(X19,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_prod(X7,X19)),tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X19),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool),X19,c_member(tc_prod(X7,X19)))),c_Product__Type_OPair(X7,X19)))),X18),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),X7,c_COMBC(X19,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_prod(X7,X19)),tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X19),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool),X19,c_member(tc_prod(X7,X19)))),c_Product__Type_OPair(X7,X19)))),X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),X18,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_cuts__eq,axiom,
! [X1,X4,X23,X2,X19,X7] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(X7,X19),X2),X23),X4) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X7,X19),X1),X23),X4)
<=> ! [X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X4)),X23))
=> hAPP(X2,X26) = hAPP(X1,X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cuts__eq) ).
fof(fact_DomainP__Domain__eq,axiom,
! [X4,X23,X19,X7] :
( c_Predicate_ODomainP(X7,X19,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),X7,c_COMBC(X19,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_prod(X7,X19)),tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X19),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool),X19,c_member(tc_prod(X7,X19)))),c_Product__Type_OPair(X7,X19)))),X23),X4)
<=> hBOOL(hAPP(hAPP(c_member(X7),X4),c_Relation_ODomain(X7,X19,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [X17,X18,X19,X7] :
( hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),X7,c_COMBC(X19,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_prod(X7,X19)),tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X19),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool),X19,c_member(tc_prod(X7,X19)))),c_Product__Type_OPair(X7,X19)))),X18) = hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),X7,c_COMBC(X19,tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X19,tc_prod(X7,X19)),tc_fun(X19,tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool)),X7,c_COMBB(tc_prod(X7,X19),tc_fun(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),tc_HOL_Obool),X19,c_member(tc_prod(X7,X19)))),c_Product__Type_OPair(X7,X19)))),X17)
<=> X18 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_adm__lemma,axiom,
! [X15,X18,X19,X7] : c_Recdef_Oadm__wf(X7,X19,X18,hAPP(hAPP(c_COMBC(tc_fun(X7,X19),tc_fun(X7,X7),tc_fun(X7,X19)),hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,X19)),tc_fun(tc_fun(X7,X7),tc_fun(X7,X19)),tc_fun(X7,X19),c_COMBS(X7,X7,X19)),hAPP(c_COMBB(tc_fun(X7,tc_fun(X7,X19)),tc_fun(X7,tc_fun(X7,X19)),tc_fun(X7,X19),c_COMBB(tc_fun(X7,X19),tc_fun(X7,X19),X7,X15)),hAPP(hAPP(c_COMBC(tc_fun(X7,X19),tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X7,tc_fun(X7,X19))),c_Recdef_Ocut(X7,X19)),X18)))),c_COMBI(X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__lemma) ).
fof(fact_extensional__funcset__fun__upd__restricts__rangeI,axiom,
! [X52,X19,X4,X2,X17,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X17))
=> hAPP(X2,X4) != hAPP(X2,X3) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional__funcset(X7,X19,hAPP(hAPP(c_Set_Oinsert(X7),X4),X17),X52)))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),c_Fun_Ofun__upd(X7,X19,X2,X4,c_HOL_Oundefined(X19))),c_FuncSet_Oextensional__funcset(X7,X19,X17,c_Groups_Ominus__class_Ominus(tc_fun(X19,tc_HOL_Obool),X52,hAPP(hAPP(c_Set_Oinsert(X19),hAPP(X2,X4)),c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool))))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__fun__upd__restricts__rangeI) ).
fof(fact_rtrancl__induct,axiom,
! [X28,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(X28,X13))
=> ( ! [X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X26)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ! [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X40)),X23))
=> ( hBOOL(hAPP(X28,X26))
=> hBOOL(hAPP(X28,X40)) ) ) )
=> hBOOL(hAPP(X28,X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
fof(fact_converse__rtrancl__induct,axiom,
! [X28,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(X28,X12))
=> ( ! [X26,X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X40)),X23))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X40),X12)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(X28,X40))
=> hBOOL(hAPP(X28,X26)) ) ) )
=> hBOOL(hAPP(X28,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
fof(fact_Pi__cong,axiom,
! [X8,X19,X1,X2,X9,X7] :
( ! [X34] :
( hBOOL(hAPP(hAPP(c_member(X7),X34),X9))
=> hAPP(X2,X34) = hAPP(X1,X34) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,X8)))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X1),c_FuncSet_OPi(X7,X19,X9,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__cong) ).
fof(fact_restrictI,axiom,
! [X8,X2,X19,X9,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X3)),hAPP(X8,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),c_FuncSet_Orestrict(X7,X19,X2,X9)),c_FuncSet_OPi(X7,X19,X9,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrictI) ).
fof(fact_Pi__I_H,axiom,
! [X8,X2,X19,X9,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X3)),hAPP(X8,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I_H) ).
fof(fact_Pi__I,axiom,
! [X8,X2,X19,X9,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X3)),hAPP(X8,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_quotient__def,axiom,
! [X23,X9,X7] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),X9,hAPP(hAPP(c_COMBC(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X7,c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X7,c_Relation_OImage(X7,X7,X23)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__def) ).
fof(fact_Image__iff,axiom,
! [X9,X23,X19,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X12),hAPP(c_Relation_OImage(X19,X7,X23),X9)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X19),X3),X9))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X3),X12)),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__iff) ).
fof(fact_conversep__noteq,axiom,
! [X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X7,X7,hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X7,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7,c_fNot)),c_fequal)),X4),X10))
<=> X4 != X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__noteq) ).
fof(fact_IIA__def,axiom,
! [X15] :
( c_Arrow__Order__Mirabelle_OIIA(X15)
<=> ! [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))
=> ! [X24] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X24),c_Arrow__Order__Mirabelle_OProf))
=> ! [X21,X22] :
( ! [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),X21),X22)),hAPP(X3,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),X21),X22)),hAPP(X24,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),X21),X22)),hAPP(X15,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),X21),X22)),hAPP(X15,X24))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact_restrict__in__funcset,axiom,
! [X8,X2,X19,X9,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X3)),X8)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),c_FuncSet_Orestrict(X7,X19,X2,X9)),c_FuncSet_OPi(X7,X19,X9,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X8)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__in__funcset) ).
fof(fact_quotient__diff1,axiom,
! [X13,X9,X23,X7] :
( c_Fun_Oinj__on(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),X7,c_Equiv__Relations_Oquotient(X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X23),X9)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),X23) = c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__diff1) ).
fof(fact_funcsetI,axiom,
! [X8,X2,X19,X9,X7] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X3)),X8)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X8)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcsetI) ).
fof(fact_Q__def,axiom,
! [X14] : hAPP(v_Q____,X14) = c_HOL_OLet(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),hAPP(hAPP(c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),hAPP(hAPP(c_fequal,v_a____),v_a_H____)),hAPP(v_P____,X14)),c_Arrow__Order__Mirabelle_Obelow(hAPP(v_P____,X14),v_a_H____,v_a____)),hAPP(hAPP(c_COMBS(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),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),hAPP(hAPP(c_fequal,v_b____),v_b_H____))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),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_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),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))),c_Arrow__Order__Mirabelle_Oabove),v_b____)),v_b_H____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Q__def) ).
fof(fact_the__inv__into__def,axiom,
! [X4,X2,X9,X19,X7] : hAPP(c_Fun_Othe__inv__into(X7,X19,X9,X2),X4) = c_HOL_OThe(X7,hAPP(hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7,c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X9))),hAPP(hAPP(c_COMBC(X7,X19,tc_HOL_Obool),hAPP(c_COMBB(X19,tc_fun(X19,tc_HOL_Obool),X7,c_fequal),X2)),X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__def) ).
fof(fact_extensional__funcset__fun__upd__extends__rangeI,axiom,
! [X4,X17,X2,X19,X52,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),X52))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X7)),X2),c_FuncSet_Oextensional__funcset(X19,X7,X17,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X52,hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X7)),c_Fun_Ofun__upd(X19,X7,X2,X4,X13)),c_FuncSet_Oextensional__funcset(X19,X7,hAPP(hAPP(c_Set_Oinsert(X19),X4),X17),X52))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__fun__upd__extends__rangeI) ).
fof(fact_fold__graph_H_Ointros_I2_J,axiom,
! [X10,X20,X2,X19,X9,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( c_Nitpick_Ofold__graph_H(X7,X19,X2,X20,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X10)
=> c_Nitpick_Ofold__graph_H(X7,X19,X2,X20,X9,hAPP(hAPP(X2,X4),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
fof(fact_in__lex__prod,axiom,
! [X29,X23,X30,X31,X12,X13,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X12)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X31),X30))),c_Wellfounded_Olex__prod(X7,X19,X23,X29)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X31)),X23))
| ( X13 = X31
& hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X19)),hAPP(hAPP(c_Product__Type_OPair(X19,X19),X12),X30)),X29)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact_dictatorI,axiom,
! [X14,X15] :
( 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))),X15),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))
=> ! [X21,X22] :
( X21 != X22
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),hAPP(X3,X14)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),hAPP(X15,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_extensional__funcset__extend__domainI,axiom,
! [X4,X17,X2,X19,X52,X10,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X10),X52))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X7)),X2),c_FuncSet_Oextensional__funcset(X19,X7,X17,X52)))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X7)),c_Fun_Ofun__upd(X19,X7,X2,X4,X10)),c_FuncSet_Oextensional__funcset(X19,X7,hAPP(hAPP(c_Set_Oinsert(X19),X4),X17),X52))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__extend__domainI) ).
fof(fact_SUP1__iff,axiom,
! [X12,X8,X9,X19,X7] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X19,tc_HOL_Obool),X9,X8),X12))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
& hBOOL(hAPP(hAPP(X8,X3),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__iff) ).
fof(fact_extensionalityI,axiom,
! [X1,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional(X7,X19,X9)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X1),c_FuncSet_Oextensional(X7,X19,X9)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> hAPP(X2,X3) = hAPP(X1,X3) )
=> X2 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensionalityI) ).
fof(fact_tranclD,axiom,
! [X18,X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Otrancl(X7,X18)))
=> ? [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X40)),X18))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X40),X10)),c_Transitive__Closure_Ortrancl(X7,X18))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD) ).
fof(fact_tranclD2,axiom,
! [X18,X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Otrancl(X7,X18)))
=> ? [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X40)),c_Transitive__Closure_Ortrancl(X7,X18)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X40),X10)),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD2) ).
fof(fact_same__fstI,axiom,
! [X7,X18,X10,X27,X19,X4,X28] :
( hBOOL(hAPP(X28,X4))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X19)),hAPP(hAPP(c_Product__Type_OPair(X19,X19),X27),X10)),hAPP(X18,X4)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X4),X27)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X4),X10))),c_Recdef_Osame__fst(X7,X19,X28,X18))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_equiv__class__nondisjoint,axiom,
! [X12,X13,X4,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).
fof(fact_inf__Int__eq,axiom,
! [X4,X17,X18,X7] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X18),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X17)),X4))
<=> hBOOL(hAPP(hAPP(c_member(X7),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X18,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_extensional__funcset__fun__upd__inj__onI,axiom,
! [X4,X13,X52,X17,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional__funcset(X7,X19,X17,c_Groups_Ominus__class_Ominus(tc_fun(X19,tc_HOL_Obool),X52,hAPP(hAPP(c_Set_Oinsert(X19),X13),c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool)))))))
=> ( c_Fun_Oinj__on(X7,X19,X2,X17)
=> c_Fun_Oinj__on(X7,X19,c_Fun_Ofun__upd(X7,X19,X2,X4,X13),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__fun__upd__inj__onI) ).
fof(fact_inv__into__funcset,axiom,
! [X8,X9,X2,X7,X19] :
( c_Set_Oimage(X19,X7,X2,X9) = X8
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),c_FuncSet_Orestrict(X7,X19,c_Hilbert__Choice_Oinv__into(X19,X7,X9,X2),X8)),c_FuncSet_OPi(X7,X19,X8,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X9)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__funcset) ).
fof(fact_unanimity__def,axiom,
! [X15] :
( c_Arrow__Order__Mirabelle_Ounanimity(X15)
<=> ! [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))
=> ! [X21,X22] :
( ! [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),X21),X22)),hAPP(X3,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),X21),X22)),hAPP(X15,X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_fun__upd__twist,axiom,
! [X63,X12,X65,X19,X7,X6,X13] :
( X13 != X6
=> c_Fun_Ofun__upd(X7,X19,c_Fun_Ofun__upd(X7,X19,X65,X13,X12),X6,X63) = c_Fun_Ofun__upd(X7,X19,c_Fun_Ofun__upd(X7,X19,X65,X6,X63),X13,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
fof(fact_in__above,axiom,
! [X10,X4,X5,X12,X13] :
( X13 != X12
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X10)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X5),X13),X12)))
<=> ( X4 != X10
& ( X4 = 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),X13),X10)),X5)) )
& ( X4 != X12
=> ( ( X10 = X12
=> ( X4 = X13
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X13)),X5)) ) )
& ( X10 != 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),X4),X10)),X5)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_the__inv__into__into,axiom,
! [X8,X4,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( hBOOL(hAPP(hAPP(c_member(X19),X4),c_Set_Oimage(X7,X19,X2,X9)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(c_Fun_Othe__inv__into(X7,X19,X9,X2),X4)),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
fof(fact_in__below,axiom,
! [X10,X4,X5,X12,X13] :
( X13 != X12
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X10)),c_Arrow__Order__Mirabelle_Obelow(X5,X13,X12)))
<=> ( X4 != X10
& ( X10 = X13
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X12)),X5)) )
& ( X10 != X13
=> ( ( X4 = X13
=> ( X10 = 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),X10)),X5)) ) )
& ( X4 != X13
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X10)),X5)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_fold__graph_H_Ointros_I1_J,axiom,
! [X20,X2,X19,X7] : c_Nitpick_Ofold__graph_H(X7,X19,X2,X20,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
fof(fact_fold__graph_H_Oequations_I1_J,axiom,
! [X32,X33,X19,X7] : c_Nitpick_Ofold__graph_H(X7,X19,X33,X32,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
fof(fact_inv__into__into,axiom,
! [X9,X2,X19,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),c_Set_Oimage(X19,X7,X2,X9)))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(c_Hilbert__Choice_Oinv__into(X19,X7,X9,X2),X4)),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).
fof(fact_total__on__def,axiom,
! [X23,X9,X7] :
( c_Relation_Ototal__on(X7,X9,X23)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> ! [X24] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),X9))
=> ( X3 != X24
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X24)),X23))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X24),X3)),X23)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__def) ).
fof(fact_single__valued__confluent,axiom,
! [X20,X10,X4,X23,X7] :
( c_Relation_Osingle__valued(X7,X7,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X20)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X20)),c_Transitive__Closure_Ortrancl(X7,X23)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X20),X10)),c_Transitive__Closure_Ortrancl(X7,X23))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_Domain__iff,axiom,
! [X23,X19,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),c_Relation_ODomain(X7,X19,X23)))
<=> ? [X26] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X26)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).
fof(fact_inv__into__injective,axiom,
! [X10,X4,X2,X9,X19,X7] :
( hAPP(c_Hilbert__Choice_Oinv__into(X7,X19,X9,X2),X4) = hAPP(c_Hilbert__Choice_Oinv__into(X7,X19,X9,X2),X10)
=> ( hBOOL(hAPP(hAPP(c_member(X19),X4),c_Set_Oimage(X7,X19,X2,X9)))
=> ( hBOOL(hAPP(hAPP(c_member(X19),X10),c_Set_Oimage(X7,X19,X2,X9)))
=> X4 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).
fof(fact_in__inv__image,axiom,
! [X2,X23,X19,X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Relation_Oinv__image(X19,X7,X23,X2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X19)),hAPP(hAPP(c_Product__Type_OPair(X19,X19),hAPP(X2,X4)),hAPP(X2,X10))),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__inv__image) ).
fof(fact_fun__upd__upd,axiom,
! [X20,X10,X4,X2,X19,X7] : c_Fun_Ofun__upd(X7,X19,c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X4,X20) = c_Fun_Ofun__upd(X7,X19,X2,X4,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
fof(fact_trancl__trans,axiom,
! [X6,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Otrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),c_Transitive__Closure_Otrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Otrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__trans) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [X20,X23,X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X20)),c_Transitive__Closure_Otrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X20)),c_Transitive__Closure_Otrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(fact_trancl__rtrancl__trancl,axiom,
! [X6,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Otrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Otrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(fact_rtrancl__trans,axiom,
! [X6,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Ortrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_trancl__into__trancl2,axiom,
! [X6,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),c_Transitive__Closure_Otrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Otrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
fof(fact_rtrancl__into__trancl2,axiom,
! [X6,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Otrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
! [X6,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Otrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),X23))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Otrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(fact_rtrancl__into__trancl1,axiom,
! [X6,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),X23))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Otrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [X6,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Ortrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [X6,X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),X23))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Ortrancl(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_r__r__into__trancl,axiom,
! [X6,X18,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X6)),X18))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X6)),c_Transitive__Closure_Otrancl(X7,X18))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
fof(fact_Image__eq__UN,axiom,
! [X8,X23,X7,X19] : hAPP(c_Relation_OImage(X19,X7,X23),X8) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X19,tc_fun(X7,tc_HOL_Obool),X8,hAPP(c_COMBB(tc_fun(X19,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X19,c_Relation_OImage(X19,X7,X23)),hAPP(hAPP(c_COMBC(X19,tc_fun(X19,tc_HOL_Obool),tc_fun(X19,tc_HOL_Obool)),c_Set_Oinsert(X19)),c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__eq__UN) ).
fof(fact_image__iff,axiom,
! [X9,X2,X19,X20,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X20),c_Set_Oimage(X19,X7,X2,X9)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X19),X3),X9))
& X20 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_trancl__converseD,axiom,
! [X23,X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Otrancl(X7,c_Relation_Oconverse(X7,X7,X23))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Relation_Oconverse(X7,X7,c_Transitive__Closure_Otrancl(X7,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseD) ).
fof(fact_single__valuedI,axiom,
! [X23,X19,X7] :
( ! [X3,X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X3),X26)),X23))
=> ! [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X3),X40)),X23))
=> X26 = X40 ) )
=> c_Relation_Osingle__valued(X7,X19,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedI) ).
fof(fact_single__valued__def,axiom,
! [X23,X19,X7] :
( c_Relation_Osingle__valued(X7,X19,X23)
<=> ! [X3,X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X3),X26)),X23))
=> ! [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X3),X40)),X23))
=> X26 = X40 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(fact_trancl__converseI,axiom,
! [X23,X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Relation_Oconverse(X7,X7,c_Transitive__Closure_Otrancl(X7,X23))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Otrancl(X7,c_Relation_Oconverse(X7,X7,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseI) ).
fof(fact_quotient__eqI,axiom,
! [X10,X4,X69,X64,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X64),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X69),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X64))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X10),X69))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),X23))
=> X64 = X69 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__eqI) ).
fof(fact_quotient__eq__iff,axiom,
! [X10,X4,X69,X64,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X64),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X69),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X64))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X10),X69))
=> ( X64 = X69
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),X23)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).
fof(fact_funcset__image,axiom,
! [X8,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X8))))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X19,tc_HOL_Obool),c_Set_Oimage(X7,X19,X2,X9),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__image) ).
fof(fact_subset__image__iff,axiom,
! [X9,X2,X19,X8,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,c_Set_Oimage(X19,X7,X2,X9))
<=> ? [X72] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X19,tc_HOL_Obool),X72,X9)
& X8 = c_Set_Oimage(X19,X7,X2,X72) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_rtrancl__converseD,axiom,
! [X23,X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Ortrancl(X7,c_Relation_Oconverse(X7,X7,X23))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X4)),c_Transitive__Closure_Ortrancl(X7,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).
fof(fact_subset__equiv__class,axiom,
! [X13,X12,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X12),X9))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__equiv__class) ).
fof(fact_funcset__mem,axiom,
! [X4,X8,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X8))))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X4)),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_single__valuedD,axiom,
! [X20,X10,X4,X23,X19,X7] :
( c_Relation_Osingle__valued(X7,X19,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X4),X10)),X23))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X4),X20)),X23))
=> X10 = X20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X7,X19] :
( class_Orderings_Oord(X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X19),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X19,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_quotientI,axiom,
! [X23,X9,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotientI) ).
fof(fact_Image__singleton__iff,axiom,
! [X13,X23,X19,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X12),hAPP(c_Relation_OImage(X19,X7,X23),hAPP(hAPP(c_Set_Oinsert(X19),X13),c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool))))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X13),X12)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
fof(fact_rtrancl__converseI,axiom,
! [X23,X4,X10,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X4)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Ortrancl(X7,c_Relation_Oconverse(X7,X7,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).
fof(fact_the__elem__def,axiom,
! [X64,X7] : c_Set_Othe__elem(X7,X64) = c_HOL_OThe(X7,hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X7,hAPP(c_fequal,X64)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),c_Set_Oinsert(X7)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__def) ).
fof(fact_const__Lin__Prof,axiom,
! [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))
=> 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,X5)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_f__the__inv__into__f,axiom,
! [X10,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( hBOOL(hAPP(hAPP(c_member(X19),X10),c_Set_Oimage(X7,X19,X2,X9)))
=> hAPP(X2,hAPP(c_Fun_Othe__inv__into(X7,X19,X9,X2),X10)) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
fof(fact_equiv__class__subset,axiom,
! [X12,X13,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__subset) ).
fof(fact_converseD,axiom,
! [X23,X12,X13,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X12)),c_Relation_Oconverse(X19,X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X12),X13)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseD) ).
fof(fact_converse__iff,axiom,
! [X23,X12,X13,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X12)),c_Relation_Oconverse(X19,X7,X23)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X12),X13)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__iff) ).
fof(fact_image__diff__subset,axiom,
! [X8,X9,X2,X19,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X19,X7,X2,X9),c_Set_Oimage(X19,X7,X2,X8)),c_Set_Oimage(X19,X7,X2,c_Groups_Ominus__class_Ominus(tc_fun(X19,tc_HOL_Obool),X9,X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__diff__subset) ).
fof(fact_image__Int__subset,axiom,
! [X8,X9,X2,X19,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X19,X7,X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19,tc_HOL_Obool),X9,X8)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X19,X7,X2,X9),c_Set_Oimage(X19,X7,X2,X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int__subset) ).
fof(fact_eq__equiv__class__iff2,axiom,
! [X10,X4,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X10),X9))
=> ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X23) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),hAPP(hAPP(c_Set_Oinsert(X7),X10),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X23)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),X23)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).
fof(fact_in__rel__def,axiom,
! [X10,X4,X18,X19,X7] :
( c_FunDef_Oin__rel(X7,X19,X18,X4,X10)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X4),X10)),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_acc_OaccI,axiom,
! [X23,X4,X7] :
( ! [X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X4)),X23))
=> hBOOL(hAPP(hAPP(c_member(X7),X26),c_Wellfounded_Oacc(X7,X23))) )
=> hBOOL(hAPP(hAPP(c_member(X7),X4),c_Wellfounded_Oacc(X7,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).
fof(fact_acc_Osimps,axiom,
! [X23,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),c_Wellfounded_Oacc(X7,X23)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X13)),X23))
=> hBOOL(hAPP(hAPP(c_member(X7),X3),c_Wellfounded_Oacc(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).
fof(fact_converseI,axiom,
! [X23,X12,X13,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X12)),X23))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X12),X13)),c_Relation_Oconverse(X7,X19,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseI) ).
fof(fact_rtrancl__eq__or__trancl,axiom,
! [X18,X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Ortrancl(X7,X18)))
<=> ( X4 = X10
| ( X4 != X10
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Otrancl(X7,X18))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
fof(fact_rtranclD,axiom,
! [X18,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Ortrancl(X7,X18)))
=> ( X13 = X12
| ( X13 != X12
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Otrancl(X7,X18))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclD) ).
fof(fact_trancl__into__rtrancl,axiom,
! [X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Otrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Ortrancl(X7,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
fof(fact_bot__empty__eq2,axiom,
! [X10,X4,X19,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_fun(X19,tc_HOL_Obool))),X4),X10))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X4),X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X19),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
fof(fact_f__inv__into__f,axiom,
! [X9,X2,X19,X10,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X10),c_Set_Oimage(X19,X7,X2,X9)))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X19,X7,X9,X2),X10)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_trancl_Or__into__trancl,axiom,
! [X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Otrancl(X7,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
fof(fact_eq__equiv__class__iff,axiom,
! [X10,X4,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X10),X9))
=> ( hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X10),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),X23)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [X23,X7] :
( c_Nitpick_Orefl_H(X7,X23)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_Pi__eq__empty,axiom,
! [X8,X9,X19,X7] :
( c_FuncSet_OPi(X7,X19,X9,X8) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,X19),tc_HOL_Obool))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
& hAPP(X8,X3) = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__eq__empty) ).
fof(fact_Image__UN,axiom,
! [X8,X9,X39,X23,X7,X19] : hAPP(c_Relation_OImage(X19,X7,X23),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X39,tc_fun(X19,tc_HOL_Obool),X9,X8)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X39,tc_fun(X7,tc_HOL_Obool),X9,hAPP(c_COMBB(tc_fun(X19,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X39,c_Relation_OImage(X19,X7,X23)),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__UN) ).
fof(fact_restrict__extensional,axiom,
! [X9,X2,X19,X7] : hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),c_FuncSet_Orestrict(X7,X19,X2,X9)),c_FuncSet_Oextensional(X7,X19,X9))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__extensional) ).
fof(fact_equiv__class__eq__iff,axiom,
! [X10,X4,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),X23))
<=> ( hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X10),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
& hBOOL(hAPP(hAPP(c_member(X7),X10),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).
fof(fact_Pi__mem,axiom,
! [X4,X8,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,X8)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X4)),hAPP(X8,X4))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_fun__upd__other,axiom,
! [X10,X2,X19,X7,X4,X20] :
( X20 != X4
=> hAPP(c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X20) = hAPP(X2,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).
fof(fact_fun__upd__apply,axiom,
! [X10,X2,X19,X7,X4,X20] :
( ( X20 = X4
=> hAPP(c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X20) = X10 )
& ( X20 != X4
=> hAPP(c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X20) = hAPP(X2,X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
fof(fact_fun__upd__def,axiom,
! [X12,X2,X19,X7,X13,X4] :
( ( X4 = X13
=> hAPP(c_Fun_Ofun__upd(X7,X19,X2,X13,X12),X4) = X12 )
& ( X4 != X13
=> hAPP(c_Fun_Ofun__upd(X7,X19,X2,X13,X12),X4) = hAPP(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).
fof(fact_extensional__funcset__mem,axiom,
! [X4,X52,X17,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional__funcset(X7,X19,X17,X52)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X17))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X4)),X52)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__mem) ).
fof(fact_fun__upd__same,axiom,
! [X10,X4,X2,X7,X19] : hAPP(c_Fun_Ofun__upd(X19,X7,X2,X4,X10),X4) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).
fof(fact_pred__subset__eq,axiom,
! [X17,X18,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X18),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X18,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_rev__ImageI,axiom,
! [X23,X12,X19,X9,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X12)),X23))
=> hBOOL(hAPP(hAPP(c_member(X19),X12),hAPP(c_Relation_OImage(X7,X19,X23),X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__ImageI) ).
fof(fact_in__mkbot,axiom,
! [X20,X5,X10,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),X10)),c_Arrow__Order__Mirabelle_Omkbot(X5,X20)))
<=> ( X10 != X20
& ( X4 = X20
=> X4 != X10 )
& ( X4 != 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),X4),X10)),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [X20,X5,X10,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),X10)),c_Arrow__Order__Mirabelle_Omktop(X5,X20)))
<=> ( X4 != X20
& ( X10 = X20
=> X4 != X10 )
& ( X10 != 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),X4),X10)),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(fact_equiv__class__eq,axiom,
! [X12,X13,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23))
=> hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__eq) ).
fof(fact_inj__on__def,axiom,
! [X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> ! [X24] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),X9))
=> ( hAPP(X2,X3) = hAPP(X2,X24)
=> X3 = X24 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact__C1_C,axiom,
! [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),v_a____),v_b____)),hAPP(v_P____,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),v_a_H____),v_b_H____)),hAPP(v_P_H____,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_eq__equiv__class,axiom,
! [X9,X12,X13,X23,X7] :
( hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> ( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X12),X9))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class) ).
fof(fact_image__inv__into__cancel,axiom,
! [X77,X70,X9,X2,X7,X19] :
( c_Set_Oimage(X19,X7,X2,X9) = X70
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X77,X70)
=> c_Set_Oimage(X19,X7,X2,c_Set_Oimage(X7,X19,c_Hilbert__Choice_Oinv__into(X19,X7,X9,X2),X77)) = X77 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_above__Lin,axiom,
! [X5,X10,X4] :
( X4 != X10
=> ( 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))
=> 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_Oabove,X5),X4),X10)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_converse__in__Lin,axiom,
! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5)),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)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__in__Lin) ).
fof(fact_acc__downwards__aux,axiom,
! [X23,X13,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X13)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X13),c_Wellfounded_Oacc(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(X7),X12),c_Wellfounded_Oacc(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_acc__downwards,axiom,
! [X12,X23,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),c_Wellfounded_Oacc(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X12),X13)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> hBOOL(hAPP(hAPP(c_member(X7),X12),c_Wellfounded_Oacc(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).
fof(fact_inj__on__image__set__diff,axiom,
! [X8,X9,X38,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X38)
=> c_Set_Oimage(X7,X19,X2,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)) = c_Groups_Ominus__class_Ominus(tc_fun(X19,tc_HOL_Obool),c_Set_Oimage(X7,X19,X2,X9),c_Set_Oimage(X7,X19,X2,X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).
fof(fact_inj__on__image__Int,axiom,
! [X8,X9,X38,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X38)
=> c_Set_Oimage(X7,X19,X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19,tc_HOL_Obool),c_Set_Oimage(X7,X19,X2,X9),c_Set_Oimage(X7,X19,X2,X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).
fof(fact_dictator__def,axiom,
! [X14,X15] :
( c_Arrow__Order__Mirabelle_Odictator(X15,X14)
<=> ! [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(X15,X3) = hAPP(X3,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_inj__on__iff__surj,axiom,
! [X70,X19,X7,X9] :
( X9 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ( ? [X53] :
( c_Fun_Oinj__on(X7,X19,X53,X9)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X19,tc_HOL_Obool),c_Set_Oimage(X7,X19,X53,X9),X70) )
<=> ? [X55] : c_Set_Oimage(X19,X7,X55,X70) = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
fof(fact_singleton__quotient,axiom,
! [X23,X4,X7] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X23) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__quotient) ).
fof(fact_congruentD,axiom,
! [X20,X10,X2,X23,X19,X7] :
( c_Equiv__Relations_Ocongruent(X7,X19,X23,X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X20)),X23))
=> hAPP(X2,X10) = hAPP(X2,X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruentD) ).
fof(fact_cut__apply,axiom,
! [X2,X19,X23,X13,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X13)),X23))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X7,X19),X2),X23),X13),X4) = hAPP(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__apply) ).
fof(fact_tfl__cut__apply,axiom,
! [X19,X13,X4,X7,X53,X54] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X13)),X54))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X7,X19),X53),X54),X13),X4) = hAPP(X53,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
fof(fact_acc__downward,axiom,
! [X13,X23,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X12),c_Wellfounded_Oacc(X7,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23))
=> hBOOL(hAPP(hAPP(c_member(X7),X13),c_Wellfounded_Oacc(X7,X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).
fof(fact_image__image,axiom,
! [X9,X1,X39,X2,X7,X19] : c_Set_Oimage(X19,X7,X2,c_Set_Oimage(X39,X19,X1,X9)) = c_Set_Oimage(X39,X7,hAPP(c_COMBB(X19,X7,X39,X2),X1),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_below__Lin,axiom,
! [X5,X10,X4] :
( X4 != X10
=> ( 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))
=> 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_Obelow(X5,X4,X10)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_DomainI,axiom,
! [X23,X12,X13,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X12)),X23))
=> hBOOL(hAPP(hAPP(c_member(X7),X13),c_Relation_ODomain(X7,X19,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).
fof(fact_funcset__id,axiom,
! [X9,X7] : hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X7)),c_COMBI(X7)),c_FuncSet_OPi(X7,X7,X9,c_COMBK(tc_fun(X7,tc_HOL_Obool),X7,X9)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(fact_fun__upd__idem__iff,axiom,
! [X10,X4,X2,X19,X7] :
( c_Fun_Ofun__upd(X7,X19,X2,X4,X10) = X2
<=> hAPP(X2,X4) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
fof(fact_refl__onD1,axiom,
! [X10,X4,X23,X9,X7] :
( c_Relation_Orefl__on(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),X23))
=> hBOOL(hAPP(hAPP(c_member(X7),X4),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD1) ).
fof(fact_refl__onD2,axiom,
! [X10,X4,X23,X9,X7] :
( c_Relation_Orefl__on(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),X23))
=> hBOOL(hAPP(hAPP(c_member(X7),X10),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD2) ).
fof(fact_Id__on__iff,axiom,
! [X9,X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Relation_OId__on(X7,X9)))
<=> ( X4 = X10
& hBOOL(hAPP(hAPP(c_member(X7),X4),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).
fof(fact_inf2D1,axiom,
! [X10,X4,X8,X9,X19,X7] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),X9,X8),X4),X10))
=> hBOOL(hAPP(hAPP(X9,X4),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).
fof(fact_inf2D2,axiom,
! [X10,X4,X8,X9,X19,X7] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),X9,X8),X4),X10))
=> hBOOL(hAPP(hAPP(X8,X4),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).
fof(fact_quotient__disj,axiom,
! [X69,X64,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X64),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X69),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23)))
=> ( X64 = X69
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X64,X69) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__disj) ).
fof(fact_inv__into__image__cancel,axiom,
! [X17,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X17,X9)
=> c_Set_Oimage(X19,X7,c_Hilbert__Choice_Oinv__into(X7,X19,X9,X2),c_Set_Oimage(X7,X19,X2,X17)) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
fof(fact_Image__Int__subset,axiom,
! [X8,X9,X18,X19,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),hAPP(c_Relation_OImage(X19,X7,X18),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19,tc_HOL_Obool),X9,X8)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(c_Relation_OImage(X19,X7,X18),X9),hAPP(c_Relation_OImage(X19,X7,X18),X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__subset) ).
fof(fact_equiv__class__self,axiom,
! [X13,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> hBOOL(hAPP(hAPP(c_member(X7),X13),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__self) ).
fof(fact_mktop__Lin,axiom,
! [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))
=> 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(X5,X4)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
fof(fact_mkbot__Lin,axiom,
! [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))
=> 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(X5,X4)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_inj__on__inv__into,axiom,
! [X9,X2,X19,X8,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,c_Set_Oimage(X19,X7,X2,X9))
=> c_Fun_Oinj__on(X7,X19,c_Hilbert__Choice_Oinv__into(X19,X7,X9,X2),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
fof(fact_the__inv__into__onto,axiom,
! [X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> c_Set_Oimage(X19,X7,c_Fun_Othe__inv__into(X7,X19,X9,X2),c_Set_Oimage(X7,X19,X2,X9)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
fof(fact_inj__on__the__inv__into,axiom,
! [X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> c_Fun_Oinj__on(X19,X7,c_Fun_Othe__inv__into(X7,X19,X9,X2),c_Set_Oimage(X7,X19,X2,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
fof(fact_UN__equiv__class,axiom,
! [X13,X2,X19,X23,X9,X7] :
( c_Equiv__Relations_Oequiv(X7,X9,X23)
=> ( c_Equiv__Relations_Ocongruent(X7,tc_fun(X19,tc_HOL_Obool),X23,X2)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X19,tc_HOL_Obool),hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X2) = hAPP(X2,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class) ).
fof(fact_UN__I,axiom,
! [X8,X12,X19,X9,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> ( hBOOL(hAPP(hAPP(c_member(X19),X12),hAPP(X8,X13)))
=> hBOOL(hAPP(hAPP(c_member(X19),X12),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X19,tc_HOL_Obool),X9,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__I) ).
fof(fact_extensional__subset,axiom,
! [X8,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional(X7,X19,X9)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional(X7,X19,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__subset) ).
fof(fact_inj__on__restrict__eq,axiom,
! [X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,c_FuncSet_Orestrict(X7,X19,X2,X9),X9)
<=> c_Fun_Oinj__on(X7,X19,X2,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__restrict__eq) ).
fof(fact_SUP1__I,axiom,
! [X19,X12,X8,X9,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> ( hBOOL(hAPP(hAPP(X8,X13),X12))
=> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X19,tc_HOL_Obool),X9,X8),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__I) ).
fof(fact_imageI,axiom,
! [X2,X19,X9,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X4)),c_Set_Oimage(X7,X19,X2,X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact_diff__single__insert,axiom,
! [X8,X4,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X8)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__single__insert) ).
fof(fact_inf2I,axiom,
! [X19,X7,X8,X10,X4,X9] :
( hBOOL(hAPP(hAPP(X9,X4),X10))
=> ( hBOOL(hAPP(hAPP(X8,X4),X10))
=> hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),X9,X8),X4),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).
fof(fact_refl__onD,axiom,
! [X13,X23,X9,X7] :
( c_Relation_Orefl__on(X7,X9,X23)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X13)),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD) ).
fof(fact_image__eqI,axiom,
! [X7,X9,X19,X4,X2,X12] :
( X12 = hAPP(X2,X4)
=> ( hBOOL(hAPP(hAPP(c_member(X19),X4),X9))
=> hBOOL(hAPP(hAPP(c_member(X7),X12),c_Set_Oimage(X19,X7,X2,X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X19,X2,X12,X9,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( X12 = hAPP(X2,X4)
=> hBOOL(hAPP(hAPP(c_member(X19),X12),c_Set_Oimage(X7,X19,X2,X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_extensional__funcset__def,axiom,
! [X52,X17,X19,X7] : c_FuncSet_Oextensional__funcset(X7,X19,X17,X52) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X7,X19),tc_HOL_Obool),c_FuncSet_OPi(X7,X19,X17,c_COMBK(tc_fun(X19,tc_HOL_Obool),X7,X52)),c_FuncSet_Oextensional(X7,X19,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__def) ).
fof(fact_Domain__Diff__subset,axiom,
! [X8,X9,X19,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Relation_ODomain(X7,X19,X9),c_Relation_ODomain(X7,X19,X8)),c_Relation_ODomain(X7,X19,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),X9,X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).
fof(fact_Domain__Int__subset,axiom,
! [X8,X9,X19,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Relation_ODomain(X7,X19,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),X9,X8)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),c_Relation_ODomain(X7,X19,X9),c_Relation_ODomain(X7,X19,X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_Id__on__eqI,axiom,
! [X9,X7,X12,X13] :
( X13 = X12
=> ( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Relation_OId__on(X7,X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_Domain__insert,axiom,
! [X23,X12,X13,X19,X7] : c_Relation_ODomain(X7,X19,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X12)),X23)) = hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Relation_ODomain(X7,X19,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__insert) ).
fof(fact_Pi__anti__mono,axiom,
! [X8,X19,X9,X70,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X70,X9)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7,X19),tc_HOL_Obool),c_FuncSet_OPi(X7,X19,X9,X8),c_FuncSet_OPi(X7,X19,X70,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_fun__upd__triv,axiom,
! [X4,X2,X19,X7] : c_Fun_Ofun__upd(X7,X19,X2,X4,hAPP(X2,X4)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
fof(fact_fun__upd__idem,axiom,
! [X7,X19,X10,X4,X2] :
( hAPP(X2,X4) = X10
=> c_Fun_Ofun__upd(X19,X7,X2,X4,X10) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
fof(fact_image__mono,axiom,
! [X2,X19,X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X19,tc_HOL_Obool),c_Set_Oimage(X7,X19,X2,X9),c_Set_Oimage(X7,X19,X2,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_inj__on__Int,axiom,
! [X8,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( c_Fun_Oinj__on(X7,X19,X2,X8)
=> c_Fun_Oinj__on(X7,X19,X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Int) ).
fof(fact_trancl__mono,axiom,
! [X29,X23,X41,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X41),c_Transitive__Closure_Otrancl(X7,X23)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X23,X29)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X41),c_Transitive__Closure_Otrancl(X7,X29))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__mono) ).
fof(fact_Id__onE,axiom,
! [X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X6),c_Relation_OId__on(X7,X9)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> X6 != hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__onE) ).
fof(fact_pred__equals__eq,axiom,
! [X17,X18,X7] :
( hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X18) = hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X17)
<=> X18 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [X23,X13,X7] : hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X13)),c_Transitive__Closure_Ortrancl(X7,X23))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_the__inv__into__f__f,axiom,
! [X4,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_Fun_Othe__inv__into(X7,X19,X9,X2),hAPP(X2,X4)) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
fof(fact_inv__into__f__f,axiom,
! [X4,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_Hilbert__Choice_Oinv__into(X7,X19,X9,X2),hAPP(X2,X4)) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
fof(fact_the__inv__into__f__eq,axiom,
! [X10,X4,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( hAPP(X2,X4) = X10
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_Fun_Othe__inv__into(X7,X19,X9,X2),X10) = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
fof(fact_inv__into__f__eq,axiom,
! [X10,X4,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( hAPP(X2,X4) = X10
=> hAPP(c_Hilbert__Choice_Oinv__into(X7,X19,X9,X2),X10) = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
fof(fact_Image__Int__eq,axiom,
! [X8,X9,X18,X19,X7] :
( c_Relation_Osingle__valued(X7,X19,c_Relation_Oconverse(X19,X7,X18))
=> hAPP(c_Relation_OImage(X19,X7,X18),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19,tc_HOL_Obool),X9,X8)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(c_Relation_OImage(X19,X7,X18),X9),hAPP(c_Relation_OImage(X19,X7,X18),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__eq) ).
fof(fact_extensional__restrict,axiom,
! [X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional(X7,X19,X9)))
=> c_FuncSet_Orestrict(X7,X19,X2,X9) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__restrict) ).
fof(conj_0,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(help_c__COMBB__1,axiom,
! [X18,X75,X28,X39,X7,X19] : hAPP(hAPP(c_COMBB(X19,X7,X39,X28),X75),X18) = hAPP(X28,hAPP(X75,X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_insert__image,axiom,
! [X2,X19,X9,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(hAPP(c_Set_Oinsert(X19),hAPP(X2,X4)),c_Set_Oimage(X7,X19,X2,X9)) = c_Set_Oimage(X7,X19,X2,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).
fof(fact_image__restrict__eq,axiom,
! [X9,X2,X7,X19] : c_Set_Oimage(X19,X7,c_FuncSet_Orestrict(X19,X7,X2,X9),X9) = c_Set_Oimage(X19,X7,X2,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__restrict__eq) ).
fof(fact_complete__Lin,axiom,
! [X12,X13] :
( X13 != X12
=> ? [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),X13),X12)),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complete__Lin) ).
fof(fact_image__insert,axiom,
! [X8,X13,X2,X7,X19] : c_Set_Oimage(X19,X7,X2,hAPP(hAPP(c_Set_Oinsert(X19),X13),X8)) = hAPP(hAPP(c_Set_Oinsert(X7),hAPP(X2,X13)),c_Set_Oimage(X19,X7,X2,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).
fof(fact_converse__inv__image,axiom,
! [X2,X18,X19,X7] : c_Relation_Oconverse(X7,X7,c_Relation_Oinv__image(X19,X7,X18,X2)) = c_Relation_Oinv__image(X19,X7,c_Relation_Oconverse(X19,X19,X18),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__inv__image) ).
fof(fact_conversep__iff,axiom,
! [X12,X13,X23,X19,X7] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X7,X19,X23),X13),X12))
<=> hBOOL(hAPP(hAPP(X23,X12),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__iff) ).
fof(fact_conversep_Oequations,axiom,
! [X33,X32,X23,X19,X7] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X7,X19,X23),X32),X33))
<=> hBOOL(hAPP(hAPP(X23,X33),X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Oequations) ).
fof(fact_conversepD,axiom,
! [X12,X13,X23,X19,X7] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X7,X19,X23),X13),X12))
=> hBOOL(hAPP(hAPP(X23,X12),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversepD) ).
fof(fact_Image__mono,axiom,
! [X9,X70,X23,X71,X19,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),X71,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X70,X9)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X19,tc_HOL_Obool),hAPP(c_Relation_OImage(X7,X19,X71),X70),hAPP(c_Relation_OImage(X7,X19,X23),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__mono) ).
fof(fact_r__into__trancl_H,axiom,
! [X23,X41,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X41),X23))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X41),c_Transitive__Closure_Otrancl(X7,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_r__into__rtrancl,axiom,
! [X23,X41,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X41),X23))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X41),c_Transitive__Closure_Ortrancl(X7,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_extensional__funcset__empty__domain,axiom,
! [X52,X19,X7] : c_FuncSet_Oextensional__funcset(X7,X19,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X52) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,X19)),c_COMBK(X19,X7,c_HOL_Oundefined(X19))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,X19),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__empty__domain) ).
fof(fact_Diff__insert2,axiom,
! [X8,X13,X9,X7] : c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert2) ).
fof(fact_singleton__iff,axiom,
! [X13,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X12),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
<=> X12 = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__iff) ).
fof(fact_singletonE,axiom,
! [X13,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X12),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))
=> X12 = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singletonE) ).
fof(fact_doubleton__eq__iff,axiom,
! [X63,X6,X12,X13,X7] :
( hAPP(hAPP(c_Set_Oinsert(X7),X13),hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X7),X6),hAPP(hAPP(c_Set_Oinsert(X7),X63),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
<=> ( ( X13 = X6
& X12 = X63 )
| ( X13 = X63
& X12 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
fof(fact_DiffE,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffE) ).
fof(fact_inj__on__diff,axiom,
! [X8,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> c_Fun_Oinj__on(X7,X19,X2,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__diff) ).
fof(fact_insert__Diff,axiom,
! [X9,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff) ).
fof(fact_inj__on__iff,axiom,
! [X10,X4,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X10),X9))
=> ( hAPP(X2,X4) = hAPP(X2,X10)
<=> X4 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__on__contraD,axiom,
! [X10,X4,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( X4 != X10
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X10),X9))
=> hAPP(X2,X4) != hAPP(X2,X10) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_inj__onD,axiom,
! [X10,X4,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( hAPP(X2,X4) = hAPP(X2,X10)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X10),X9))
=> X4 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).
fof(fact_subset__inj__on,axiom,
! [X9,X8,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> c_Fun_Oinj__on(X7,X19,X2,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_DiffD1,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD1) ).
fof(fact_Int__iff,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
& hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD1,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).
fof(fact_IntD2,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).
fof(fact_IntI,axiom,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X8))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).
fof(fact_Image__closed__trancl,axiom,
! [X64,X23,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),hAPP(c_Relation_OImage(X7,X7,X23),X64),X64)
=> hAPP(c_Relation_OImage(X7,X7,c_Transitive__Closure_Ortrancl(X7,X23)),X64) = X64 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).
fof(fact_insert__Diff__single,axiom,
! [X9,X13,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X7),X13),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
fof(fact_extensional__empty,axiom,
! [X19,X7] : c_FuncSet_Oextensional(X7,X19,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X7,X19)),c_COMBK(X19,X7,c_HOL_Oundefined(X19))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,X19),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__empty) ).
fof(fact_converse__Int,axiom,
! [X29,X23,X7,X19] : c_Relation_Oconverse(X19,X7,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X19,X7),tc_HOL_Obool),X23,X29)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),c_Relation_Oconverse(X19,X7,X23),c_Relation_Oconverse(X19,X7,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Int) ).
fof(fact_converse__meet,axiom,
! [X29,X23,X7,X19] : c_Predicate_Oconversep(X19,X7,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19,tc_fun(X7,tc_HOL_Obool)),X23,X29)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),c_Predicate_Oconversep(X19,X7,X23),c_Predicate_Oconversep(X19,X7,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__meet) ).
fof(fact_conversep_Ointros,axiom,
! [X19,X7,X12,X13,X23] :
( hBOOL(hAPP(hAPP(X23,X13),X12))
=> hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X7,X19,X23),X12),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Ointros) ).
fof(fact_disjoint__iff__not__equal,axiom,
! [X8,X9,X7] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
=> ! [X24] :
( hBOOL(hAPP(hAPP(c_member(X7),X24),X8))
=> X3 != X24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
fof(fact_refl__on__Int,axiom,
! [X29,X8,X23,X9,X7] :
( c_Relation_Orefl__on(X7,X9,X23)
=> ( c_Relation_Orefl__on(X7,X8,X29)
=> c_Relation_Orefl__on(X7,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X23,X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Int) ).
fof(fact_Diff__mono,axiom,
! [X8,X35,X38,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X35,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X38,X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__mono) ).
fof(fact_Int__mono,axiom,
! [X35,X8,X38,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X35)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X38,X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).
fof(fact_image__constant,axiom,
! [X6,X19,X9,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Set_Oimage(X7,X19,c_COMBK(X19,X7,X6),X9) = hAPP(hAPP(c_Set_Oinsert(X19),X6),c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__constant) ).
fof(fact_Diff__insert,axiom,
! [X8,X13,X9,X7] : c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8),hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert) ).
fof(fact_Diff__Int2,axiom,
! [X8,X38,X9,X7] : c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X38),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38)) = c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X38),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int2) ).
fof(fact_Diff__Int__distrib2,axiom,
! [X38,X8,X9,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8),X38) = c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X38),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).
fof(fact_Diff__Int__distrib,axiom,
! [X8,X9,X38,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X38,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)) = c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X38,X9),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X38,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).
fof(fact_insert__iff,axiom,
! [X9,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),hAPP(hAPP(c_Set_Oinsert(X7),X12),X9)))
<=> ( X13 = X12
| hBOOL(hAPP(hAPP(c_member(X7),X13),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X9,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),hAPP(hAPP(c_Set_Oinsert(X7),X12),X9)))
=> ( X13 != X12
=> hBOOL(hAPP(hAPP(c_member(X7),X13),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_linear__alt,axiom,
? [X11] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X11),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linear__alt) ).
fof(fact_accp_Osimps,axiom,
! [X13,X23,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X23),X13))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X23,X3),X13))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X23),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
fof(fact_accp_Oequations,axiom,
! [X13,X23,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X23),X13))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X23,X3),X13))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X23),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
fof(help_c__COMBS__1,axiom,
! [X18,X75,X28,X7,X39,X19] : hAPP(hAPP(hAPP(c_COMBS(X19,X39,X7),X28),X75),X18) = hAPP(hAPP(X28,X18),hAPP(X75,X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_subset__singletonD,axiom,
! [X4,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> ( X9 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
| X9 = hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__singletonD) ).
fof(fact_RangeP_Oequations,axiom,
! [X32,X23,X19,X7] :
( c_Predicate_ORangeP(X7,X19,X23,X32)
<=> ? [X21] : hBOOL(hAPP(hAPP(X23,X21),X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
fof(help_c__COMBC__1,axiom,
! [X18,X75,X28,X7,X39,X19] : hAPP(hAPP(hAPP(c_COMBC(X19,X39,X7),X28),X75),X18) = hAPP(hAPP(X28,X18),X75),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_inf1D1,axiom,
! [X4,X8,X9,X7] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),X4))
=> hBOOL(hAPP(X9,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).
fof(fact_inf1D2,axiom,
! [X4,X8,X9,X7] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),X4))
=> hBOOL(hAPP(X8,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).
fof(fact_Int__insert__left__if1,axiom,
! [X8,X38,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),X38))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X13),X8),X38) = hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
fof(fact_Int__insert__right__if1,axiom,
! [X8,X9,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
fof(fact_the__eq__trivial,axiom,
! [X13,X7] : c_HOL_OThe(X7,hAPP(hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal),X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__eq__trivial) ).
fof(fact_Domain__mono,axiom,
! [X29,X23,X19,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),X23,X29)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Relation_ODomain(X7,X19,X23),c_Relation_ODomain(X7,X19,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__mono) ).
fof(fact_image__constant__conv,axiom,
! [X6,X19,X7,X9] :
( ( X9 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Set_Oimage(X7,X19,c_COMBK(X19,X7,X6),X9) = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool)) )
& ( X9 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Set_Oimage(X7,X19,c_COMBK(X19,X7,X6),X9) = hAPP(hAPP(c_Set_Oinsert(X19),X6),c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__constant__conv) ).
fof(fact_insert__inter__insert,axiom,
! [X8,X9,X13,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X13),X9),hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
fof(fact_insertI2,axiom,
! [X12,X8,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),X8))
=> hBOOL(hAPP(hAPP(c_member(X7),X13),hAPP(hAPP(c_Set_Oinsert(X7),X12),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
fof(fact_rtrancl__subset,axiom,
! [X17,X18,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X18,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X17,c_Transitive__Closure_Ortrancl(X7,X18))
=> c_Transitive__Closure_Ortrancl(X7,X17) = c_Transitive__Closure_Ortrancl(X7,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_double__diff,axiom,
! [X38,X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X38)
=> c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X8,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X38,X9)) = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__diff) ).
fof(fact_Int__greatest,axiom,
! [X8,X9,X38,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X38,X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X38,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X38,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).
fof(fact_insert__subset,axiom,
! [X8,X9,X4,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9),X8)
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X8))
& c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_bot__empty__eq,axiom,
! [X4,X7] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X4))
<=> hBOOL(hAPP(hAPP(c_member(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
fof(fact_Int__Diff,axiom,
! [X38,X8,X9,X7] : c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),X38) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X8,X38)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Diff) ).
fof(fact_Int__assoc,axiom,
! [X38,X8,X9,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),X38) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).
fof(fact_Int__left__commute,axiom,
! [X38,X8,X9,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X38)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).
fof(fact_empty__is__image,axiom,
! [X9,X2,X19,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = c_Set_Oimage(X19,X7,X2,X9)
<=> X9 = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__is__image) ).
fof(fact_image__is__empty,axiom,
! [X9,X2,X7,X19] :
( c_Set_Oimage(X19,X7,X2,X9) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> X9 = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__is__empty) ).
fof(fact_inf__mono,axiom,
! [X76,X60,X59,X61,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X61,X59)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X60,X76)
=> c_Orderings_Oord__class_Oless__eq(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60),c_Lattices_Osemilattice__inf__class_Oinf(X7,X59,X76)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).
fof(fact_inf1I,axiom,
! [X7,X8,X4,X9] :
( hBOOL(hAPP(X9,X4))
=> ( hBOOL(hAPP(X8,X4))
=> hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [X29,X23,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X23,c_Transitive__Closure_Ortrancl(X7,X29))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X7,X23),c_Transitive__Closure_Ortrancl(X7,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_insert__Diff1,axiom,
! [X9,X8,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X8))
=> c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9),X8) = c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff1) ).
fof(fact_predicate2D,axiom,
! [X10,X4,X75,X28,X19,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),X28,X75)
=> ( hBOOL(hAPP(hAPP(X28,X4),X10))
=> hBOOL(hAPP(hAPP(X75,X4),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X75,X19,X7,X10,X4,X28] :
( hBOOL(hAPP(hAPP(X28,X4),X10))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),X28,X75)
=> hBOOL(hAPP(hAPP(X75,X4),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_extensional__funcset__empty__range,axiom,
! [X19,X7,X17] :
( X17 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_FuncSet_Oextensional__funcset(X7,X19,X17,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,X19),tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__empty__range) ).
fof(fact_insert__mono,axiom,
! [X13,X35,X38,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X38,X35)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X13),X38),hAPP(hAPP(c_Set_Oinsert(X7),X13),X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(fact_insert__code,axiom,
! [X4,X9,X10,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X7),X10),X9),X4))
<=> ( X10 = X4
| hBOOL(hAPP(X9,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_set__rev__mp,axiom,
! [X8,X9,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> hBOOL(hAPP(hAPP(c_member(X7),X4),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_set__mp,axiom,
! [X4,X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hBOOL(hAPP(hAPP(c_member(X7),X4),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_in__mono,axiom,
! [X4,X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hBOOL(hAPP(hAPP(c_member(X7),X4),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_subsetD,axiom,
! [X6,X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_rtrancl__mono,axiom,
! [X29,X23,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X23,X29)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X7,X23),c_Transitive__Closure_Ortrancl(X7,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_DomainP_Ointros,axiom,
! [X19,X7,X12,X13,X23] :
( hBOOL(hAPP(hAPP(X23,X13),X12))
=> c_Predicate_ODomainP(X7,X19,X23,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_RangeP_Ointros,axiom,
! [X19,X7,X12,X13,X23] :
( hBOOL(hAPP(hAPP(X23,X13),X12))
=> c_Predicate_ORangeP(X7,X19,X23,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_single__valued__subset,axiom,
! [X29,X23,X19,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X19),tc_HOL_Obool),X23,X29)
=> ( c_Relation_Osingle__valued(X7,X19,X29)
=> c_Relation_Osingle__valued(X7,X19,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__subset) ).
fof(fact_le__inf__iff,axiom,
! [X20,X10,X4,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X4,c_Lattices_Osemilattice__inf__class_Oinf(X7,X10,X20))
<=> ( c_Orderings_Oord__class_Oless__eq(X7,X4,X10)
& c_Orderings_Oord__class_Oless__eq(X7,X4,X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).
fof(fact_le__infI,axiom,
! [X60,X61,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,X61)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,X60)
=> c_Orderings_Oord__class_Oless__eq(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).
fof(fact_inf__greatest,axiom,
! [X56,X57,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,X57)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,X56)
=> c_Orderings_Oord__class_Oless__eq(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X57,X56)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).
fof(fact_accp__downward,axiom,
! [X13,X12,X23,X7] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X23),X12))
=> ( hBOOL(hAPP(hAPP(X23,X13),X12))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X23),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
fof(fact_acc__subset,axiom,
! [X73,X74,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X74,X73)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Wellfounded_Oacc(X7,X73),c_Wellfounded_Oacc(X7,X74)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__subset) ).
fof(fact_inf_Oassoc,axiom,
! [X59,X60,X61,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60),X59) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,c_Lattices_Osemilattice__inf__class_Oinf(X7,X60,X59)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
fof(fact_inf__assoc,axiom,
! [X56,X57,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57),X56) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X57,X56)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).
fof(fact_inf__sup__aci_I2_J,axiom,
! [X56,X57,X58,X7] :
( class_Lattices_Olattice(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57),X56) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X57,X56)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
fof(fact_inf_Oleft__commute,axiom,
! [X59,X61,X60,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X60,c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X59)) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,c_Lattices_Osemilattice__inf__class_Oinf(X7,X60,X59)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
fof(fact_inf__left__commute,axiom,
! [X56,X57,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X57,X56)) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X57,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X56)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf__sup__aci_I3_J,axiom,
! [X56,X57,X58,X7] :
( class_Lattices_Olattice(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X57,X56)) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X57,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X56)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
fof(fact_singleton__inject,axiom,
! [X12,X13,X7] :
( hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))
=> X13 = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__inject) ).
fof(fact_accp__subset,axiom,
! [X73,X74,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_fun(X7,tc_HOL_Obool)),X74,X73)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Wellfounded_Oaccp(X7,X73),c_Wellfounded_Oaccp(X7,X74)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__subset) ).
fof(fact_image__empty,axiom,
! [X2,X7,X19] : c_Set_Oimage(X19,X7,X2,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__empty) ).
fof(fact_subset__trans,axiom,
! [X38,X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X38)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X38) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X63,X6,X12,X13,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( c_Groups_Ominus__class_Ominus(X7,X13,X12) = c_Groups_Ominus__class_Ominus(X7,X6,X63)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X13,X12)
<=> c_Orderings_Oord__class_Oless__eq(X7,X6,X63) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_insertI1,axiom,
! [X8,X13,X7] : hBOOL(hAPP(hAPP(c_member(X7),X13),hAPP(hAPP(c_Set_Oinsert(X7),X13),X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_refl__on__converse,axiom,
! [X23,X9,X7] :
( c_Relation_Orefl__on(X7,X9,c_Relation_Oconverse(X7,X7,X23))
<=> c_Relation_Orefl__on(X7,X9,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__converse) ).
fof(fact_total__on__converse,axiom,
! [X23,X9,X7] :
( c_Relation_Ototal__on(X7,X9,c_Relation_Oconverse(X7,X7,X23))
<=> c_Relation_Ototal__on(X7,X9,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__converse) ).
fof(fact_insert__commute,axiom,
! [X9,X10,X4,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X4),hAPP(hAPP(c_Set_Oinsert(X7),X10),X9)) = hAPP(hAPP(c_Set_Oinsert(X7),X10),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_Diff__idemp,axiom,
! [X8,X9,X7] : c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8),X8) = c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__idemp) ).
fof(fact_Int__left__absorb,axiom,
! [X8,X9,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_subset__insertI2,axiom,
! [X12,X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X12),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_inj__on__empty,axiom,
! [X2,X19,X7] : c_Fun_Oinj__on(X7,X19,X2,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__empty) ).
fof(fact_fun__diff__def,axiom,
! [X4,X8,X9,X19,X7] :
( class_Groups_Ominus(X7)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19,X7),X9,X8),X4) = c_Groups_Ominus__class_Ominus(X7,hAPP(X9,X4),hAPP(X8,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__diff__def) ).
fof(fact_minus__apply,axiom,
! [X4,X8,X9,X19,X7] :
( class_Groups_Ominus(X7)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19,X7),X9,X8),X4) = c_Groups_Ominus__class_Ominus(X7,hAPP(X9,X4),hAPP(X8,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(fact_inf__apply,axiom,
! [X4,X1,X2,X19,X7] :
( class_Lattices_Olattice(X7)
=> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19,X7),X2,X1),X4) = c_Lattices_Osemilattice__inf__class_Oinf(X7,hAPP(X2,X4),hAPP(X1,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__apply) ).
fof(fact_inf__fun__def,axiom,
! [X4,X1,X2,X19,X7] :
( class_Lattices_Olattice(X7)
=> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X19,X7),X2,X1),X4) = c_Lattices_Osemilattice__inf__class_Oinf(X7,hAPP(X2,X4),hAPP(X1,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).
fof(fact_refl__on__empty,axiom,
! [X7] : c_Relation_Orefl__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__empty) ).
fof(fact_Diff__disjoint,axiom,
! [X8,X9,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X8,X9)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__disjoint) ).
fof(fact_less__by__empty,axiom,
! [X8,X7,X9] :
( X9 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__by__empty) ).
fof(fact_le__infI1,axiom,
! [X60,X58,X61,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X61,X58)
=> c_Orderings_Oord__class_Oless__eq(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60),X58) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).
fof(fact_le__infI2,axiom,
! [X61,X58,X60,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X60,X58)
=> c_Orderings_Oord__class_Oless__eq(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60),X58) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).
fof(fact_image__ident,axiom,
! [X69,X7] : c_Set_Oimage(X7,X7,c_COMBI(X7),X69) = X69,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_inj__on__id2,axiom,
! [X9,X7] : c_Fun_Oinj__on(X7,X7,c_COMBI(X7),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(fact_Image__Id__on,axiom,
! [X8,X9,X7] : hAPP(c_Relation_OImage(X7,X7,c_Relation_OId__on(X7,X9)),X8) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id__on) ).
fof(fact_trancl__empty,axiom,
! [X7] : c_Transitive__Closure_Otrancl(X7,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__empty) ).
fof(fact_set__eq__subset,axiom,
! [X7,X8,X9] :
( X9 = X8
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X9)
=> X9 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_Diff__triv,axiom,
! [X8,X9,X7] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__triv) ).
fof(fact_eq__mem,axiom,
! [X10,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),hAPP(c_fequal,X10)))
<=> X4 = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_le__funD,axiom,
! [X4,X1,X2,X7,X19] :
( class_Orderings_Oord(X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X19),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(X2,X4),hAPP(X1,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X4,X1,X2,X7,X19] :
( class_Orderings_Oord(X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X19),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X19,hAPP(X2,X4),hAPP(X1,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_acyclic__subset,axiom,
! [X23,X29,X7] :
( c_Wellfounded_Oacyclic(X7,X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),X23,X29)
=> c_Wellfounded_Oacyclic(X7,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__subset) ).
fof(fact_ex__in__conv,axiom,
! [X9,X7] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
<=> X9 != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__in__conv) ).
fof(fact_Domain__empty,axiom,
! [X19,X7] : c_Relation_ODomain(X7,X19,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X19),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty) ).
fof(fact_order__trans,axiom,
! [X56,X57,X58,X7] :
( class_Orderings_Opreorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,X57)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X57,X56)
=> c_Orderings_Oord__class_Oless__eq(X7,X58,X56) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X56,X58,X57,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X57,X58)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X56,X57)
=> c_Orderings_Oord__class_Oless__eq(X7,X56,X58) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_subset__empty,axiom,
! [X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))
<=> X9 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__empty) ).
fof(fact_Diff__subset,axiom,
! [X8,X9,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset) ).
fof(fact_Int__lower1,axiom,
! [X8,X9,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).
fof(fact_Int__lower2,axiom,
! [X8,X9,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).
fof(fact_quotient__empty,axiom,
! [X23,X7] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X23) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__empty) ).
fof(fact_quotient__is__empty2,axiom,
! [X23,X9,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23)
<=> X9 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).
fof(fact_quotient__is__empty,axiom,
! [X23,X9,X7] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool))
<=> X9 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__is__empty) ).
fof(fact_inf_Oleft__idem,axiom,
! [X60,X61,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60)) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
fof(fact_inf__left__idem,axiom,
! [X57,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57)) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).
fof(fact_inf__sup__aci_I4_J,axiom,
! [X57,X58,X7] :
( class_Lattices_Olattice(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57)) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
fof(fact_insert__absorb,axiom,
! [X9,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> hAPP(hAPP(c_Set_Oinsert(X7),X13),X9) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_the__elem__eq,axiom,
! [X4,X7] : c_Set_Othe__elem(X7,hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__eq) ).
fof(fact_Domain__empty__iff,axiom,
! [X23,X19,X7] :
( c_Relation_ODomain(X7,X19,X23) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> X23 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X19),tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
fof(fact_insert__absorb2,axiom,
! [X9,X4,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X4),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9)) = hAPP(hAPP(c_Set_Oinsert(X7),X4),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(fact_acyclic__converse,axiom,
! [X23,X7] :
( c_Wellfounded_Oacyclic(X7,c_Relation_Oconverse(X7,X7,X23))
<=> c_Wellfounded_Oacyclic(X7,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__converse) ).
fof(fact_trancl__converse,axiom,
! [X23,X7] : c_Transitive__Closure_Otrancl(X7,c_Relation_Oconverse(X7,X7,X23)) = c_Relation_Oconverse(X7,X7,c_Transitive__Closure_Otrancl(X7,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converse) ).
fof(fact_rtrancl__converse,axiom,
! [X23,X7] : c_Transitive__Closure_Ortrancl(X7,c_Relation_Oconverse(X7,X7,X23)) = c_Relation_Oconverse(X7,X7,c_Transitive__Closure_Ortrancl(X7,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converse) ).
fof(fact_Int__absorb2,axiom,
! [X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).
fof(fact_Int__absorb1,axiom,
! [X9,X8,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X9)
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).
fof(fact_predicate1D,axiom,
! [X4,X75,X28,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X28,X75)
=> ( hBOOL(hAPP(X28,X4))
=> hBOOL(hAPP(X75,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X75,X7,X4,X28] :
( hBOOL(hAPP(X28,X4))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X28,X75)
=> hBOOL(hAPP(X75,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_Image__empty,axiom,
! [X18,X7,X19] : hAPP(c_Relation_OImage(X19,X7,X18),c_Orderings_Obot__class_Obot(tc_fun(X19,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__empty) ).
fof(fact_mem__def,axiom,
! [X9,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
<=> hBOOL(hAPP(X9,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X63,X6,X12,X13,X7] :
( class_Groups_Oab__group__add(X7)
=> ( c_Groups_Ominus__class_Ominus(X7,X13,X12) = c_Groups_Ominus__class_Ominus(X7,X6,X63)
=> ( X13 = X12
<=> X6 = X63 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_order__eq__iff,axiom,
! [X10,X4,X7] :
( class_Orderings_Oorder(X7)
=> ( X4 = X10
<=> ( c_Orderings_Oord__class_Oless__eq(X7,X4,X10)
& c_Orderings_Oord__class_Oless__eq(X7,X10,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X4,X10,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X10,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X4,X10)
<=> X4 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X57,X58,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,X57)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X57,X58)
=> X58 = X57 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X58,X57,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X57,X58)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,X57)
=> X58 = X57 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_subset__insertI,axiom,
! [X13,X8,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_inf__le1,axiom,
! [X57,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Orderings_Oord__class_Oless__eq(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57),X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I1_J,axiom,
! [X57,X58,X7] :
( class_Lattices_Olattice(X7)
=> c_Orderings_Oord__class_Oless__eq(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57),X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_inf__le2,axiom,
! [X57,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Orderings_Oord__class_Oless__eq(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57),X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [X57,X58,X7] :
( class_Lattices_Olattice(X7)
=> c_Orderings_Oord__class_Oless__eq(X7,c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57),X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_conversep__conversep,axiom,
! [X23,X7,X19] : c_Predicate_Oconversep(X19,X7,c_Predicate_Oconversep(X7,X19,X23)) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__conversep) ).
fof(fact_converse__converse,axiom,
! [X23,X7,X19] : c_Relation_Oconverse(X19,X7,c_Relation_Oconverse(X7,X19,X23)) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(fact_empty__Diff,axiom,
! [X9,X7] : c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X9) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Diff) ).
fof(fact_Int__empty__left,axiom,
! [X8,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X8) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__left) ).
fof(fact_Int__empty__right,axiom,
! [X9,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__right) ).
fof(fact_Int__commute,axiom,
! [X8,X9,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).
fof(fact_le__iff__inf,axiom,
! [X10,X4,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X4,X10)
<=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X4,X10) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).
fof(fact_inf__absorb1,axiom,
! [X57,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,X57)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57) = X58 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).
fof(fact_inf__absorb2,axiom,
! [X58,X57,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X57,X58)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57) = X57 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).
fof(fact_Id__on__empty,axiom,
! [X7] : c_Relation_OId__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__empty) ).
fof(fact_trancl__domain,axiom,
! [X23,X7] : c_Relation_ODomain(X7,X7,c_Transitive__Closure_Otrancl(X7,X23)) = c_Relation_ODomain(X7,X7,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__domain) ).
fof(fact_Diff__empty,axiom,
! [X9,X7] : c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__empty) ).
fof(fact_empty__subsetI,axiom,
! [X9,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_insert__not__empty,axiom,
! [X9,X13,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X13),X9) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__not__empty) ).
fof(fact_empty__not__insert,axiom,
! [X9,X13,X7] : c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X7),X13),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__not__insert) ).
fof(help_c__COMBK__1,axiom,
! [X81,X80,X19,X7] : hAPP(c_COMBK(X7,X19,X80),X81) = X80,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_linorder__linear,axiom,
! [X57,X58,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,X57)
| c_Orderings_Oord__class_Oless__eq(X7,X57,X58) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_inf_Ocommute,axiom,
! [X60,X61,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X60,X61) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
fof(fact_inf__commute,axiom,
! [X57,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X57,X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).
fof(fact_inf__sup__aci_I1_J,axiom,
! [X57,X58,X7] :
( class_Lattices_Olattice(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X57) = c_Lattices_Osemilattice__inf__class_Oinf(X7,X57,X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
fof(fact_total__on__empty,axiom,
! [X23,X7] : c_Relation_Ototal__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__empty) ).
fof(fact_Diff__cancel,axiom,
! [X9,X7] : c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X9) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).
fof(fact_converse__Id__on,axiom,
! [X9,X7] : c_Relation_Oconverse(X7,X7,c_Relation_OId__on(X7,X9)) = c_Relation_OId__on(X7,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id__on) ).
fof(fact_bot__apply,axiom,
! [X4,X19,X7] :
( class_Orderings_Obot(X7)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X19,X7)),X4) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(fact_bot__fun__def,axiom,
! [X4,X19,X7] :
( class_Orderings_Obot(X7)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X19,X7)),X4) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(fact_Domain__Id__on,axiom,
! [X9,X7] : c_Relation_ODomain(X7,X7,c_Relation_OId__on(X7,X9)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_equalityD1,axiom,
! [X7,X8,X9] :
( X9 = X8
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X7,X8,X9] :
( X9 = X8
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_single__valued__Id__on,axiom,
! [X9,X7] : c_Relation_Osingle__valued(X7,X7,c_Relation_OId__on(X7,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
fof(fact_refl__on__Id__on,axiom,
! [X9,X7] : c_Relation_Orefl__on(X7,X9,c_Relation_OId__on(X7,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
fof(help_c__fequal__2,axiom,
! [X10,X4] :
( X4 != X10
| hBOOL(hAPP(hAPP(c_fequal,X4),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_Int__absorb,axiom,
! [X9,X7] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X9) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(fact_subset__refl,axiom,
! [X9,X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_inf__bot__left,axiom,
! [X58,X7] :
( class_Lattices_Obounded__lattice__bot(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,c_Orderings_Obot__class_Obot(X7),X58) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__left) ).
fof(fact_inf__bot__right,axiom,
! [X58,X7] :
( class_Lattices_Obounded__lattice__bot(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,c_Orderings_Obot__class_Obot(X7)) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__right) ).
fof(fact_bot__least,axiom,
! [X58,X7] :
( class_Orderings_Obot(X7)
=> c_Orderings_Oord__class_Oless__eq(X7,c_Orderings_Obot__class_Obot(X7),X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__least) ).
fof(fact_order__eq__refl,axiom,
! [X57,X58,X7] :
( class_Orderings_Opreorder(X7)
=> ( X58 = X57
=> c_Orderings_Oord__class_Oless__eq(X7,X58,X57) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_inf_Oidem,axiom,
! [X61,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X61) = X61 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).
fof(fact_inf__idem,axiom,
! [X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(X7,X58,X58) = X58 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).
fof(fact_order__refl,axiom,
! [X58,X7] :
( class_Orderings_Opreorder(X7)
=> c_Orderings_Oord__class_Oless__eq(X7,X58,X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_rtrancl__trancl__absorb,axiom,
! [X18,X7] : c_Transitive__Closure_Otrancl(X7,c_Transitive__Closure_Ortrancl(X7,X18)) = c_Transitive__Closure_Ortrancl(X7,X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
fof(fact_trancl__rtrancl__absorb,axiom,
! [X18,X7] : c_Transitive__Closure_Ortrancl(X7,c_Transitive__Closure_Otrancl(X7,X18)) = c_Transitive__Closure_Ortrancl(X7,X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(fact_rtrancl__idemp,axiom,
! [X23,X7] : c_Transitive__Closure_Ortrancl(X7,c_Transitive__Closure_Ortrancl(X7,X23)) = c_Transitive__Closure_Ortrancl(X7,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_conversep__eq,axiom,
! [X7] : c_Predicate_Oconversep(X7,X7,c_fequal) = c_fequal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__eq) ).
fof(fact_the__sym__eq__trivial,axiom,
! [X4,X7] : c_HOL_OThe(X7,hAPP(c_fequal,X4)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(arity_fun__Lattices_Obounded__lattice,axiom,
! [X78,X79] :
( class_Lattices_Obounded__lattice(X79)
=> class_Lattices_Obounded__lattice(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X78,X79] :
( class_Orderings_Oorder(X79)
=> class_Orderings_Oorder(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X78,X79] :
( class_Orderings_Oord(X79)
=> class_Orderings_Oord(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X78,X79] :
( class_Orderings_Opreorder(X79)
=> class_Orderings_Opreorder(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Groups_Ominus,axiom,
! [X78,X79] :
( class_Groups_Ominus(X79)
=> class_Groups_Ominus(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_fun__Orderings_Obot,axiom,
! [X78,X79] :
( class_Orderings_Obot(X79)
=> class_Orderings_Obot(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
! [X78,X79] :
( class_Lattices_Obounded__lattice(X79)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(arity_fun__Lattices_Osemilattice__inf,axiom,
! [X78,X79] :
( class_Lattices_Olattice(X79)
=> class_Lattices_Osemilattice__inf(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(arity_fun__Lattices_Olattice,axiom,
! [X78,X79] :
( class_Lattices_Olattice(X79)
=> class_Lattices_Olattice(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(help_c__COMBI__1,axiom,
! [X80,X7] : hAPP(c_COMBI(X7),X80) = X80,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_assms_I1_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(fact__096P_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
fof(fact__096P_H_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_H_A_058_AProf_096) ).
fof(fact__096Q_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_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Q_A_058_AProf_096) ).
fof(fact__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096,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____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(arity_HOL__Obool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).
fof(fact_d1_I1_J,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d1_I1_J) ).
fof(fact_d2_I1_J,axiom,
v_a____ != v_b_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d2_I1_J) ).
fof(fact_d2_I2_J,axiom,
v_b____ != v_a_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d2_I2_J) ).
fof(fact_d1_I2_J,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d1_I2_J) ).
fof(i_0_516,plain,
! [X23,X19,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X12),c_Relation_ORange(X19,X7,X23)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X3),X12)),X23)) ),
inference(fof_simplification,[status(thm)],[fact_RangeE]) ).
fof(i_0_517,plain,
! [X23,X48,X49,X50,X51,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X51),X50)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X49),X48))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X19),X23)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X7,X19),X51),X50) != hAPP(hAPP(c_Product__Type_OPair(X7,X19),X49),X48)
=> ~ ! [X21,X22] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X51),X50)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X21),X22))),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X19),tc_prod(X7,X19))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X19),tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X21),X22)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X49),X48))),c_Transitive__Closure_Ortrancl(tc_prod(X7,X19),X23))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_converse__rtranclE2]) ).
fof(i_0_518,plain,
! [X2376,X2377,X2378,X2379] :
( ( ~ c_Predicate_ORangeP(X2379,X2378,hAPP(hAPP(c_COMBC(X2379,tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_fun(X2378,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2378,tc_fun(tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_fun(X2378,tc_HOL_Obool)),X2379,c_COMBC(X2378,tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2378,tc_prod(X2379,X2378)),tc_fun(X2378,tc_fun(tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_HOL_Obool)),X2379,c_COMBB(tc_prod(X2379,X2378),tc_fun(tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_HOL_Obool),X2378,c_member(tc_prod(X2379,X2378)))),c_Product__Type_OPair(X2379,X2378)))),X2377),X2376)
| hBOOL(hAPP(hAPP(c_member(X2378),X2376),c_Relation_ORange(X2379,X2378,X2377))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2378),X2376),c_Relation_ORange(X2379,X2378,X2377)))
| c_Predicate_ORangeP(X2379,X2378,hAPP(hAPP(c_COMBC(X2379,tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_fun(X2378,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2378,tc_fun(tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_fun(X2378,tc_HOL_Obool)),X2379,c_COMBC(X2378,tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2378,tc_prod(X2379,X2378)),tc_fun(X2378,tc_fun(tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_HOL_Obool)),X2379,c_COMBB(tc_prod(X2379,X2378),tc_fun(tc_fun(tc_prod(X2379,X2378),tc_HOL_Obool),tc_HOL_Obool),X2378,c_member(tc_prod(X2379,X2378)))),c_Product__Type_OPair(X2379,X2378)))),X2377),X2376) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).
fof(i_0_519,plain,
! [X2469,X2470,X2471] : c_Relation_ORange(X2471,X2470,X2469) = c_Relation_ODomain(X2470,X2471,c_Relation_Oconverse(X2471,X2470,X2469)),
inference(variable_rename,[status(thm)],[fact_Range__def]) ).
fof(i_0_520,plain,
! [X9,X23,X19,X12,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X12),hAPP(c_Relation_OImage(X19,X7,X23),X9)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X3),X12)),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(X19),X3),X9)) ) ),
inference(fof_simplification,[status(thm)],[fact_ImageE]) ).
fof(i_0_521,plain,
! [X2504,X2505,X2506,X2507,X2508,X2509,X2510,X2511,X2512,X2513,X2514] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2514,X2513)),X2512),c_FuncSet_OPi(X2514,X2513,X2511,c_COMBK(tc_fun(X2513,tc_HOL_Obool),X2514,X2510))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2513,X2509)),X2508),c_FuncSet_OPi(X2513,X2509,X2510,c_COMBK(tc_fun(X2509,tc_HOL_Obool),X2513,X2507))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2509,X2506)),X2505),c_FuncSet_OPi(X2509,X2506,X2507,c_COMBK(tc_fun(X2506,tc_HOL_Obool),X2509,X2504))))
| c_FuncSet_Ocompose(X2514,X2509,X2506,X2511,X2505,c_FuncSet_Ocompose(X2514,X2513,X2509,X2511,X2508,X2512)) = c_FuncSet_Ocompose(X2514,X2513,X2506,X2511,c_FuncSet_Ocompose(X2513,X2509,X2506,X2510,X2505,X2508),X2512) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__assoc])]) ).
fof(i_0_522,plain,
! [X2736,X2737,X2738,X2739,X2740,X2741] : c_FuncSet_Ocompose(X2741,X2740,X2739,X2738,X2737,X2736) = c_FuncSet_Orestrict(X2741,X2739,hAPP(c_COMBB(X2740,X2739,X2741,X2737),X2736),X2738),
inference(variable_rename,[status(thm)],[fact_compose__def]) ).
fof(i_0_523,plain,
! [X2515,X2516,X2517,X2518,X2519,X2520,X2521,X2522] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2522,X2521)),X2520),c_FuncSet_OPi(X2522,X2521,X2519,c_COMBK(tc_fun(X2521,tc_HOL_Obool),X2522,X2518))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2521,X2517)),X2516),c_FuncSet_OPi(X2521,X2517,X2518,c_COMBK(tc_fun(X2517,tc_HOL_Obool),X2521,X2515))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2522,X2517)),c_FuncSet_Ocompose(X2522,X2521,X2517,X2519,X2516,X2520)),c_FuncSet_OPi(X2522,X2517,X2519,c_COMBK(tc_fun(X2517,tc_HOL_Obool),X2522,X2515)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__compose])]) ).
fof(i_0_524,plain,
! [X52,X2,X19,X17,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X17))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional__funcset(X7,X19,hAPP(hAPP(c_Set_Oinsert(X7),X4),X17),X52)))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),c_Fun_Ofun__upd(X7,X19,X2,X4,c_HOL_Oundefined(X19))),c_FuncSet_Oextensional__funcset(X7,X19,X17,X52))) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__funcset__restrict__domain]) ).
fof(i_0_525,plain,
! [X23,X25,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),X25),c_Relation_Oconverse(X19,X7,X23)))
=> ~ ! [X3,X26] :
( X25 = hAPP(hAPP(c_Product__Type_OPair(X7,X19),X26),X3)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X19,X7)),hAPP(hAPP(c_Product__Type_OPair(X19,X7),X3),X26)),X23)) ) ),
inference(fof_simplification,[status(thm)],[fact_converseE]) ).
fof(i_0_526,plain,
! [X23,X20,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X20)),c_Transitive__Closure_Otrancl(X7,X23)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X20)),X23))
=> ~ ! [X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X26)),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X20)),c_Transitive__Closure_Otrancl(X7,X23))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_converse__tranclE]) ).
fof(i_0_527,plain,
! [X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Otrancl(X7,X23)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),X23))
=> ~ ! [X62] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X62)),c_Transitive__Closure_Otrancl(X7,X23)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X62),X12)),X23)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_tranclE]) ).
fof(i_0_528,plain,
! [X23,X20,X4,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X20)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( X4 != X20
=> ~ ! [X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X26)),X23))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X20)),c_Transitive__Closure_Ortrancl(X7,X23))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_converse__rtranclE]) ).
fof(i_0_529,plain,
! [X23,X12,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X12)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ( X13 != X12
=> ~ ! [X26] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X13),X26)),c_Transitive__Closure_Ortrancl(X7,X23)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X12)),X23)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_rtranclE]) ).
fof(i_0_530,plain,
! [X2581,X2582,X2583,X2584,X2585,X2586] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2586,X2585)),c_FuncSet_Ocompose(X2586,X2584,X2585,X2583,X2582,X2581)),c_FuncSet_Oextensional(X2586,X2585,X2583))),
inference(variable_rename,[status(thm)],[fact_compose__extensional]) ).
fof(i_0_531,plain,
! [X2392,X2393,X2394,X2395] :
( ~ hBOOL(hAPP(hAPP(c_member(X2395),X2394),c_Relation_ORange(X2393,X2395,X2392)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2393,X2395)),hAPP(hAPP(c_Product__Type_OPair(X2393,X2395),esk23_4(X2392,X2393,X2394,X2395)),X2394)),X2392)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_516])])]) ).
fof(i_0_532,plain,
! [X2366,X2367,X2368,X2369,X2371,X2372,X2373,X2374,X2375] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2369),X2368),c_Relation_ORange(X2367,X2369,X2366)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2367,X2369)),hAPP(hAPP(c_Product__Type_OPair(X2367,X2369),esk21_4(X2366,X2367,X2368,X2369)),X2368)),X2366)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2372,X2374)),hAPP(hAPP(c_Product__Type_OPair(X2372,X2374),X2375),X2373)),X2371))
| hBOOL(hAPP(hAPP(c_member(X2374),X2373),c_Relation_ORange(X2372,X2374,X2371))) ) ),
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_533,plain,
! [X2676,X2677,X2678,X2679,X2680] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2680,X2679)),X2678),c_FuncSet_OPi(X2680,X2679,X2677,c_COMBK(tc_fun(X2679,tc_HOL_Obool),X2680,X2676))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2680,X2679)),X2678),c_FuncSet_Oextensional(X2680,X2679,X2677)))
| c_FuncSet_Ocompose(X2680,X2679,X2679,X2677,c_FuncSet_Orestrict(X2679,X2679,c_COMBI(X2679),X2676),X2678) = X2678 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__compose])]) ).
fof(i_0_534,plain,
! [X2671,X2672,X2673,X2674,X2675] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2675,X2674)),X2673),c_FuncSet_OPi(X2675,X2674,X2672,c_COMBK(tc_fun(X2674,tc_HOL_Obool),X2675,X2671))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2675,X2674)),X2673),c_FuncSet_Oextensional(X2675,X2674,X2672)))
| c_FuncSet_Ocompose(X2675,X2675,X2674,X2672,X2673,c_FuncSet_Orestrict(X2675,X2675,c_COMBI(X2675),X2672)) = X2673 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__Id])]) ).
fof(i_0_535,plain,
! [X9,X13,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,hAPP(hAPP(c_Set_Oinsert(X7),X13),X9))
<=> ( c_Fun_Oinj__on(X7,X19,X2,X9)
& ~ hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X13)),c_Set_Oimage(X7,X19,X2,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))) ) ),
inference(fof_simplification,[status(thm)],[fact_inj__on__insert]) ).
fof(i_0_536,plain,
! [X23,X19,X13,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X13),c_Relation_ODomain(X7,X19,X23)))
=> ~ ! [X26] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X19)),hAPP(hAPP(c_Product__Type_OPair(X7,X19),X13),X26)),X23)) ),
inference(fof_simplification,[status(thm)],[fact_DomainE]) ).
fof(i_0_537,plain,
! [X3751,X3752,X3753,X3754,X3755] :
( c_Set_Oimage(X3755,X3754,X3753,X3752) != X3751
| c_FuncSet_Ocompose(X3754,X3755,X3754,X3751,X3753,c_FuncSet_Orestrict(X3754,X3755,c_Hilbert__Choice_Oinv__into(X3755,X3754,X3752,X3753),X3751)) = c_FuncSet_Orestrict(X3754,X3754,c_COMBI(X3754),X3751) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__id__inv__into])]) ).
fof(i_0_538,plain,
! [X10,X2,X19,X9,X4,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Set_Oimage(X7,X19,c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X9) = hAPP(hAPP(c_Set_Oinsert(X19),X10),c_Set_Oimage(X7,X19,X2,c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Set_Oimage(X7,X19,c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X9) = c_Set_Oimage(X7,X19,X2,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__upd__image]) ).
fof(i_0_539,plain,
! [X4,X10,X9,X2,X19,X7] :
( c_Fun_Oinj__on(X7,X19,X2,X9)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X19),X10),c_Set_Oimage(X7,X19,X2,X9)))
=> c_Fun_Oinj__on(X7,X19,c_Fun_Ofun__upd(X7,X19,X2,X4,X10),X9) ) ),
inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI]) ).
fof(i_0_540,plain,
! [X10,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))
=> ( X4 != 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),X4),X10)),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),X10),X4)),X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).
fof(i_0_541,plain,
! [X12,X13,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))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X13),X12)),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),X12),X13)),X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_542,plain,
! [X3671,X3672,X3673,X3674,X3675,X3676,X3677,X3678] :
( c_Set_Oimage(X3678,X3677,X3676,X3675) != X3674
| c_Set_Oimage(X3677,X3673,X3672,X3674) != X3671
| c_Set_Oimage(X3678,X3673,c_FuncSet_Ocompose(X3678,X3677,X3673,X3675,X3672,X3676),X3675) = X3671 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__compose])]) ).
fof(i_0_543,plain,
! [X23,X4,X10,X7] :
( c_Wellfounded_Oacyclic(X7,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X4)),X23))
<=> ( c_Wellfounded_Oacyclic(X7,X23)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Ortrancl(X7,X23))) ) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__insert]) ).
fof(i_0_544,plain,
! [X23,X9,X64,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X64),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X9),X23)))
=> ~ ! [X3] :
( X64 = hAPP(c_Relation_OImage(X7,X7,X23),hAPP(hAPP(c_Set_Oinsert(X7),X3),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X9)) ) ),
inference(fof_simplification,[status(thm)],[fact_quotientE]) ).
fof(i_0_545,plain,
! [X18,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),c_Wellfounded_Oacc(X7,X18)))
=> ~ ! [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X40),X4)),X18))
=> hBOOL(hAPP(hAPP(c_member(X7),X40),c_Wellfounded_Oacc(X7,X18))) ) ),
inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).
fof(i_0_546,plain,
! [X4129,X4130,X4131,X4132] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4132,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4132,tc_HOL_Obool),c_Relation_ORange(X4131,X4132,X4130),c_Relation_ORange(X4131,X4132,X4129)),c_Relation_ORange(X4131,X4132,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4131,X4132),tc_HOL_Obool),X4130,X4129))),
inference(variable_rename,[status(thm)],[fact_Range__Diff__subset]) ).
fof(i_0_547,plain,
! [X4172,X4173,X4174,X4175] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4175,tc_HOL_Obool),c_Relation_ORange(X4174,X4175,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4174,X4175),tc_HOL_Obool),X4173,X4172)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4175,tc_HOL_Obool),c_Relation_ORange(X4174,X4175,X4173),c_Relation_ORange(X4174,X4175,X4172))),
inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).
fof(i_0_548,plain,
! [X2556,X2557,X2558,X2559,X2560,X2561,X2562] :
( ~ hBOOL(hAPP(hAPP(c_member(X2562),X2561),X2560))
| hAPP(c_FuncSet_Ocompose(X2562,X2559,X2558,X2560,X2557,X2556),X2561) = hAPP(X2557,hAPP(X2556,X2561)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__eq])]) ).
fof(i_0_549,plain,
! [X3169,X3170,X3171,X3172,X3173] : c_Relation_ORange(X3173,X3172,hAPP(hAPP(c_Set_Oinsert(tc_prod(X3173,X3172)),hAPP(hAPP(c_Product__Type_OPair(X3173,X3172),X3171),X3170)),X3169)) = hAPP(hAPP(c_Set_Oinsert(X3172),X3170),c_Relation_ORange(X3173,X3172,X3169)),
inference(variable_rename,[status(thm)],[fact_Range__insert]) ).
fof(i_0_550,plain,
! [X4,X8,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_OPi(X7,X19,X9,X8)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X19),hAPP(X2,X4)),hAPP(X8,X4)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9)) ) ),
inference(fof_simplification,[status(thm)],[fact_PiE]) ).
fof(i_0_551,plain,
! [X2346,X2347,X2348,X2349,X2350] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2350,X2349)),hAPP(hAPP(c_Product__Type_OPair(X2350,X2349),X2348),X2347)),X2346))
| hBOOL(hAPP(hAPP(c_member(X2349),X2347),c_Relation_ORange(X2350,X2349,X2346))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).
fof(i_0_552,plain,
! [X4,X23,X7] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),c_Relation_Oconverse(X7,X7,X23),c_Transitive__Closure_Ortrancl(X7,X23)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X4)),c_Transitive__Closure_Otrancl(X7,X23))) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI]) ).
fof(i_0_553,plain,
! [X12,X9,X7] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> c_Partial__Function_Oflat__lub(X7,X12,X9) = X12 )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))
=> c_Partial__Function_Oflat__lub(X7,X12,X9) = c_HOL_OThe(X7,hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X12),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))) ) ),
inference(fof_simplification,[status(thm)],[fact_flat__lub__def]) ).
fof(i_0_554,plain,
! [X4,X52,X17,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional__funcset(X7,X19,X17,X52)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X17))
=> hAPP(X2,X4) = c_HOL_Oundefined(X19) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__funcset__arb]) ).
fof(i_0_555,plain,
! [X2,X19,X23,X4,X10,X7] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X4)),X23))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X7,X19),X2),X23),X4),X10) = hAPP(X2,X10) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X10),X4)),X23))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X7,X19),X2),X23),X4),X10) = c_HOL_Oundefined(X19) ) ),
inference(fof_simplification,[status(thm)],[fact_cut__def]) ).
fof(i_0_556,plain,
! [X10,X18,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),c_Relation_ODomain(X7,X7,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X4),X10)),c_Transitive__Closure_Ortrancl(X7,X18)))
<=> X4 = X10 ) ),
inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).
fof(i_0_557,plain,
! [X10,X4,X8,X9,X19,X7] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X19,tc_HOL_Obool)),X9,X8),X4),X10))
=> ~ ( hBOOL(hAPP(hAPP(X9,X4),X10))
=> ~ hBOOL(hAPP(hAPP(X8,X4),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf2E]) ).
fof(i_0_558,plain,
! [X23,X7] :
( c_Wellfounded_Oacyclic(X7,X23)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),c_Transitive__Closure_Otrancl(X7,X23))) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).
fof(i_0_559,plain,
! [X23,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),c_Transitive__Closure_Otrancl(X7,X23)))
=> c_Wellfounded_Oacyclic(X7,X23) ),
inference(fof_simplification,[status(thm)],[fact_acyclicI]) ).
fof(i_0_560,plain,
! [X23,X7] :
( c_Relation_Oirrefl(X7,X23)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X3)),X23)) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).
fof(i_0_561,plain,
! [X8,X4,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),X8))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X8) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8) ) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert__iff]) ).
fof(i_0_562,plain,
! [X10,X4,X19,X7] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_fun(X19,tc_HOL_Obool))),X4),X10)),
inference(fof_simplification,[status(thm)],[fact_bot2E]) ).
fof(i_0_563,plain,
! [X4,X9,X2,X19,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X19)),X2),c_FuncSet_Oextensional(X7,X19,X9)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(X2,X4) = c_HOL_Oundefined(X19) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__arb]) ).
fof(i_0_564,plain,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)))
<=> ( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
& ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_Diff__iff]) ).
fof(i_0_565,plain,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ),
inference(fof_simplification,[status(thm)],[fact_DiffD2]) ).
fof(i_0_566,plain,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_IntE]) ).
fof(i_0_567,plain,
! [X2,X19,X9,X4,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_FuncSet_Orestrict(X7,X19,X2,X9),X4) = hAPP(X2,X4) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_FuncSet_Orestrict(X7,X19,X2,X9),X4) = c_HOL_Oundefined(X19) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__def]) ).
fof(i_0_568,plain,
! [X2,X19,X9,X4,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_FuncSet_Orestrict(X7,X19,X2,X9),X4) = hAPP(X2,X4) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> hAPP(c_FuncSet_Orestrict(X7,X19,X2,X9),X4) = c_HOL_Oundefined(X19) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__apply]) ).
fof(i_0_569,plain,
! [X8,X9,X6,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X6),X9))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X6),X8))
=> hBOOL(hAPP(hAPP(c_member(X7),X6),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8))) ) ),
inference(fof_simplification,[status(thm)],[fact_DiffI]) ).
fof(i_0_570,plain,
! [X4,X8,X9,X7] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8),X4))
=> ~ ( hBOOL(hAPP(X9,X4))
=> ~ hBOOL(hAPP(X8,X4)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf1E]) ).
fof(i_0_571,plain,
! [X8,X38,X13,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X13),X38))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X13),X8),X38) = hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X38))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X13),X8),X38) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38) ) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__left]) ).
fof(i_0_572,plain,
! [X8,X9,X13,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = hAPP(hAPP(c_Set_Oinsert(X7),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__right]) ).
fof(i_0_573,plain,
! [X3258,X3259] : c_Relation_ORange(X3259,X3258,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3259,X3258),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X3258,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Range__empty]) ).
fof(i_0_574,plain,
! [X9,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9),hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X9 ),
inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb]) ).
fof(i_0_575,plain,
! [X9,X8,X4,X7] :
( ( hBOOL(hAPP(hAPP(c_member(X7),X4),X8))
=> c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9),X8) = c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X8))
=> c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X4),X9),X8) = hAPP(hAPP(c_Set_Oinsert(X7),X4),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool),X9,X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__Diff__if]) ).
fof(i_0_576,plain,
! [X12,X8,X13,X7] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X8))
=> X13 = X12 )
=> hBOOL(hAPP(hAPP(c_member(X7),X13),hAPP(hAPP(c_Set_Oinsert(X7),X12),X8))) ),
inference(fof_simplification,[status(thm)],[fact_insertCI]) ).
fof(i_0_577,plain,
! [X8,X9,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X4),X8))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).
fof(i_0_578,plain,
! [X2475,X2476,X2477] : c_Relation_ORange(X2477,X2476,c_Relation_Oconverse(X2476,X2477,X2475)) = c_Relation_ODomain(X2476,X2477,X2475),
inference(variable_rename,[status(thm)],[fact_Range__converse]) ).
fof(i_0_579,plain,
! [X8,X9,X4,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X9))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),X4),X8))
=> ( hAPP(hAPP(c_Set_Oinsert(X7),X4),X9) = hAPP(hAPP(c_Set_Oinsert(X7),X4),X8)
<=> X9 = X8 ) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).
fof(i_0_580,plain,
! [X3260,X3261,X3262] :
( ( c_Relation_ORange(X3262,X3261,X3260) != c_Orderings_Obot__class_Obot(tc_fun(X3261,tc_HOL_Obool))
| X3260 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3262,X3261),tc_HOL_Obool)) )
& ( X3260 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3262,X3261),tc_HOL_Obool))
| c_Relation_ORange(X3262,X3261,X3260) = c_Orderings_Obot__class_Obot(tc_fun(X3261,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])]) ).
fof(i_0_581,plain,
! [X2944,X2945] : c_Relation_ORange(X2945,X2945,c_Transitive__Closure_Otrancl(X2945,X2944)) = c_Relation_ORange(X2945,X2945,X2944),
inference(variable_rename,[status(thm)],[fact_trancl__range]) ).
fof(i_0_582,plain,
! [X8,X38,X13,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X38))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X7),X13),X8),X38) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X8,X38) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__left__if0]) ).
fof(i_0_583,plain,
! [X8,X9,X13,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X9))
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,hAPP(hAPP(c_Set_Oinsert(X7),X13),X8)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool),X9,X8) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if0]) ).
fof(i_0_584,plain,
! [X6,X7] : ~ hBOOL(hAPP(hAPP(c_member(X7),X6),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).
fof(i_0_585,plain,
! [X13,X7] : ~ hBOOL(hAPP(hAPP(c_member(X7),X13),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_emptyE]) ).
fof(i_0_586,plain,
! [X60,X61,X58,X7] :
( class_Lattices_Osemilattice__inf(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X58,c_Lattices_Osemilattice__inf__class_Oinf(X7,X61,X60))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X7,X58,X61)
=> ~ c_Orderings_Oord__class_Oless__eq(X7,X58,X60) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__infE]) ).
fof(i_0_587,plain,
! [X9,X7] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X7),X3),X9))
<=> X9 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).
fof(i_0_588,plain,
! [X2362,X2363] : c_Relation_ORange(X2363,X2363,c_Relation_OId__on(X2363,X2362)) = X2362,
inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).
fof(i_0_589,plain,
! [X13,X7,X9] :
( X9 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X13),X9)) ),
inference(fof_simplification,[status(thm)],[fact_equals0D]) ).
fof(i_0_590,plain,
! [X75,X28] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X28),X75))
| hBOOL(X28) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(i_0_591,plain,
! [X75,X28] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X28),X75))
| hBOOL(X75) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).
fof(i_0_592,plain,
! [X10,X4] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X4),X10))
| X4 = X10 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_593,plain,
! [X57,X58,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X7,X58,X57)
=> c_Orderings_Oord__class_Oless__eq(X7,X57,X58) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_594,plain,
! [X75,X28] :
( ~ hBOOL(X28)
| ~ hBOOL(X75)
| hBOOL(hAPP(hAPP(c_fconj,X28),X75)) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).
fof(i_0_595,plain,
! [X7,X8,X9] :
( X9 = X8
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X9,X8)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X8,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_596,plain,
! [X28] :
( ~ hBOOL(hAPP(c_fNot,X28))
| ~ hBOOL(X28) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(i_0_597,plain,
! [X28] :
( hBOOL(X28)
| hBOOL(hAPP(c_fNot,X28)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
fof(i_0_598,plain,
! [X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2693,X2692),tc_prod(X2693,X2692))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2693,X2692),tc_prod(X2693,X2692)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),X2691),X2690)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),esk38_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693)),esk39_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693)))),c_Transitive__Closure_Ortrancl(tc_prod(X2693,X2692),X2687)))
| hBOOL(hAPP(hAPP(X2686,X2689),X2688))
| ~ hBOOL(hAPP(hAPP(X2686,X2691),X2690))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2693,X2692),tc_prod(X2693,X2692))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2693,X2692),tc_prod(X2693,X2692)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),X2691),X2690)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),X2689),X2688))),c_Transitive__Closure_Ortrancl(tc_prod(X2693,X2692),X2687))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2693,X2692),tc_prod(X2693,X2692))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2693,X2692),tc_prod(X2693,X2692)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),esk38_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693)),esk39_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693))),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),esk40_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693)),esk41_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693)))),X2687))
| hBOOL(hAPP(hAPP(X2686,X2689),X2688))
| ~ hBOOL(hAPP(hAPP(X2686,X2691),X2690))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2693,X2692),tc_prod(X2693,X2692))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2693,X2692),tc_prod(X2693,X2692)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),X2691),X2690)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),X2689),X2688))),c_Transitive__Closure_Ortrancl(tc_prod(X2693,X2692),X2687))) )
& ( hBOOL(hAPP(hAPP(X2686,esk38_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693)),esk39_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693)))
| hBOOL(hAPP(hAPP(X2686,X2689),X2688))
| ~ hBOOL(hAPP(hAPP(X2686,X2691),X2690))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2693,X2692),tc_prod(X2693,X2692))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2693,X2692),tc_prod(X2693,X2692)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),X2691),X2690)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),X2689),X2688))),c_Transitive__Closure_Ortrancl(tc_prod(X2693,X2692),X2687))) )
& ( ~ hBOOL(hAPP(hAPP(X2686,esk40_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693)),esk41_8(X2686,X2687,X2688,X2689,X2690,X2691,X2692,X2693)))
| hBOOL(hAPP(hAPP(X2686,X2689),X2688))
| ~ hBOOL(hAPP(hAPP(X2686,X2691),X2690))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2693,X2692),tc_prod(X2693,X2692))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2693,X2692),tc_prod(X2693,X2692)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),X2691),X2690)),hAPP(hAPP(c_Product__Type_OPair(X2693,X2692),X2689),X2688))),c_Transitive__Closure_Ortrancl(tc_prod(X2693,X2692),X2687))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__induct2])])])]) ).
fof(i_0_599,plain,
! [X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2705,X2704),tc_prod(X2705,X2704))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2705,X2704),tc_prod(X2705,X2704)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),esk42_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705)),esk43_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705))),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),esk44_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705)),esk45_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705)))),X2699))
| hBOOL(hAPP(hAPP(X2698,X2703),X2702))
| ~ hBOOL(hAPP(hAPP(X2698,X2701),X2700))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2705,X2704),tc_prod(X2705,X2704))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2705,X2704),tc_prod(X2705,X2704)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),X2703),X2702)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),X2701),X2700))),c_Transitive__Closure_Ortrancl(tc_prod(X2705,X2704),X2699))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2705,X2704),tc_prod(X2705,X2704))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2705,X2704),tc_prod(X2705,X2704)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),esk44_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705)),esk45_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705))),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),X2701),X2700))),c_Transitive__Closure_Ortrancl(tc_prod(X2705,X2704),X2699)))
| hBOOL(hAPP(hAPP(X2698,X2703),X2702))
| ~ hBOOL(hAPP(hAPP(X2698,X2701),X2700))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2705,X2704),tc_prod(X2705,X2704))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2705,X2704),tc_prod(X2705,X2704)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),X2703),X2702)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),X2701),X2700))),c_Transitive__Closure_Ortrancl(tc_prod(X2705,X2704),X2699))) )
& ( hBOOL(hAPP(hAPP(X2698,esk44_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705)),esk45_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705)))
| hBOOL(hAPP(hAPP(X2698,X2703),X2702))
| ~ hBOOL(hAPP(hAPP(X2698,X2701),X2700))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2705,X2704),tc_prod(X2705,X2704))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2705,X2704),tc_prod(X2705,X2704)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),X2703),X2702)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),X2701),X2700))),c_Transitive__Closure_Ortrancl(tc_prod(X2705,X2704),X2699))) )
& ( ~ hBOOL(hAPP(hAPP(X2698,esk42_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705)),esk43_8(X2698,X2699,X2700,X2701,X2702,X2703,X2704,X2705)))
| hBOOL(hAPP(hAPP(X2698,X2703),X2702))
| ~ hBOOL(hAPP(hAPP(X2698,X2701),X2700))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2705,X2704),tc_prod(X2705,X2704))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2705,X2704),tc_prod(X2705,X2704)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),X2703),X2702)),hAPP(hAPP(c_Product__Type_OPair(X2705,X2704),X2701),X2700))),c_Transitive__Closure_Ortrancl(tc_prod(X2705,X2704),X2699))) ) ),
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_600,plain,
! [X2710,X2711,X2712,X2713,X2714,X2715,X2716] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2716,X2715),tc_prod(X2716,X2715))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2716,X2715),tc_prod(X2716,X2715)),hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2714),X2713)),hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),esk46_7(X2710,X2711,X2712,X2713,X2714,X2715,X2716)),esk47_7(X2710,X2711,X2712,X2713,X2714,X2715,X2716)))),X2710))
| hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2714),X2713) = hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2712),X2711)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2716,X2715),tc_prod(X2716,X2715))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2716,X2715),tc_prod(X2716,X2715)),hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2714),X2713)),hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2712),X2711))),c_Transitive__Closure_Ortrancl(tc_prod(X2716,X2715),X2710))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2716,X2715),tc_prod(X2716,X2715))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2716,X2715),tc_prod(X2716,X2715)),hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),esk46_7(X2710,X2711,X2712,X2713,X2714,X2715,X2716)),esk47_7(X2710,X2711,X2712,X2713,X2714,X2715,X2716))),hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2712),X2711))),c_Transitive__Closure_Ortrancl(tc_prod(X2716,X2715),X2710)))
| hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2714),X2713) = hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2712),X2711)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2716,X2715),tc_prod(X2716,X2715))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2716,X2715),tc_prod(X2716,X2715)),hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2714),X2713)),hAPP(hAPP(c_Product__Type_OPair(X2716,X2715),X2712),X2711))),c_Transitive__Closure_Ortrancl(tc_prod(X2716,X2715),X2710))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_517])])])]) ).
fof(i_0_601,plain,
! [X3048,X3049,X3050,X3051,X3052,X3053] :
( ( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3053,tc_fun(X3052,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3053,tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_fun(X3052,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3052,tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_fun(X3052,tc_HOL_Obool)),X3053,c_COMBC(X3052,tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3052,tc_prod(X3053,X3052)),tc_fun(X3052,tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),X3053,c_COMBB(tc_prod(X3053,X3052),tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool),X3052,c_member(tc_prod(X3053,X3052)))),c_Product__Type_OPair(X3053,X3052)))),X3051),hAPP(hAPP(c_COMBC(X3053,tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_fun(X3052,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3052,tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_fun(X3052,tc_HOL_Obool)),X3053,c_COMBC(X3052,tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3052,tc_prod(X3053,X3052)),tc_fun(X3052,tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),X3053,c_COMBB(tc_prod(X3053,X3052),tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool),X3052,c_member(tc_prod(X3053,X3052)))),c_Product__Type_OPair(X3053,X3052)))),X3050)),X3049),X3048))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3053,X3052)),hAPP(hAPP(c_Product__Type_OPair(X3053,X3052),X3049),X3048)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),X3051,X3050))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3053,X3052)),hAPP(hAPP(c_Product__Type_OPair(X3053,X3052),X3049),X3048)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),X3051,X3050)))
| hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3053,tc_fun(X3052,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3053,tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_fun(X3052,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3052,tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_fun(X3052,tc_HOL_Obool)),X3053,c_COMBC(X3052,tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3052,tc_prod(X3053,X3052)),tc_fun(X3052,tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),X3053,c_COMBB(tc_prod(X3053,X3052),tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool),X3052,c_member(tc_prod(X3053,X3052)))),c_Product__Type_OPair(X3053,X3052)))),X3051),hAPP(hAPP(c_COMBC(X3053,tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_fun(X3052,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3052,tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_fun(X3052,tc_HOL_Obool)),X3053,c_COMBC(X3052,tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3052,tc_prod(X3053,X3052)),tc_fun(X3052,tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool)),X3053,c_COMBB(tc_prod(X3053,X3052),tc_fun(tc_fun(tc_prod(X3053,X3052),tc_HOL_Obool),tc_HOL_Obool),X3052,c_member(tc_prod(X3053,X3052)))),c_Product__Type_OPair(X3053,X3052)))),X3050)),X3049),X3048)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).
fof(i_0_602,plain,
! [X3032,X3033,X3034,X3035,X3036,X3037,X3038,X3040,X3041,X3042,X3043,X3047] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3035,X3035)),hAPP(hAPP(c_Product__Type_OPair(X3035,X3035),esk67_7(X3032,X3033,X3034,X3035,X3036,X3037,X3038)),X3038)),X3033))
| hAPP(hAPP(X3032,X3036),X3038) = hAPP(hAPP(X3032,X3037),X3038)
| ~ c_Recdef_Oadm__wf(X3035,X3034,X3033,X3032) )
& ( hAPP(X3036,esk67_7(X3032,X3033,X3034,X3035,X3036,X3037,X3038)) != hAPP(X3037,esk67_7(X3032,X3033,X3034,X3035,X3036,X3037,X3038))
| hAPP(hAPP(X3032,X3036),X3038) = hAPP(hAPP(X3032,X3037),X3038)
| ~ c_Recdef_Oadm__wf(X3035,X3034,X3033,X3032) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3043,X3043)),hAPP(hAPP(c_Product__Type_OPair(X3043,X3043),X3047),esk70_4(X3040,X3041,X3042,X3043))),X3041))
| hAPP(esk68_4(X3040,X3041,X3042,X3043),X3047) = hAPP(esk69_4(X3040,X3041,X3042,X3043),X3047)
| c_Recdef_Oadm__wf(X3043,X3042,X3041,X3040) )
& ( hAPP(hAPP(X3040,esk68_4(X3040,X3041,X3042,X3043)),esk70_4(X3040,X3041,X3042,X3043)) != hAPP(hAPP(X3040,esk69_4(X3040,X3041,X3042,X3043)),esk70_4(X3040,X3041,X3042,X3043))
| c_Recdef_Oadm__wf(X3043,X3042,X3041,X3040) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_adm__wf__def])])])])])]) ).
fof(i_0_603,plain,
! [X2408,X2409,X2410,X2411,X2412] :
( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2412,X2411,hAPP(hAPP(c_COMBC(X2412,tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_fun(X2411,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2411,tc_fun(tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_fun(X2411,tc_HOL_Obool)),X2412,c_COMBC(X2411,tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2411,tc_prod(X2412,X2411)),tc_fun(X2411,tc_fun(tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_HOL_Obool)),X2412,c_COMBB(tc_prod(X2412,X2411),tc_fun(tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_HOL_Obool),X2411,c_member(tc_prod(X2412,X2411)))),c_Product__Type_OPair(X2412,X2411)))),X2410)),X2409),X2408))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2411,X2412)),hAPP(hAPP(c_Product__Type_OPair(X2411,X2412),X2409),X2408)),c_Relation_Oconverse(X2412,X2411,X2410))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2411,X2412)),hAPP(hAPP(c_Product__Type_OPair(X2411,X2412),X2409),X2408)),c_Relation_Oconverse(X2412,X2411,X2410)))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2412,X2411,hAPP(hAPP(c_COMBC(X2412,tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_fun(X2411,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2411,tc_fun(tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_fun(X2411,tc_HOL_Obool)),X2412,c_COMBC(X2411,tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2411,tc_prod(X2412,X2411)),tc_fun(X2411,tc_fun(tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_HOL_Obool)),X2412,c_COMBB(tc_prod(X2412,X2411),tc_fun(tc_fun(tc_prod(X2412,X2411),tc_HOL_Obool),tc_HOL_Obool),X2411,c_member(tc_prod(X2412,X2411)))),c_Product__Type_OPair(X2412,X2411)))),X2410)),X2409),X2408)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq])]) ).
fof(i_0_604,plain,
! [X3573,X3574,X3575,X3576,X3577,X3578,X3579,X3582,X3583,X3584,X3585,X3586,X3587,X3588,X3589,X3590] :
( ( hAPP(hAPP(X3577,X3574),X3573) = hAPP(hAPP(X3577,esk82_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579)),esk83_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579))
| X3575 = c_Orderings_Obot__class_Obot(tc_fun(X3579,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X3579,X3578,X3577,X3576,X3575,hAPP(hAPP(X3577,X3574),X3573)) )
& ( hBOOL(hAPP(hAPP(c_member(X3579),esk82_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579)),X3575))
| X3575 = c_Orderings_Obot__class_Obot(tc_fun(X3579,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X3579,X3578,X3577,X3576,X3575,hAPP(hAPP(X3577,X3574),X3573)) )
& ( c_Nitpick_Ofold__graph_H(X3579,X3578,X3577,X3576,c_Groups_Ominus__class_Ominus(tc_fun(X3579,tc_HOL_Obool),X3575,hAPP(hAPP(c_Set_Oinsert(X3579),esk82_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579)),c_Orderings_Obot__class_Obot(tc_fun(X3579,tc_HOL_Obool)))),esk83_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579))
| X3575 = c_Orderings_Obot__class_Obot(tc_fun(X3579,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X3579,X3578,X3577,X3576,X3575,hAPP(hAPP(X3577,X3574),X3573)) )
& ( hAPP(hAPP(X3577,X3574),X3573) = hAPP(hAPP(X3577,esk82_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579)),esk83_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579))
| hAPP(hAPP(X3577,X3574),X3573) = X3576
| ~ c_Nitpick_Ofold__graph_H(X3579,X3578,X3577,X3576,X3575,hAPP(hAPP(X3577,X3574),X3573)) )
& ( hBOOL(hAPP(hAPP(c_member(X3579),esk82_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579)),X3575))
| hAPP(hAPP(X3577,X3574),X3573) = X3576
| ~ c_Nitpick_Ofold__graph_H(X3579,X3578,X3577,X3576,X3575,hAPP(hAPP(X3577,X3574),X3573)) )
& ( c_Nitpick_Ofold__graph_H(X3579,X3578,X3577,X3576,c_Groups_Ominus__class_Ominus(tc_fun(X3579,tc_HOL_Obool),X3575,hAPP(hAPP(c_Set_Oinsert(X3579),esk82_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579)),c_Orderings_Obot__class_Obot(tc_fun(X3579,tc_HOL_Obool)))),esk83_7(X3573,X3574,X3575,X3576,X3577,X3578,X3579))
| hAPP(hAPP(X3577,X3574),X3573) = X3576
| ~ c_Nitpick_Ofold__graph_H(X3579,X3578,X3577,X3576,X3575,hAPP(hAPP(X3577,X3574),X3573)) )
& ( X3584 != c_Orderings_Obot__class_Obot(tc_fun(X3588,tc_HOL_Obool))
| hAPP(hAPP(X3586,X3583),X3582) != X3585
| c_Nitpick_Ofold__graph_H(X3588,X3587,X3586,X3585,X3584,hAPP(hAPP(X3586,X3583),X3582)) )
& ( hAPP(hAPP(X3586,X3583),X3582) != hAPP(hAPP(X3586,X3589),X3590)
| ~ hBOOL(hAPP(hAPP(c_member(X3588),X3589),X3584))
| ~ c_Nitpick_Ofold__graph_H(X3588,X3587,X3586,X3585,c_Groups_Ominus__class_Ominus(tc_fun(X3588,tc_HOL_Obool),X3584,hAPP(hAPP(c_Set_Oinsert(X3588),X3589),c_Orderings_Obot__class_Obot(tc_fun(X3588,tc_HOL_Obool)))),X3590)
| c_Nitpick_Ofold__graph_H(X3588,X3587,X3586,X3585,X3584,hAPP(hAPP(X3586,X3583),X3582)) ) ),
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_fold__graph_H_Oequations_I2_J])])])])])]) ).
fof(i_0_605,plain,
! [X2570,X2571,X2572] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2572,hAPP(hAPP(c_COMBC(X2572,tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_fun(X2572,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2572,tc_fun(tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_fun(X2572,tc_HOL_Obool)),X2572,c_COMBC(X2572,tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2572,tc_prod(X2572,X2572)),tc_fun(X2572,tc_fun(tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_HOL_Obool)),X2572,c_COMBB(tc_prod(X2572,X2572),tc_fun(tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_HOL_Obool),X2572,c_member(tc_prod(X2572,X2572)))),c_Product__Type_OPair(X2572,X2572)))),X2571)),X2570))
| hBOOL(hAPP(hAPP(c_member(X2572),X2570),c_Wellfounded_Oacc(X2572,X2571))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2572),X2570),c_Wellfounded_Oacc(X2572,X2571)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2572,hAPP(hAPP(c_COMBC(X2572,tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_fun(X2572,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2572,tc_fun(tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_fun(X2572,tc_HOL_Obool)),X2572,c_COMBC(X2572,tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2572,tc_prod(X2572,X2572)),tc_fun(X2572,tc_fun(tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_HOL_Obool)),X2572,c_COMBB(tc_prod(X2572,X2572),tc_fun(tc_fun(tc_prod(X2572,X2572),tc_HOL_Obool),tc_HOL_Obool),X2572,c_member(tc_prod(X2572,X2572)))),c_Product__Type_OPair(X2572,X2572)))),X2571)),X2570)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).
fof(i_0_606,plain,
! [X4235,X4236,X4237,X4238] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4238,tc_fun(X4237,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4238,tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_fun(X4237,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4237,tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_fun(X4237,tc_HOL_Obool)),X4238,c_COMBC(X4237,tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4237,tc_prod(X4238,X4237)),tc_fun(X4237,tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),X4238,c_COMBB(tc_prod(X4238,X4237),tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool),X4237,c_member(tc_prod(X4238,X4237)))),c_Product__Type_OPair(X4238,X4237)))),X4236),hAPP(hAPP(c_COMBC(X4238,tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_fun(X4237,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4237,tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_fun(X4237,tc_HOL_Obool)),X4238,c_COMBC(X4237,tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4237,tc_prod(X4238,X4237)),tc_fun(X4237,tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),X4238,c_COMBB(tc_prod(X4238,X4237),tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool),X4237,c_member(tc_prod(X4238,X4237)))),c_Product__Type_OPair(X4238,X4237)))),X4235))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),X4236,X4235) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),X4236,X4235)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4238,tc_fun(X4237,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4238,tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_fun(X4237,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4237,tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_fun(X4237,tc_HOL_Obool)),X4238,c_COMBC(X4237,tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4237,tc_prod(X4238,X4237)),tc_fun(X4237,tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),X4238,c_COMBB(tc_prod(X4238,X4237),tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool),X4237,c_member(tc_prod(X4238,X4237)))),c_Product__Type_OPair(X4238,X4237)))),X4236),hAPP(hAPP(c_COMBC(X4238,tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_fun(X4237,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4237,tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_fun(X4237,tc_HOL_Obool)),X4238,c_COMBC(X4237,tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4237,tc_prod(X4238,X4237)),tc_fun(X4237,tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool)),X4238,c_COMBB(tc_prod(X4238,X4237),tc_fun(tc_fun(tc_prod(X4238,X4237),tc_HOL_Obool),tc_HOL_Obool),X4237,c_member(tc_prod(X4238,X4237)))),c_Product__Type_OPair(X4238,X4237)))),X4235)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_607,plain,
! [X2823,X2824,X2825,X2826,X2827,X2828,X2829,X2830,X2831,X2832,X2833,X2834,X2835] :
( ( hAPP(hAPP(hAPP(c_Recdef_Ocut(X2828,X2827),X2826),X2825),X2824) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X2828,X2827),X2823),X2825),X2824)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2828,X2828)),hAPP(hAPP(c_Product__Type_OPair(X2828,X2828),X2829),X2824)),X2825))
| hAPP(X2826,X2829) = hAPP(X2823,X2829) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2835,X2835)),hAPP(hAPP(c_Product__Type_OPair(X2835,X2835),esk59_6(X2830,X2831,X2832,X2833,X2834,X2835)),X2831)),X2832))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X2835,X2834),X2833),X2832),X2831) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X2835,X2834),X2830),X2832),X2831) )
& ( hAPP(X2833,esk59_6(X2830,X2831,X2832,X2833,X2834,X2835)) != hAPP(X2830,esk59_6(X2830,X2831,X2832,X2833,X2834,X2835))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X2835,X2834),X2833),X2832),X2831) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X2835,X2834),X2830),X2832),X2831) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cuts__eq])])])])])]) ).
cnf(i_0_608,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(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(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,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_518]) ).
cnf(i_0_609,plain,
c_Relation_ORange(X1,X2,X3) = c_Relation_ODomain(X2,X1,c_Relation_Oconverse(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_519]) ).
fof(i_0_610,plain,
! [X2488,X2489,X2490,X2491] :
( ( ~ c_Predicate_ODomainP(X2491,X2490,hAPP(hAPP(c_COMBC(X2491,tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_fun(X2490,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2490,tc_fun(tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_fun(X2490,tc_HOL_Obool)),X2491,c_COMBC(X2490,tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2490,tc_prod(X2491,X2490)),tc_fun(X2490,tc_fun(tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_HOL_Obool)),X2491,c_COMBB(tc_prod(X2491,X2490),tc_fun(tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_HOL_Obool),X2490,c_member(tc_prod(X2491,X2490)))),c_Product__Type_OPair(X2491,X2490)))),X2489),X2488)
| hBOOL(hAPP(hAPP(c_member(X2491),X2488),c_Relation_ODomain(X2491,X2490,X2489))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2491),X2488),c_Relation_ODomain(X2491,X2490,X2489)))
| c_Predicate_ODomainP(X2491,X2490,hAPP(hAPP(c_COMBC(X2491,tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_fun(X2490,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2490,tc_fun(tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_fun(X2490,tc_HOL_Obool)),X2491,c_COMBC(X2490,tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2490,tc_prod(X2491,X2490)),tc_fun(X2490,tc_fun(tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_HOL_Obool)),X2491,c_COMBB(tc_prod(X2491,X2490),tc_fun(tc_fun(tc_prod(X2491,X2490),tc_HOL_Obool),tc_HOL_Obool),X2490,c_member(tc_prod(X2491,X2490)))),c_Product__Type_OPair(X2491,X2490)))),X2489),X2488) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).
fof(i_0_611,plain,
! [X2235,X2236,X2237,X2238] :
( ( hAPP(hAPP(c_COMBC(X2238,tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_fun(X2237,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2237,tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_fun(X2237,tc_HOL_Obool)),X2238,c_COMBC(X2237,tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2237,tc_prod(X2238,X2237)),tc_fun(X2237,tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),X2238,c_COMBB(tc_prod(X2238,X2237),tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool),X2237,c_member(tc_prod(X2238,X2237)))),c_Product__Type_OPair(X2238,X2237)))),X2236) != hAPP(hAPP(c_COMBC(X2238,tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_fun(X2237,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2237,tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_fun(X2237,tc_HOL_Obool)),X2238,c_COMBC(X2237,tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2237,tc_prod(X2238,X2237)),tc_fun(X2237,tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),X2238,c_COMBB(tc_prod(X2238,X2237),tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool),X2237,c_member(tc_prod(X2238,X2237)))),c_Product__Type_OPair(X2238,X2237)))),X2235)
| X2236 = X2235 )
& ( X2236 != X2235
| hAPP(hAPP(c_COMBC(X2238,tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_fun(X2237,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2237,tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_fun(X2237,tc_HOL_Obool)),X2238,c_COMBC(X2237,tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2237,tc_prod(X2238,X2237)),tc_fun(X2237,tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),X2238,c_COMBB(tc_prod(X2238,X2237),tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool),X2237,c_member(tc_prod(X2238,X2237)))),c_Product__Type_OPair(X2238,X2237)))),X2236) = hAPP(hAPP(c_COMBC(X2238,tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_fun(X2237,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2237,tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_fun(X2237,tc_HOL_Obool)),X2238,c_COMBC(X2237,tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2237,tc_prod(X2238,X2237)),tc_fun(X2237,tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool)),X2238,c_COMBB(tc_prod(X2238,X2237),tc_fun(tc_fun(tc_prod(X2238,X2237),tc_HOL_Obool),tc_HOL_Obool),X2237,c_member(tc_prod(X2238,X2237)))),c_Product__Type_OPair(X2238,X2237)))),X2235) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_612,plain,
! [X2843,X2844,X2845,X2846] : c_Recdef_Oadm__wf(X2846,X2845,X2844,hAPP(hAPP(c_COMBC(tc_fun(X2846,X2845),tc_fun(X2846,X2846),tc_fun(X2846,X2845)),hAPP(c_COMBB(tc_fun(X2846,tc_fun(X2846,X2845)),tc_fun(tc_fun(X2846,X2846),tc_fun(X2846,X2845)),tc_fun(X2846,X2845),c_COMBS(X2846,X2846,X2845)),hAPP(c_COMBB(tc_fun(X2846,tc_fun(X2846,X2845)),tc_fun(X2846,tc_fun(X2846,X2845)),tc_fun(X2846,X2845),c_COMBB(tc_fun(X2846,X2845),tc_fun(X2846,X2845),X2846,X2843)),hAPP(hAPP(c_COMBC(tc_fun(X2846,X2845),tc_fun(tc_prod(X2846,X2846),tc_HOL_Obool),tc_fun(X2846,tc_fun(X2846,X2845))),c_Recdef_Ocut(X2846,X2845)),X2844)))),c_COMBI(X2846))),
inference(variable_rename,[status(thm)],[fact_adm__lemma]) ).
cnf(i_0_613,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(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(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,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_518]) ).
fof(i_0_614,plain,
! [X3495,X3496,X3497,X3498,X3499,X3500] :
( ( hBOOL(hAPP(hAPP(c_member(X3500),esk79_6(X3495,X3496,X3497,X3498,X3499,X3500)),X3499))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3500,X3496)),X3498),c_FuncSet_Oextensional__funcset(X3500,X3496,hAPP(hAPP(c_Set_Oinsert(X3500),X3497),X3499),X3495)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3500,X3496)),c_Fun_Ofun__upd(X3500,X3496,X3498,X3497,c_HOL_Oundefined(X3496))),c_FuncSet_Oextensional__funcset(X3500,X3496,X3499,c_Groups_Ominus__class_Ominus(tc_fun(X3496,tc_HOL_Obool),X3495,hAPP(hAPP(c_Set_Oinsert(X3496),hAPP(X3498,X3497)),c_Orderings_Obot__class_Obot(tc_fun(X3496,tc_HOL_Obool))))))) )
& ( hAPP(X3498,X3497) = hAPP(X3498,esk79_6(X3495,X3496,X3497,X3498,X3499,X3500))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3500,X3496)),X3498),c_FuncSet_Oextensional__funcset(X3500,X3496,hAPP(hAPP(c_Set_Oinsert(X3500),X3497),X3499),X3495)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3500,X3496)),c_Fun_Ofun__upd(X3500,X3496,X3498,X3497,c_HOL_Oundefined(X3496))),c_FuncSet_Oextensional__funcset(X3500,X3496,X3499,c_Groups_Ominus__class_Ominus(tc_fun(X3496,tc_HOL_Obool),X3495,hAPP(hAPP(c_Set_Oinsert(X3496),hAPP(X3498,X3497)),c_Orderings_Obot__class_Obot(tc_fun(X3496,tc_HOL_Obool))))))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__fun__upd__restricts__rangeI])])])]) ).
fof(i_0_615,plain,
! [X2804,X2805,X2806,X2807,X2808] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2808,X2808)),hAPP(hAPP(c_Product__Type_OPair(X2808,X2808),X2807),esk57_5(X2804,X2805,X2806,X2807,X2808))),c_Transitive__Closure_Ortrancl(X2808,X2805)))
| hBOOL(hAPP(X2804,X2806))
| ~ hBOOL(hAPP(X2804,X2807))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2808,X2808)),hAPP(hAPP(c_Product__Type_OPair(X2808,X2808),X2807),X2806)),c_Transitive__Closure_Ortrancl(X2808,X2805))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2808,X2808)),hAPP(hAPP(c_Product__Type_OPair(X2808,X2808),esk57_5(X2804,X2805,X2806,X2807,X2808)),esk58_5(X2804,X2805,X2806,X2807,X2808))),X2805))
| hBOOL(hAPP(X2804,X2806))
| ~ hBOOL(hAPP(X2804,X2807))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2808,X2808)),hAPP(hAPP(c_Product__Type_OPair(X2808,X2808),X2807),X2806)),c_Transitive__Closure_Ortrancl(X2808,X2805))) )
& ( hBOOL(hAPP(X2804,esk57_5(X2804,X2805,X2806,X2807,X2808)))
| hBOOL(hAPP(X2804,X2806))
| ~ hBOOL(hAPP(X2804,X2807))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2808,X2808)),hAPP(hAPP(c_Product__Type_OPair(X2808,X2808),X2807),X2806)),c_Transitive__Closure_Ortrancl(X2808,X2805))) )
& ( ~ hBOOL(hAPP(X2804,esk58_5(X2804,X2805,X2806,X2807,X2808)))
| hBOOL(hAPP(X2804,X2806))
| ~ hBOOL(hAPP(X2804,X2807))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2808,X2808)),hAPP(hAPP(c_Product__Type_OPair(X2808,X2808),X2807),X2806)),c_Transitive__Closure_Ortrancl(X2808,X2805))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__induct])])])]) ).
fof(i_0_616,plain,
! [X2861,X2862,X2863,X2864,X2865] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2865,X2865)),hAPP(hAPP(c_Product__Type_OPair(X2865,X2865),esk62_5(X2861,X2862,X2863,X2864,X2865)),esk63_5(X2861,X2862,X2863,X2864,X2865))),X2862))
| hBOOL(hAPP(X2861,X2864))
| ~ hBOOL(hAPP(X2861,X2863))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2865,X2865)),hAPP(hAPP(c_Product__Type_OPair(X2865,X2865),X2864),X2863)),c_Transitive__Closure_Ortrancl(X2865,X2862))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2865,X2865)),hAPP(hAPP(c_Product__Type_OPair(X2865,X2865),esk63_5(X2861,X2862,X2863,X2864,X2865)),X2863)),c_Transitive__Closure_Ortrancl(X2865,X2862)))
| hBOOL(hAPP(X2861,X2864))
| ~ hBOOL(hAPP(X2861,X2863))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2865,X2865)),hAPP(hAPP(c_Product__Type_OPair(X2865,X2865),X2864),X2863)),c_Transitive__Closure_Ortrancl(X2865,X2862))) )
& ( hBOOL(hAPP(X2861,esk63_5(X2861,X2862,X2863,X2864,X2865)))
| hBOOL(hAPP(X2861,X2864))
| ~ hBOOL(hAPP(X2861,X2863))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2865,X2865)),hAPP(hAPP(c_Product__Type_OPair(X2865,X2865),X2864),X2863)),c_Transitive__Closure_Ortrancl(X2865,X2862))) )
& ( ~ hBOOL(hAPP(X2861,esk62_5(X2861,X2862,X2863,X2864,X2865)))
| hBOOL(hAPP(X2861,X2864))
| ~ hBOOL(hAPP(X2861,X2863))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2865,X2865)),hAPP(hAPP(c_Product__Type_OPair(X2865,X2865),X2864),X2863)),c_Transitive__Closure_Ortrancl(X2865,X2862))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__induct])])])]) ).
fof(i_0_617,plain,
! [X2497,X2498,X2499,X2500,X2501,X2502] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2502,X2498)),X2500),c_FuncSet_OPi(X2502,X2498,X2501,X2497)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2502,X2498)),X2499),c_FuncSet_OPi(X2502,X2498,X2501,X2497)))
| hBOOL(hAPP(hAPP(c_member(X2502),esk30_6(X2497,X2498,X2499,X2500,X2501,X2502)),X2501)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2502,X2498)),X2499),c_FuncSet_OPi(X2502,X2498,X2501,X2497)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2502,X2498)),X2500),c_FuncSet_OPi(X2502,X2498,X2501,X2497)))
| hBOOL(hAPP(hAPP(c_member(X2502),esk30_6(X2497,X2498,X2499,X2500,X2501,X2502)),X2501)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2502,X2498)),X2500),c_FuncSet_OPi(X2502,X2498,X2501,X2497)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2502,X2498)),X2499),c_FuncSet_OPi(X2502,X2498,X2501,X2497)))
| hAPP(X2500,esk30_6(X2497,X2498,X2499,X2500,X2501,X2502)) != hAPP(X2499,esk30_6(X2497,X2498,X2499,X2500,X2501,X2502)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2502,X2498)),X2499),c_FuncSet_OPi(X2502,X2498,X2501,X2497)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2502,X2498)),X2500),c_FuncSet_OPi(X2502,X2498,X2501,X2497)))
| hAPP(X2500,esk30_6(X2497,X2498,X2499,X2500,X2501,X2502)) != hAPP(X2499,esk30_6(X2497,X2498,X2499,X2500,X2501,X2502)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__cong])])])]) ).
fof(i_0_618,plain,
! [X2768,X2769,X2770,X2771,X2772] :
( ( hBOOL(hAPP(hAPP(c_member(X2772),esk51_5(X2768,X2769,X2770,X2771,X2772)),X2771))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2772,X2770)),c_FuncSet_Orestrict(X2772,X2770,X2769,X2771)),c_FuncSet_OPi(X2772,X2770,X2771,X2768))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2770),hAPP(X2769,esk51_5(X2768,X2769,X2770,X2771,X2772))),hAPP(X2768,esk51_5(X2768,X2769,X2770,X2771,X2772))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2772,X2770)),c_FuncSet_Orestrict(X2772,X2770,X2769,X2771)),c_FuncSet_OPi(X2772,X2770,X2771,X2768))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrictI])])])]) ).
fof(i_0_619,plain,
! [X2419,X2420,X2421,X2422,X2423] :
( ( hBOOL(hAPP(hAPP(c_member(X2423),esk26_5(X2419,X2420,X2421,X2422,X2423)),X2422))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2423,X2421)),X2420),c_FuncSet_OPi(X2423,X2421,X2422,X2419))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2421),hAPP(X2420,esk26_5(X2419,X2420,X2421,X2422,X2423))),hAPP(X2419,esk26_5(X2419,X2420,X2421,X2422,X2423))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2423,X2421)),X2420),c_FuncSet_OPi(X2423,X2421,X2422,X2419))) ) ),
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_620,plain,
! [X2322,X2323,X2324,X2325,X2326] :
( ( hBOOL(hAPP(hAPP(c_member(X2326),esk17_5(X2322,X2323,X2324,X2325,X2326)),X2325))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2326,X2324)),X2323),c_FuncSet_OPi(X2326,X2324,X2325,X2322))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2324),hAPP(X2323,esk17_5(X2322,X2323,X2324,X2325,X2326))),hAPP(X2322,esk17_5(X2322,X2323,X2324,X2325,X2326))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2326,X2324)),X2323),c_FuncSet_OPi(X2326,X2324,X2325,X2322))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_621,plain,
! [X4296,X4297,X4298] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X4298),X4297),X4296) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4298,tc_fun(tc_fun(X4298,tc_HOL_Obool),tc_HOL_Obool),X4297,hAPP(hAPP(c_COMBC(X4298,tc_fun(tc_fun(X4298,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4298,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4298,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X4298,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4298,tc_HOL_Obool),tc_HOL_Obool)),X4298,c_Set_Oinsert(tc_fun(X4298,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(X4298,tc_HOL_Obool),tc_fun(X4298,tc_HOL_Obool),X4298,c_Relation_OImage(X4298,X4298,X4296)),hAPP(hAPP(c_COMBC(X4298,tc_fun(X4298,tc_HOL_Obool),tc_fun(X4298,tc_HOL_Obool)),c_Set_Oinsert(X4298)),c_Orderings_Obot__class_Obot(tc_fun(X4298,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4298,tc_HOL_Obool),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_quotient__def]) ).
fof(i_0_622,plain,
! [X3725,X3726,X3727,X3728,X3729] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3727,X3729)),hAPP(hAPP(c_Product__Type_OPair(X3727,X3729),esk86_5(X3725,X3726,X3727,X3728,X3729)),X3728)),X3726))
| ~ hBOOL(hAPP(hAPP(c_member(X3729),X3728),hAPP(c_Relation_OImage(X3727,X3729,X3726),X3725))) )
& ( hBOOL(hAPP(hAPP(c_member(X3727),esk86_5(X3725,X3726,X3727,X3728,X3729)),X3725))
| ~ hBOOL(hAPP(hAPP(c_member(X3729),X3728),hAPP(c_Relation_OImage(X3727,X3729,X3726),X3725))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_520])])])]) ).
fof(i_0_623,plain,
! [X3697,X3698,X3699,X3700,X3701,X3703,X3704,X3705,X3706,X3707,X3708] :
( ( hBOOL(hAPP(hAPP(c_member(X3699),esk85_5(X3697,X3698,X3699,X3700,X3701)),X3697))
| ~ hBOOL(hAPP(hAPP(c_member(X3701),X3700),hAPP(c_Relation_OImage(X3699,X3701,X3698),X3697))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3699,X3701)),hAPP(hAPP(c_Product__Type_OPair(X3699,X3701),esk85_5(X3697,X3698,X3699,X3700,X3701)),X3700)),X3698))
| ~ hBOOL(hAPP(hAPP(c_member(X3701),X3700),hAPP(c_Relation_OImage(X3699,X3701,X3698),X3697))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3705),X3708),X3703))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3705,X3707)),hAPP(hAPP(c_Product__Type_OPair(X3705,X3707),X3708),X3706)),X3704))
| hBOOL(hAPP(hAPP(c_member(X3707),X3706),hAPP(c_Relation_OImage(X3705,X3707,X3704),X3703))) ) ),
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_624,plain,
! [X2464,X2465,X2466] :
( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2466,X2466,hAPP(c_COMBB(tc_fun(X2466,tc_HOL_Obool),tc_fun(X2466,tc_HOL_Obool),X2466,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2466,c_fNot)),c_fequal)),X2465),X2464))
| X2465 != X2464 )
& ( X2465 = X2464
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2466,X2466,hAPP(c_COMBB(tc_fun(X2466,tc_HOL_Obool),tc_fun(X2466,tc_HOL_Obool),X2466,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2466,c_fNot)),c_fequal)),X2465),X2464)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__noteq])]) ).
fof(i_0_625,plain,
! [X2290,X2291,X2292,X2293,X2294,X2296,X2301,X2302] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2290,X2291)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2290,X2292)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2291,esk7_5(X2290,X2291,X2292,X2293,X2294))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2292,esk7_5(X2290,X2291,X2292,X2293,X2294))))
| ~ 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))),X2292),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))),X2291),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2290) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2290,X2292)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2290,X2291)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2291,esk7_5(X2290,X2291,X2292,X2293,X2294))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2292,esk7_5(X2290,X2291,X2292,X2293,X2294))))
| ~ 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))),X2292),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))),X2291),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2290) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2290,X2291)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2290,X2292)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2291,esk7_5(X2290,X2291,X2292,X2293,X2294))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2292,esk7_5(X2290,X2291,X2292,X2293,X2294))))
| ~ 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))),X2292),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))),X2291),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2290) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2290,X2292)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2290,X2291)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2291,esk7_5(X2290,X2291,X2292,X2293,X2294))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2293),X2294)),hAPP(X2292,esk7_5(X2290,X2291,X2292,X2293,X2294))))
| ~ 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))),X2292),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))),X2291),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2290) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk8_1(X2296)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2296) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk9_1(X2296)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2296) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X2296)),esk11_1(X2296))),hAPP(esk8_1(X2296),X2301)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X2296)),esk11_1(X2296))),hAPP(esk9_1(X2296),X2301)))
| c_Arrow__Order__Mirabelle_OIIA(X2296) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X2296)),esk11_1(X2296))),hAPP(esk9_1(X2296),X2302)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X2296)),esk11_1(X2296))),hAPP(esk8_1(X2296),X2302)))
| c_Arrow__Order__Mirabelle_OIIA(X2296) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X2296)),esk11_1(X2296))),hAPP(X2296,esk8_1(X2296))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X2296)),esk11_1(X2296))),hAPP(X2296,esk9_1(X2296))))
| c_Arrow__Order__Mirabelle_OIIA(X2296) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X2296)),esk11_1(X2296))),hAPP(X2296,esk8_1(X2296))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X2296)),esk11_1(X2296))),hAPP(X2296,esk9_1(X2296))))
| c_Arrow__Order__Mirabelle_OIIA(X2296) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IIA__def])])])])])]) ).
fof(i_0_626,plain,
! [X2774,X2775,X2776,X2777,X2778] :
( ( hBOOL(hAPP(hAPP(c_member(X2778),esk52_5(X2774,X2775,X2776,X2777,X2778)),X2777))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2778,X2776)),c_FuncSet_Orestrict(X2778,X2776,X2775,X2777)),c_FuncSet_OPi(X2778,X2776,X2777,c_COMBK(tc_fun(X2776,tc_HOL_Obool),X2778,X2774)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2776),hAPP(X2775,esk52_5(X2774,X2775,X2776,X2777,X2778))),X2774))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2778,X2776)),c_FuncSet_Orestrict(X2778,X2776,X2775,X2777)),c_FuncSet_OPi(X2778,X2776,X2777,c_COMBK(tc_fun(X2776,tc_HOL_Obool),X2778,X2774)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrict__in__funcset])])])]) ).
fof(i_0_627,plain,
! [X4197,X4198,X4199,X4200] :
( ~ c_Fun_Oinj__on(X4200,tc_fun(tc_fun(X4200,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4200,tc_fun(tc_prod(X4200,X4200),tc_HOL_Obool),tc_fun(tc_fun(X4200,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4200,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X4200,X4200),tc_HOL_Obool),tc_fun(tc_fun(X4200,tc_HOL_Obool),tc_HOL_Obool)),X4200,c_Equiv__Relations_Oquotient(X4200)),hAPP(hAPP(c_COMBC(X4200,tc_fun(X4200,tc_HOL_Obool),tc_fun(X4200,tc_HOL_Obool)),c_Set_Oinsert(X4200)),c_Orderings_Obot__class_Obot(tc_fun(X4200,tc_HOL_Obool))))),X4199),X4198)
| ~ hBOOL(hAPP(hAPP(c_member(X4200),X4197),X4198))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X4200),c_Groups_Ominus__class_Ominus(tc_fun(X4200,tc_HOL_Obool),X4198,hAPP(hAPP(c_Set_Oinsert(X4200),X4197),c_Orderings_Obot__class_Obot(tc_fun(X4200,tc_HOL_Obool))))),X4199) = c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X4200,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4200),X4198),X4199),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4200),hAPP(hAPP(c_Set_Oinsert(X4200),X4197),c_Orderings_Obot__class_Obot(tc_fun(X4200,tc_HOL_Obool)))),X4199)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__diff1])]) ).
fof(i_0_628,plain,
! [X2397,X2398,X2399,X2400,X2401] :
( ( hBOOL(hAPP(hAPP(c_member(X2401),esk24_5(X2397,X2398,X2399,X2400,X2401)),X2400))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2401,X2399)),X2398),c_FuncSet_OPi(X2401,X2399,X2400,c_COMBK(tc_fun(X2399,tc_HOL_Obool),X2401,X2397)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2399),hAPP(X2398,esk24_5(X2397,X2398,X2399,X2400,X2401))),X2397))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2401,X2399)),X2398),c_FuncSet_OPi(X2401,X2399,X2400,c_COMBK(tc_fun(X2399,tc_HOL_Obool),X2401,X2397)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcsetI])])])]) ).
cnf(i_0_629,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_521]) ).
cnf(i_0_630,plain,
c_FuncSet_Ocompose(X1,X2,X3,X4,X5,X6) = c_FuncSet_Orestrict(X1,X3,hAPP(c_COMBB(X2,X3,X1,X5),X6),X4),
inference(split_conjunct,[status(thm)],[i_0_522]) ).
fof(i_0_631,plain,
! [X2222] : hAPP(v_Q____,X2222) = c_HOL_OLet(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),hAPP(hAPP(c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),hAPP(hAPP(c_fequal,v_a____),v_a_H____)),hAPP(v_P____,X2222)),c_Arrow__Order__Mirabelle_Obelow(hAPP(v_P____,X2222),v_a_H____,v_a____)),hAPP(hAPP(c_COMBS(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),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),hAPP(hAPP(c_fequal,v_b____),v_b_H____))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),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_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),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))),c_Arrow__Order__Mirabelle_Oabove),v_b____)),v_b_H____))),
inference(variable_rename,[status(thm)],[fact_Q__def]) ).
fof(i_0_632,plain,
! [X4286,X4287,X4288,X4289,X4290] : hAPP(c_Fun_Othe__inv__into(X4290,X4289,X4288,X4287),X4286) = c_HOL_OThe(X4290,hAPP(hAPP(c_COMBS(X4290,tc_HOL_Obool,tc_HOL_Obool),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4290,c_fconj),hAPP(hAPP(c_COMBC(X4290,tc_fun(X4290,tc_HOL_Obool),tc_HOL_Obool),c_member(X4290)),X4288))),hAPP(hAPP(c_COMBC(X4290,X4289,tc_HOL_Obool),hAPP(c_COMBB(X4289,tc_fun(X4289,tc_HOL_Obool),X4290,c_fequal),X4287)),X4286))),
inference(variable_rename,[status(thm)],[fact_the__inv__into__def]) ).
cnf(i_0_633,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_523]) ).
fof(i_0_634,plain,
! [X3350,X3351,X3352,X3353,X3354,X3355,X3356] :
( ~ hBOOL(hAPP(hAPP(c_member(X3356),X3355),X3354))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3353,X3356)),X3352),c_FuncSet_Oextensional__funcset(X3353,X3356,X3351,c_Groups_Ominus__class_Ominus(tc_fun(X3356,tc_HOL_Obool),X3354,hAPP(hAPP(c_Set_Oinsert(X3356),X3355),c_Orderings_Obot__class_Obot(tc_fun(X3356,tc_HOL_Obool)))))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3353,X3356)),c_Fun_Ofun__upd(X3353,X3356,X3352,X3350,X3355)),c_FuncSet_Oextensional__funcset(X3353,X3356,hAPP(hAPP(c_Set_Oinsert(X3353),X3350),X3351),X3354))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__fun__upd__extends__rangeI])]) ).
fof(i_0_635,plain,
! [X3502,X3503,X3504,X3505,X3506,X3507,X3508] :
( ~ hBOOL(hAPP(hAPP(c_member(X3508),X3507),X3506))
| ~ c_Nitpick_Ofold__graph_H(X3508,X3505,X3504,X3503,c_Groups_Ominus__class_Ominus(tc_fun(X3508,tc_HOL_Obool),X3506,hAPP(hAPP(c_Set_Oinsert(X3508),X3507),c_Orderings_Obot__class_Obot(tc_fun(X3508,tc_HOL_Obool)))),X3502)
| c_Nitpick_Ofold__graph_H(X3508,X3505,X3504,X3503,X3506,hAPP(hAPP(X3504,X3507),X3502)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])]) ).
fof(i_0_636,plain,
! [X2380,X2381,X2382,X2383,X2384,X2385,X2386,X2387] :
( ( X2385 = X2383
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2387,X2387)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2387),X2385),X2383)),X2381))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2387,X2386),tc_prod(X2387,X2386))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2387,X2386),tc_prod(X2387,X2386)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2386),X2385),X2384)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2386),X2383),X2382))),c_Wellfounded_Olex__prod(X2387,X2386,X2381,X2380))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2386,X2386)),hAPP(hAPP(c_Product__Type_OPair(X2386,X2386),X2384),X2382)),X2380))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2387,X2387)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2387),X2385),X2383)),X2381))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2387,X2386),tc_prod(X2387,X2386))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2387,X2386),tc_prod(X2387,X2386)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2386),X2385),X2384)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2386),X2383),X2382))),c_Wellfounded_Olex__prod(X2387,X2386,X2381,X2380))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2387,X2387)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2387),X2385),X2383)),X2381))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2387,X2386),tc_prod(X2387,X2386))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2387,X2386),tc_prod(X2387,X2386)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2386),X2385),X2384)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2386),X2383),X2382))),c_Wellfounded_Olex__prod(X2387,X2386,X2381,X2380))) )
& ( X2385 != X2383
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2386,X2386)),hAPP(hAPP(c_Product__Type_OPair(X2386,X2386),X2384),X2382)),X2380))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2387,X2386),tc_prod(X2387,X2386))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2387,X2386),tc_prod(X2387,X2386)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2386),X2385),X2384)),hAPP(hAPP(c_Product__Type_OPair(X2387,X2386),X2383),X2382))),c_Wellfounded_Olex__prod(X2387,X2386,X2381,X2380))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_637,plain,
! [X2256,X2257] :
( ( 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))),esk4_2(X2256,X2257)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2257,X2256)
| ~ 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))),X2257),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)))) )
& ( esk5_2(X2256,X2257) != esk6_2(X2256,X2257)
| c_Arrow__Order__Mirabelle_Odictator(X2257,X2256)
| ~ 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))),X2257),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),esk5_2(X2256,X2257)),esk6_2(X2256,X2257))),hAPP(esk4_2(X2256,X2257),X2256)))
| c_Arrow__Order__Mirabelle_Odictator(X2257,X2256)
| ~ 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))),X2257),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),esk5_2(X2256,X2257)),esk6_2(X2256,X2257))),hAPP(X2257,esk4_2(X2256,X2257))))
| c_Arrow__Order__Mirabelle_Odictator(X2257,X2256)
| ~ 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))),X2257),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_638,plain,
! [X3324,X3325,X3326,X3327,X3328,X3329] :
( hBOOL(hAPP(hAPP(c_member(X3329),X3328),X3327))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3329,X3326)),X3325),c_FuncSet_Oextensional__funcset(X3329,X3326,hAPP(hAPP(c_Set_Oinsert(X3329),X3328),X3327),X3324)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3329,X3326)),c_Fun_Ofun__upd(X3329,X3326,X3325,X3328,c_HOL_Oundefined(X3326))),c_FuncSet_Oextensional__funcset(X3329,X3326,X3327,X3324))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])]) ).
fof(i_0_639,plain,
! [X2333,X2334,X2335,X2336] :
( ( X2334 = hAPP(hAPP(c_Product__Type_OPair(X2336,X2335),esk19_4(X2333,X2334,X2335,X2336)),esk18_4(X2333,X2334,X2335,X2336))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2336,X2335)),X2334),c_Relation_Oconverse(X2335,X2336,X2333))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2335,X2336)),hAPP(hAPP(c_Product__Type_OPair(X2335,X2336),esk18_4(X2333,X2334,X2335,X2336)),esk19_4(X2333,X2334,X2335,X2336))),X2333))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2336,X2335)),X2334),c_Relation_Oconverse(X2335,X2336,X2333))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])])])]) ).
fof(i_0_640,plain,
! [X3339,X3340,X3341,X3342,X3343,X3344,X3345] :
( ~ hBOOL(hAPP(hAPP(c_member(X3345),X3344),X3343))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3342,X3345)),X3341),c_FuncSet_Oextensional__funcset(X3342,X3345,X3340,X3343)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3342,X3345)),c_Fun_Ofun__upd(X3342,X3345,X3341,X3339,X3344)),c_FuncSet_Oextensional__funcset(X3342,X3345,hAPP(hAPP(c_Set_Oinsert(X3342),X3339),X3340),X3343))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__extend__domainI])]) ).
fof(i_0_641,plain,
! [X3125,X3126,X3127,X3128] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3128,X3128)),hAPP(hAPP(c_Product__Type_OPair(X3128,X3128),X3127),esk73_4(X3125,X3126,X3127,X3128))),X3125))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3128,X3128)),hAPP(hAPP(c_Product__Type_OPair(X3128,X3128),X3127),X3126)),X3125))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3128,X3128)),hAPP(hAPP(c_Product__Type_OPair(X3128,X3128),X3127),X3126)),c_Transitive__Closure_Otrancl(X3128,X3125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3128,X3128)),hAPP(hAPP(c_Product__Type_OPair(X3128,X3128),esk73_4(X3125,X3126,X3127,X3128)),X3126)),c_Transitive__Closure_Otrancl(X3128,X3125)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3128,X3128)),hAPP(hAPP(c_Product__Type_OPair(X3128,X3128),X3127),X3126)),X3125))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3128,X3128)),hAPP(hAPP(c_Product__Type_OPair(X3128,X3128),X3127),X3126)),c_Transitive__Closure_Otrancl(X3128,X3125))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_526])])])]) ).
fof(i_0_642,plain,
! [X3120,X3121,X3122,X3123] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3123,X3123)),hAPP(hAPP(c_Product__Type_OPair(X3123,X3123),X3122),esk72_4(X3120,X3121,X3122,X3123))),c_Transitive__Closure_Otrancl(X3123,X3120)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3123,X3123)),hAPP(hAPP(c_Product__Type_OPair(X3123,X3123),X3122),X3121)),X3120))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3123,X3123)),hAPP(hAPP(c_Product__Type_OPair(X3123,X3123),X3122),X3121)),c_Transitive__Closure_Otrancl(X3123,X3120))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3123,X3123)),hAPP(hAPP(c_Product__Type_OPair(X3123,X3123),esk72_4(X3120,X3121,X3122,X3123)),X3121)),X3120))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3123,X3123)),hAPP(hAPP(c_Product__Type_OPair(X3123,X3123),X3122),X3121)),X3120))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3123,X3123)),hAPP(hAPP(c_Product__Type_OPair(X3123,X3123),X3122),X3121)),c_Transitive__Closure_Otrancl(X3123,X3120))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])])])]) ).
fof(i_0_643,plain,
! [X4311,X4312,X4313,X4314,X4315,X4317,X4318,X4319,X4320,X4321,X4322] :
( ( hBOOL(hAPP(hAPP(c_member(X4315),esk92_5(X4311,X4312,X4313,X4314,X4315)),X4313))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4315,tc_fun(X4314,tc_HOL_Obool),X4313,X4312),X4311)) )
& ( hBOOL(hAPP(hAPP(X4312,esk92_5(X4311,X4312,X4313,X4314,X4315)),X4311))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4315,tc_fun(X4314,tc_HOL_Obool),X4313,X4312),X4311)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4321),X4322),X4319))
| ~ hBOOL(hAPP(hAPP(X4318,X4322),X4317))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4321,tc_fun(X4320,tc_HOL_Obool),X4319,X4318),X4317)) ) ),
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_SUP1__iff])])])])])]) ).
fof(i_0_644,plain,
! [X2792,X2793,X2794,X2795,X2796] :
( ( hBOOL(hAPP(hAPP(c_member(X2796),esk53_5(X2792,X2793,X2794,X2795,X2796)),X2793))
| X2794 = X2792
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2796,X2795)),X2792),c_FuncSet_Oextensional(X2796,X2795,X2793)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2796,X2795)),X2794),c_FuncSet_Oextensional(X2796,X2795,X2793))) )
& ( hAPP(X2794,esk53_5(X2792,X2793,X2794,X2795,X2796)) != hAPP(X2792,esk53_5(X2792,X2793,X2794,X2795,X2796))
| X2794 = X2792
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2796,X2795)),X2792),c_FuncSet_Oextensional(X2796,X2795,X2793)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2796,X2795)),X2794),c_FuncSet_Oextensional(X2796,X2795,X2793))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensionalityI])])])]) ).
fof(i_0_645,plain,
! [X2856,X2857,X2858,X2859] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2859,X2859)),hAPP(hAPP(c_Product__Type_OPair(X2859,X2859),X2858),esk61_4(X2856,X2857,X2858,X2859))),X2856))
| X2858 = X2857
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2859,X2859)),hAPP(hAPP(c_Product__Type_OPair(X2859,X2859),X2858),X2857)),c_Transitive__Closure_Ortrancl(X2859,X2856))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2859,X2859)),hAPP(hAPP(c_Product__Type_OPair(X2859,X2859),esk61_4(X2856,X2857,X2858,X2859)),X2857)),c_Transitive__Closure_Ortrancl(X2859,X2856)))
| X2858 = X2857
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2859,X2859)),hAPP(hAPP(c_Product__Type_OPair(X2859,X2859),X2858),X2857)),c_Transitive__Closure_Ortrancl(X2859,X2856))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])])]) ).
fof(i_0_646,plain,
! [X3016,X3017,X3018,X3019] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3019,X3019)),hAPP(hAPP(c_Product__Type_OPair(X3019,X3019),X3018),esk64_4(X3016,X3017,X3018,X3019))),X3016))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3019,X3019)),hAPP(hAPP(c_Product__Type_OPair(X3019,X3019),X3018),X3017)),c_Transitive__Closure_Otrancl(X3019,X3016))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3019,X3019)),hAPP(hAPP(c_Product__Type_OPair(X3019,X3019),esk64_4(X3016,X3017,X3018,X3019)),X3017)),c_Transitive__Closure_Ortrancl(X3019,X3016)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3019,X3019)),hAPP(hAPP(c_Product__Type_OPair(X3019,X3019),X3018),X3017)),c_Transitive__Closure_Otrancl(X3019,X3016))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD])])])]) ).
fof(i_0_647,plain,
! [X2851,X2852,X2853,X2854] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2854,X2854)),hAPP(hAPP(c_Product__Type_OPair(X2854,X2854),X2853),esk60_4(X2851,X2852,X2853,X2854))),c_Transitive__Closure_Ortrancl(X2854,X2851)))
| X2853 = X2852
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2854,X2854)),hAPP(hAPP(c_Product__Type_OPair(X2854,X2854),X2853),X2852)),c_Transitive__Closure_Ortrancl(X2854,X2851))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2854,X2854)),hAPP(hAPP(c_Product__Type_OPair(X2854,X2854),esk60_4(X2851,X2852,X2853,X2854)),X2852)),X2851))
| X2853 = X2852
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2854,X2854)),hAPP(hAPP(c_Product__Type_OPair(X2854,X2854),X2853),X2852)),c_Transitive__Closure_Ortrancl(X2854,X2851))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])])])]) ).
fof(i_0_648,plain,
! [X3021,X3022,X3023,X3024] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3024,X3024)),hAPP(hAPP(c_Product__Type_OPair(X3024,X3024),X3023),esk65_4(X3021,X3022,X3023,X3024))),c_Transitive__Closure_Ortrancl(X3024,X3021)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3024,X3024)),hAPP(hAPP(c_Product__Type_OPair(X3024,X3024),X3023),X3022)),c_Transitive__Closure_Otrancl(X3024,X3021))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3024,X3024)),hAPP(hAPP(c_Product__Type_OPair(X3024,X3024),esk65_4(X3021,X3022,X3023,X3024)),X3022)),X3021))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3024,X3024)),hAPP(hAPP(c_Product__Type_OPair(X3024,X3024),X3023),X3022)),c_Transitive__Closure_Otrancl(X3024,X3021))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD2])])])]) ).
fof(i_0_649,plain,
! [X2339,X2340,X2341,X2342,X2343,X2344,X2345] :
( ~ hBOOL(hAPP(X2345,X2344))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2343,X2343)),hAPP(hAPP(c_Product__Type_OPair(X2343,X2343),X2342),X2341)),hAPP(X2340,X2344)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2339,X2343),tc_prod(X2339,X2343))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2339,X2343),tc_prod(X2339,X2343)),hAPP(hAPP(c_Product__Type_OPair(X2339,X2343),X2344),X2342)),hAPP(hAPP(c_Product__Type_OPair(X2339,X2343),X2344),X2341))),c_Recdef_Osame__fst(X2339,X2343,X2345,X2340))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
cnf(i_0_650,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),c_FuncSet_Ocompose(X1,X3,X2,X4,X5,X6)),c_FuncSet_Oextensional(X1,X2,X4))),
inference(split_conjunct,[status(thm)],[i_0_530]) ).
cnf(i_0_651,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk23_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_531]) ).
cnf(i_0_652,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk21_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_532]) ).
fof(i_0_653,plain,
! [X3731,X3732,X3733,X3734,X3735,X3736] :
( ~ c_Equiv__Relations_Oequiv(X3736,X3735,X3734)
| ~ hBOOL(hAPP(hAPP(c_member(X3736),X3733),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3736,tc_HOL_Obool),hAPP(c_Relation_OImage(X3736,X3736,X3734),hAPP(hAPP(c_Set_Oinsert(X3736),X3732),c_Orderings_Obot__class_Obot(tc_fun(X3736,tc_HOL_Obool)))),hAPP(c_Relation_OImage(X3736,X3736,X3734),hAPP(hAPP(c_Set_Oinsert(X3736),X3731),c_Orderings_Obot__class_Obot(tc_fun(X3736,tc_HOL_Obool)))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3736,X3736)),hAPP(hAPP(c_Product__Type_OPair(X3736,X3736),X3732),X3731)),X3734)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint])]) ).
fof(i_0_654,plain,
! [X2946,X2947,X2948,X2949] :
( ( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2949,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2949,tc_fun(X2949,tc_HOL_Obool),tc_HOL_Obool),c_member(X2949)),X2948),hAPP(hAPP(c_COMBC(X2949,tc_fun(X2949,tc_HOL_Obool),tc_HOL_Obool),c_member(X2949)),X2947)),X2946))
| hBOOL(hAPP(hAPP(c_member(X2949),X2946),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2949,tc_HOL_Obool),X2948,X2947))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2949),X2946),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2949,tc_HOL_Obool),X2948,X2947)))
| hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2949,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2949,tc_fun(X2949,tc_HOL_Obool),tc_HOL_Obool),c_member(X2949)),X2948),hAPP(hAPP(c_COMBC(X2949,tc_fun(X2949,tc_HOL_Obool),tc_HOL_Obool),c_member(X2949)),X2947)),X2946)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).
fof(i_0_655,plain,
! [X3509,X3510,X3511,X3512,X3513,X3514,X3515] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3515,X3514)),X3513),c_FuncSet_Oextensional__funcset(X3515,X3514,X3512,c_Groups_Ominus__class_Ominus(tc_fun(X3514,tc_HOL_Obool),X3511,hAPP(hAPP(c_Set_Oinsert(X3514),X3510),c_Orderings_Obot__class_Obot(tc_fun(X3514,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(X3515,X3514,X3513,X3512)
| c_Fun_Oinj__on(X3515,X3514,c_Fun_Ofun__upd(X3515,X3514,X3513,X3509,X3510),X3512) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__fun__upd__inj__onI])]) ).
fof(i_0_656,plain,
! [X3737,X3738,X3739,X3740,X3741] :
( c_Set_Oimage(X3741,X3740,X3739,X3738) != X3737
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3740,X3741)),c_FuncSet_Orestrict(X3740,X3741,c_Hilbert__Choice_Oinv__into(X3741,X3740,X3738,X3739),X3737)),c_FuncSet_OPi(X3740,X3741,X3737,c_COMBK(tc_fun(X3741,tc_HOL_Obool),X3740,X3738)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__funcset])]) ).
fof(i_0_657,plain,
! [X2303,X2304,X2305,X2306,X2308,X2312] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2303)
| ~ 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))),X2304),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),X2305),X2306)),hAPP(X2304,esk12_4(X2303,X2304,X2305,X2306))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2305),X2306)),hAPP(X2303,X2304))) )
& ( 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))),esk13_1(X2308)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X2308) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk14_1(X2308)),esk15_1(X2308))),hAPP(esk13_1(X2308),X2312)))
| c_Arrow__Order__Mirabelle_Ounanimity(X2308) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk14_1(X2308)),esk15_1(X2308))),hAPP(X2308,esk13_1(X2308))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2308) ) ),
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_658,plain,
! [X3477,X3478,X3479,X3480,X3481,X3482,X3483] :
( X3483 = X3482
| c_Fun_Ofun__upd(X3481,X3480,c_Fun_Ofun__upd(X3481,X3480,X3479,X3483,X3478),X3482,X3477) = c_Fun_Ofun__upd(X3481,X3480,c_Fun_Ofun__upd(X3481,X3480,X3479,X3482,X3477),X3483,X3478) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__twist])]) ).
cnf(i_0_659,plain,
( c_FuncSet_Ocompose(X1,X2,X2,X4,c_FuncSet_Orestrict(X2,X2,c_COMBI(X2),X5),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_533]) ).
fof(i_0_660,plain,
! [X2217,X2218,X2219,X2220,X2221] :
( ( X2218 != X2217
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2218 != X2220
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2221),X2217)),X2219))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2217 != X2220
| X2218 = 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),X2218),X2221)),X2219))
| X2218 = X2220
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2217 = X2220
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),X2219))
| X2218 = X2220
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2218 != X2220
| X2218 = X2220
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2217 != X2220
| X2217 = X2220
| X2218 = X2220
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),X2219))
| X2217 = X2220
| X2218 = X2220
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2217 != X2220
| X2218 != X2221
| X2218 = X2220
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),X2219))
| X2218 != X2221
| X2218 = X2220
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2217 != X2220
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2221)),X2219))
| X2218 = X2220
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),X2219))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2221)),X2219))
| X2218 = X2220
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2218 != X2220
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2221),X2217)),X2219))
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2217 != X2220
| X2217 = X2220
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2221),X2217)),X2219))
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),X2219))
| X2217 = X2220
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2221),X2217)),X2219))
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2217 != X2220
| X2218 != 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),X2221),X2217)),X2219))
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),X2219))
| X2218 != 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),X2221),X2217)),X2219))
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( X2217 != X2220
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2221)),X2219))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2221),X2217)),X2219))
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),X2219))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2221)),X2219))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2221),X2217)),X2219))
| X2218 = X2217
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2219),X2221),X2220)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| X2221 = X2220 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_661,plain,
! [X4244,X4245,X4246,X4247,X4248,X4249] :
( ~ c_Fun_Oinj__on(X4249,X4248,X4247,X4246)
| ~ hBOOL(hAPP(hAPP(c_member(X4248),X4245),c_Set_Oimage(X4249,X4248,X4247,X4246)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4249,tc_HOL_Obool),X4246,X4244)
| hBOOL(hAPP(hAPP(c_member(X4249),hAPP(c_Fun_Othe__inv__into(X4249,X4248,X4246,X4247),X4245)),X4244)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])]) ).
fof(i_0_662,plain,
! [X2212,X2213,X2214,X2215,X2216] :
( ( X2213 != 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2212 != 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),X2213),X2215)),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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2213 != X2216
| X2212 = X2215
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2212)),X2214))
| X2212 = 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),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2213 = 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),X2213),X2212)),X2214))
| X2212 = 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),X2213),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2212 != X2216
| X2212 = X2216
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2213 != X2216
| X2213 = X2216
| X2212 = X2216
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2212)),X2214))
| X2213 = X2216
| X2212 = X2216
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2213 != X2216
| X2212 != X2215
| X2212 = X2216
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2212)),X2214))
| X2212 != X2215
| X2212 = X2216
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2213 != X2216
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2212)),X2214))
| X2212 = X2216
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2212)),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),X2215),X2212)),X2214))
| X2212 = X2216
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2212 != 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),X2213),X2215)),X2214))
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2213 != X2216
| X2213 = 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),X2213),X2215)),X2214))
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2212)),X2214))
| X2213 = 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),X2213),X2215)),X2214))
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2213 != X2216
| X2212 != X2215
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2215)),X2214))
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2212)),X2214))
| X2212 != X2215
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2215)),X2214))
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( X2213 != X2216
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2212)),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),X2215)),X2214))
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2212)),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),X2215),X2212)),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),X2215)),X2214))
| X2213 = 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),X2212)),c_Arrow__Order__Mirabelle_Obelow(X2214,X2216,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2214),c_Arrow__Order__Mirabelle_OLin))
| X2216 = X2215 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
cnf(i_0_663,plain,
( c_FuncSet_Ocompose(X1,X1,X2,X4,X3,c_FuncSet_Orestrict(X1,X1,c_COMBI(X1),X4)) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_534]) ).
fof(i_0_664,plain,
! [X3569,X3570,X3571,X3572] : c_Nitpick_Ofold__graph_H(X3572,X3571,X3570,X3569,c_Orderings_Obot__class_Obot(tc_fun(X3572,tc_HOL_Obool)),X3569),
inference(variable_rename,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).
fof(i_0_665,plain,
! [X3565,X3566,X3567,X3568] : c_Nitpick_Ofold__graph_H(X3568,X3567,X3566,X3565,c_Orderings_Obot__class_Obot(tc_fun(X3568,tc_HOL_Obool)),X3565),
inference(variable_rename,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).
fof(i_0_666,plain,
! [X3606,X3607,X3608,X3609,X3610] :
( ( c_Fun_Oinj__on(X3610,X3609,X3608,X3606)
| ~ c_Fun_Oinj__on(X3610,X3609,X3608,hAPP(hAPP(c_Set_Oinsert(X3610),X3607),X3606)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3609),hAPP(X3608,X3607)),c_Set_Oimage(X3610,X3609,X3608,c_Groups_Ominus__class_Ominus(tc_fun(X3610,tc_HOL_Obool),X3606,hAPP(hAPP(c_Set_Oinsert(X3610),X3607),c_Orderings_Obot__class_Obot(tc_fun(X3610,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(X3610,X3609,X3608,hAPP(hAPP(c_Set_Oinsert(X3610),X3607),X3606)) )
& ( ~ c_Fun_Oinj__on(X3610,X3609,X3608,X3606)
| hBOOL(hAPP(hAPP(c_member(X3609),hAPP(X3608,X3607)),c_Set_Oimage(X3610,X3609,X3608,c_Groups_Ominus__class_Ominus(tc_fun(X3610,tc_HOL_Obool),X3606,hAPP(hAPP(c_Set_Oinsert(X3610),X3607),c_Orderings_Obot__class_Obot(tc_fun(X3610,tc_HOL_Obool)))))))
| c_Fun_Oinj__on(X3610,X3609,X3608,hAPP(hAPP(c_Set_Oinsert(X3610),X3607),X3606)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_535])])]) ).
fof(i_0_667,plain,
! [X3793,X3794,X3795,X3796,X3797] :
( ~ hBOOL(hAPP(hAPP(c_member(X3797),X3796),c_Set_Oimage(X3795,X3797,X3794,X3793)))
| hBOOL(hAPP(hAPP(c_member(X3795),hAPP(c_Hilbert__Choice_Oinv__into(X3795,X3797,X3793,X3794),X3796)),X3793)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).
fof(i_0_668,plain,
! [X2535,X2536,X2537,X2538,X2539,X2540,X2541,X2542] :
( ( ~ c_Relation_Ototal__on(X2537,X2536,X2535)
| ~ hBOOL(hAPP(hAPP(c_member(X2537),X2538),X2536))
| ~ hBOOL(hAPP(hAPP(c_member(X2537),X2539),X2536))
| X2538 = X2539
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2537,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2537,X2537),X2538),X2539)),X2535))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2537,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2537,X2537),X2539),X2538)),X2535)) )
& ( hBOOL(hAPP(hAPP(c_member(X2542),esk32_3(X2540,X2541,X2542)),X2541))
| c_Relation_Ototal__on(X2542,X2541,X2540) )
& ( hBOOL(hAPP(hAPP(c_member(X2542),esk33_3(X2540,X2541,X2542)),X2541))
| c_Relation_Ototal__on(X2542,X2541,X2540) )
& ( esk32_3(X2540,X2541,X2542) != esk33_3(X2540,X2541,X2542)
| c_Relation_Ototal__on(X2542,X2541,X2540) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2542,X2542)),hAPP(hAPP(c_Product__Type_OPair(X2542,X2542),esk32_3(X2540,X2541,X2542)),esk33_3(X2540,X2541,X2542))),X2540))
| c_Relation_Ototal__on(X2542,X2541,X2540) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2542,X2542)),hAPP(hAPP(c_Product__Type_OPair(X2542,X2542),esk33_3(X2540,X2541,X2542)),esk32_3(X2540,X2541,X2542))),X2540))
| c_Relation_Ototal__on(X2542,X2541,X2540) ) ),
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_total__on__def])])])])])]) ).
fof(i_0_669,plain,
! [X2681,X2682,X2683,X2684,X2685] :
( ~ c_Relation_Osingle__valued(X2685,X2685,X2684)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2685,X2685)),hAPP(hAPP(c_Product__Type_OPair(X2685,X2685),X2683),X2682)),c_Transitive__Closure_Ortrancl(X2685,X2684)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2685,X2685)),hAPP(hAPP(c_Product__Type_OPair(X2685,X2685),X2683),X2681)),c_Transitive__Closure_Ortrancl(X2685,X2684)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2685,X2685)),hAPP(hAPP(c_Product__Type_OPair(X2685,X2685),X2682),X2681)),c_Transitive__Closure_Ortrancl(X2685,X2684)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2685,X2685)),hAPP(hAPP(c_Product__Type_OPair(X2685,X2685),X2681),X2682)),c_Transitive__Closure_Ortrancl(X2685,X2684))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).
fof(i_0_670,plain,
! [X2492,X2493,X2494,X2495] :
( ~ hBOOL(hAPP(hAPP(c_member(X2495),X2494),c_Relation_ODomain(X2495,X2493,X2492)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2495,X2493)),hAPP(hAPP(c_Product__Type_OPair(X2495,X2493),X2494),esk29_4(X2492,X2493,X2494,X2495))),X2492)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_536])])]) ).
fof(i_0_671,plain,
! [X2478,X2479,X2480,X2481,X2483,X2484,X2485,X2486,X2487] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2481),X2480),c_Relation_ODomain(X2481,X2479,X2478)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2481,X2479)),hAPP(hAPP(c_Product__Type_OPair(X2481,X2479),X2480),esk28_4(X2478,X2479,X2480,X2481))),X2478)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2486,X2484)),hAPP(hAPP(c_Product__Type_OPair(X2486,X2484),X2485),X2487)),X2483))
| hBOOL(hAPP(hAPP(c_member(X2486),X2485),c_Relation_ODomain(X2486,X2484,X2483))) ) ),
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_672,plain,
! [X3782,X3783,X3784,X3785,X3786,X3787] :
( hAPP(c_Hilbert__Choice_Oinv__into(X3787,X3786,X3785,X3784),X3783) != hAPP(c_Hilbert__Choice_Oinv__into(X3787,X3786,X3785,X3784),X3782)
| ~ hBOOL(hAPP(hAPP(c_member(X3786),X3783),c_Set_Oimage(X3787,X3786,X3784,X3785)))
| ~ hBOOL(hAPP(hAPP(c_member(X3786),X3782),c_Set_Oimage(X3787,X3786,X3784,X3785)))
| X3783 = X3782 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).
cnf(i_0_673,plain,
( c_FuncSet_Ocompose(X2,X1,X2,X5,X3,c_FuncSet_Orestrict(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5)) = c_FuncSet_Orestrict(X2,X2,c_COMBI(X2),X5)
| c_Set_Oimage(X1,X2,X3,X4) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_537]) ).
fof(i_0_674,plain,
! [X2545,X2546,X2547,X2548,X2549,X2550] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2550,X2550)),hAPP(hAPP(c_Product__Type_OPair(X2550,X2550),X2549),X2548)),c_Relation_Oinv__image(X2547,X2550,X2546,X2545)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2547,X2547)),hAPP(hAPP(c_Product__Type_OPair(X2547,X2547),hAPP(X2545,X2549)),hAPP(X2545,X2548))),X2546)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2547,X2547)),hAPP(hAPP(c_Product__Type_OPair(X2547,X2547),hAPP(X2545,X2549)),hAPP(X2545,X2548))),X2546))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2550,X2550)),hAPP(hAPP(c_Product__Type_OPair(X2550,X2550),X2549),X2548)),c_Relation_Oinv__image(X2547,X2550,X2546,X2545))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])]) ).
fof(i_0_675,plain,
! [X3460,X3461,X3462,X3463,X3464,X3465] : c_Fun_Ofun__upd(X3465,X3464,c_Fun_Ofun__upd(X3465,X3464,X3463,X3462,X3461),X3462,X3460) = c_Fun_Ofun__upd(X3465,X3464,X3463,X3462,X3460),
inference(variable_rename,[status(thm)],[fact_fun__upd__upd]) ).
fof(i_0_676,plain,
! [X2950,X2951,X2952,X2953,X2954] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2954,X2954)),hAPP(hAPP(c_Product__Type_OPair(X2954,X2954),X2953),X2952)),c_Transitive__Closure_Otrancl(X2954,X2951)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2954,X2954)),hAPP(hAPP(c_Product__Type_OPair(X2954,X2954),X2952),X2950)),c_Transitive__Closure_Otrancl(X2954,X2951)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2954,X2954)),hAPP(hAPP(c_Product__Type_OPair(X2954,X2954),X2953),X2950)),c_Transitive__Closure_Otrancl(X2954,X2951))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__trans])]) ).
fof(i_0_677,plain,
! [X2993,X2994,X2995,X2996,X2997] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2997,X2997)),hAPP(hAPP(c_Product__Type_OPair(X2997,X2997),X2996),X2995)),c_Transitive__Closure_Ortrancl(X2997,X2994)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2997,X2997)),hAPP(hAPP(c_Product__Type_OPair(X2997,X2997),X2995),X2993)),c_Transitive__Closure_Otrancl(X2997,X2994)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2997,X2997)),hAPP(hAPP(c_Product__Type_OPair(X2997,X2997),X2996),X2993)),c_Transitive__Closure_Otrancl(X2997,X2994))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl])]) ).
fof(i_0_678,plain,
! [X2988,X2989,X2990,X2991,X2992] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2992,X2992)),hAPP(hAPP(c_Product__Type_OPair(X2992,X2992),X2991),X2990)),c_Transitive__Closure_Otrancl(X2992,X2989)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2992,X2992)),hAPP(hAPP(c_Product__Type_OPair(X2992,X2992),X2990),X2988)),c_Transitive__Closure_Ortrancl(X2992,X2989)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2992,X2992)),hAPP(hAPP(c_Product__Type_OPair(X2992,X2992),X2991),X2988)),c_Transitive__Closure_Otrancl(X2992,X2989))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl])]) ).
fof(i_0_679,plain,
! [X2652,X2653,X2654,X2655,X2656] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2656,X2656)),hAPP(hAPP(c_Product__Type_OPair(X2656,X2656),X2655),X2654)),c_Transitive__Closure_Ortrancl(X2656,X2653)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2656,X2656)),hAPP(hAPP(c_Product__Type_OPair(X2656,X2656),X2654),X2652)),c_Transitive__Closure_Ortrancl(X2656,X2653)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2656,X2656)),hAPP(hAPP(c_Product__Type_OPair(X2656,X2656),X2655),X2652)),c_Transitive__Closure_Ortrancl(X2656,X2653))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).
fof(i_0_680,plain,
! [X3600,X3601,X3602,X3603,X3604,X3605] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3605),X3604),X3603))
| c_Set_Oimage(X3605,X3602,c_Fun_Ofun__upd(X3605,X3602,X3601,X3604,X3600),X3603) = hAPP(hAPP(c_Set_Oinsert(X3602),X3600),c_Set_Oimage(X3605,X3602,X3601,c_Groups_Ominus__class_Ominus(tc_fun(X3605,tc_HOL_Obool),X3603,hAPP(hAPP(c_Set_Oinsert(X3605),X3604),c_Orderings_Obot__class_Obot(tc_fun(X3605,tc_HOL_Obool)))))) )
& ( hBOOL(hAPP(hAPP(c_member(X3605),X3604),X3603))
| c_Set_Oimage(X3605,X3602,c_Fun_Ofun__upd(X3605,X3602,X3601,X3604,X3600),X3603) = c_Set_Oimage(X3605,X3602,X3601,X3603) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_538])]) ).
fof(i_0_681,plain,
! [X2960,X2961,X2962,X2963,X2964] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2964,X2964)),hAPP(hAPP(c_Product__Type_OPair(X2964,X2964),X2963),X2962)),X2961))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2964,X2964)),hAPP(hAPP(c_Product__Type_OPair(X2964,X2964),X2962),X2960)),c_Transitive__Closure_Otrancl(X2964,X2961)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2964,X2964)),hAPP(hAPP(c_Product__Type_OPair(X2964,X2964),X2963),X2960)),c_Transitive__Closure_Otrancl(X2964,X2961))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])]) ).
fof(i_0_682,plain,
! [X2974,X2975,X2976,X2977,X2978] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2978,X2978)),hAPP(hAPP(c_Product__Type_OPair(X2978,X2978),X2977),X2976)),X2975))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2978,X2978)),hAPP(hAPP(c_Product__Type_OPair(X2978,X2978),X2976),X2974)),c_Transitive__Closure_Ortrancl(X2978,X2975)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2978,X2978)),hAPP(hAPP(c_Product__Type_OPair(X2978,X2978),X2977),X2974)),c_Transitive__Closure_Otrancl(X2978,X2975))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2])]) ).
fof(i_0_683,plain,
! [X2955,X2956,X2957,X2958,X2959] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2959,X2959)),hAPP(hAPP(c_Product__Type_OPair(X2959,X2959),X2958),X2957)),c_Transitive__Closure_Otrancl(X2959,X2956)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2959,X2959)),hAPP(hAPP(c_Product__Type_OPair(X2959,X2959),X2957),X2955)),X2956))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2959,X2959)),hAPP(hAPP(c_Product__Type_OPair(X2959,X2959),X2958),X2955)),c_Transitive__Closure_Otrancl(X2959,X2956))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])]) ).
fof(i_0_684,plain,
! [X2983,X2984,X2985,X2986,X2987] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2987,X2987)),hAPP(hAPP(c_Product__Type_OPair(X2987,X2987),X2986),X2985)),c_Transitive__Closure_Ortrancl(X2987,X2984)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2987,X2987)),hAPP(hAPP(c_Product__Type_OPair(X2987,X2987),X2985),X2983)),X2984))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2987,X2987)),hAPP(hAPP(c_Product__Type_OPair(X2987,X2987),X2986),X2983)),c_Transitive__Closure_Otrancl(X2987,X2984))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])]) ).
fof(i_0_685,plain,
! [X2666,X2667,X2668,X2669,X2670] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2670,X2670)),hAPP(hAPP(c_Product__Type_OPair(X2670,X2670),X2669),X2668)),X2667))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2670,X2670)),hAPP(hAPP(c_Product__Type_OPair(X2670,X2670),X2668),X2666)),c_Transitive__Closure_Ortrancl(X2670,X2667)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2670,X2670)),hAPP(hAPP(c_Product__Type_OPair(X2670,X2670),X2669),X2666)),c_Transitive__Closure_Ortrancl(X2670,X2667))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).
fof(i_0_686,plain,
! [X2657,X2658,X2659,X2660,X2661] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2661,X2661)),hAPP(hAPP(c_Product__Type_OPair(X2661,X2661),X2660),X2659)),c_Transitive__Closure_Ortrancl(X2661,X2658)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2661,X2661)),hAPP(hAPP(c_Product__Type_OPair(X2661,X2661),X2659),X2657)),X2658))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2661,X2661)),hAPP(hAPP(c_Product__Type_OPair(X2661,X2661),X2660),X2657)),c_Transitive__Closure_Ortrancl(X2661,X2658))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).
fof(i_0_687,plain,
! [X2965,X2966,X2967,X2968,X2969] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2969,X2969)),hAPP(hAPP(c_Product__Type_OPair(X2969,X2969),X2968),X2967)),X2966))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2969,X2969)),hAPP(hAPP(c_Product__Type_OPair(X2969,X2969),X2967),X2965)),X2966))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2969,X2969)),hAPP(hAPP(c_Product__Type_OPair(X2969,X2969),X2968),X2965)),c_Transitive__Closure_Otrancl(X2969,X2966))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
fof(i_0_688,plain,
! [X3691,X3692,X3693,X3694,X3695,X3696] :
( ~ c_Fun_Oinj__on(X3696,X3695,X3694,X3693)
| hBOOL(hAPP(hAPP(c_member(X3695),X3692),c_Set_Oimage(X3696,X3695,X3694,X3693)))
| c_Fun_Oinj__on(X3696,X3695,c_Fun_Ofun__upd(X3696,X3695,X3694,X3691,X3692),X3693) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])]) ).
fof(i_0_689,plain,
! [X4335,X4336,X4337,X4338] : hAPP(c_Relation_OImage(X4338,X4337,X4336),X4335) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4338,tc_fun(X4337,tc_HOL_Obool),X4335,hAPP(c_COMBB(tc_fun(X4338,tc_HOL_Obool),tc_fun(X4337,tc_HOL_Obool),X4338,c_Relation_OImage(X4338,X4337,X4336)),hAPP(hAPP(c_COMBC(X4338,tc_fun(X4338,tc_HOL_Obool),tc_fun(X4338,tc_HOL_Obool)),c_Set_Oinsert(X4338)),c_Orderings_Obot__class_Obot(tc_fun(X4338,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_Image__eq__UN]) ).
fof(i_0_690,plain,
! [X3659,X3660,X3661,X3662,X3663,X3665,X3666,X3667,X3668,X3669,X3670] :
( ( hBOOL(hAPP(hAPP(c_member(X3661),esk84_4(X3659,X3660,X3661,X3662)),X3659))
| ~ hBOOL(hAPP(hAPP(c_member(X3663),X3662),c_Set_Oimage(X3661,X3663,X3660,X3659))) )
& ( X3662 = hAPP(X3660,esk84_4(X3659,X3660,X3661,X3662))
| ~ hBOOL(hAPP(hAPP(c_member(X3663),X3662),c_Set_Oimage(X3661,X3663,X3660,X3659))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3667),X3669),X3665))
| X3668 != hAPP(X3666,X3669)
| hBOOL(hAPP(hAPP(c_member(X3670),X3668),c_Set_Oimage(X3667,X3670,X3666,X3665))) ) ),
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_691,plain,
! [X2230,X2231,X2232] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2231),X2230)),X2232))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2230),X2231)),X2232))
| X2231 = X2230
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2232),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),X2230),X2231)),X2232))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2231),X2230)),X2232))
| X2231 = X2230
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2232),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])])]) ).
fof(i_0_692,plain,
! [X2227,X2228,X2229] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2229),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2228),X2227)),X2229))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2228)),X2229)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])]) ).
fof(i_0_693,plain,
! [X2998,X2999,X3000,X3001] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3001,X3001)),hAPP(hAPP(c_Product__Type_OPair(X3001,X3001),X3000),X2999)),c_Transitive__Closure_Otrancl(X3001,c_Relation_Oconverse(X3001,X3001,X2998))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3001,X3001)),hAPP(hAPP(c_Product__Type_OPair(X3001,X3001),X3000),X2999)),c_Relation_Oconverse(X3001,X3001,c_Transitive__Closure_Otrancl(X3001,X2998)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseD])]) ).
fof(i_0_694,plain,
! [X2798,X2799,X2800] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2800,X2799)),hAPP(hAPP(c_Product__Type_OPair(X2800,X2799),esk54_3(X2798,X2799,X2800)),esk55_3(X2798,X2799,X2800))),X2798))
| c_Relation_Osingle__valued(X2800,X2799,X2798) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2800,X2799)),hAPP(hAPP(c_Product__Type_OPair(X2800,X2799),esk54_3(X2798,X2799,X2800)),esk56_3(X2798,X2799,X2800))),X2798))
| c_Relation_Osingle__valued(X2800,X2799,X2798) )
& ( esk55_3(X2798,X2799,X2800) != esk56_3(X2798,X2799,X2800)
| c_Relation_Osingle__valued(X2800,X2799,X2798) ) ),
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,
! [X2756,X2757,X2758,X2759,X2760,X2761,X2762,X2763,X2764] :
( ( ~ c_Relation_Osingle__valued(X2758,X2757,X2756)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2758,X2757)),hAPP(hAPP(c_Product__Type_OPair(X2758,X2757),X2759),X2760)),X2756))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2758,X2757)),hAPP(hAPP(c_Product__Type_OPair(X2758,X2757),X2759),X2761)),X2756))
| X2760 = X2761 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2764,X2763)),hAPP(hAPP(c_Product__Type_OPair(X2764,X2763),esk48_3(X2762,X2763,X2764)),esk49_3(X2762,X2763,X2764))),X2762))
| c_Relation_Osingle__valued(X2764,X2763,X2762) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2764,X2763)),hAPP(hAPP(c_Product__Type_OPair(X2764,X2763),esk48_3(X2762,X2763,X2764)),esk50_3(X2762,X2763,X2764))),X2762))
| c_Relation_Osingle__valued(X2764,X2763,X2762) )
& ( esk49_3(X2762,X2763,X2764) != esk50_3(X2762,X2763,X2764)
| c_Relation_Osingle__valued(X2764,X2763,X2762) ) ),
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,
! [X3002,X3003,X3004,X3005] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3005,X3005)),hAPP(hAPP(c_Product__Type_OPair(X3005,X3005),X3004),X3003)),c_Relation_Oconverse(X3005,X3005,c_Transitive__Closure_Otrancl(X3005,X3002))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3005,X3005)),hAPP(hAPP(c_Product__Type_OPair(X3005,X3005),X3004),X3003)),c_Transitive__Closure_Otrancl(X3005,c_Relation_Oconverse(X3005,X3005,X3002)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseI])]) ).
fof(i_0_697,plain,
! [X4217,X4218,X4219,X4220,X4221,X4222,X4223] :
( ~ c_Equiv__Relations_Oequiv(X4223,X4222,X4221)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4223,tc_HOL_Obool)),X4220),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4223),X4222),X4221)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4223,tc_HOL_Obool)),X4219),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4223),X4222),X4221)))
| ~ hBOOL(hAPP(hAPP(c_member(X4223),X4218),X4220))
| ~ hBOOL(hAPP(hAPP(c_member(X4223),X4217),X4219))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4223,X4223)),hAPP(hAPP(c_Product__Type_OPair(X4223,X4223),X4218),X4217)),X4221))
| X4220 = X4219 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eqI])]) ).
fof(i_0_698,plain,
! [X4210,X4211,X4212,X4213,X4214,X4215,X4216] :
( ( X4213 != X4212
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4216,X4216)),hAPP(hAPP(c_Product__Type_OPair(X4216,X4216),X4211),X4210)),X4214))
| ~ hBOOL(hAPP(hAPP(c_member(X4216),X4210),X4212))
| ~ hBOOL(hAPP(hAPP(c_member(X4216),X4211),X4213))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4216,tc_HOL_Obool)),X4212),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4216),X4215),X4214)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4216,tc_HOL_Obool)),X4213),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4216),X4215),X4214)))
| ~ c_Equiv__Relations_Oequiv(X4216,X4215,X4214) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4216,X4216)),hAPP(hAPP(c_Product__Type_OPair(X4216,X4216),X4211),X4210)),X4214))
| X4213 = X4212
| ~ hBOOL(hAPP(hAPP(c_member(X4216),X4210),X4212))
| ~ hBOOL(hAPP(hAPP(c_member(X4216),X4211),X4213))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4216,tc_HOL_Obool)),X4212),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4216),X4215),X4214)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4216,tc_HOL_Obool)),X4213),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4216),X4215),X4214)))
| ~ c_Equiv__Relations_Oequiv(X4216,X4215,X4214) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff])])]) ).
fof(i_0_699,plain,
! [X4176,X4177,X4178,X4179,X4180] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4180,X4179)),X4178),c_FuncSet_OPi(X4180,X4179,X4177,c_COMBK(tc_fun(X4179,tc_HOL_Obool),X4180,X4176))))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4179,tc_HOL_Obool),c_Set_Oimage(X4180,X4179,X4178,X4177),X4176) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).
fof(i_0_700,plain,
! [X3834,X3835,X3836,X3837,X3838,X3840,X3841,X3842,X3843,X3844,X3845] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3836,tc_HOL_Obool),esk87_5(X3834,X3835,X3836,X3837,X3838),X3834)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3838,tc_HOL_Obool),X3837,c_Set_Oimage(X3836,X3838,X3835,X3834)) )
& ( X3837 = c_Set_Oimage(X3836,X3838,X3835,esk87_5(X3834,X3835,X3836,X3837,X3838))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3838,tc_HOL_Obool),X3837,c_Set_Oimage(X3836,X3838,X3835,X3834)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3842,tc_HOL_Obool),X3845,X3840)
| X3843 != c_Set_Oimage(X3842,X3844,X3841,X3845)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3844,tc_HOL_Obool),X3843,c_Set_Oimage(X3842,X3844,X3841,X3840)) ) ),
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_701,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_542]) ).
fof(i_0_702,plain,
! [X2644,X2645,X2646,X2647] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2647,X2647)),hAPP(hAPP(c_Product__Type_OPair(X2647,X2647),X2646),X2645)),c_Transitive__Closure_Ortrancl(X2647,c_Relation_Oconverse(X2647,X2647,X2644))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2647,X2647)),hAPP(hAPP(c_Product__Type_OPair(X2647,X2647),X2645),X2646)),c_Transitive__Closure_Ortrancl(X2647,X2644))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD])]) ).
fof(i_0_703,plain,
! [X3803,X3804,X3805,X3806,X3807] :
( ~ c_Equiv__Relations_Oequiv(X3807,X3806,X3805)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3807,tc_HOL_Obool),hAPP(c_Relation_OImage(X3807,X3807,X3805),hAPP(hAPP(c_Set_Oinsert(X3807),X3804),c_Orderings_Obot__class_Obot(tc_fun(X3807,tc_HOL_Obool)))),hAPP(c_Relation_OImage(X3807,X3807,X3805),hAPP(hAPP(c_Set_Oinsert(X3807),X3803),c_Orderings_Obot__class_Obot(tc_fun(X3807,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(hAPP(c_member(X3807),X3804),X3806))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3807,X3807)),hAPP(hAPP(c_Product__Type_OPair(X3807,X3807),X3803),X3804)),X3805)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__equiv__class])]) ).
fof(i_0_704,plain,
! [X2261,X2262,X2263,X2264,X2265,X2266] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2266,X2265)),X2264),c_FuncSet_OPi(X2266,X2265,X2263,c_COMBK(tc_fun(X2265,tc_HOL_Obool),X2266,X2262))))
| ~ hBOOL(hAPP(hAPP(c_member(X2266),X2261),X2263))
| hBOOL(hAPP(hAPP(c_member(X2265),hAPP(X2264,X2261)),X2262)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
fof(i_0_705,plain,
! [X3116,X3117,X3118,X3119] :
( ( c_Wellfounded_Oacyclic(X3119,X3116)
| ~ c_Wellfounded_Oacyclic(X3119,hAPP(hAPP(c_Set_Oinsert(tc_prod(X3119,X3119)),hAPP(hAPP(c_Product__Type_OPair(X3119,X3119),X3118),X3117)),X3116)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3119,X3119)),hAPP(hAPP(c_Product__Type_OPair(X3119,X3119),X3117),X3118)),c_Transitive__Closure_Ortrancl(X3119,X3116)))
| ~ c_Wellfounded_Oacyclic(X3119,hAPP(hAPP(c_Set_Oinsert(tc_prod(X3119,X3119)),hAPP(hAPP(c_Product__Type_OPair(X3119,X3119),X3118),X3117)),X3116)) )
& ( ~ c_Wellfounded_Oacyclic(X3119,X3116)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3119,X3119)),hAPP(hAPP(c_Product__Type_OPair(X3119,X3119),X3117),X3118)),c_Transitive__Closure_Ortrancl(X3119,X3116)))
| c_Wellfounded_Oacyclic(X3119,hAPP(hAPP(c_Set_Oinsert(tc_prod(X3119,X3119)),hAPP(hAPP(c_Product__Type_OPair(X3119,X3119),X3118),X3117)),X3116)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])])]) ).
fof(i_0_706,plain,
! [X2750,X2751,X2752,X2753,X2754,X2755] :
( ~ c_Relation_Osingle__valued(X2755,X2754,X2753)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2755,X2754)),hAPP(hAPP(c_Product__Type_OPair(X2755,X2754),X2752),X2751)),X2753))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2755,X2754)),hAPP(hAPP(c_Product__Type_OPair(X2755,X2754),X2752),X2750)),X2753))
| X2751 = X2750 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).
fof(i_0_707,plain,
! [X3923,X3924,X3925,X3926,X3927] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3925,X3926),X3924,X3923)
| c_Orderings_Oord__class_Oless__eq(X3926,hAPP(X3924,X3927),hAPP(X3923,X3927))
| ~ class_Orderings_Oord(X3926) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3926,hAPP(X3924,esk88_4(X3923,X3924,X3925,X3926)),hAPP(X3923,esk88_4(X3923,X3924,X3925,X3926)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3925,X3926),X3924,X3923)
| ~ class_Orderings_Oord(X3926) ) ),
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_708,plain,
! [X4201,X4202,X4203,X4204] :
( ~ hBOOL(hAPP(hAPP(c_member(X4204),X4203),X4202))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X4204,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4204,X4204,X4201),hAPP(hAPP(c_Set_Oinsert(X4204),X4203),c_Orderings_Obot__class_Obot(tc_fun(X4204,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4204),X4202),X4201))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotientI])]) ).
fof(i_0_709,plain,
! [X3595,X3596,X3597,X3598,X3599] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3599),X3598),hAPP(c_Relation_OImage(X3597,X3599,X3596),hAPP(hAPP(c_Set_Oinsert(X3597),X3595),c_Orderings_Obot__class_Obot(tc_fun(X3597,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3597,X3599)),hAPP(hAPP(c_Product__Type_OPair(X3597,X3599),X3595),X3598)),X3596)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3597,X3599)),hAPP(hAPP(c_Product__Type_OPair(X3597,X3599),X3595),X3598)),X3596))
| hBOOL(hAPP(hAPP(c_member(X3599),X3598),hAPP(c_Relation_OImage(X3597,X3599,X3596),hAPP(hAPP(c_Set_Oinsert(X3597),X3595),c_Orderings_Obot__class_Obot(tc_fun(X3597,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])]) ).
fof(i_0_710,plain,
! [X2648,X2649,X2650,X2651] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2651,X2651)),hAPP(hAPP(c_Product__Type_OPair(X2651,X2651),X2650),X2649)),c_Transitive__Closure_Ortrancl(X2651,X2648)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2651,X2651)),hAPP(hAPP(c_Product__Type_OPair(X2651,X2651),X2649),X2650)),c_Transitive__Closure_Ortrancl(X2651,c_Relation_Oconverse(X2651,X2651,X2648)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI])]) ).
fof(i_0_711,plain,
! [X3357,X3358] : c_Set_Othe__elem(X3358,X3357) = c_HOL_OThe(X3358,hAPP(c_COMBB(tc_fun(X3358,tc_HOL_Obool),tc_HOL_Obool,X3358,hAPP(c_fequal,X3357)),hAPP(hAPP(c_COMBC(X3358,tc_fun(X3358,tc_HOL_Obool),tc_fun(X3358,tc_HOL_Obool)),c_Set_Oinsert(X3358)),c_Orderings_Obot__class_Obot(tc_fun(X3358,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_the__elem__def]) ).
fof(i_0_712,plain,
! [X2233] :
( ~ 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_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,X2233)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_713,plain,
! [X4291,X4292,X4293,X4294,X4295] :
( ~ c_Fun_Oinj__on(X4295,X4294,X4293,X4292)
| ~ hBOOL(hAPP(hAPP(c_member(X4294),X4291),c_Set_Oimage(X4295,X4294,X4293,X4292)))
| hAPP(X4293,hAPP(c_Fun_Othe__inv__into(X4295,X4294,X4292,X4293),X4291)) = X4291 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f])]) ).
fof(i_0_714,plain,
! [X4205,X4206,X4207,X4208,X4209] :
( ~ c_Equiv__Relations_Oequiv(X4209,X4208,X4207)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4209,X4209)),hAPP(hAPP(c_Product__Type_OPair(X4209,X4209),X4206),X4205)),X4207))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4209,tc_HOL_Obool),hAPP(c_Relation_OImage(X4209,X4209,X4207),hAPP(hAPP(c_Set_Oinsert(X4209),X4206),c_Orderings_Obot__class_Obot(tc_fun(X4209,tc_HOL_Obool)))),hAPP(c_Relation_OImage(X4209,X4209,X4207),hAPP(hAPP(c_Set_Oinsert(X4209),X4205),c_Orderings_Obot__class_Obot(tc_fun(X4209,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__subset])]) ).
fof(i_0_715,plain,
! [X4227,X4228,X4229,X4230] :
( ( X4229 = hAPP(c_Relation_OImage(X4230,X4230,X4227),hAPP(hAPP(c_Set_Oinsert(X4230),esk91_4(X4227,X4228,X4229,X4230)),c_Orderings_Obot__class_Obot(tc_fun(X4230,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4230,tc_HOL_Obool)),X4229),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4230),X4228),X4227))) )
& ( hBOOL(hAPP(hAPP(c_member(X4230),esk91_4(X4227,X4228,X4229,X4230)),X4228))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4230,tc_HOL_Obool)),X4229),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4230),X4228),X4227))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])])])]) ).
fof(i_0_716,plain,
! [X2283,X2284,X2285,X2286,X2287] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2287,X2286)),hAPP(hAPP(c_Product__Type_OPair(X2287,X2286),X2285),X2284)),c_Relation_Oconverse(X2286,X2287,X2283)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2286,X2287)),hAPP(hAPP(c_Product__Type_OPair(X2286,X2287),X2284),X2285)),X2283)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseD])]) ).
fof(i_0_717,plain,
! [X2273,X2274,X2275,X2276,X2277] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2277,X2276)),hAPP(hAPP(c_Product__Type_OPair(X2277,X2276),X2275),X2274)),c_Relation_Oconverse(X2276,X2277,X2273)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2276,X2277)),hAPP(hAPP(c_Product__Type_OPair(X2276,X2277),X2274),X2275)),X2273)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2276,X2277)),hAPP(hAPP(c_Product__Type_OPair(X2276,X2277),X2274),X2275)),X2273))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2277,X2276)),hAPP(hAPP(c_Product__Type_OPair(X2277,X2276),X2275),X2274)),c_Relation_Oconverse(X2276,X2277,X2273))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__iff])]) ).
fof(i_0_718,plain,
! [X4087,X4088,X4089,X4090,X4091] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4091,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4091,tc_HOL_Obool),c_Set_Oimage(X4090,X4091,X4089,X4088),c_Set_Oimage(X4090,X4091,X4089,X4087)),c_Set_Oimage(X4090,X4091,X4089,c_Groups_Ominus__class_Ominus(tc_fun(X4090,tc_HOL_Obool),X4088,X4087))),
inference(variable_rename,[status(thm)],[fact_image__diff__subset]) ).
fof(i_0_719,plain,
! [X4092,X4093,X4094,X4095,X4096] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4096,tc_HOL_Obool),c_Set_Oimage(X4095,X4096,X4094,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4095,tc_HOL_Obool),X4093,X4092)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4096,tc_HOL_Obool),c_Set_Oimage(X4095,X4096,X4094,X4093),c_Set_Oimage(X4095,X4096,X4094,X4092))),
inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).
fof(i_0_720,plain,
! [X3798,X3799,X3800,X3801,X3802] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X3802),hAPP(hAPP(c_Set_Oinsert(X3802),X3799),c_Orderings_Obot__class_Obot(tc_fun(X3802,tc_HOL_Obool)))),X3800) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X3802),hAPP(hAPP(c_Set_Oinsert(X3802),X3798),c_Orderings_Obot__class_Obot(tc_fun(X3802,tc_HOL_Obool)))),X3800)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3802,X3802)),hAPP(hAPP(c_Product__Type_OPair(X3802,X3802),X3799),X3798)),X3800))
| ~ hBOOL(hAPP(hAPP(c_member(X3802),X3798),X3801))
| ~ hBOOL(hAPP(hAPP(c_member(X3802),X3799),X3801))
| ~ c_Equiv__Relations_Oequiv(X3802,X3801,X3800) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3802,X3802)),hAPP(hAPP(c_Product__Type_OPair(X3802,X3802),X3799),X3798)),X3800))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X3802),hAPP(hAPP(c_Set_Oinsert(X3802),X3799),c_Orderings_Obot__class_Obot(tc_fun(X3802,tc_HOL_Obool)))),X3800) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X3802),hAPP(hAPP(c_Set_Oinsert(X3802),X3798),c_Orderings_Obot__class_Obot(tc_fun(X3802,tc_HOL_Obool)))),X3800)
| ~ hBOOL(hAPP(hAPP(c_member(X3802),X3798),X3801))
| ~ hBOOL(hAPP(hAPP(c_member(X3802),X3799),X3801))
| ~ c_Equiv__Relations_Oequiv(X3802,X3801,X3800) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2])])]) ).
fof(i_0_721,plain,
! [X2328,X2329,X2330,X2331,X2332] :
( ( ~ c_FunDef_Oin__rel(X2332,X2331,X2330,X2329,X2328)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2332,X2331)),hAPP(hAPP(c_Product__Type_OPair(X2332,X2331),X2329),X2328)),X2330)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2332,X2331)),hAPP(hAPP(c_Product__Type_OPair(X2332,X2331),X2329),X2328)),X2330))
| c_FunDef_Oin__rel(X2332,X2331,X2330,X2329,X2328) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_722,plain,
! [X2577,X2578,X2579] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2579,X2579)),hAPP(hAPP(c_Product__Type_OPair(X2579,X2579),esk35_3(X2577,X2578,X2579)),X2578)),X2577))
| hBOOL(hAPP(hAPP(c_member(X2579),X2578),c_Wellfounded_Oacc(X2579,X2577))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2579),esk35_3(X2577,X2578,X2579)),c_Wellfounded_Oacc(X2579,X2577)))
| hBOOL(hAPP(hAPP(c_member(X2579),X2578),c_Wellfounded_Oacc(X2579,X2577))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])])])]) ).
fof(i_0_723,plain,
! [X2573,X2574,X2575] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2575,X2575)),hAPP(hAPP(c_Product__Type_OPair(X2575,X2575),esk34_3(X2573,X2574,X2575)),X2574)),X2573))
| hBOOL(hAPP(hAPP(c_member(X2575),X2574),c_Wellfounded_Oacc(X2575,X2573))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2575),esk34_3(X2573,X2574,X2575)),c_Wellfounded_Oacc(X2575,X2573)))
| hBOOL(hAPP(hAPP(c_member(X2575),X2574),c_Wellfounded_Oacc(X2575,X2573))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).
fof(i_0_724,plain,
! [X2527,X2528,X2529,X2530,X2531,X2532,X2533] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2529),X2528),c_Wellfounded_Oacc(X2529,X2527)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2529,X2529)),hAPP(hAPP(c_Product__Type_OPair(X2529,X2529),X2530),X2528)),X2527))
| hBOOL(hAPP(hAPP(c_member(X2529),X2530),c_Wellfounded_Oacc(X2529,X2527))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2533,X2533)),hAPP(hAPP(c_Product__Type_OPair(X2533,X2533),esk31_3(X2531,X2532,X2533)),X2532)),X2531))
| hBOOL(hAPP(hAPP(c_member(X2533),X2532),c_Wellfounded_Oacc(X2533,X2531))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2533),esk31_3(X2531,X2532,X2533)),c_Wellfounded_Oacc(X2533,X2531)))
| hBOOL(hAPP(hAPP(c_member(X2533),X2532),c_Wellfounded_Oacc(X2533,X2531))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_Osimps])])])])])]) ).
fof(i_0_725,plain,
! [X2278,X2279,X2280,X2281,X2282] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2282,X2281)),hAPP(hAPP(c_Product__Type_OPair(X2282,X2281),X2280),X2279)),X2278))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2281,X2282)),hAPP(hAPP(c_Product__Type_OPair(X2281,X2282),X2279),X2280)),c_Relation_Oconverse(X2282,X2281,X2278))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseI])]) ).
cnf(i_0_726,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Relation_ORange(X2,X1,X3),c_Relation_ORange(X2,X1,X4)),c_Relation_ORange(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3,X4))),
inference(split_conjunct,[status(thm)],[i_0_546]) ).
cnf(i_0_727,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ORange(X2,X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3,X4)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Relation_ORange(X2,X1,X3),c_Relation_ORange(X2,X1,X4))),
inference(split_conjunct,[status(thm)],[i_0_547]) ).
fof(i_0_728,plain,
! [X2970,X2971,X2972,X2973] :
( ( X2972 != X2971
| X2972 = X2971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2973,X2973)),hAPP(hAPP(c_Product__Type_OPair(X2973,X2973),X2972),X2971)),c_Transitive__Closure_Ortrancl(X2973,X2970))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2973,X2973)),hAPP(hAPP(c_Product__Type_OPair(X2973,X2973),X2972),X2971)),c_Transitive__Closure_Otrancl(X2973,X2970)))
| X2972 = X2971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2973,X2973)),hAPP(hAPP(c_Product__Type_OPair(X2973,X2973),X2972),X2971)),c_Transitive__Closure_Ortrancl(X2973,X2970))) )
& ( X2972 != X2971
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2973,X2973)),hAPP(hAPP(c_Product__Type_OPair(X2973,X2973),X2972),X2971)),c_Transitive__Closure_Ortrancl(X2973,X2970))) )
& ( X2972 = X2971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2973,X2973)),hAPP(hAPP(c_Product__Type_OPair(X2973,X2973),X2972),X2971)),c_Transitive__Closure_Otrancl(X2973,X2970)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2973,X2973)),hAPP(hAPP(c_Product__Type_OPair(X2973,X2973),X2972),X2971)),c_Transitive__Closure_Ortrancl(X2973,X2970))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl])])]) ).
fof(i_0_729,plain,
! [X2979,X2980,X2981,X2982] :
( ( X2981 != X2980
| X2981 = X2980
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2982,X2982)),hAPP(hAPP(c_Product__Type_OPair(X2982,X2982),X2981),X2980)),c_Transitive__Closure_Ortrancl(X2982,X2979))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2982,X2982)),hAPP(hAPP(c_Product__Type_OPair(X2982,X2982),X2981),X2980)),c_Transitive__Closure_Otrancl(X2982,X2979)))
| X2981 = X2980
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2982,X2982)),hAPP(hAPP(c_Product__Type_OPair(X2982,X2982),X2981),X2980)),c_Transitive__Closure_Ortrancl(X2982,X2979))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtranclD])])]) ).
fof(i_0_730,plain,
! [X2868,X2869,X2870,X2871] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2871,X2871)),hAPP(hAPP(c_Product__Type_OPair(X2871,X2871),X2870),X2869)),c_Transitive__Closure_Otrancl(X2871,X2868)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2871,X2871)),hAPP(hAPP(c_Product__Type_OPair(X2871,X2871),X2870),X2869)),c_Transitive__Closure_Ortrancl(X2871,X2868))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl])]) ).
fof(i_0_731,plain,
! [X3335,X3336,X3337,X3338] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3338,tc_fun(X3337,tc_HOL_Obool))),X3336),X3335))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3338,X3337)),hAPP(hAPP(c_Product__Type_OPair(X3338,X3337),X3336),X3335)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3338,X3337),tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3338,X3337)),hAPP(hAPP(c_Product__Type_OPair(X3338,X3337),X3336),X3335)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3338,X3337),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3338,tc_fun(X3337,tc_HOL_Obool))),X3336),X3335)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2])]) ).
fof(i_0_732,plain,
! [X3788,X3789,X3790,X3791,X3792] :
( ~ hBOOL(hAPP(hAPP(c_member(X3792),X3791),c_Set_Oimage(X3790,X3792,X3789,X3788)))
| hAPP(X3789,hAPP(c_Hilbert__Choice_Oinv__into(X3790,X3792,X3788,X3789),X3791)) = X3791 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).
cnf(i_0_733,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_548]) ).
fof(i_0_734,plain,
! [X2888,X2889,X2890,X2891] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2891,X2891)),hAPP(hAPP(c_Product__Type_OPair(X2891,X2891),X2890),X2889)),X2888))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2891,X2891)),hAPP(hAPP(c_Product__Type_OPair(X2891,X2891),X2890),X2889)),c_Transitive__Closure_Otrancl(X2891,X2888))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl])]) ).
fof(i_0_735,plain,
! [X3761,X3762,X3763,X3764,X3765] :
( ( hAPP(c_Relation_OImage(X3765,X3765,X3763),hAPP(hAPP(c_Set_Oinsert(X3765),X3762),c_Orderings_Obot__class_Obot(tc_fun(X3765,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X3765,X3765,X3763),hAPP(hAPP(c_Set_Oinsert(X3765),X3761),c_Orderings_Obot__class_Obot(tc_fun(X3765,tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3765,X3765)),hAPP(hAPP(c_Product__Type_OPair(X3765,X3765),X3762),X3761)),X3763))
| ~ hBOOL(hAPP(hAPP(c_member(X3765),X3761),X3764))
| ~ hBOOL(hAPP(hAPP(c_member(X3765),X3762),X3764))
| ~ c_Equiv__Relations_Oequiv(X3765,X3764,X3763) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3765,X3765)),hAPP(hAPP(c_Product__Type_OPair(X3765,X3765),X3762),X3761)),X3763))
| hAPP(c_Relation_OImage(X3765,X3765,X3763),hAPP(hAPP(c_Set_Oinsert(X3765),X3762),c_Orderings_Obot__class_Obot(tc_fun(X3765,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X3765,X3765,X3763),hAPP(hAPP(c_Set_Oinsert(X3765),X3761),c_Orderings_Obot__class_Obot(tc_fun(X3765,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X3765),X3761),X3764))
| ~ hBOOL(hAPP(hAPP(c_member(X3765),X3762),X3764))
| ~ c_Equiv__Relations_Oequiv(X3765,X3764,X3763) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff])])]) ).
fof(i_0_736,plain,
! [X2413,X2414,X2415,X2416,X2417] :
( ( ~ c_Nitpick_Orefl_H(X2414,X2413)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2414,X2414)),hAPP(hAPP(c_Product__Type_OPair(X2414,X2414),X2415),X2415)),X2413)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2417,X2417)),hAPP(hAPP(c_Product__Type_OPair(X2417,X2417),esk25_2(X2416,X2417)),esk25_2(X2416,X2417))),X2416))
| c_Nitpick_Orefl_H(X2417,X2416) ) ),
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_737,plain,
c_Relation_ORange(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Relation_ORange(X1,X2,X5)),
inference(split_conjunct,[status(thm)],[i_0_549]) ).
fof(i_0_738,plain,
! [X3216,X3217,X3218,X3219,X3221,X3222,X3223,X3224,X3225] :
( ( hBOOL(hAPP(hAPP(c_member(X3219),esk76_4(X3216,X3217,X3218,X3219)),X3217))
| c_FuncSet_OPi(X3219,X3218,X3217,X3216) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3219,X3218),tc_HOL_Obool)) )
& ( hAPP(X3216,esk76_4(X3216,X3217,X3218,X3219)) = c_Orderings_Obot__class_Obot(tc_fun(X3218,tc_HOL_Obool))
| c_FuncSet_OPi(X3219,X3218,X3217,X3216) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3219,X3218),tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3224),X3225),X3222))
| hAPP(X3221,X3225) != c_Orderings_Obot__class_Obot(tc_fun(X3223,tc_HOL_Obool))
| c_FuncSet_OPi(X3224,X3223,X3222,X3221) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3224,X3223),tc_HOL_Obool)) ) ),
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_Pi__eq__empty])])])])])]) ).
fof(i_0_739,plain,
! [X4323,X4324,X4325,X4326,X4327,X4328] : hAPP(c_Relation_OImage(X4328,X4327,X4326),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4325,tc_fun(X4328,tc_HOL_Obool),X4324,X4323)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4325,tc_fun(X4327,tc_HOL_Obool),X4324,hAPP(c_COMBB(tc_fun(X4328,tc_HOL_Obool),tc_fun(X4327,tc_HOL_Obool),X4325,c_Relation_OImage(X4328,X4327,X4326)),X4323)),
inference(variable_rename,[status(thm)],[fact_Image__UN]) ).
fof(i_0_740,plain,
! [X2742,X2743,X2744,X2745] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2745,X2744)),c_FuncSet_Orestrict(X2745,X2744,X2743,X2742)),c_FuncSet_Oextensional(X2745,X2744,X2742))),
inference(variable_rename,[status(thm)],[fact_restrict__extensional]) ).
fof(i_0_741,plain,
! [X3766,X3767,X3768,X3769,X3770] :
( ( hAPP(c_Relation_OImage(X3770,X3770,X3768),hAPP(hAPP(c_Set_Oinsert(X3770),X3767),c_Orderings_Obot__class_Obot(tc_fun(X3770,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X3770,X3770,X3768),hAPP(hAPP(c_Set_Oinsert(X3770),X3766),c_Orderings_Obot__class_Obot(tc_fun(X3770,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3770,X3770)),hAPP(hAPP(c_Product__Type_OPair(X3770,X3770),X3767),X3766)),X3768))
| ~ c_Equiv__Relations_Oequiv(X3770,X3769,X3768) )
& ( hBOOL(hAPP(hAPP(c_member(X3770),X3767),X3769))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3770,X3770)),hAPP(hAPP(c_Product__Type_OPair(X3770,X3770),X3767),X3766)),X3768))
| ~ c_Equiv__Relations_Oequiv(X3770,X3769,X3768) )
& ( hBOOL(hAPP(hAPP(c_member(X3770),X3766),X3769))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3770,X3770)),hAPP(hAPP(c_Product__Type_OPair(X3770,X3770),X3767),X3766)),X3768))
| ~ c_Equiv__Relations_Oequiv(X3770,X3769,X3768) )
& ( hAPP(c_Relation_OImage(X3770,X3770,X3768),hAPP(hAPP(c_Set_Oinsert(X3770),X3767),c_Orderings_Obot__class_Obot(tc_fun(X3770,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X3770,X3770,X3768),hAPP(hAPP(c_Set_Oinsert(X3770),X3766),c_Orderings_Obot__class_Obot(tc_fun(X3770,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X3770),X3767),X3769))
| ~ hBOOL(hAPP(hAPP(c_member(X3770),X3766),X3769))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3770,X3770)),hAPP(hAPP(c_Product__Type_OPair(X3770,X3770),X3767),X3766)),X3768))
| ~ c_Equiv__Relations_Oequiv(X3770,X3769,X3768) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])]) ).
fof(i_0_742,plain,
! [X2267,X2268,X2269,X2270,X2271,X2272] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2272,X2271)),X2270),c_FuncSet_OPi(X2272,X2271,X2269,X2268)))
| ~ hBOOL(hAPP(hAPP(c_member(X2272),X2267),X2269))
| hBOOL(hAPP(hAPP(c_member(X2271),hAPP(X2270,X2267)),hAPP(X2268,X2267))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_743,plain,
! [X2250,X2251,X2252,X2253,X2254,X2255] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2255,X2254)),X2253),c_FuncSet_OPi(X2255,X2254,X2252,X2251)))
| hBOOL(hAPP(hAPP(c_member(X2254),hAPP(X2253,X2250)),hAPP(X2251,X2250)))
| ~ hBOOL(hAPP(hAPP(c_member(X2255),X2250),X2252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])]) ).
fof(i_0_744,plain,
! [X3484,X3485,X3486,X3487,X3488,X3489] :
( X3489 = X3488
| hAPP(c_Fun_Ofun__upd(X3487,X3486,X3485,X3488,X3484),X3489) = hAPP(X3485,X3489) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__other])]) ).
fof(i_0_745,plain,
! [X3471,X3472,X3473,X3474,X3475,X3476] :
( ( X3476 != X3475
| hAPP(c_Fun_Ofun__upd(X3474,X3473,X3472,X3475,X3471),X3476) = X3471 )
& ( X3476 = X3475
| hAPP(c_Fun_Ofun__upd(X3474,X3473,X3472,X3475,X3471),X3476) = hAPP(X3472,X3476) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__apply])]) ).
fof(i_0_746,plain,
! [X3359,X3360,X3361,X3362,X3363,X3364] :
( ( X3364 != X3363
| hAPP(c_Fun_Ofun__upd(X3362,X3361,X3360,X3363,X3359),X3364) = X3359 )
& ( X3364 = X3363
| hAPP(c_Fun_Ofun__upd(X3362,X3361,X3360,X3363,X3359),X3364) = hAPP(X3360,X3364) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__def])]) ).
fof(i_0_747,plain,
! [X2811,X2812,X2813,X2814,X2815,X2816] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2816,X2815)),X2814),c_FuncSet_Oextensional__funcset(X2816,X2815,X2813,X2812)))
| ~ hBOOL(hAPP(hAPP(c_member(X2816),X2811),X2813))
| hBOOL(hAPP(hAPP(c_member(X2815),hAPP(X2814,X2811)),X2812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__mem])]) ).
fof(i_0_748,plain,
! [X3466,X3467,X3468,X3469,X3470] : hAPP(c_Fun_Ofun__upd(X3470,X3469,X3468,X3467,X3466),X3467) = X3466,
inference(variable_rename,[status(thm)],[fact_fun__upd__same]) ).
fof(i_0_749,plain,
! [X3936,X3937,X3938] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3938,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3938,tc_fun(X3938,tc_HOL_Obool),tc_HOL_Obool),c_member(X3938)),X3937),hAPP(hAPP(c_COMBC(X3938,tc_fun(X3938,tc_HOL_Obool),tc_HOL_Obool),c_member(X3938)),X3936))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3938,tc_HOL_Obool),X3937,X3936) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3938,tc_HOL_Obool),X3937,X3936)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3938,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3938,tc_fun(X3938,tc_HOL_Obool),tc_HOL_Obool),c_member(X3938)),X3937),hAPP(hAPP(c_COMBC(X3938,tc_fun(X3938,tc_HOL_Obool),tc_HOL_Obool),c_member(X3938)),X3936)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_750,plain,
! [X3709,X3710,X3711,X3712,X3713,X3714] :
( ~ hBOOL(hAPP(hAPP(c_member(X3714),X3713),X3712))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3714,X3711)),hAPP(hAPP(c_Product__Type_OPair(X3714,X3711),X3713),X3710)),X3709))
| hBOOL(hAPP(hAPP(c_member(X3711),X3710),hAPP(c_Relation_OImage(X3714,X3711,X3709),X3712))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__ImageI])]) ).
fof(i_0_751,plain,
! [X2246,X2247,X2248,X2249] :
( ( X2248 != X2246
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),c_Arrow__Order__Mirabelle_Omkbot(X2247,X2246))) )
& ( X2249 != X2246
| X2249 != X2248
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),c_Arrow__Order__Mirabelle_Omkbot(X2247,X2246))) )
& ( X2249 = X2246
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),X2247))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),c_Arrow__Order__Mirabelle_Omkbot(X2247,X2246))) )
& ( X2249 != X2246
| X2249 = X2246
| X2248 = X2246
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),c_Arrow__Order__Mirabelle_Omkbot(X2247,X2246))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),X2247))
| X2249 = X2246
| X2248 = X2246
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),c_Arrow__Order__Mirabelle_Omkbot(X2247,X2246))) )
& ( X2249 != X2246
| X2249 = X2248
| X2248 = X2246
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),c_Arrow__Order__Mirabelle_Omkbot(X2247,X2246))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),X2247))
| X2249 = X2248
| X2248 = X2246
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2249),X2248)),c_Arrow__Order__Mirabelle_Omkbot(X2247,X2246))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_752,plain,
! [X2242,X2243,X2244,X2245] :
( ( X2245 != X2242
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),c_Arrow__Order__Mirabelle_Omktop(X2243,X2242))) )
& ( X2244 != X2242
| X2245 != X2244
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),c_Arrow__Order__Mirabelle_Omktop(X2243,X2242))) )
& ( X2244 = X2242
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),X2243))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),c_Arrow__Order__Mirabelle_Omktop(X2243,X2242))) )
& ( X2244 != X2242
| X2244 = X2242
| X2245 = X2242
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),c_Arrow__Order__Mirabelle_Omktop(X2243,X2242))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),X2243))
| X2244 = X2242
| X2245 = X2242
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),c_Arrow__Order__Mirabelle_Omktop(X2243,X2242))) )
& ( X2244 != X2242
| X2245 = X2244
| X2245 = X2242
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),c_Arrow__Order__Mirabelle_Omktop(X2243,X2242))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),X2243))
| X2245 = X2244
| X2245 = X2242
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2245),X2244)),c_Arrow__Order__Mirabelle_Omktop(X2243,X2242))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
cnf(i_0_753,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_532]) ).
cnf(i_0_754,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_551]) ).
fof(i_0_755,plain,
! [X3746,X3747,X3748,X3749,X3750] :
( ~ c_Equiv__Relations_Oequiv(X3750,X3749,X3748)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3750,X3750)),hAPP(hAPP(c_Product__Type_OPair(X3750,X3750),X3747),X3746)),X3748))
| hAPP(c_Relation_OImage(X3750,X3750,X3748),hAPP(hAPP(c_Set_Oinsert(X3750),X3747),c_Orderings_Obot__class_Obot(tc_fun(X3750,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X3750,X3750,X3748),hAPP(hAPP(c_Set_Oinsert(X3750),X3746),c_Orderings_Obot__class_Obot(tc_fun(X3750,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq])]) ).
fof(i_0_756,plain,
! [X3539,X3540,X3541,X3542,X3543,X3544,X3545,X3546,X3547,X3548] :
( ( ~ c_Fun_Oinj__on(X3542,X3541,X3540,X3539)
| ~ hBOOL(hAPP(hAPP(c_member(X3542),X3543),X3539))
| ~ hBOOL(hAPP(hAPP(c_member(X3542),X3544),X3539))
| hAPP(X3540,X3543) != hAPP(X3540,X3544)
| X3543 = X3544 )
& ( hBOOL(hAPP(hAPP(c_member(X3548),esk80_4(X3545,X3546,X3547,X3548)),X3545))
| c_Fun_Oinj__on(X3548,X3547,X3546,X3545) )
& ( hBOOL(hAPP(hAPP(c_member(X3548),esk81_4(X3545,X3546,X3547,X3548)),X3545))
| c_Fun_Oinj__on(X3548,X3547,X3546,X3545) )
& ( hAPP(X3546,esk80_4(X3545,X3546,X3547,X3548)) = hAPP(X3546,esk81_4(X3545,X3546,X3547,X3548))
| c_Fun_Oinj__on(X3548,X3547,X3546,X3545) )
& ( esk80_4(X3545,X3546,X3547,X3548) != esk81_4(X3545,X3546,X3547,X3548)
| c_Fun_Oinj__on(X3548,X3547,X3546,X3545) ) ),
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_inj__on__def])])])])])]) ).
fof(i_0_757,plain,
! [X2234] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X2234)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X2234))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X2234)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X2234))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])]) ).
fof(i_0_758,plain,
! [X3756,X3757,X3758,X3759,X3760] :
( hAPP(c_Relation_OImage(X3760,X3760,X3759),hAPP(hAPP(c_Set_Oinsert(X3760),X3758),c_Orderings_Obot__class_Obot(tc_fun(X3760,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X3760,X3760,X3759),hAPP(hAPP(c_Set_Oinsert(X3760),X3757),c_Orderings_Obot__class_Obot(tc_fun(X3760,tc_HOL_Obool))))
| ~ c_Equiv__Relations_Oequiv(X3760,X3756,X3759)
| ~ hBOOL(hAPP(hAPP(c_member(X3760),X3757),X3756))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3760,X3760)),hAPP(hAPP(c_Product__Type_OPair(X3760,X3760),X3758),X3757)),X3759)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class])]) ).
fof(i_0_759,plain,
! [X3110,X3111,X3112] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3112,X3112),tc_HOL_Obool),c_Relation_Oconverse(X3112,X3112,X3111),c_Transitive__Closure_Ortrancl(X3112,X3111)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3112,X3112),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3112,X3112)),hAPP(hAPP(c_Product__Type_OPair(X3112,X3112),X3110),X3110)),c_Transitive__Closure_Otrancl(X3112,X3111))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])]) ).
fof(i_0_760,plain,
! [X4119,X4120,X4121,X4122,X4123,X4124] :
( c_Set_Oimage(X4124,X4123,X4122,X4121) != X4120
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4123,tc_HOL_Obool),X4119,X4120)
| c_Set_Oimage(X4124,X4123,X4122,c_Set_Oimage(X4123,X4124,c_Hilbert__Choice_Oinv__into(X4124,X4123,X4121,X4122),X4119)) = X4119 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).
fof(i_0_761,plain,
! [X2184,X2185,X2186] :
( X2186 = X2185
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2184),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_Oabove,X2184),X2186),X2185)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_762,plain,
! [X2226] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2226)),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)),X2226),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)),X2226),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_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2226)),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__in__Lin])]) ).
fof(i_0_763,plain,
! [X4224,X4225,X4226] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4226,tc_HOL_Obool),X4225,hAPP(hAPP(c_Set_Oinsert(X4226),X4224),c_Orderings_Obot__class_Obot(tc_fun(X4226,tc_HOL_Obool))))
| c_Partial__Function_Oflat__lub(X4226,X4224,X4225) = X4224 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4226,tc_HOL_Obool),X4225,hAPP(hAPP(c_Set_Oinsert(X4226),X4224),c_Orderings_Obot__class_Obot(tc_fun(X4226,tc_HOL_Obool))))
| c_Partial__Function_Oflat__lub(X4226,X4224,X4225) = c_HOL_OThe(X4226,hAPP(hAPP(c_COMBC(X4226,tc_fun(X4226,tc_HOL_Obool),tc_HOL_Obool),c_member(X4226)),c_Groups_Ominus__class_Ominus(tc_fun(X4226,tc_HOL_Obool),X4225,hAPP(hAPP(c_Set_Oinsert(X4226),X4224),c_Orderings_Obot__class_Obot(tc_fun(X4226,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])]) ).
fof(i_0_764,plain,
! [X2786,X2787,X2788,X2789,X2790,X2791] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2791,X2790)),X2789),c_FuncSet_Oextensional__funcset(X2791,X2790,X2788,X2787)))
| hBOOL(hAPP(hAPP(c_member(X2791),X2786),X2788))
| hAPP(X2789,X2786) = c_HOL_Oundefined(X2790) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])]) ).
fof(i_0_765,plain,
! [X2591,X2592,X2593,X2594] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2594,X2594)),hAPP(hAPP(c_Product__Type_OPair(X2594,X2594),X2593),X2592)),c_Transitive__Closure_Ortrancl(X2594,X2591)))
| ~ hBOOL(hAPP(hAPP(c_member(X2594),X2592),c_Wellfounded_Oacc(X2594,X2591)))
| hBOOL(hAPP(hAPP(c_member(X2594),X2593),c_Wellfounded_Oacc(X2594,X2591))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).
fof(i_0_766,plain,
! [X2587,X2588,X2589,X2590] :
( ~ hBOOL(hAPP(hAPP(c_member(X2590),X2589),c_Wellfounded_Oacc(X2590,X2588)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2590,X2590)),hAPP(hAPP(c_Product__Type_OPair(X2590,X2590),X2587),X2589)),c_Transitive__Closure_Ortrancl(X2590,X2588)))
| hBOOL(hAPP(hAPP(c_member(X2590),X2587),c_Wellfounded_Oacc(X2590,X2588))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).
fof(i_0_767,plain,
! [X4152,X4153,X4154,X4155,X4156,X4157] :
( ~ c_Fun_Oinj__on(X4157,X4156,X4155,X4154)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4157,tc_HOL_Obool),X4153,X4154)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4157,tc_HOL_Obool),X4152,X4154)
| c_Set_Oimage(X4157,X4156,X4155,c_Groups_Ominus__class_Ominus(tc_fun(X4157,tc_HOL_Obool),X4153,X4152)) = c_Groups_Ominus__class_Ominus(tc_fun(X4156,tc_HOL_Obool),c_Set_Oimage(X4157,X4156,X4155,X4153),c_Set_Oimage(X4157,X4156,X4155,X4152)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff])]) ).
fof(i_0_768,plain,
! [X4146,X4147,X4148,X4149,X4150,X4151] :
( ~ c_Fun_Oinj__on(X4151,X4150,X4149,X4148)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4151,tc_HOL_Obool),X4147,X4148)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4151,tc_HOL_Obool),X4146,X4148)
| c_Set_Oimage(X4151,X4150,X4149,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4151,tc_HOL_Obool),X4147,X4146)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4150,tc_HOL_Obool),c_Set_Oimage(X4151,X4150,X4149,X4147),c_Set_Oimage(X4151,X4150,X4149,X4146)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int])]) ).
fof(i_0_769,plain,
! [X2206,X2207,X2208,X2209,X2210] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2207,X2206)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2208),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X2207,X2208) = hAPP(X2208,X2206) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk3_2(X2209,X2210)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2210,X2209) )
& ( hAPP(X2210,esk3_2(X2209,X2210)) != hAPP(esk3_2(X2209,X2210),X2209)
| c_Arrow__Order__Mirabelle_Odictator(X2210,X2209) ) ),
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_770,plain,
! [X4138,X4139,X4140,X4141,X4142,X4144] :
( ( ~ c_Fun_Oinj__on(X4140,X4139,X4142,X4141)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4139,tc_HOL_Obool),c_Set_Oimage(X4140,X4139,X4142,X4141),X4138)
| c_Set_Oimage(X4139,X4140,esk89_4(X4138,X4139,X4140,X4141),X4138) = X4141
| X4141 = c_Orderings_Obot__class_Obot(tc_fun(X4140,tc_HOL_Obool)) )
& ( c_Fun_Oinj__on(X4140,X4139,esk90_4(X4138,X4139,X4140,X4141),X4141)
| c_Set_Oimage(X4139,X4140,X4144,X4138) != X4141
| X4141 = c_Orderings_Obot__class_Obot(tc_fun(X4140,tc_HOL_Obool)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4139,tc_HOL_Obool),c_Set_Oimage(X4140,X4139,esk90_4(X4138,X4139,X4140,X4141),X4141),X4138)
| c_Set_Oimage(X4139,X4140,X4144,X4138) != X4141
| X4141 = c_Orderings_Obot__class_Obot(tc_fun(X4140,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj])])])])]) ).
fof(i_0_771,plain,
! [X4181,X4182,X4183] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X4183),hAPP(hAPP(c_Set_Oinsert(X4183),X4182),c_Orderings_Obot__class_Obot(tc_fun(X4183,tc_HOL_Obool)))),X4181) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X4183,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4183,X4183,X4181),hAPP(hAPP(c_Set_Oinsert(X4183),X4182),c_Orderings_Obot__class_Obot(tc_fun(X4183,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4183,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__quotient]) ).
fof(i_0_772,plain,
! [X4299,X4300,X4301,X4302,X4303,X4304] :
( ~ c_Equiv__Relations_Ocongruent(X4304,X4303,X4302,X4301)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4304,X4304)),hAPP(hAPP(c_Product__Type_OPair(X4304,X4304),X4300),X4299)),X4302))
| hAPP(X4301,X4300) = hAPP(X4301,X4299) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentD])]) ).
fof(i_0_773,plain,
! [X2837,X2838,X2839,X2840,X2841,X2842] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2842,X2842)),hAPP(hAPP(c_Product__Type_OPair(X2842,X2842),X2841),X2840)),X2839))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X2842,X2838),X2837),X2839),X2840),X2841) = hAPP(X2837,X2841) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut__apply])]) ).
fof(i_0_774,plain,
! [X2817,X2818,X2819,X2820,X2821,X2822] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2820,X2820)),hAPP(hAPP(c_Product__Type_OPair(X2820,X2820),X2819),X2818)),X2822))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X2820,X2817),X2821),X2822),X2818),X2819) = hAPP(X2821,X2819) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__cut__apply])]) ).
fof(i_0_775,plain,
! [X2780,X2781,X2782,X2783,X2784,X2785] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2785,X2785)),hAPP(hAPP(c_Product__Type_OPair(X2785,X2785),X2784),X2783)),X2782))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X2785,X2781),X2780),X2782),X2783),X2784) = hAPP(X2780,X2784) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2785,X2785)),hAPP(hAPP(c_Product__Type_OPair(X2785,X2785),X2784),X2783)),X2782))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X2785,X2781),X2780),X2782),X2783),X2784) = c_HOL_Oundefined(X2781) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])]) ).
fof(i_0_776,plain,
! [X2523,X2524,X2525,X2526] :
( ~ hBOOL(hAPP(hAPP(c_member(X2526),X2525),c_Wellfounded_Oacc(X2526,X2524)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2526,X2526)),hAPP(hAPP(c_Product__Type_OPair(X2526,X2526),X2523),X2525)),X2524))
| hBOOL(hAPP(hAPP(c_member(X2526),X2523),c_Wellfounded_Oacc(X2526,X2524))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).
fof(i_0_777,plain,
! [X2640,X2641,X2642,X2643] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2643,X2643)),hAPP(hAPP(c_Product__Type_OPair(X2643,X2643),X2642),X2640)),c_Transitive__Closure_Ortrancl(X2643,X2641)))
| X2642 = X2640
| hBOOL(hAPP(hAPP(c_member(X2643),X2642),c_Relation_ODomain(X2643,X2643,X2641))) )
& ( X2642 != X2640
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2643,X2643)),hAPP(hAPP(c_Product__Type_OPair(X2643,X2643),X2642),X2640)),c_Transitive__Closure_Ortrancl(X2643,X2641)))
| hBOOL(hAPP(hAPP(c_member(X2643),X2642),c_Relation_ODomain(X2643,X2643,X2641))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])])]) ).
fof(i_0_778,plain,
! [X3642,X3643,X3644,X3645,X3646,X3647] : c_Set_Oimage(X3647,X3646,X3645,c_Set_Oimage(X3644,X3647,X3643,X3642)) = c_Set_Oimage(X3644,X3646,hAPP(c_COMBB(X3647,X3646,X3644,X3645),X3643),X3642),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_779,plain,
! [X2187,X2188,X2189] :
( X2189 = X2188
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2187),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_Obelow(X2187,X2189,X2188)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_780,plain,
! [X2403,X2404,X2405,X2406,X2407] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2407,X2406)),hAPP(hAPP(c_Product__Type_OPair(X2407,X2406),X2405),X2404)),X2403))
| hBOOL(hAPP(hAPP(c_member(X2407),X2405),c_Relation_ODomain(X2407,X2406,X2403))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).
fof(i_0_781,plain,
! [X2288,X2289] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2289,X2289)),c_COMBI(X2289)),c_FuncSet_OPi(X2289,X2289,X2288,c_COMBK(tc_fun(X2289,tc_HOL_Obool),X2289,X2288)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_782,plain,
! [X3455,X3456,X3457,X3458,X3459] :
( ( c_Fun_Ofun__upd(X3459,X3458,X3457,X3456,X3455) != X3457
| hAPP(X3457,X3456) = X3455 )
& ( hAPP(X3457,X3456) != X3455
| c_Fun_Ofun__upd(X3459,X3458,X3457,X3456,X3455) = X3457 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])]) ).
fof(i_0_783,plain,
! [X2599,X2600,X2601,X2602,X2603] :
( ~ c_Relation_Orefl__on(X2603,X2602,X2601)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2603,X2603)),hAPP(hAPP(c_Product__Type_OPair(X2603,X2603),X2600),X2599)),X2601))
| hBOOL(hAPP(hAPP(c_member(X2603),X2600),X2602)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD1])]) ).
fof(i_0_784,plain,
! [X2629,X2630,X2631,X2632,X2633] :
( ~ c_Relation_Orefl__on(X2633,X2632,X2631)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2633,X2633)),hAPP(hAPP(c_Product__Type_OPair(X2633,X2633),X2630),X2629)),X2631))
| hBOOL(hAPP(hAPP(c_member(X2633),X2629),X2632)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD2])]) ).
fof(i_0_785,plain,
! [X2358,X2359,X2360,X2361] :
( ( X2360 = X2359
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2361,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2361),X2360),X2359)),c_Relation_OId__on(X2361,X2358))) )
& ( hBOOL(hAPP(hAPP(c_member(X2361),X2360),X2358))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2361,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2361),X2360),X2359)),c_Relation_OId__on(X2361,X2358))) )
& ( X2360 != X2359
| ~ hBOOL(hAPP(hAPP(c_member(X2361),X2360),X2358))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2361,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2361),X2360),X2359)),c_Relation_OId__on(X2361,X2358))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).
fof(i_0_786,plain,
! [X3130,X3131,X3132,X3133,X3134,X3135] :
( ( hBOOL(hAPP(hAPP(X3133,X3131),X3130))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3135,tc_fun(X3134,tc_HOL_Obool)),X3133,X3132),X3131),X3130)) )
& ( hBOOL(hAPP(hAPP(X3132,X3131),X3130))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3135,tc_fun(X3134,tc_HOL_Obool)),X3133,X3132),X3131),X3130)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])])]) ).
fof(i_0_787,plain,
! [X3158,X3159,X3160,X3161,X3162,X3163] :
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3163,tc_fun(X3162,tc_HOL_Obool)),X3161,X3160),X3159),X3158))
| hBOOL(hAPP(hAPP(X3161,X3159),X3158)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).
fof(i_0_788,plain,
! [X3152,X3153,X3154,X3155,X3156,X3157] :
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3157,tc_fun(X3156,tc_HOL_Obool)),X3155,X3154),X3153),X3152))
| hBOOL(hAPP(hAPP(X3154,X3153),X3152)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).
fof(i_0_789,plain,
! [X4192,X4193,X4194,X4195,X4196] :
( ~ c_Equiv__Relations_Oequiv(X4196,X4195,X4194)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4196,tc_HOL_Obool)),X4193),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4196),X4195),X4194)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4196,tc_HOL_Obool)),X4192),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4196),X4195),X4194)))
| X4193 = X4192
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4196,tc_HOL_Obool),X4193,X4192) = c_Orderings_Obot__class_Obot(tc_fun(X4196,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__disj])]) ).
fof(i_0_790,plain,
! [X4158,X4159,X4160,X4161,X4162] :
( ~ c_Fun_Oinj__on(X4162,X4161,X4160,X4159)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4162,tc_HOL_Obool),X4158,X4159)
| c_Set_Oimage(X4161,X4162,c_Hilbert__Choice_Oinv__into(X4162,X4161,X4159,X4160),c_Set_Oimage(X4162,X4161,X4160,X4158)) = X4158 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).
fof(i_0_791,plain,
! [X3026,X3027,X3028,X3029,X3030] :
( ( ~ c_Wellfounded_Oacyclic(X3027,X3026)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3027,X3027)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3027),X3028),X3028)),c_Transitive__Closure_Otrancl(X3027,X3026))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3030,X3030)),hAPP(hAPP(c_Product__Type_OPair(X3030,X3030),esk66_2(X3029,X3030)),esk66_2(X3029,X3030))),c_Transitive__Closure_Otrancl(X3030,X3029)))
| c_Wellfounded_Oacyclic(X3030,X3029) ) ),
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_558])])])])]) ).
fof(i_0_792,plain,
! [X3823,X3824,X3825,X3826,X3827] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3827,tc_HOL_Obool),hAPP(c_Relation_OImage(X3826,X3827,X3825),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3826,tc_HOL_Obool),X3824,X3823)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3827,tc_HOL_Obool),hAPP(c_Relation_OImage(X3826,X3827,X3825),X3824),hAPP(c_Relation_OImage(X3826,X3827,X3825),X3823))),
inference(variable_rename,[status(thm)],[fact_Image__Int__subset]) ).
fof(i_0_793,plain,
! [X3113,X3114] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3114,X3114)),hAPP(hAPP(c_Product__Type_OPair(X3114,X3114),esk71_2(X3113,X3114)),esk71_2(X3113,X3114))),c_Transitive__Closure_Otrancl(X3114,X3113)))
| c_Wellfounded_Oacyclic(X3114,X3113) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])])]) ).
fof(i_0_794,plain,
! [X2316,X2317,X2318,X2319,X2320] :
( ( ~ c_Relation_Oirrefl(X2317,X2316)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2317,X2317)),hAPP(hAPP(c_Product__Type_OPair(X2317,X2317),X2318),X2318)),X2316)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2320,X2320)),hAPP(hAPP(c_Product__Type_OPair(X2320,X2320),esk16_2(X2319,X2320)),esk16_2(X2319,X2320))),X2319))
| c_Relation_Oirrefl(X2320,X2319) ) ),
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_560])])])])]) ).
fof(i_0_795,plain,
! [X3742,X3743,X3744,X3745] :
( ~ c_Equiv__Relations_Oequiv(X3745,X3744,X3743)
| ~ hBOOL(hAPP(hAPP(c_member(X3745),X3742),X3744))
| hBOOL(hAPP(hAPP(c_member(X3745),X3742),hAPP(c_Relation_OImage(X3745,X3745,X3743),hAPP(hAPP(c_Set_Oinsert(X3745),X3742),c_Orderings_Obot__class_Obot(tc_fun(X3745,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__self])]) ).
fof(i_0_796,plain,
! [X2178,X2179] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2179),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(X2179,X2178)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_797,plain,
! [X2176,X2177] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2177),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(X2177,X2176)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_798,plain,
! [X4163,X4164,X4165,X4166,X4167] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4167,tc_HOL_Obool),X4166,c_Set_Oimage(X4165,X4167,X4164,X4163))
| c_Fun_Oinj__on(X4167,X4165,c_Hilbert__Choice_Oinv__into(X4165,X4167,X4163,X4164),X4166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).
fof(i_0_799,plain,
! [X4282,X4283,X4284,X4285] :
( ~ c_Fun_Oinj__on(X4285,X4284,X4283,X4282)
| c_Set_Oimage(X4284,X4285,c_Fun_Othe__inv__into(X4285,X4284,X4282,X4283),c_Set_Oimage(X4285,X4284,X4283,X4282)) = X4282 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).
fof(i_0_800,plain,
! [X4278,X4279,X4280,X4281] :
( ~ c_Fun_Oinj__on(X4281,X4280,X4279,X4278)
| c_Fun_Oinj__on(X4280,X4281,c_Fun_Othe__inv__into(X4281,X4280,X4278,X4279),c_Set_Oimage(X4281,X4280,X4279,X4278)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into])]) ).
fof(i_0_801,plain,
! [X4329,X4330,X4331,X4332,X4333,X4334] :
( ~ c_Equiv__Relations_Oequiv(X4334,X4333,X4332)
| ~ c_Equiv__Relations_Ocongruent(X4334,tc_fun(X4331,tc_HOL_Obool),X4332,X4330)
| ~ hBOOL(hAPP(hAPP(c_member(X4334),X4329),X4333))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4334,tc_fun(X4331,tc_HOL_Obool),hAPP(c_Relation_OImage(X4334,X4334,X4332),hAPP(hAPP(c_Set_Oinsert(X4334),X4329),c_Orderings_Obot__class_Obot(tc_fun(X4334,tc_HOL_Obool)))),X4330) = hAPP(X4330,X4329) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class])]) ).
fof(i_0_802,plain,
! [X4339,X4340,X4341,X4342,X4343,X4344] :
( ~ hBOOL(hAPP(hAPP(c_member(X4344),X4343),X4342))
| ~ hBOOL(hAPP(hAPP(c_member(X4341),X4340),hAPP(X4339,X4343)))
| hBOOL(hAPP(hAPP(c_member(X4341),X4340),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4344,tc_fun(X4341,tc_HOL_Obool),X4342,X4339))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__I])]) ).
fof(i_0_803,plain,
! [X4133,X4134,X4135,X4136,X4137] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4137,X4136)),X4135),c_FuncSet_Oextensional(X4137,X4136,X4134)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4137,tc_HOL_Obool),X4134,X4133)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X4137,X4136)),X4135),c_FuncSet_Oextensional(X4137,X4136,X4133))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__subset])]) ).
fof(i_0_804,plain,
! [X3561,X3562,X3563,X3564] :
( ( ~ c_Fun_Oinj__on(X3564,X3563,c_FuncSet_Orestrict(X3564,X3563,X3562,X3561),X3561)
| c_Fun_Oinj__on(X3564,X3563,X3562,X3561) )
& ( ~ c_Fun_Oinj__on(X3564,X3563,X3562,X3561)
| c_Fun_Oinj__on(X3564,X3563,c_FuncSet_Orestrict(X3564,X3563,X3562,X3561),X3561) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__restrict__eq])]) ).
fof(i_0_805,plain,
! [X4305,X4306,X4307,X4308,X4309,X4310] :
( ~ hBOOL(hAPP(hAPP(c_member(X4310),X4309),X4308))
| ~ hBOOL(hAPP(hAPP(X4307,X4309),X4306))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4310,tc_fun(X4305,tc_HOL_Obool),X4308,X4307),X4306)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__I])]) ).
fof(i_0_806,plain,
! [X3654,X3655,X3656,X3657,X3658] :
( ~ hBOOL(hAPP(hAPP(c_member(X3658),X3657),X3656))
| hBOOL(hAPP(hAPP(c_member(X3655),hAPP(X3654,X3657)),c_Set_Oimage(X3658,X3655,X3654,X3656))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_807,plain,
! [X4184,X4185,X4186,X4187] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4187,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4187,tc_HOL_Obool),X4186,hAPP(hAPP(c_Set_Oinsert(X4187),X4185),c_Orderings_Obot__class_Obot(tc_fun(X4187,tc_HOL_Obool)))),X4184)
| ~ hBOOL(hAPP(hAPP(c_member(X4187),X4185),X4186))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4187,tc_HOL_Obool),X4186,hAPP(hAPP(c_Set_Oinsert(X4187),X4185),X4184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__single__insert])]) ).
fof(i_0_808,plain,
! [X4188,X4189,X4190,X4191] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X4191),X4189),X4190))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4191,tc_HOL_Obool),X4190,hAPP(hAPP(c_Set_Oinsert(X4191),X4189),c_Orderings_Obot__class_Obot(tc_fun(X4191,tc_HOL_Obool)))),X4188)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),X4190,hAPP(hAPP(c_Set_Oinsert(X4191),X4189),X4188)) )
& ( hBOOL(hAPP(hAPP(c_member(X4191),X4189),X4190))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),X4190,X4188)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),X4190,hAPP(hAPP(c_Set_Oinsert(X4191),X4189),X4188)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4191),X4189),X4190))
| hBOOL(hAPP(hAPP(c_member(X4191),X4189),X4190))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),X4190,hAPP(hAPP(c_Set_Oinsert(X4191),X4189),X4188)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),X4190,X4188)
| hBOOL(hAPP(hAPP(c_member(X4191),X4189),X4190))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),X4190,hAPP(hAPP(c_Set_Oinsert(X4191),X4189),X4188)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4191),X4189),X4190))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4191,tc_HOL_Obool),X4190,hAPP(hAPP(c_Set_Oinsert(X4191),X4189),c_Orderings_Obot__class_Obot(tc_fun(X4191,tc_HOL_Obool)))),X4188)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),X4190,hAPP(hAPP(c_Set_Oinsert(X4191),X4189),X4188)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),X4190,X4188)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4191,tc_HOL_Obool),X4190,hAPP(hAPP(c_Set_Oinsert(X4191),X4189),c_Orderings_Obot__class_Obot(tc_fun(X4191,tc_HOL_Obool)))),X4188)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4191,tc_HOL_Obool),X4190,hAPP(hAPP(c_Set_Oinsert(X4191),X4189),X4188)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])])]) ).
fof(i_0_809,plain,
! [X3136,X3137,X3138,X3139,X3140,X3141] :
( ~ hBOOL(hAPP(hAPP(X3141,X3140),X3139))
| ~ hBOOL(hAPP(hAPP(X3138,X3140),X3139))
| hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3137,tc_fun(X3136,tc_HOL_Obool)),X3141,X3138),X3140),X3139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).
fof(i_0_810,plain,
! [X2595,X2596,X2597,X2598] :
( ~ c_Relation_Orefl__on(X2598,X2597,X2596)
| ~ hBOOL(hAPP(hAPP(c_member(X2598),X2595),X2597))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2598,X2598)),hAPP(hAPP(c_Product__Type_OPair(X2598,X2598),X2595),X2595)),X2596)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD])]) ).
fof(i_0_811,plain,
! [X3611,X3612,X3613,X3614,X3615,X3616] :
( X3616 != hAPP(X3615,X3614)
| ~ hBOOL(hAPP(hAPP(c_member(X3613),X3614),X3612))
| hBOOL(hAPP(hAPP(c_member(X3611),X3616),c_Set_Oimage(X3613,X3611,X3615,X3612))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_812,plain,
! [X3648,X3649,X3650,X3651,X3652,X3653] :
( ~ hBOOL(hAPP(hAPP(c_member(X3653),X3652),X3651))
| X3650 != hAPP(X3649,X3652)
| hBOOL(hAPP(hAPP(c_member(X3648),X3650),c_Set_Oimage(X3653,X3648,X3649,X3651))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_813,plain,
! [X2847,X2848,X2849,X2850] : c_FuncSet_Oextensional__funcset(X2850,X2849,X2848,X2847) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X2850,X2849),tc_HOL_Obool),c_FuncSet_OPi(X2850,X2849,X2848,c_COMBK(tc_fun(X2849,tc_HOL_Obool),X2850,X2847)),c_FuncSet_Oextensional(X2850,X2849,X2848)),
inference(variable_rename,[status(thm)],[fact_extensional__funcset__def]) ).
fof(i_0_814,plain,
! [X4125,X4126,X4127,X4128] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4128,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X4128,tc_HOL_Obool),c_Relation_ODomain(X4128,X4127,X4126),c_Relation_ODomain(X4128,X4127,X4125)),c_Relation_ODomain(X4128,X4127,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4128,X4127),tc_HOL_Obool),X4126,X4125))),
inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset]) ).
fof(i_0_815,plain,
! [X4168,X4169,X4170,X4171] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4171,tc_HOL_Obool),c_Relation_ODomain(X4171,X4170,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4171,X4170),tc_HOL_Obool),X4169,X4168)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4171,tc_HOL_Obool),c_Relation_ODomain(X4171,X4170,X4169),c_Relation_ODomain(X4171,X4170,X4168))),
inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).
fof(i_0_816,plain,
! [X2354,X2355,X2356,X2357] :
( X2357 != X2356
| ~ hBOOL(hAPP(hAPP(c_member(X2355),X2357),X2354))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2355,X2355)),hAPP(hAPP(c_Product__Type_OPair(X2355,X2355),X2357),X2356)),c_Relation_OId__on(X2355,X2354))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).
fof(i_0_817,plain,
! [X3164,X3165,X3166,X3167,X3168] : c_Relation_ODomain(X3168,X3167,hAPP(hAPP(c_Set_Oinsert(tc_prod(X3168,X3167)),hAPP(hAPP(c_Product__Type_OPair(X3168,X3167),X3166),X3165)),X3164)) = hAPP(hAPP(c_Set_Oinsert(X3168),X3166),c_Relation_ODomain(X3168,X3167,X3164)),
inference(variable_rename,[status(thm)],[fact_Domain__insert]) ).
fof(i_0_818,plain,
! [X3954,X3955,X3956,X3957,X3958] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3958,tc_HOL_Obool),X3957,X3956)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X3958,X3955),tc_HOL_Obool),c_FuncSet_OPi(X3958,X3955,X3956,X3954),c_FuncSet_OPi(X3958,X3955,X3957,X3954)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_819,plain,
! [X3346,X3347,X3348,X3349] : c_Fun_Ofun__upd(X3349,X3348,X3347,X3346,hAPP(X3347,X3346)) = X3347,
inference(variable_rename,[status(thm)],[fact_fun__upd__triv]) ).
fof(i_0_820,plain,
! [X3490,X3491,X3492,X3493,X3494] :
( hAPP(X3494,X3493) != X3492
| c_Fun_Ofun__upd(X3491,X3490,X3494,X3493,X3492) = X3494 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem])]) ).
fof(i_0_821,plain,
! [X3846,X3847,X3848,X3849,X3850] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3850,tc_HOL_Obool),X3849,X3848)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3847,tc_HOL_Obool),c_Set_Oimage(X3850,X3847,X3846,X3849),c_Set_Oimage(X3850,X3847,X3846,X3848)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_822,plain,
! [X3556,X3557,X3558,X3559,X3560] :
( ~ c_Fun_Oinj__on(X3560,X3559,X3558,X3557)
| ~ c_Fun_Oinj__on(X3560,X3559,X3558,X3556)
| c_Fun_Oinj__on(X3560,X3559,X3558,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3560,tc_HOL_Obool),X3557,X3556)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Int])]) ).
fof(i_0_823,plain,
! [X3819,X3820,X3821,X3822] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3822,X3822)),X3821),c_Transitive__Closure_Otrancl(X3822,X3820)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3822,X3822),tc_HOL_Obool),X3820,X3819)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3822,X3822)),X3821),c_Transitive__Closure_Otrancl(X3822,X3819))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__mono])]) ).
fof(i_0_824,plain,
! [X2388,X2389,X2390] :
( ( hBOOL(hAPP(hAPP(c_member(X2390),esk22_3(X2388,X2389,X2390)),X2388))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2390,X2390)),X2389),c_Relation_OId__on(X2390,X2388))) )
& ( X2389 = hAPP(hAPP(c_Product__Type_OPair(X2390,X2390),esk22_3(X2388,X2389,X2390)),esk22_3(X2388,X2389,X2390))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2390,X2390)),X2389),c_Relation_OId__on(X2390,X2388))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).
fof(i_0_825,plain,
! [X2239,X2240,X2241] :
( ( hAPP(hAPP(c_COMBC(X2241,tc_fun(X2241,tc_HOL_Obool),tc_HOL_Obool),c_member(X2241)),X2240) != hAPP(hAPP(c_COMBC(X2241,tc_fun(X2241,tc_HOL_Obool),tc_HOL_Obool),c_member(X2241)),X2239)
| X2240 = X2239 )
& ( X2240 != X2239
| hAPP(hAPP(c_COMBC(X2241,tc_fun(X2241,tc_HOL_Obool),tc_HOL_Obool),c_member(X2241)),X2240) = hAPP(hAPP(c_COMBC(X2241,tc_fun(X2241,tc_HOL_Obool),tc_HOL_Obool),c_member(X2241)),X2239) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_826,plain,
! [X2634,X2635,X2636] : hBOOL(hAPP(hAPP(c_member(tc_prod(X2636,X2636)),hAPP(hAPP(c_Product__Type_OPair(X2636,X2636),X2635),X2635)),c_Transitive__Closure_Ortrancl(X2636,X2634))),
inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
fof(i_0_827,plain,
! [X4273,X4274,X4275,X4276,X4277] :
( ~ c_Fun_Oinj__on(X4277,X4276,X4275,X4274)
| ~ hBOOL(hAPP(hAPP(c_member(X4277),X4273),X4274))
| hAPP(c_Fun_Othe__inv__into(X4277,X4276,X4274,X4275),hAPP(X4275,X4273)) = X4273 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f])]) ).
fof(i_0_828,plain,
! [X3777,X3778,X3779,X3780,X3781] :
( ~ c_Fun_Oinj__on(X3781,X3780,X3779,X3778)
| ~ hBOOL(hAPP(hAPP(c_member(X3781),X3777),X3778))
| hAPP(c_Hilbert__Choice_Oinv__into(X3781,X3780,X3778,X3779),hAPP(X3779,X3777)) = X3777 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).
fof(i_0_829,plain,
! [X4267,X4268,X4269,X4270,X4271,X4272] :
( ~ c_Fun_Oinj__on(X4272,X4271,X4270,X4269)
| hAPP(X4270,X4268) != X4267
| ~ hBOOL(hAPP(hAPP(c_member(X4272),X4268),X4269))
| hAPP(c_Fun_Othe__inv__into(X4272,X4271,X4269,X4270),X4267) = X4268 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq])]) ).
fof(i_0_830,plain,
! [X3771,X3772,X3773,X3774,X3775,X3776] :
( ~ c_Fun_Oinj__on(X3776,X3775,X3774,X3773)
| ~ hBOOL(hAPP(hAPP(c_member(X3776),X3772),X3773))
| hAPP(X3774,X3772) != X3771
| hAPP(c_Hilbert__Choice_Oinv__into(X3776,X3775,X3773,X3774),X3771) = X3772 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).
fof(i_0_831,plain,
! [X3720,X3721,X3722,X3723,X3724] :
( ~ c_Relation_Osingle__valued(X3724,X3723,c_Relation_Oconverse(X3723,X3724,X3722))
| hAPP(c_Relation_OImage(X3723,X3724,X3722),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3723,tc_HOL_Obool),X3721,X3720)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3724,tc_HOL_Obool),hAPP(c_Relation_OImage(X3723,X3724,X3722),X3721),hAPP(c_Relation_OImage(X3723,X3724,X3722),X3720)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__Int__eq])]) ).
fof(i_0_832,plain,
! [X2746,X2747,X2748,X2749] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2749,X2748)),X2747),c_FuncSet_Oextensional(X2749,X2748,X2746)))
| c_FuncSet_Orestrict(X2749,X2748,X2747,X2746) = X2747 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__restrict])]) ).
fof(i_0_833,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_834,plain,
! [X3373,X3374,X3375,X3376] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3376,tc_fun(X3375,tc_HOL_Obool))),X3374),X3373)),
inference(variable_rename,[status(thm)],[i_0_562]) ).
fof(i_0_835,plain,
! [X4369,X4370,X4371,X4372,X4373,X4374] : hAPP(hAPP(c_COMBB(X4374,X4373,X4372,X4371),X4370),X4369) = hAPP(X4371,hAPP(X4370,X4369)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_836,plain,
! [X3679,X3680,X3681,X3682,X3683] :
( ~ hBOOL(hAPP(hAPP(c_member(X3683),X3682),X3681))
| hAPP(hAPP(c_Set_Oinsert(X3680),hAPP(X3679,X3682)),c_Set_Oimage(X3683,X3680,X3679,X3681)) = c_Set_Oimage(X3683,X3680,X3679,X3681) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
fof(i_0_837,plain,
! [X3638,X3639,X3640,X3641] : c_Set_Oimage(X3641,X3640,c_FuncSet_Orestrict(X3641,X3640,X3639,X3638),X3638) = c_Set_Oimage(X3641,X3640,X3639,X3638),
inference(variable_rename,[status(thm)],[fact_image__restrict__eq]) ).
fof(i_0_838,plain,
! [X2719,X2720,X2721,X2722,X2723] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2723,X2722)),X2721),c_FuncSet_Oextensional(X2723,X2722,X2720)))
| hBOOL(hAPP(hAPP(c_member(X2723),X2719),X2720))
| hAPP(X2721,X2719) = c_HOL_Oundefined(X2722) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).
fof(i_0_839,plain,
! [X2351,X2352] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk20_2(X2351,X2352)),c_Arrow__Order__Mirabelle_OLin))
| X2352 = X2351 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2352),X2351)),esk20_2(X2351,X2352)))
| X2352 = X2351 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_complete__Lin])])])]) ).
fof(i_0_840,plain,
! [X3621,X3622,X3623,X3624,X3625] : c_Set_Oimage(X3625,X3624,X3623,hAPP(hAPP(c_Set_Oinsert(X3625),X3622),X3621)) = hAPP(hAPP(c_Set_Oinsert(X3624),hAPP(X3623,X3622)),c_Set_Oimage(X3625,X3624,X3623,X3621)),
inference(variable_rename,[status(thm)],[fact_image__insert]) ).
fof(i_0_841,plain,
! [X2563,X2564,X2565,X2566] : c_Relation_Oconverse(X2566,X2566,c_Relation_Oinv__image(X2565,X2566,X2564,X2563)) = c_Relation_Oinv__image(X2565,X2566,c_Relation_Oconverse(X2565,X2565,X2564),X2563),
inference(variable_rename,[status(thm)],[fact_converse__inv__image]) ).
fof(i_0_842,plain,
! [X2455,X2456,X2457,X2458,X2459] :
( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2459,X2458,X2457),X2456),X2455))
| hBOOL(hAPP(hAPP(X2457,X2455),X2456)) )
& ( ~ hBOOL(hAPP(hAPP(X2457,X2455),X2456))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2459,X2458,X2457),X2456),X2455)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__iff])]) ).
fof(i_0_843,plain,
! [X2450,X2451,X2452,X2453,X2454] :
( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2454,X2453,X2452),X2451),X2450))
| hBOOL(hAPP(hAPP(X2452,X2450),X2451)) )
& ( ~ hBOOL(hAPP(hAPP(X2452,X2450),X2451))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2454,X2453,X2452),X2451),X2450)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Oequations])]) ).
fof(i_0_844,plain,
! [X2440,X2441,X2442,X2443,X2444] :
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2444,X2443,X2442),X2441),X2440))
| hBOOL(hAPP(hAPP(X2442,X2440),X2441)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversepD])]) ).
fof(i_0_845,plain,
! [X3828,X3829,X3830,X3831,X3832,X3833] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3833,X3832),tc_HOL_Obool),X3831,X3830)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3833,tc_HOL_Obool),X3829,X3828)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3832,tc_HOL_Obool),hAPP(c_Relation_OImage(X3833,X3832,X3831),X3829),hAPP(c_Relation_OImage(X3833,X3832,X3830),X3828)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__mono])]) ).
fof(i_0_846,plain,
! [X2933,X2934,X2935] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2935,X2935)),X2934),X2933))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2935,X2935)),X2934),c_Transitive__Closure_Otrancl(X2935,X2933))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])]) ).
fof(i_0_847,plain,
! [X2637,X2638,X2639] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2639,X2639)),X2638),X2637))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2639,X2639)),X2638),c_Transitive__Closure_Ortrancl(X2639,X2637))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).
fof(i_0_848,plain,
! [X3330,X3331,X3332] : c_FuncSet_Oextensional__funcset(X3332,X3331,c_Orderings_Obot__class_Obot(tc_fun(X3332,tc_HOL_Obool)),X3330) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X3332,X3331)),c_COMBK(X3331,X3332,c_HOL_Oundefined(X3331))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3332,X3331),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_extensional__funcset__empty__domain]) ).
fof(i_0_849,plain,
! [X3435,X3436,X3437,X3438] : c_Groups_Ominus__class_Ominus(tc_fun(X3438,tc_HOL_Obool),X3437,hAPP(hAPP(c_Set_Oinsert(X3438),X3436),X3435)) = c_Groups_Ominus__class_Ominus(tc_fun(X3438,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3438,tc_HOL_Obool),X3437,hAPP(hAPP(c_Set_Oinsert(X3438),X3436),c_Orderings_Obot__class_Obot(tc_fun(X3438,tc_HOL_Obool)))),X3435),
inference(variable_rename,[status(thm)],[fact_Diff__insert2]) ).
fof(i_0_850,plain,
! [X3230,X3231,X3232] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3232),X3231),hAPP(hAPP(c_Set_Oinsert(X3232),X3230),c_Orderings_Obot__class_Obot(tc_fun(X3232,tc_HOL_Obool)))))
| X3231 = X3230 )
& ( X3231 != X3230
| hBOOL(hAPP(hAPP(c_member(X3232),X3231),hAPP(hAPP(c_Set_Oinsert(X3232),X3230),c_Orderings_Obot__class_Obot(tc_fun(X3232,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])]) ).
fof(i_0_851,plain,
! [X3227,X3228,X3229] :
( ~ hBOOL(hAPP(hAPP(c_member(X3229),X3228),hAPP(hAPP(c_Set_Oinsert(X3229),X3227),c_Orderings_Obot__class_Obot(tc_fun(X3229,tc_HOL_Obool)))))
| X3228 = X3227 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singletonE])]) ).
fof(i_0_852,plain,
! [X3240,X3241,X3242,X3243,X3244] :
( ( X3243 = X3240
| X3243 = X3241
| hAPP(hAPP(c_Set_Oinsert(X3244),X3243),hAPP(hAPP(c_Set_Oinsert(X3244),X3242),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X3244),X3241),hAPP(hAPP(c_Set_Oinsert(X3244),X3240),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) )
& ( X3242 = X3241
| X3243 = X3241
| hAPP(hAPP(c_Set_Oinsert(X3244),X3243),hAPP(hAPP(c_Set_Oinsert(X3244),X3242),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X3244),X3241),hAPP(hAPP(c_Set_Oinsert(X3244),X3240),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) )
& ( X3243 = X3240
| X3242 = X3240
| hAPP(hAPP(c_Set_Oinsert(X3244),X3243),hAPP(hAPP(c_Set_Oinsert(X3244),X3242),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X3244),X3241),hAPP(hAPP(c_Set_Oinsert(X3244),X3240),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) )
& ( X3242 = X3241
| X3242 = X3240
| hAPP(hAPP(c_Set_Oinsert(X3244),X3243),hAPP(hAPP(c_Set_Oinsert(X3244),X3242),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X3244),X3241),hAPP(hAPP(c_Set_Oinsert(X3244),X3240),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) )
& ( X3243 != X3241
| X3242 != X3240
| hAPP(hAPP(c_Set_Oinsert(X3244),X3243),hAPP(hAPP(c_Set_Oinsert(X3244),X3242),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X3244),X3241),hAPP(hAPP(c_Set_Oinsert(X3244),X3240),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) )
& ( X3243 != X3240
| X3242 != X3241
| hAPP(hAPP(c_Set_Oinsert(X3244),X3243),hAPP(hAPP(c_Set_Oinsert(X3244),X3242),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X3244),X3241),hAPP(hAPP(c_Set_Oinsert(X3244),X3240),c_Orderings_Obot__class_Obot(tc_fun(X3244,tc_HOL_Obool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])]) ).
fof(i_0_853,plain,
! [X3393,X3394,X3395,X3396] :
( ( hBOOL(hAPP(hAPP(c_member(X3396),X3395),X3394))
| ~ hBOOL(hAPP(hAPP(c_member(X3396),X3395),c_Groups_Ominus__class_Ominus(tc_fun(X3396,tc_HOL_Obool),X3394,X3393))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3396),X3395),X3393))
| ~ hBOOL(hAPP(hAPP(c_member(X3396),X3395),c_Groups_Ominus__class_Ominus(tc_fun(X3396,tc_HOL_Obool),X3394,X3393))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3396),X3395),X3394))
| hBOOL(hAPP(hAPP(c_member(X3396),X3395),X3393))
| hBOOL(hAPP(hAPP(c_member(X3396),X3395),c_Groups_Ominus__class_Ominus(tc_fun(X3396,tc_HOL_Obool),X3394,X3393))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])])]) ).
fof(i_0_854,plain,
! [X3369,X3370,X3371,X3372] :
( ( hBOOL(hAPP(hAPP(c_member(X3372),X3371),X3370))
| ~ hBOOL(hAPP(hAPP(c_member(X3372),X3371),c_Groups_Ominus__class_Ominus(tc_fun(X3372,tc_HOL_Obool),X3370,X3369))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3372),X3371),X3369))
| ~ hBOOL(hAPP(hAPP(c_member(X3372),X3371),c_Groups_Ominus__class_Ominus(tc_fun(X3372,tc_HOL_Obool),X3370,X3369))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffE])])]) ).
fof(i_0_855,plain,
! [X3401,X3402,X3403,X3404] :
( ~ hBOOL(hAPP(hAPP(c_member(X3404),X3403),c_Groups_Ominus__class_Ominus(tc_fun(X3404,tc_HOL_Obool),X3402,X3401)))
| ~ hBOOL(hAPP(hAPP(c_member(X3404),X3403),X3401)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])]) ).
fof(i_0_856,plain,
! [X3551,X3552,X3553,X3554,X3555] :
( ~ c_Fun_Oinj__on(X3555,X3554,X3553,X3552)
| c_Fun_Oinj__on(X3555,X3554,X3553,c_Groups_Ominus__class_Ominus(tc_fun(X3555,tc_HOL_Obool),X3552,X3551)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff])]) ).
fof(i_0_857,plain,
! [X3452,X3453,X3454] :
( ~ hBOOL(hAPP(hAPP(c_member(X3454),X3453),X3452))
| hAPP(hAPP(c_Set_Oinsert(X3454),X3453),c_Groups_Ominus__class_Ominus(tc_fun(X3454,tc_HOL_Obool),X3452,hAPP(hAPP(c_Set_Oinsert(X3454),X3453),c_Orderings_Obot__class_Obot(tc_fun(X3454,tc_HOL_Obool))))) = X3452 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff])]) ).
fof(i_0_858,plain,
! [X3525,X3526,X3527,X3528,X3529,X3530] :
( ( hAPP(X3528,X3526) != hAPP(X3528,X3525)
| X3526 = X3525
| ~ hBOOL(hAPP(hAPP(c_member(X3530),X3525),X3527))
| ~ hBOOL(hAPP(hAPP(c_member(X3530),X3526),X3527))
| ~ c_Fun_Oinj__on(X3530,X3529,X3528,X3527) )
& ( X3526 != X3525
| hAPP(X3528,X3526) = hAPP(X3528,X3525)
| ~ hBOOL(hAPP(hAPP(c_member(X3530),X3525),X3527))
| ~ hBOOL(hAPP(hAPP(c_member(X3530),X3526),X3527))
| ~ c_Fun_Oinj__on(X3530,X3529,X3528,X3527) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_859,plain,
! [X3531,X3532,X3533,X3534,X3535,X3536] :
( ~ c_Fun_Oinj__on(X3536,X3535,X3534,X3533)
| X3532 = X3531
| ~ hBOOL(hAPP(hAPP(c_member(X3536),X3532),X3533))
| ~ hBOOL(hAPP(hAPP(c_member(X3536),X3531),X3533))
| hAPP(X3534,X3532) != hAPP(X3534,X3531) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_860,plain,
! [X3519,X3520,X3521,X3522,X3523,X3524] :
( ~ c_Fun_Oinj__on(X3524,X3523,X3522,X3521)
| hAPP(X3522,X3520) != hAPP(X3522,X3519)
| ~ hBOOL(hAPP(hAPP(c_member(X3524),X3520),X3521))
| ~ hBOOL(hAPP(hAPP(c_member(X3524),X3519),X3521))
| X3520 = X3519 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_861,plain,
! [X3851,X3852,X3853,X3854,X3855] :
( ~ c_Fun_Oinj__on(X3855,X3854,X3853,X3852)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3855,tc_HOL_Obool),X3851,X3852)
| c_Fun_Oinj__on(X3855,X3854,X3853,X3851) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_862,plain,
! [X3397,X3398,X3399,X3400] :
( ~ hBOOL(hAPP(hAPP(c_member(X3400),X3399),c_Groups_Ominus__class_Ominus(tc_fun(X3400,tc_HOL_Obool),X3398,X3397)))
| hBOOL(hAPP(hAPP(c_member(X3400),X3399),X3398)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffD1])]) ).
fof(i_0_863,plain,
! [X2929,X2930,X2931,X2932] :
( ( hBOOL(hAPP(hAPP(c_member(X2932),X2931),X2930))
| ~ hBOOL(hAPP(hAPP(c_member(X2932),X2931),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2932,tc_HOL_Obool),X2930,X2929))) )
& ( hBOOL(hAPP(hAPP(c_member(X2932),X2931),X2929))
| ~ hBOOL(hAPP(hAPP(c_member(X2932),X2931),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2932,tc_HOL_Obool),X2930,X2929))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2932),X2931),X2930))
| ~ hBOOL(hAPP(hAPP(c_member(X2932),X2931),X2929))
| hBOOL(hAPP(hAPP(c_member(X2932),X2931),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2932,tc_HOL_Obool),X2930,X2929))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).
fof(i_0_864,plain,
! [X2925,X2926,X2927,X2928] :
( ~ hBOOL(hAPP(hAPP(c_member(X2928),X2927),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2928,tc_HOL_Obool),X2926,X2925)))
| hBOOL(hAPP(hAPP(c_member(X2928),X2927),X2926)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).
fof(i_0_865,plain,
! [X2880,X2881,X2882,X2883] :
( ( hBOOL(hAPP(hAPP(c_member(X2883),X2882),X2881))
| ~ hBOOL(hAPP(hAPP(c_member(X2883),X2882),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2883,tc_HOL_Obool),X2881,X2880))) )
& ( hBOOL(hAPP(hAPP(c_member(X2883),X2882),X2880))
| ~ hBOOL(hAPP(hAPP(c_member(X2883),X2882),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2883,tc_HOL_Obool),X2881,X2880))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])])]) ).
fof(i_0_866,plain,
! [X2921,X2922,X2923,X2924] :
( ~ hBOOL(hAPP(hAPP(c_member(X2924),X2923),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2924,tc_HOL_Obool),X2922,X2921)))
| hBOOL(hAPP(hAPP(c_member(X2924),X2923),X2921)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).
fof(i_0_867,plain,
! [X2884,X2885,X2886,X2887] :
( ~ hBOOL(hAPP(hAPP(c_member(X2887),X2886),X2885))
| ~ hBOOL(hAPP(hAPP(c_member(X2887),X2886),X2884))
| hBOOL(hAPP(hAPP(c_member(X2887),X2886),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2887,tc_HOL_Obool),X2885,X2884))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).
fof(i_0_868,plain,
! [X2729,X2730,X2731,X2732,X2733] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2733),X2732),X2731))
| hAPP(c_FuncSet_Orestrict(X2733,X2730,X2729,X2731),X2732) = hAPP(X2729,X2732) )
& ( hBOOL(hAPP(hAPP(c_member(X2733),X2732),X2731))
| hAPP(c_FuncSet_Orestrict(X2733,X2730,X2729,X2731),X2732) = c_HOL_Oundefined(X2730) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_869,plain,
! [X2724,X2725,X2726,X2727,X2728] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2728),X2727),X2726))
| hAPP(c_FuncSet_Orestrict(X2728,X2725,X2724,X2726),X2727) = hAPP(X2724,X2727) )
& ( hBOOL(hAPP(hAPP(c_member(X2728),X2727),X2726))
| hAPP(c_FuncSet_Orestrict(X2728,X2725,X2724,X2726),X2727) = c_HOL_Oundefined(X2725) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_870,plain,
! [X3365,X3366,X3367,X3368] :
( ~ hBOOL(hAPP(hAPP(c_member(X3368),X3367),X3366))
| hBOOL(hAPP(hAPP(c_member(X3368),X3367),X3365))
| hBOOL(hAPP(hAPP(c_member(X3368),X3367),c_Groups_Ominus__class_Ominus(tc_fun(X3368,tc_HOL_Obool),X3366,X3365))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).
fof(i_0_871,plain,
! [X4116,X4117,X4118] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4118,tc_HOL_Obool),hAPP(c_Relation_OImage(X4118,X4118,X4117),X4116),X4116)
| hAPP(c_Relation_OImage(X4118,X4118,c_Transitive__Closure_Ortrancl(X4118,X4117)),X4116) = X4116 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl])]) ).
fof(i_0_872,plain,
! [X3432,X3433,X3434] : hAPP(hAPP(c_Set_Oinsert(X3434),X3433),c_Groups_Ominus__class_Ominus(tc_fun(X3434,tc_HOL_Obool),X3432,hAPP(hAPP(c_Set_Oinsert(X3434),X3433),c_Orderings_Obot__class_Obot(tc_fun(X3434,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X3434),X3433),X3432),
inference(variable_rename,[status(thm)],[fact_insert__Diff__single]) ).
fof(i_0_873,plain,
! [X3333,X3334] : c_FuncSet_Oextensional(X3334,X3333,c_Orderings_Obot__class_Obot(tc_fun(X3334,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X3334,X3333)),c_COMBK(X3333,X3334,c_HOL_Oundefined(X3333))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3334,X3333),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_extensional__empty]) ).
fof(i_0_874,plain,
! [X3058,X3059,X3060,X3061] : c_Relation_Oconverse(X3061,X3060,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3061,X3060),tc_HOL_Obool),X3059,X3058)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3060,X3061),tc_HOL_Obool),c_Relation_Oconverse(X3061,X3060,X3059),c_Relation_Oconverse(X3061,X3060,X3058)),
inference(variable_rename,[status(thm)],[fact_converse__Int]) ).
fof(i_0_875,plain,
! [X3054,X3055,X3056,X3057] : c_Predicate_Oconversep(X3057,X3056,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3057,tc_fun(X3056,tc_HOL_Obool)),X3055,X3054)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3056,tc_fun(X3057,tc_HOL_Obool)),c_Predicate_Oconversep(X3057,X3056,X3055),c_Predicate_Oconversep(X3057,X3056,X3054)),
inference(variable_rename,[status(thm)],[fact_converse__meet]) ).
fof(i_0_876,plain,
! [X2445,X2446,X2447,X2448,X2449] :
( ~ hBOOL(hAPP(hAPP(X2449,X2448),X2447))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2446,X2445,X2449),X2447),X2448)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Ointros])]) ).
fof(i_0_877,plain,
! [X3269,X3270,X3271,X3272,X3273,X3274,X3275,X3276] :
( ( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3271,tc_HOL_Obool),X3270,X3269) != c_Orderings_Obot__class_Obot(tc_fun(X3271,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X3271),X3272),X3270))
| ~ hBOOL(hAPP(hAPP(c_member(X3271),X3273),X3269))
| X3272 != X3273 )
& ( hBOOL(hAPP(hAPP(c_member(X3276),esk77_3(X3274,X3275,X3276)),X3275))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3276,tc_HOL_Obool),X3275,X3274) = c_Orderings_Obot__class_Obot(tc_fun(X3276,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X3276),esk78_3(X3274,X3275,X3276)),X3274))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3276,tc_HOL_Obool),X3275,X3274) = c_Orderings_Obot__class_Obot(tc_fun(X3276,tc_HOL_Obool)) )
& ( esk77_3(X3274,X3275,X3276) = esk78_3(X3274,X3275,X3276)
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3276,tc_HOL_Obool),X3275,X3274) = c_Orderings_Obot__class_Obot(tc_fun(X3276,tc_HOL_Obool)) ) ),
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_disjoint__iff__not__equal])])])])])]) ).
fof(i_0_878,plain,
! [X2916,X2917,X2918,X2919,X2920] :
( ~ c_Relation_Orefl__on(X2920,X2919,X2918)
| ~ c_Relation_Orefl__on(X2920,X2917,X2916)
| c_Relation_Orefl__on(X2920,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2920,tc_HOL_Obool),X2919,X2917),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2920,X2920),tc_HOL_Obool),X2918,X2916)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Int])]) ).
fof(i_0_879,plain,
! [X3860,X3861,X3862,X3863,X3864] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3864,tc_HOL_Obool),X3863,X3862)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3864,tc_HOL_Obool),X3861,X3860)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3864,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3864,tc_HOL_Obool),X3863,X3860),c_Groups_Ominus__class_Ominus(tc_fun(X3864,tc_HOL_Obool),X3862,X3861)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__mono])]) ).
fof(i_0_880,plain,
! [X4014,X4015,X4016,X4017,X4018] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4018,tc_HOL_Obool),X4017,X4016)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4018,tc_HOL_Obool),X4015,X4014)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4018,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4018,tc_HOL_Obool),X4017,X4015),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4018,tc_HOL_Obool),X4016,X4014)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).
fof(i_0_881,plain,
! [X3715,X3716,X3717,X3718,X3719] :
( ~ hBOOL(hAPP(hAPP(c_member(X3719),X3718),X3717))
| c_Set_Oimage(X3719,X3716,c_COMBK(X3716,X3719,X3715),X3717) = hAPP(hAPP(c_Set_Oinsert(X3716),X3715),c_Orderings_Obot__class_Obot(tc_fun(X3716,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant])]) ).
fof(i_0_882,plain,
! [X3439,X3440,X3441,X3442] : c_Groups_Ominus__class_Ominus(tc_fun(X3442,tc_HOL_Obool),X3441,hAPP(hAPP(c_Set_Oinsert(X3442),X3440),X3439)) = c_Groups_Ominus__class_Ominus(tc_fun(X3442,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3442,tc_HOL_Obool),X3441,X3439),hAPP(hAPP(c_Set_Oinsert(X3442),X3440),c_Orderings_Obot__class_Obot(tc_fun(X3442,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_Diff__insert]) ).
fof(i_0_883,plain,
! [X3408,X3409,X3410,X3411] : c_Groups_Ominus__class_Ominus(tc_fun(X3411,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3411,tc_HOL_Obool),X3410,X3409),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3411,tc_HOL_Obool),X3408,X3409)) = c_Groups_Ominus__class_Ominus(tc_fun(X3411,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3411,tc_HOL_Obool),X3410,X3409),X3408),
inference(variable_rename,[status(thm)],[fact_Diff__Int2]) ).
fof(i_0_884,plain,
! [X3412,X3413,X3414,X3415] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3415,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3415,tc_HOL_Obool),X3414,X3413),X3412) = c_Groups_Ominus__class_Ominus(tc_fun(X3415,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3415,tc_HOL_Obool),X3414,X3412),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3415,tc_HOL_Obool),X3413,X3412)),
inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2]) ).
fof(i_0_885,plain,
! [X3420,X3421,X3422,X3423] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3423,tc_HOL_Obool),X3422,c_Groups_Ominus__class_Ominus(tc_fun(X3423,tc_HOL_Obool),X3421,X3420)) = c_Groups_Ominus__class_Ominus(tc_fun(X3423,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3423,tc_HOL_Obool),X3422,X3421),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3423,tc_HOL_Obool),X3422,X3420)),
inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib]) ).
fof(i_0_886,plain,
! [X3177,X3178,X3179,X3180] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3180),X3179),hAPP(hAPP(c_Set_Oinsert(X3180),X3178),X3177)))
| X3179 = X3178
| hBOOL(hAPP(hAPP(c_member(X3180),X3179),X3177)) )
& ( X3179 != X3178
| hBOOL(hAPP(hAPP(c_member(X3180),X3179),hAPP(hAPP(c_Set_Oinsert(X3180),X3178),X3177))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3180),X3179),X3177))
| hBOOL(hAPP(hAPP(c_member(X3180),X3179),hAPP(hAPP(c_Set_Oinsert(X3180),X3178),X3177))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_887,plain,
! [X3148,X3149,X3150,X3151] :
( ~ hBOOL(hAPP(hAPP(c_member(X3151),X3150),hAPP(hAPP(c_Set_Oinsert(X3151),X3149),X3148)))
| X3150 = X3149
| hBOOL(hAPP(hAPP(c_member(X3151),X3150),X3148)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).
fof(i_0_888,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk2_0),c_Arrow__Order__Mirabelle_OLin)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_linear__alt])]) ).
fof(i_0_889,plain,
! [X2616,X2617,X2618,X2619,X2620,X2621,X2622] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2618,X2617),X2616))
| ~ hBOOL(hAPP(hAPP(X2617,X2619),X2616))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2618,X2617),X2619)) )
& ( hBOOL(hAPP(hAPP(X2621,esk37_3(X2620,X2621,X2622)),X2620))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2622,X2621),X2620)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2622,X2621),esk37_3(X2620,X2621,X2622)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2622,X2621),X2620)) ) ),
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_890,plain,
! [X2608,X2609,X2610,X2611,X2612,X2613,X2614] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2610,X2609),X2608))
| ~ hBOOL(hAPP(hAPP(X2609,X2611),X2608))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2610,X2609),X2611)) )
& ( hBOOL(hAPP(hAPP(X2613,esk36_3(X2612,X2613,X2614)),X2612))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2614,X2613),X2612)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2614,X2613),esk36_3(X2612,X2613,X2614)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2614,X2613),X2612)) ) ),
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_891,plain,
! [X4381,X4382,X4383,X4384,X4385,X4386] : hAPP(hAPP(hAPP(c_COMBS(X4386,X4385,X4384),X4383),X4382),X4381) = hAPP(hAPP(X4383,X4381),hAPP(X4382,X4381)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_892,plain,
! [X4097,X4098,X4099] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4099,tc_HOL_Obool),X4098,hAPP(hAPP(c_Set_Oinsert(X4099),X4097),c_Orderings_Obot__class_Obot(tc_fun(X4099,tc_HOL_Obool))))
| X4098 = c_Orderings_Obot__class_Obot(tc_fun(X4099,tc_HOL_Obool))
| X4098 = hAPP(hAPP(c_Set_Oinsert(X4099),X4097),c_Orderings_Obot__class_Obot(tc_fun(X4099,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__singletonD])]) ).
fof(i_0_893,plain,
! [X2430,X2431,X2432,X2433,X2435,X2436,X2437,X2438,X2439] :
( ( ~ c_Predicate_ORangeP(X2433,X2432,X2431,X2430)
| hBOOL(hAPP(hAPP(X2431,esk27_2(X2430,X2431)),X2430)) )
& ( ~ hBOOL(hAPP(hAPP(X2436,X2437),X2435))
| c_Predicate_ORangeP(X2439,X2438,X2436,X2435) ) ),
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_894,plain,
! [X4375,X4376,X4377,X4378,X4379,X4380] : hAPP(hAPP(hAPP(c_COMBC(X4380,X4379,X4378),X4377),X4376),X4375) = hAPP(hAPP(X4377,X4375),X4376),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_895,plain,
! [X2872,X2873,X2874,X2875] :
( ( hBOOL(hAPP(X2874,X2872))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2875,tc_HOL_Obool),X2874,X2873),X2872)) )
& ( hBOOL(hAPP(X2873,X2872))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2875,tc_HOL_Obool),X2874,X2873),X2872)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])])]) ).
fof(i_0_896,plain,
! [X2896,X2897,X2898,X2899] :
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2899,tc_HOL_Obool),X2898,X2897),X2896))
| hBOOL(hAPP(X2898,X2896)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).
fof(i_0_897,plain,
! [X2892,X2893,X2894,X2895] :
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2895,tc_HOL_Obool),X2894,X2893),X2892))
| hBOOL(hAPP(X2893,X2892)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).
fof(i_0_898,plain,
! [X3308,X3309,X3310,X3311] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3311),X3310),X3309))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3311,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X3311),X3310),X3308),X3309) = hAPP(hAPP(c_Set_Oinsert(X3311),X3310),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3311,tc_HOL_Obool),X3308,X3309)) )
& ( hBOOL(hAPP(hAPP(c_member(X3311),X3310),X3309))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3311,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X3311),X3310),X3308),X3309) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3311,tc_HOL_Obool),X3308,X3309) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])]) ).
fof(i_0_899,plain,
! [X3292,X3293,X3294,X3295] :
( ~ hBOOL(hAPP(hAPP(c_member(X3295),X3294),X3293))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3295,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X3295),X3294),X3292),X3293) = hAPP(hAPP(c_Set_Oinsert(X3295),X3294),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3295,tc_HOL_Obool),X3292,X3293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1])]) ).
fof(i_0_900,plain,
! [X3312,X3313,X3314,X3315] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3315),X3314),X3313))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3315,tc_HOL_Obool),X3313,hAPP(hAPP(c_Set_Oinsert(X3315),X3314),X3312)) = hAPP(hAPP(c_Set_Oinsert(X3315),X3314),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3315,tc_HOL_Obool),X3313,X3312)) )
& ( hBOOL(hAPP(hAPP(c_member(X3315),X3314),X3313))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3315,tc_HOL_Obool),X3313,hAPP(hAPP(c_Set_Oinsert(X3315),X3314),X3312)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3315,tc_HOL_Obool),X3313,X3312) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).
fof(i_0_901,plain,
! [X3296,X3297,X3298,X3299] :
( ~ hBOOL(hAPP(hAPP(c_member(X3299),X3298),X3297))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3299,tc_HOL_Obool),X3297,hAPP(hAPP(c_Set_Oinsert(X3299),X3298),X3296)) = hAPP(hAPP(c_Set_Oinsert(X3299),X3298),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3299,tc_HOL_Obool),X3297,X3296)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1])]) ).
fof(i_0_902,plain,
! [X3593,X3594] : c_HOL_OThe(X3594,hAPP(hAPP(c_COMBC(X3594,X3594,tc_HOL_Obool),c_fequal),X3593)) = X3593,
inference(variable_rename,[status(thm)],[fact_the__eq__trivial]) ).
cnf(i_0_903,plain,
c_Relation_ORange(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_573]) ).
fof(i_0_904,plain,
! [X3985,X3986,X3987,X3988] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3988,X3987),tc_HOL_Obool),X3986,X3985)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3988,tc_HOL_Obool),c_Relation_ODomain(X3988,X3987,X3986),c_Relation_ODomain(X3988,X3987,X3985)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).
fof(i_0_905,plain,
! [X3449,X3450,X3451] :
( hBOOL(hAPP(hAPP(c_member(X3451),X3450),X3449))
| c_Groups_Ominus__class_Ominus(tc_fun(X3451,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X3451),X3450),X3449),hAPP(hAPP(c_Set_Oinsert(X3451),X3450),c_Orderings_Obot__class_Obot(tc_fun(X3451,tc_HOL_Obool)))) = X3449 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_574])]) ).
fof(i_0_906,plain,
! [X3428,X3429,X3430,X3431] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3431),X3430),X3429))
| c_Groups_Ominus__class_Ominus(tc_fun(X3431,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X3431),X3430),X3428),X3429) = c_Groups_Ominus__class_Ominus(tc_fun(X3431,tc_HOL_Obool),X3428,X3429) )
& ( hBOOL(hAPP(hAPP(c_member(X3431),X3430),X3429))
| c_Groups_Ominus__class_Ominus(tc_fun(X3431,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X3431),X3430),X3428),X3429) = hAPP(hAPP(c_Set_Oinsert(X3431),X3430),c_Groups_Ominus__class_Ominus(tc_fun(X3431,tc_HOL_Obool),X3428,X3429)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_575])]) ).
fof(i_0_907,plain,
! [X3684,X3685,X3686,X3687] :
( ( X3687 != c_Orderings_Obot__class_Obot(tc_fun(X3686,tc_HOL_Obool))
| c_Set_Oimage(X3686,X3685,c_COMBK(X3685,X3686,X3684),X3687) = c_Orderings_Obot__class_Obot(tc_fun(X3685,tc_HOL_Obool)) )
& ( X3687 = c_Orderings_Obot__class_Obot(tc_fun(X3686,tc_HOL_Obool))
| c_Set_Oimage(X3686,X3685,c_COMBK(X3685,X3686,X3684),X3687) = hAPP(hAPP(c_Set_Oinsert(X3685),X3684),c_Orderings_Obot__class_Obot(tc_fun(X3685,tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant__conv])]) ).
fof(i_0_908,plain,
! [X3192,X3193,X3194,X3195] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3195,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X3195),X3194),X3193),hAPP(hAPP(c_Set_Oinsert(X3195),X3194),X3192)) = hAPP(hAPP(c_Set_Oinsert(X3195),X3194),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3195,tc_HOL_Obool),X3193,X3192)),
inference(variable_rename,[status(thm)],[fact_insert__inter__insert]) ).
fof(i_0_909,plain,
! [X3185,X3186,X3187,X3188] :
( ~ hBOOL(hAPP(hAPP(c_member(X3188),X3187),X3186))
| hBOOL(hAPP(hAPP(c_member(X3188),X3187),hAPP(hAPP(c_Set_Oinsert(X3188),X3185),X3186))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_910,plain,
! [X3144,X3145,X3146,X3147] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3147),X3146),X3145))
| hBOOL(hAPP(hAPP(c_member(X3147),X3146),hAPP(hAPP(c_Set_Oinsert(X3147),X3144),X3145))) )
& ( X3146 != X3144
| hBOOL(hAPP(hAPP(c_member(X3147),X3146),hAPP(hAPP(c_Set_Oinsert(X3147),X3144),X3145))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_576])])]) ).
fof(i_0_911,plain,
! [X3992,X3993,X3994] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3994,X3994),tc_HOL_Obool),X3993,X3992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3994,X3994),tc_HOL_Obool),X3992,c_Transitive__Closure_Ortrancl(X3994,X3993))
| c_Transitive__Closure_Ortrancl(X3994,X3992) = c_Transitive__Closure_Ortrancl(X3994,X3993) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).
fof(i_0_912,plain,
! [X3856,X3857,X3858,X3859] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3859,tc_HOL_Obool),X3858,X3857)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3859,tc_HOL_Obool),X3857,X3856)
| c_Groups_Ominus__class_Ominus(tc_fun(X3859,tc_HOL_Obool),X3857,c_Groups_Ominus__class_Ominus(tc_fun(X3859,tc_HOL_Obool),X3856,X3858)) = X3858 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__diff])]) ).
fof(i_0_913,plain,
! [X4010,X4011,X4012,X4013] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4013,tc_HOL_Obool),X4012,X4011)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4013,tc_HOL_Obool),X4012,X4010)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4013,tc_HOL_Obool),X4012,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4013,tc_HOL_Obool),X4011,X4010)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).
fof(i_0_914,plain,
! [X4100,X4101,X4102,X4103] :
( ( hBOOL(hAPP(hAPP(c_member(X4103),X4102),X4100))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4103,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X4103),X4102),X4101),X4100) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4103,tc_HOL_Obool),X4101,X4100)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4103,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X4103),X4102),X4101),X4100) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4103),X4102),X4100))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4103,tc_HOL_Obool),X4101,X4100)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4103,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X4103),X4102),X4101),X4100) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_915,plain,
! [X4104,X4105,X4106,X4107] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4107,tc_HOL_Obool),X4105,hAPP(hAPP(c_Set_Oinsert(X4107),X4106),X4104))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4107,tc_HOL_Obool),X4105,X4104)
| hBOOL(hAPP(hAPP(c_member(X4107),X4106),X4105)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4107,tc_HOL_Obool),X4105,X4104)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4107,tc_HOL_Obool),X4105,hAPP(hAPP(c_Set_Oinsert(X4107),X4106),X4104))
| hBOOL(hAPP(hAPP(c_member(X4107),X4106),X4105)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_577])])]) ).
fof(i_0_916,plain,
! [X3284,X3285] :
( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3285,tc_HOL_Obool)),X3284))
| hBOOL(hAPP(hAPP(c_member(X3285),X3284),c_Orderings_Obot__class_Obot(tc_fun(X3285,tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3285),X3284),c_Orderings_Obot__class_Obot(tc_fun(X3285,tc_HOL_Obool))))
| hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3285,tc_HOL_Obool)),X3284)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])]) ).
fof(i_0_917,plain,
! [X3416,X3417,X3418,X3419] : c_Groups_Ominus__class_Ominus(tc_fun(X3419,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3419,tc_HOL_Obool),X3418,X3417),X3416) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3419,tc_HOL_Obool),X3418,c_Groups_Ominus__class_Ominus(tc_fun(X3419,tc_HOL_Obool),X3417,X3416)),
inference(variable_rename,[status(thm)],[fact_Int__Diff]) ).
fof(i_0_918,plain,
! [X2900,X2901,X2902,X2903] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2903,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2903,tc_HOL_Obool),X2902,X2901),X2900) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2903,tc_HOL_Obool),X2902,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2903,tc_HOL_Obool),X2901,X2900)),
inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).
fof(i_0_919,plain,
! [X2904,X2905,X2906,X2907] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2907,tc_HOL_Obool),X2906,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2907,tc_HOL_Obool),X2905,X2904)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2907,tc_HOL_Obool),X2905,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2907,tc_HOL_Obool),X2906,X2904)),
inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).
fof(i_0_920,plain,
! [X3629,X3630,X3631,X3632] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X3632,tc_HOL_Obool)) != c_Set_Oimage(X3631,X3632,X3630,X3629)
| X3629 = c_Orderings_Obot__class_Obot(tc_fun(X3631,tc_HOL_Obool)) )
& ( X3629 != c_Orderings_Obot__class_Obot(tc_fun(X3631,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X3632,tc_HOL_Obool)) = c_Set_Oimage(X3631,X3632,X3630,X3629) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])]) ).
fof(i_0_921,plain,
! [X3617,X3618,X3619,X3620] :
( ( c_Set_Oimage(X3620,X3619,X3618,X3617) != c_Orderings_Obot__class_Obot(tc_fun(X3619,tc_HOL_Obool))
| X3617 = c_Orderings_Obot__class_Obot(tc_fun(X3620,tc_HOL_Obool)) )
& ( X3617 != c_Orderings_Obot__class_Obot(tc_fun(X3620,tc_HOL_Obool))
| c_Set_Oimage(X3620,X3619,X3618,X3617) = c_Orderings_Obot__class_Obot(tc_fun(X3619,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])]) ).
fof(i_0_922,plain,
! [X4023,X4024,X4025,X4026,X4027] :
( ~ class_Lattices_Osemilattice__inf(X4027)
| ~ c_Orderings_Oord__class_Oless__eq(X4027,X4026,X4025)
| ~ c_Orderings_Oord__class_Oless__eq(X4027,X4024,X4023)
| c_Orderings_Oord__class_Oless__eq(X4027,c_Lattices_Osemilattice__inf__class_Oinf(X4027,X4026,X4024),c_Lattices_Osemilattice__inf__class_Oinf(X4027,X4025,X4023)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).
fof(i_0_923,plain,
! [X2876,X2877,X2878,X2879] :
( ~ hBOOL(hAPP(X2879,X2878))
| ~ hBOOL(hAPP(X2877,X2878))
| hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2876,tc_HOL_Obool),X2879,X2877),X2878)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).
cnf(i_0_924,plain,
c_Relation_ORange(X1,X2,c_Relation_Oconverse(X2,X1,X3)) = c_Relation_ODomain(X2,X1,X3),
inference(split_conjunct,[status(thm)],[i_0_578]) ).
fof(i_0_925,plain,
! [X3995,X3996,X3997] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3997,X3997),tc_HOL_Obool),X3996,c_Transitive__Closure_Ortrancl(X3997,X3995))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3997,X3997),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X3997,X3996),c_Transitive__Closure_Ortrancl(X3997,X3995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).
fof(i_0_926,plain,
! [X3424,X3425,X3426,X3427] :
( ~ hBOOL(hAPP(hAPP(c_member(X3427),X3426),X3425))
| c_Groups_Ominus__class_Ominus(tc_fun(X3427,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X3427),X3426),X3424),X3425) = c_Groups_Ominus__class_Ominus(tc_fun(X3427,tc_HOL_Obool),X3424,X3425) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff1])]) ).
fof(i_0_927,plain,
! [X4256,X4257,X4258,X4259,X4260,X4261] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4261,tc_fun(X4260,tc_HOL_Obool)),X4259,X4258)
| ~ hBOOL(hAPP(hAPP(X4259,X4257),X4256))
| hBOOL(hAPP(hAPP(X4258,X4257),X4256)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_928,plain,
! [X4250,X4251,X4252,X4253,X4254,X4255] :
( ~ hBOOL(hAPP(hAPP(X4255,X4254),X4253))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4252,tc_fun(X4251,tc_HOL_Obool)),X4255,X4250)
| hBOOL(hAPP(hAPP(X4250,X4254),X4253)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_929,plain,
! [X3213,X3214,X3215] :
( X3215 = c_Orderings_Obot__class_Obot(tc_fun(X3214,tc_HOL_Obool))
| c_FuncSet_Oextensional__funcset(X3214,X3213,X3215,c_Orderings_Obot__class_Obot(tc_fun(X3213,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3214,X3213),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__empty__range])]) ).
fof(i_0_930,plain,
! [X4078,X4079,X4080,X4081] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4081,tc_HOL_Obool),X4080,X4079)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4081,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X4081),X4078),X4080),hAPP(hAPP(c_Set_Oinsert(X4081),X4078),X4079)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
fof(i_0_931,plain,
! [X3236,X3237,X3238,X3239] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3239),X3238),X3237),X3236))
| X3238 = X3236
| hBOOL(hAPP(X3237,X3236)) )
& ( X3238 != X3236
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3239),X3238),X3237),X3236)) )
& ( ~ hBOOL(hAPP(X3237,X3236))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3239),X3238),X3237),X3236)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_932,plain,
! [X3943,X3944,X3945,X3946] :
( ~ hBOOL(hAPP(hAPP(c_member(X3946),X3945),X3944))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3946,tc_HOL_Obool),X3944,X3943)
| hBOOL(hAPP(hAPP(c_member(X3946),X3945),X3943)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_933,plain,
! [X3947,X3948,X3949,X3950] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3950,tc_HOL_Obool),X3949,X3948)
| ~ hBOOL(hAPP(hAPP(c_member(X3950),X3947),X3949))
| hBOOL(hAPP(hAPP(c_member(X3950),X3947),X3948)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_934,plain,
! [X3939,X3940,X3941,X3942] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3942,tc_HOL_Obool),X3941,X3940)
| ~ hBOOL(hAPP(hAPP(c_member(X3942),X3939),X3941))
| hBOOL(hAPP(hAPP(c_member(X3942),X3939),X3940)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_935,plain,
! [X3813,X3814,X3815,X3816] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3816,tc_HOL_Obool),X3815,X3814)
| ~ hBOOL(hAPP(hAPP(c_member(X3816),X3813),X3815))
| hBOOL(hAPP(hAPP(c_member(X3816),X3813),X3814)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_936,plain,
! [X3989,X3990,X3991] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3991,X3991),tc_HOL_Obool),X3990,X3989)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3991,X3991),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X3991,X3990),c_Transitive__Closure_Ortrancl(X3991,X3989)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).
fof(i_0_937,plain,
! [X3181,X3182,X3183,X3184] :
( ( hAPP(hAPP(c_Set_Oinsert(X3184),X3183),X3182) != hAPP(hAPP(c_Set_Oinsert(X3184),X3183),X3181)
| X3182 = X3181
| hBOOL(hAPP(hAPP(c_member(X3184),X3183),X3181))
| hBOOL(hAPP(hAPP(c_member(X3184),X3183),X3182)) )
& ( X3182 != X3181
| hAPP(hAPP(c_Set_Oinsert(X3184),X3183),X3182) = hAPP(hAPP(c_Set_Oinsert(X3184),X3183),X3181)
| hBOOL(hAPP(hAPP(c_member(X3184),X3183),X3181))
| hBOOL(hAPP(hAPP(c_member(X3184),X3183),X3182)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_579])])]) ).
fof(i_0_938,plain,
! [X2551,X2552,X2553,X2554,X2555] :
( ~ hBOOL(hAPP(hAPP(X2555,X2554),X2553))
| c_Predicate_ODomainP(X2552,X2551,X2555,X2554) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).
fof(i_0_939,plain,
! [X2425,X2426,X2427,X2428,X2429] :
( ~ hBOOL(hAPP(hAPP(X2429,X2428),X2427))
| c_Predicate_ORangeP(X2426,X2425,X2429,X2427) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).
cnf(i_0_940,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))
| c_Relation_ORange(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_580]) ).
cnf(i_0_941,plain,
c_Relation_ORange(X1,X1,c_Transitive__Closure_Otrancl(X1,X2)) = c_Relation_ORange(X1,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_581]) ).
fof(i_0_942,plain,
! [X3300,X3301,X3302,X3303] :
( hBOOL(hAPP(hAPP(c_member(X3303),X3302),X3301))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3303,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X3303),X3302),X3300),X3301) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3303,tc_HOL_Obool),X3300,X3301) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_582])]) ).
fof(i_0_943,plain,
! [X3304,X3305,X3306,X3307] :
( hBOOL(hAPP(hAPP(c_member(X3307),X3306),X3305))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3307,tc_HOL_Obool),X3305,hAPP(hAPP(c_Set_Oinsert(X3307),X3306),X3304)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3307,tc_HOL_Obool),X3305,X3304) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_583])]) ).
fof(i_0_944,plain,
! [X3932,X3933,X3934,X3935] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3935,X3934),tc_HOL_Obool),X3933,X3932)
| ~ c_Relation_Osingle__valued(X3935,X3934,X3932)
| c_Relation_Osingle__valued(X3935,X3934,X3933) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).
fof(i_0_945,plain,
! [X4050,X4051,X4052,X4053] :
( ( c_Orderings_Oord__class_Oless__eq(X4053,X4052,X4051)
| ~ c_Orderings_Oord__class_Oless__eq(X4053,X4052,c_Lattices_Osemilattice__inf__class_Oinf(X4053,X4051,X4050))
| ~ class_Lattices_Osemilattice__inf(X4053) )
& ( c_Orderings_Oord__class_Oless__eq(X4053,X4052,X4050)
| ~ c_Orderings_Oord__class_Oless__eq(X4053,X4052,c_Lattices_Osemilattice__inf__class_Oinf(X4053,X4051,X4050))
| ~ class_Lattices_Osemilattice__inf(X4053) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4053,X4052,X4051)
| ~ c_Orderings_Oord__class_Oless__eq(X4053,X4052,X4050)
| c_Orderings_Oord__class_Oless__eq(X4053,X4052,c_Lattices_Osemilattice__inf__class_Oinf(X4053,X4051,X4050))
| ~ class_Lattices_Osemilattice__inf(X4053) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).
fof(i_0_946,plain,
! [X4032,X4033,X4034,X4035] :
( ~ class_Lattices_Osemilattice__inf(X4035)
| ~ c_Orderings_Oord__class_Oless__eq(X4035,X4034,X4033)
| ~ c_Orderings_Oord__class_Oless__eq(X4035,X4034,X4032)
| c_Orderings_Oord__class_Oless__eq(X4035,X4034,c_Lattices_Osemilattice__inf__class_Oinf(X4035,X4033,X4032)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).
fof(i_0_947,plain,
! [X4028,X4029,X4030,X4031] :
( ~ class_Lattices_Osemilattice__inf(X4031)
| ~ c_Orderings_Oord__class_Oless__eq(X4031,X4030,X4029)
| ~ c_Orderings_Oord__class_Oless__eq(X4031,X4030,X4028)
| c_Orderings_Oord__class_Oless__eq(X4031,X4030,c_Lattices_Osemilattice__inf__class_Oinf(X4031,X4029,X4028)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).
fof(i_0_948,plain,
! [X2604,X2605,X2606,X2607] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2607,X2606),X2605))
| ~ hBOOL(hAPP(hAPP(X2606,X2604),X2605))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2607,X2606),X2604)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).
fof(i_0_949,plain,
! [X3951,X3952,X3953] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3953,X3953),tc_HOL_Obool),X3952,X3951)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3953,tc_HOL_Obool),c_Wellfounded_Oacc(X3953,X3951),c_Wellfounded_Oacc(X3953,X3952)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).
fof(i_0_950,plain,
! [X3208,X3209] : ~ hBOOL(hAPP(hAPP(c_member(X3209),X3208),c_Orderings_Obot__class_Obot(tc_fun(X3209,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_584]) ).
fof(i_0_951,plain,
! [X3142,X3143] : ~ hBOOL(hAPP(hAPP(c_member(X3143),X3142),c_Orderings_Obot__class_Obot(tc_fun(X3143,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_585]) ).
fof(i_0_952,plain,
! [X3072,X3073,X3074,X3075] :
( ~ class_Lattices_Osemilattice__inf(X3075)
| c_Lattices_Osemilattice__inf__class_Oinf(X3075,c_Lattices_Osemilattice__inf__class_Oinf(X3075,X3074,X3073),X3072) = c_Lattices_Osemilattice__inf__class_Oinf(X3075,X3074,c_Lattices_Osemilattice__inf__class_Oinf(X3075,X3073,X3072)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).
fof(i_0_953,plain,
! [X3064,X3065,X3066,X3067] :
( ~ class_Lattices_Osemilattice__inf(X3067)
| c_Lattices_Osemilattice__inf__class_Oinf(X3067,c_Lattices_Osemilattice__inf__class_Oinf(X3067,X3066,X3065),X3064) = c_Lattices_Osemilattice__inf__class_Oinf(X3067,X3066,c_Lattices_Osemilattice__inf__class_Oinf(X3067,X3065,X3064)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).
fof(i_0_954,plain,
! [X3068,X3069,X3070,X3071] :
( ~ class_Lattices_Olattice(X3071)
| c_Lattices_Osemilattice__inf__class_Oinf(X3071,c_Lattices_Osemilattice__inf__class_Oinf(X3071,X3070,X3069),X3068) = c_Lattices_Osemilattice__inf__class_Oinf(X3071,X3070,c_Lattices_Osemilattice__inf__class_Oinf(X3071,X3069,X3068)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).
fof(i_0_955,plain,
! [X3084,X3085,X3086,X3087] :
( ~ class_Lattices_Osemilattice__inf(X3087)
| c_Lattices_Osemilattice__inf__class_Oinf(X3087,X3086,c_Lattices_Osemilattice__inf__class_Oinf(X3087,X3085,X3084)) = c_Lattices_Osemilattice__inf__class_Oinf(X3087,X3085,c_Lattices_Osemilattice__inf__class_Oinf(X3087,X3086,X3084)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).
fof(i_0_956,plain,
! [X3076,X3077,X3078,X3079] :
( ~ class_Lattices_Osemilattice__inf(X3079)
| c_Lattices_Osemilattice__inf__class_Oinf(X3079,X3078,c_Lattices_Osemilattice__inf__class_Oinf(X3079,X3077,X3076)) = c_Lattices_Osemilattice__inf__class_Oinf(X3079,X3077,c_Lattices_Osemilattice__inf__class_Oinf(X3079,X3078,X3076)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).
fof(i_0_957,plain,
! [X3080,X3081,X3082,X3083] :
( ~ class_Lattices_Olattice(X3083)
| c_Lattices_Osemilattice__inf__class_Oinf(X3083,X3082,c_Lattices_Osemilattice__inf__class_Oinf(X3083,X3081,X3080)) = c_Lattices_Osemilattice__inf__class_Oinf(X3083,X3081,c_Lattices_Osemilattice__inf__class_Oinf(X3083,X3082,X3080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).
fof(i_0_958,plain,
! [X3233,X3234,X3235] :
( hAPP(hAPP(c_Set_Oinsert(X3235),X3234),c_Orderings_Obot__class_Obot(tc_fun(X3235,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X3235),X3233),c_Orderings_Obot__class_Obot(tc_fun(X3235,tc_HOL_Obool)))
| X3234 = X3233 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])]) ).
fof(i_0_959,plain,
! [X4232,X4233,X4234] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4234,tc_fun(X4234,tc_HOL_Obool)),X4233,X4232)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4234,tc_HOL_Obool),c_Wellfounded_Oaccp(X4234,X4232),c_Wellfounded_Oaccp(X4234,X4233)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).
fof(i_0_960,plain,
! [X3626,X3627,X3628] : c_Set_Oimage(X3628,X3627,X3626,c_Orderings_Obot__class_Obot(tc_fun(X3628,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X3627,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_image__empty]) ).
fof(i_0_961,plain,
! [X3970,X3971,X3972,X3973] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3973,tc_HOL_Obool),X3972,X3971)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3973,tc_HOL_Obool),X3971,X3970)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3973,tc_HOL_Obool),X3972,X3970) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_962,plain,
! [X4239,X4240,X4241,X4242,X4243] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4243,X4242,X4241)
| c_Orderings_Oord__class_Oless__eq(X4243,X4240,X4239)
| c_Groups_Ominus__class_Ominus(X4243,X4242,X4241) != c_Groups_Ominus__class_Ominus(X4243,X4240,X4239)
| ~ class_Groups_Oordered__ab__group__add(X4243) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4243,X4240,X4239)
| c_Orderings_Oord__class_Oless__eq(X4243,X4242,X4241)
| c_Groups_Ominus__class_Ominus(X4243,X4242,X4241) != c_Groups_Ominus__class_Ominus(X4243,X4240,X4239)
| ~ class_Groups_Oordered__ab__group__add(X4243) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).
fof(i_0_963,plain,
! [X4019,X4020,X4021,X4022] :
( ( c_Orderings_Oord__class_Oless__eq(X4022,X4021,X4020)
| ~ c_Orderings_Oord__class_Oless__eq(X4022,X4021,c_Lattices_Osemilattice__inf__class_Oinf(X4022,X4020,X4019))
| ~ class_Lattices_Osemilattice__inf(X4022) )
& ( c_Orderings_Oord__class_Oless__eq(X4022,X4021,X4019)
| ~ c_Orderings_Oord__class_Oless__eq(X4022,X4021,c_Lattices_Osemilattice__inf__class_Oinf(X4022,X4020,X4019))
| ~ class_Lattices_Osemilattice__inf(X4022) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_586])])]) ).
cnf(i_0_964,plain,
( c_Relation_ORange(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_580]) ).
fof(i_0_965,plain,
! [X3174,X3175,X3176] : hBOOL(hAPP(hAPP(c_member(X3176),X3175),hAPP(hAPP(c_Set_Oinsert(X3176),X3175),X3174))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_966,plain,
! [X2624,X2625,X2626] :
( ( ~ c_Relation_Orefl__on(X2626,X2625,c_Relation_Oconverse(X2626,X2626,X2624))
| c_Relation_Orefl__on(X2626,X2625,X2624) )
& ( ~ c_Relation_Orefl__on(X2626,X2625,X2624)
| c_Relation_Orefl__on(X2626,X2625,c_Relation_Oconverse(X2626,X2626,X2624)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])]) ).
fof(i_0_967,plain,
! [X2567,X2568,X2569] :
( ( ~ c_Relation_Ototal__on(X2569,X2568,c_Relation_Oconverse(X2569,X2569,X2567))
| c_Relation_Ototal__on(X2569,X2568,X2567) )
& ( ~ c_Relation_Ototal__on(X2569,X2568,X2567)
| c_Relation_Ototal__on(X2569,X2568,c_Relation_Oconverse(X2569,X2569,X2567)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])]) ).
fof(i_0_968,plain,
! [X3245,X3246,X3247,X3248] : hAPP(hAPP(c_Set_Oinsert(X3248),X3247),hAPP(hAPP(c_Set_Oinsert(X3248),X3246),X3245)) = hAPP(hAPP(c_Set_Oinsert(X3248),X3246),hAPP(hAPP(c_Set_Oinsert(X3248),X3247),X3245)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_969,plain,
! [X3405,X3406,X3407] : c_Groups_Ominus__class_Ominus(tc_fun(X3407,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3407,tc_HOL_Obool),X3406,X3405),X3405) = c_Groups_Ominus__class_Ominus(tc_fun(X3407,tc_HOL_Obool),X3406,X3405),
inference(variable_rename,[status(thm)],[fact_Diff__idemp]) ).
fof(i_0_970,plain,
! [X2908,X2909,X2910] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2910,tc_HOL_Obool),X2909,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2910,tc_HOL_Obool),X2909,X2908)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2910,tc_HOL_Obool),X2909,X2908),
inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).
fof(i_0_971,plain,
! [X4074,X4075,X4076,X4077] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4077,tc_HOL_Obool),X4076,X4075)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4077,tc_HOL_Obool),X4076,hAPP(hAPP(c_Set_Oinsert(X4077),X4074),X4075)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_972,plain,
! [X3516,X3517,X3518] : c_Fun_Oinj__on(X3518,X3517,X3516,c_Orderings_Obot__class_Obot(tc_fun(X3518,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_inj__on__empty]) ).
fof(i_0_973,plain,
! [X3388,X3389,X3390,X3391,X3392] :
( ~ class_Groups_Ominus(X3392)
| hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3391,X3392),X3390,X3389),X3388) = c_Groups_Ominus__class_Ominus(X3392,hAPP(X3390,X3388),hAPP(X3389,X3388)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__diff__def])]) ).
fof(i_0_974,plain,
! [X3383,X3384,X3385,X3386,X3387] :
( ~ class_Groups_Ominus(X3387)
| hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3386,X3387),X3385,X3384),X3383) = c_Groups_Ominus__class_Ominus(X3387,hAPP(X3385,X3383),hAPP(X3384,X3383)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).
fof(i_0_975,plain,
! [X3011,X3012,X3013,X3014,X3015] :
( ~ class_Lattices_Olattice(X3015)
| hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3014,X3015),X3013,X3012),X3011) = c_Lattices_Osemilattice__inf__class_Oinf(X3015,hAPP(X3013,X3011),hAPP(X3012,X3011)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).
fof(i_0_976,plain,
! [X3006,X3007,X3008,X3009,X3010] :
( ~ class_Lattices_Olattice(X3010)
| hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3009,X3010),X3008,X3007),X3006) = c_Lattices_Osemilattice__inf__class_Oinf(X3010,hAPP(X3008,X3006),hAPP(X3007,X3006)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).
fof(i_0_977,plain,
! [X3268] : c_Relation_Orefl__on(X3268,c_Orderings_Obot__class_Obot(tc_fun(X3268,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3268,X3268),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_refl__on__empty]) ).
fof(i_0_978,plain,
! [X3446,X3447,X3448] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3448,tc_HOL_Obool),X3447,c_Groups_Ominus__class_Ominus(tc_fun(X3448,tc_HOL_Obool),X3446,X3447)) = c_Orderings_Obot__class_Obot(tc_fun(X3448,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__disjoint]) ).
fof(i_0_979,plain,
! [X4084,X4085,X4086] :
( X4086 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4085,X4085),tc_HOL_Obool))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4085,X4085),tc_HOL_Obool),X4086,X4084) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__by__empty])]) ).
fof(i_0_980,plain,
! [X4046,X4047,X4048,X4049] :
( ~ class_Lattices_Osemilattice__inf(X4049)
| ~ c_Orderings_Oord__class_Oless__eq(X4049,X4048,X4047)
| c_Orderings_Oord__class_Oless__eq(X4049,c_Lattices_Osemilattice__inf__class_Oinf(X4049,X4048,X4046),X4047) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).
fof(i_0_981,plain,
! [X4042,X4043,X4044,X4045] :
( ~ class_Lattices_Osemilattice__inf(X4045)
| ~ c_Orderings_Oord__class_Oless__eq(X4045,X4044,X4043)
| c_Orderings_Oord__class_Oless__eq(X4045,c_Lattices_Osemilattice__inf__class_Oinf(X4045,X4042,X4044),X4043) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).
fof(i_0_982,plain,
! [X3636,X3637] : c_Set_Oimage(X3637,X3637,c_COMBI(X3637),X3636) = X3636,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_983,plain,
! [X3537,X3538] : c_Fun_Oinj__on(X3538,X3538,c_COMBI(X3538),X3537),
inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).
fof(i_0_984,plain,
! [X3688,X3689,X3690] : hAPP(c_Relation_OImage(X3690,X3690,c_Relation_OId__on(X3690,X3689)),X3688) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3690,tc_HOL_Obool),X3689,X3688),
inference(variable_rename,[status(thm)],[fact_Image__Id__on]) ).
fof(i_0_985,plain,
! [X3283] : c_Transitive__Closure_Otrancl(X3283,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3283,X3283),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3283,X3283),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_trancl__empty]) ).
fof(i_0_986,plain,
! [X3980,X3981,X3982] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3980,tc_HOL_Obool),X3982,X3981)
| X3982 != X3981 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3980,tc_HOL_Obool),X3981,X3982)
| X3982 != X3981 )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3980,tc_HOL_Obool),X3982,X3981)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3980,tc_HOL_Obool),X3981,X3982)
| X3982 = X3981 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_987,plain,
! [X3810,X3811,X3812] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3812,tc_HOL_Obool),X3811,X3810)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3812,tc_HOL_Obool),X3810,X3811)
| X3811 = X3810 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_988,plain,
! [X3443,X3444,X3445] :
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3445,tc_HOL_Obool),X3444,X3443) != c_Orderings_Obot__class_Obot(tc_fun(X3445,tc_HOL_Obool))
| c_Groups_Ominus__class_Ominus(tc_fun(X3445,tc_HOL_Obool),X3444,X3443) = X3444 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__triv])]) ).
fof(i_0_989,plain,
! [X2223,X2224,X2225] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2225),X2224),hAPP(c_fequal,X2223)))
| X2224 = X2223 )
& ( X2224 != X2223
| hBOOL(hAPP(hAPP(c_member(X2225),X2224),hAPP(c_fequal,X2223))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_990,plain,
! [X3909,X3910,X3911,X3912,X3913] :
( ~ class_Orderings_Oord(X3913)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3912,X3913),X3911,X3910)
| c_Orderings_Oord__class_Oless__eq(X3913,hAPP(X3911,X3909),hAPP(X3910,X3909)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_991,plain,
! [X3871,X3872,X3873,X3874,X3875] :
( ~ class_Orderings_Oord(X3875)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3874,X3875),X3873,X3872)
| c_Orderings_Oord__class_Oless__eq(X3875,hAPP(X3873,X3871),hAPP(X3872,X3871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_992,plain,
! [X3929,X3930,X3931] :
( ~ c_Wellfounded_Oacyclic(X3931,X3930)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3931,X3931),tc_HOL_Obool),X3929,X3930)
| c_Wellfounded_Oacyclic(X3931,X3929) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__subset])]) ).
fof(i_0_993,plain,
! [X3202,X3203,X3204,X3205,X3206] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3203),X3204),X3202))
| X3202 != c_Orderings_Obot__class_Obot(tc_fun(X3203,tc_HOL_Obool)) )
& ( X3205 = c_Orderings_Obot__class_Obot(tc_fun(X3206,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X3206),esk75_2(X3205,X3206)),X3205)) ) ),
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_ex__in__conv])])])])]) ).
fof(i_0_994,plain,
! [X3196,X3197,X3199,X3200,X3201] :
( ( hBOOL(hAPP(hAPP(c_member(X3197),esk74_2(X3196,X3197)),X3196))
| X3196 = c_Orderings_Obot__class_Obot(tc_fun(X3197,tc_HOL_Obool)) )
& ( X3199 != c_Orderings_Obot__class_Obot(tc_fun(X3200,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X3200),X3201),X3199)) ) ),
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_587])])])])]) ).
fof(i_0_995,plain,
! [X3263,X3264] : c_Relation_ODomain(X3264,X3263,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3264,X3263),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X3264,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Domain__empty]) ).
fof(i_0_996,plain,
! [X3883,X3884,X3885,X3886] :
( ~ class_Orderings_Opreorder(X3886)
| ~ c_Orderings_Oord__class_Oless__eq(X3886,X3885,X3884)
| ~ c_Orderings_Oord__class_Oless__eq(X3886,X3884,X3883)
| c_Orderings_Oord__class_Oless__eq(X3886,X3885,X3883) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_997,plain,
! [X3876,X3877,X3878,X3879] :
( ~ class_Orderings_Oorder(X3879)
| ~ c_Orderings_Oord__class_Oless__eq(X3879,X3878,X3877)
| ~ c_Orderings_Oord__class_Oless__eq(X3879,X3876,X3878)
| c_Orderings_Oord__class_Oless__eq(X3879,X3876,X3877) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_998,plain,
! [X4072,X4073] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4073,tc_HOL_Obool),X4072,c_Orderings_Obot__class_Obot(tc_fun(X4073,tc_HOL_Obool)))
| X4072 = c_Orderings_Obot__class_Obot(tc_fun(X4073,tc_HOL_Obool)) )
& ( X4072 != c_Orderings_Obot__class_Obot(tc_fun(X4073,tc_HOL_Obool))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4073,tc_HOL_Obool),X4072,c_Orderings_Obot__class_Obot(tc_fun(X4073,tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])]) ).
fof(i_0_999,plain,
! [X3865,X3866,X3867] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3867,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3867,tc_HOL_Obool),X3866,X3865),X3866),
inference(variable_rename,[status(thm)],[fact_Diff__subset]) ).
fof(i_0_1000,plain,
! [X3998,X3999,X4000] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4000,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4000,tc_HOL_Obool),X3999,X3998),X3999),
inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).
fof(i_0_1001,plain,
! [X4001,X4002,X4003] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4003,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4003,tc_HOL_Obool),X4002,X4001),X4001),
inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).
fof(i_0_1002,plain,
! [X4108,X4109] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X4109),c_Orderings_Obot__class_Obot(tc_fun(X4109,tc_HOL_Obool))),X4108) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4109,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_quotient__empty]) ).
fof(i_0_1003,plain,
! [X4110,X4111,X4112] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4112,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X4112),X4111),X4110)
| X4111 = c_Orderings_Obot__class_Obot(tc_fun(X4112,tc_HOL_Obool)) )
& ( X4111 != c_Orderings_Obot__class_Obot(tc_fun(X4112,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4112,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X4112),X4111),X4110) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2])]) ).
fof(i_0_1004,plain,
! [X4113,X4114,X4115] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X4115),X4114),X4113) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4115,tc_HOL_Obool),tc_HOL_Obool))
| X4114 = c_Orderings_Obot__class_Obot(tc_fun(X4115,tc_HOL_Obool)) )
& ( X4114 != c_Orderings_Obot__class_Obot(tc_fun(X4115,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X4115),X4114),X4113) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4115,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty])]) ).
fof(i_0_1005,plain,
! [X3094,X3095,X3096] :
( ~ class_Lattices_Osemilattice__inf(X3096)
| c_Lattices_Osemilattice__inf__class_Oinf(X3096,X3095,c_Lattices_Osemilattice__inf__class_Oinf(X3096,X3095,X3094)) = c_Lattices_Osemilattice__inf__class_Oinf(X3096,X3095,X3094) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).
fof(i_0_1006,plain,
! [X3088,X3089,X3090] :
( ~ class_Lattices_Osemilattice__inf(X3090)
| c_Lattices_Osemilattice__inf__class_Oinf(X3090,X3089,c_Lattices_Osemilattice__inf__class_Oinf(X3090,X3089,X3088)) = c_Lattices_Osemilattice__inf__class_Oinf(X3090,X3089,X3088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).
fof(i_0_1007,plain,
! [X3091,X3092,X3093] :
( ~ class_Lattices_Olattice(X3093)
| c_Lattices_Osemilattice__inf__class_Oinf(X3093,X3092,c_Lattices_Osemilattice__inf__class_Oinf(X3093,X3092,X3091)) = c_Lattices_Osemilattice__inf__class_Oinf(X3093,X3092,X3091) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).
fof(i_0_1008,plain,
! [X3189,X3190,X3191] :
( ~ hBOOL(hAPP(hAPP(c_member(X3191),X3190),X3189))
| hAPP(hAPP(c_Set_Oinsert(X3191),X3190),X3189) = X3189 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_1009,plain,
! [X3316,X3317] : c_Set_Othe__elem(X3317,hAPP(hAPP(c_Set_Oinsert(X3317),X3316),c_Orderings_Obot__class_Obot(tc_fun(X3317,tc_HOL_Obool)))) = X3316,
inference(variable_rename,[status(thm)],[fact_the__elem__eq]) ).
cnf(i_0_1010,plain,
c_Relation_ORange(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_588]) ).
fof(i_0_1011,plain,
! [X3210,X3211,X3212] :
( X3212 != c_Orderings_Obot__class_Obot(tc_fun(X3211,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X3211),X3210),X3212)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_589])]) ).
fof(i_0_1012,plain,
! [X3265,X3266,X3267] :
( ( c_Relation_ODomain(X3267,X3266,X3265) != c_Orderings_Obot__class_Obot(tc_fun(X3267,tc_HOL_Obool))
| X3265 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3267,X3266),tc_HOL_Obool)) )
& ( X3265 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3267,X3266),tc_HOL_Obool))
| c_Relation_ODomain(X3267,X3266,X3265) = c_Orderings_Obot__class_Obot(tc_fun(X3267,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])]) ).
fof(i_0_1013,plain,
! [X3249,X3250,X3251] : hAPP(hAPP(c_Set_Oinsert(X3251),X3250),hAPP(hAPP(c_Set_Oinsert(X3251),X3250),X3249)) = hAPP(hAPP(c_Set_Oinsert(X3251),X3250),X3249),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
fof(i_0_1014,plain,
! [X3062,X3063] :
( ( ~ c_Wellfounded_Oacyclic(X3063,c_Relation_Oconverse(X3063,X3063,X3062))
| c_Wellfounded_Oacyclic(X3063,X3062) )
& ( ~ c_Wellfounded_Oacyclic(X3063,X3062)
| c_Wellfounded_Oacyclic(X3063,c_Relation_Oconverse(X3063,X3063,X3062)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])]) ).
fof(i_0_1015,plain,
! [X2940,X2941] : c_Transitive__Closure_Otrancl(X2941,c_Relation_Oconverse(X2941,X2941,X2940)) = c_Relation_Oconverse(X2941,X2941,c_Transitive__Closure_Otrancl(X2941,X2940)),
inference(variable_rename,[status(thm)],[fact_trancl__converse]) ).
fof(i_0_1016,plain,
! [X2664,X2665] : c_Transitive__Closure_Ortrancl(X2665,c_Relation_Oconverse(X2665,X2665,X2664)) = c_Relation_Oconverse(X2665,X2665,c_Transitive__Closure_Ortrancl(X2665,X2664)),
inference(variable_rename,[status(thm)],[fact_rtrancl__converse]) ).
fof(i_0_1017,plain,
! [X4004,X4005,X4006] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4006,tc_HOL_Obool),X4005,X4004)
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4006,tc_HOL_Obool),X4005,X4004) = X4005 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).
fof(i_0_1018,plain,
! [X4007,X4008,X4009] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4009,tc_HOL_Obool),X4008,X4007)
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4009,tc_HOL_Obool),X4007,X4008) = X4008 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).
fof(i_0_1019,plain,
! [X3959,X3960,X3961,X3962] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3962,tc_HOL_Obool),X3961,X3960)
| ~ hBOOL(hAPP(X3961,X3959))
| hBOOL(hAPP(X3960,X3959)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_1020,plain,
! [X3963,X3964,X3965,X3966] :
( ~ hBOOL(hAPP(X3966,X3965))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3964,tc_HOL_Obool),X3966,X3963)
| hBOOL(hAPP(X3963,X3965)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_1021,plain,
! [X3633,X3634,X3635] : hAPP(c_Relation_OImage(X3635,X3634,X3633),c_Orderings_Obot__class_Obot(tc_fun(X3635,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X3634,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Image__empty]) ).
fof(i_0_1022,plain,
! [X2191,X2192,X2193] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2193),X2192),X2191))
| hBOOL(hAPP(X2191,X2192)) )
& ( ~ hBOOL(hAPP(X2191,X2192))
| hBOOL(hAPP(hAPP(c_member(X2193),X2192),X2191)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_1023,plain,
! [X4262,X4263,X4264,X4265,X4266] :
( ( X4265 != X4264
| X4263 = X4262
| c_Groups_Ominus__class_Ominus(X4266,X4265,X4264) != c_Groups_Ominus__class_Ominus(X4266,X4263,X4262)
| ~ class_Groups_Oab__group__add(X4266) )
& ( X4263 != X4262
| X4265 = X4264
| c_Groups_Ominus__class_Ominus(X4266,X4265,X4264) != c_Groups_Ominus__class_Ominus(X4266,X4263,X4262)
| ~ class_Groups_Oab__group__add(X4266) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
fof(i_0_1024,plain,
! [X3917,X3918,X3919] :
( ( c_Orderings_Oord__class_Oless__eq(X3919,X3918,X3917)
| X3918 != X3917
| ~ class_Orderings_Oorder(X3919) )
& ( c_Orderings_Oord__class_Oless__eq(X3919,X3917,X3918)
| X3918 != X3917
| ~ class_Orderings_Oorder(X3919) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3919,X3918,X3917)
| ~ c_Orderings_Oord__class_Oless__eq(X3919,X3917,X3918)
| X3918 = X3917
| ~ class_Orderings_Oorder(X3919) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_1025,plain,
! [X3906,X3907,X3908] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3908,X3906,X3907)
| X3906 = X3907
| ~ c_Orderings_Oord__class_Oless__eq(X3908,X3907,X3906)
| ~ class_Orderings_Oorder(X3908) )
& ( X3906 != X3907
| c_Orderings_Oord__class_Oless__eq(X3908,X3906,X3907)
| ~ c_Orderings_Oord__class_Oless__eq(X3908,X3907,X3906)
| ~ class_Orderings_Oorder(X3908) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_1026,plain,
! [X3887,X3888,X3889] :
( ~ class_Orderings_Oorder(X3889)
| ~ c_Orderings_Oord__class_Oless__eq(X3889,X3888,X3887)
| ~ c_Orderings_Oord__class_Oless__eq(X3889,X3887,X3888)
| X3888 = X3887 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_1027,plain,
! [X3880,X3881,X3882] :
( ~ class_Orderings_Oorder(X3882)
| ~ c_Orderings_Oord__class_Oless__eq(X3882,X3881,X3880)
| ~ c_Orderings_Oord__class_Oless__eq(X3882,X3880,X3881)
| X3880 = X3881 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_1028,plain,
! [X4069,X4070,X4071] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4071,tc_HOL_Obool),X4070,hAPP(hAPP(c_Set_Oinsert(X4071),X4069),X4070)),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_1029,plain,
! [X4063,X4064,X4065] :
( ~ class_Lattices_Osemilattice__inf(X4065)
| c_Orderings_Oord__class_Oless__eq(X4065,c_Lattices_Osemilattice__inf__class_Oinf(X4065,X4064,X4063),X4064) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).
fof(i_0_1030,plain,
! [X4066,X4067,X4068] :
( ~ class_Lattices_Olattice(X4068)
| c_Orderings_Oord__class_Oless__eq(X4068,c_Lattices_Osemilattice__inf__class_Oinf(X4068,X4067,X4066),X4067) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).
fof(i_0_1031,plain,
! [X4057,X4058,X4059] :
( ~ class_Lattices_Osemilattice__inf(X4059)
| c_Orderings_Oord__class_Oless__eq(X4059,c_Lattices_Osemilattice__inf__class_Oinf(X4059,X4058,X4057),X4057) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).
fof(i_0_1032,plain,
! [X4060,X4061,X4062] :
( ~ class_Lattices_Olattice(X4062)
| c_Orderings_Oord__class_Oless__eq(X4062,c_Lattices_Osemilattice__inf__class_Oinf(X4062,X4061,X4060),X4060) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).
fof(i_0_1033,plain,
! [X2460,X2461,X2462] : c_Predicate_Oconversep(X2462,X2461,c_Predicate_Oconversep(X2461,X2462,X2460)) = X2460,
inference(variable_rename,[status(thm)],[fact_conversep__conversep]) ).
fof(i_0_1034,plain,
! [X2313,X2314,X2315] : c_Relation_Oconverse(X2315,X2314,c_Relation_Oconverse(X2314,X2315,X2313)) = X2313,
inference(variable_rename,[status(thm)],[fact_converse__converse]) ).
fof(i_0_1035,plain,
! [X3381,X3382] : c_Groups_Ominus__class_Ominus(tc_fun(X3382,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X3382,tc_HOL_Obool)),X3381) = c_Orderings_Obot__class_Obot(tc_fun(X3382,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_empty__Diff]) ).
fof(i_0_1036,plain,
! [X3281,X3282] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3282,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X3282,tc_HOL_Obool)),X3281) = c_Orderings_Obot__class_Obot(tc_fun(X3282,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Int__empty__left]) ).
fof(i_0_1037,plain,
! [X3279,X3280] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3280,tc_HOL_Obool),X3279,c_Orderings_Obot__class_Obot(tc_fun(X3280,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X3280,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Int__empty__right]) ).
fof(i_0_1038,plain,
! [X2911,X2912,X2913] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2913,tc_HOL_Obool),X2912,X2911) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2913,tc_HOL_Obool),X2911,X2912),
inference(variable_rename,[status(thm)],[fact_Int__commute]) ).
fof(i_0_1039,plain,
! [X4054,X4055,X4056] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4056,X4055,X4054)
| c_Lattices_Osemilattice__inf__class_Oinf(X4056,X4055,X4054) = X4055
| ~ class_Lattices_Osemilattice__inf(X4056) )
& ( c_Lattices_Osemilattice__inf__class_Oinf(X4056,X4055,X4054) != X4055
| c_Orderings_Oord__class_Oless__eq(X4056,X4055,X4054)
| ~ class_Lattices_Osemilattice__inf(X4056) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).
fof(i_0_1040,plain,
! [X4039,X4040,X4041] :
( ~ class_Lattices_Osemilattice__inf(X4041)
| ~ c_Orderings_Oord__class_Oless__eq(X4041,X4040,X4039)
| c_Lattices_Osemilattice__inf__class_Oinf(X4041,X4040,X4039) = X4040 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).
fof(i_0_1041,plain,
! [X4036,X4037,X4038] :
( ~ class_Lattices_Osemilattice__inf(X4038)
| ~ c_Orderings_Oord__class_Oless__eq(X4038,X4037,X4036)
| c_Lattices_Osemilattice__inf__class_Oinf(X4038,X4036,X4037) = X4037 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).
fof(i_0_1042,plain,
! [X3226] : c_Relation_OId__on(X3226,c_Orderings_Obot__class_Obot(tc_fun(X3226,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3226,X3226),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Id__on__empty]) ).
fof(i_0_1043,plain,
! [X2942,X2943] : c_Relation_ODomain(X2943,X2943,c_Transitive__Closure_Otrancl(X2943,X2942)) = c_Relation_ODomain(X2943,X2943,X2942),
inference(variable_rename,[status(thm)],[fact_trancl__domain]) ).
fof(i_0_1044,plain,
! [X3379,X3380] : c_Groups_Ominus__class_Ominus(tc_fun(X3380,tc_HOL_Obool),X3379,c_Orderings_Obot__class_Obot(tc_fun(X3380,tc_HOL_Obool))) = X3379,
inference(variable_rename,[status(thm)],[fact_Diff__empty]) ).
fof(i_0_1045,plain,
! [X3817,X3818] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3818,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X3818,tc_HOL_Obool)),X3817),
inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).
fof(i_0_1046,plain,
! [X2173,X2174] :
( hAPP(X2174,esk1_2(X2173,X2174)) != hAPP(X2173,esk1_2(X2173,X2174))
| X2174 = X2173 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_1047,plain,
! [X3252,X3253,X3254] : hAPP(hAPP(c_Set_Oinsert(X3254),X3253),X3252) != c_Orderings_Obot__class_Obot(tc_fun(X3254,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_insert__not__empty]) ).
fof(i_0_1048,plain,
! [X3255,X3256,X3257] : c_Orderings_Obot__class_Obot(tc_fun(X3257,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X3257),X3256),X3255),
inference(variable_rename,[status(thm)],[fact_empty__not__insert]) ).
fof(i_0_1049,plain,
! [X4395,X4396] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4396),X4395))
| hBOOL(X4396) ),
inference(variable_rename,[status(thm)],[i_0_590]) ).
fof(i_0_1050,plain,
! [X4397,X4398] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4398),X4397))
| hBOOL(X4397) ),
inference(variable_rename,[status(thm)],[i_0_591]) ).
fof(i_0_1051,plain,
! [X4387,X4388] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X4388),X4387))
| X4388 = X4387 ),
inference(variable_rename,[status(thm)],[i_0_592]) ).
fof(i_0_1052,plain,
! [X4365,X4366,X4367,X4368] : hAPP(c_COMBK(X4368,X4367,X4366),X4365) = X4366,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_1053,plain,
! [X3920,X3921,X3922] :
( ~ class_Orderings_Olinorder(X3922)
| c_Orderings_Oord__class_Oless__eq(X3922,X3921,X3920)
| c_Orderings_Oord__class_Oless__eq(X3922,X3920,X3921) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_1054,plain,
! [X3868,X3869,X3870] :
( ~ class_Orderings_Olinorder(X3870)
| c_Orderings_Oord__class_Oless__eq(X3870,X3869,X3868)
| c_Orderings_Oord__class_Oless__eq(X3870,X3868,X3869) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_593])]) ).
fof(i_0_1055,plain,
! [X3103,X3104,X3105] :
( ~ class_Lattices_Osemilattice__inf(X3105)
| c_Lattices_Osemilattice__inf__class_Oinf(X3105,X3104,X3103) = c_Lattices_Osemilattice__inf__class_Oinf(X3105,X3103,X3104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).
fof(i_0_1056,plain,
! [X3097,X3098,X3099] :
( ~ class_Lattices_Osemilattice__inf(X3099)
| c_Lattices_Osemilattice__inf__class_Oinf(X3099,X3098,X3097) = c_Lattices_Osemilattice__inf__class_Oinf(X3099,X3097,X3098) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).
fof(i_0_1057,plain,
! [X3100,X3101,X3102] :
( ~ class_Lattices_Olattice(X3102)
| c_Lattices_Osemilattice__inf__class_Oinf(X3102,X3101,X3100) = c_Lattices_Osemilattice__inf__class_Oinf(X3102,X3100,X3101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).
fof(i_0_1058,plain,
! [X3286,X3287] : c_Relation_Ototal__on(X3287,c_Orderings_Obot__class_Obot(tc_fun(X3287,tc_HOL_Obool)),X3286),
inference(variable_rename,[status(thm)],[fact_total__on__empty]) ).
fof(i_0_1059,plain,
! [X3377,X3378] : c_Groups_Ominus__class_Ominus(tc_fun(X3378,tc_HOL_Obool),X3377,X3377) = c_Orderings_Obot__class_Obot(tc_fun(X3378,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).
fof(i_0_1060,plain,
! [X2364,X2365] : c_Relation_Oconverse(X2365,X2365,c_Relation_OId__on(X2365,X2364)) = c_Relation_OId__on(X2365,X2364),
inference(variable_rename,[status(thm)],[fact_converse__Id__on]) ).
fof(i_0_1061,plain,
! [X4393,X4394] :
( ~ hBOOL(X4394)
| ~ hBOOL(X4393)
| hBOOL(hAPP(hAPP(c_fconj,X4394),X4393)) ),
inference(variable_rename,[status(thm)],[i_0_594]) ).
fof(i_0_1062,plain,
! [X3321,X3322,X3323] :
( ~ class_Orderings_Obot(X3323)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3322,X3323)),X3321) = c_Orderings_Obot__class_Obot(X3323) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).
fof(i_0_1063,plain,
! [X3318,X3319,X3320] :
( ~ class_Orderings_Obot(X3320)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3319,X3320)),X3318) = c_Orderings_Obot__class_Obot(X3320) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).
fof(i_0_1064,plain,
! [X2467,X2468] : c_Relation_ODomain(X2468,X2468,c_Relation_OId__on(X2468,X2467)) = X2467,
inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).
fof(i_0_1065,plain,
! [X3967,X3968,X3969] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3967,tc_HOL_Obool),X3969,X3968)
| X3969 != X3968 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3967,tc_HOL_Obool),X3968,X3969)
| X3969 != X3968 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_595])])]) ).
fof(i_0_1066,plain,
! [X3977,X3978,X3979] :
( X3979 != X3978
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3977,tc_HOL_Obool),X3979,X3978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_1067,plain,
! [X3974,X3975,X3976] :
( X3976 != X3975
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3974,tc_HOL_Obool),X3975,X3976) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_1068,plain,
! [X2734,X2735] : c_Relation_Osingle__valued(X2735,X2735,c_Relation_OId__on(X2735,X2734)),
inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).
fof(i_0_1069,plain,
! [X2627,X2628] : c_Relation_Orefl__on(X2628,X2627,c_Relation_OId__on(X2628,X2627)),
inference(variable_rename,[status(thm)],[fact_refl__on__Id__on]) ).
fof(i_0_1070,plain,
! [X4389,X4390] :
( X4390 != X4389
| hBOOL(hAPP(hAPP(c_fequal,X4390),X4389)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1071,plain,
! [X2914,X2915] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2915,tc_HOL_Obool),X2914,X2914) = X2914,
inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).
fof(i_0_1072,plain,
! [X3983,X3984] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3984,tc_HOL_Obool),X3983,X3983),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_1073,plain,
! [X3290,X3291] :
( ~ class_Lattices_Obounded__lattice__bot(X3291)
| c_Lattices_Osemilattice__inf__class_Oinf(X3291,c_Orderings_Obot__class_Obot(X3291),X3290) = c_Orderings_Obot__class_Obot(X3291) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])]) ).
fof(i_0_1074,plain,
! [X3288,X3289] :
( ~ class_Lattices_Obounded__lattice__bot(X3289)
| c_Lattices_Osemilattice__inf__class_Oinf(X3289,X3288,c_Orderings_Obot__class_Obot(X3289)) = c_Orderings_Obot__class_Obot(X3289) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__right])]) ).
fof(i_0_1075,plain,
! [X4082,X4083] :
( ~ class_Orderings_Obot(X4083)
| c_Orderings_Oord__class_Oless__eq(X4083,c_Orderings_Obot__class_Obot(X4083),X4082) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])]) ).
fof(i_0_1076,plain,
! [X3914,X3915,X3916] :
( ~ class_Orderings_Opreorder(X3916)
| X3915 != X3914
| c_Orderings_Oord__class_Oless__eq(X3916,X3915,X3914) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1077,plain,
! [X3108,X3109] :
( ~ class_Lattices_Osemilattice__inf(X3109)
| c_Lattices_Osemilattice__inf__class_Oinf(X3109,X3108,X3108) = X3108 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).
fof(i_0_1078,plain,
! [X3106,X3107] :
( ~ class_Lattices_Osemilattice__inf(X3107)
| c_Lattices_Osemilattice__inf__class_Oinf(X3107,X3106,X3106) = X3106 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).
fof(i_0_1079,plain,
! [X3808,X3809] :
( ~ class_Orderings_Opreorder(X3809)
| c_Orderings_Oord__class_Oless__eq(X3809,X3808,X3808) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1080,plain,
! [X2938,X2939] : c_Transitive__Closure_Otrancl(X2939,c_Transitive__Closure_Ortrancl(X2939,X2938)) = c_Transitive__Closure_Ortrancl(X2939,X2938),
inference(variable_rename,[status(thm)],[fact_rtrancl__trancl__absorb]) ).
fof(i_0_1081,plain,
! [X2936,X2937] : c_Transitive__Closure_Ortrancl(X2937,c_Transitive__Closure_Otrancl(X2937,X2936)) = c_Transitive__Closure_Ortrancl(X2937,X2936),
inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb]) ).
fof(i_0_1082,plain,
! [X2662,X2663] : c_Transitive__Closure_Ortrancl(X2663,c_Transitive__Closure_Ortrancl(X2663,X2662)) = c_Transitive__Closure_Ortrancl(X2663,X2662),
inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).
fof(i_0_1083,plain,
! [X2463] : c_Predicate_Oconversep(X2463,X2463,c_fequal) = c_fequal,
inference(variable_rename,[status(thm)],[fact_conversep__eq]) ).
fof(i_0_1084,plain,
! [X4391] :
( ~ hBOOL(hAPP(c_fNot,X4391))
| ~ hBOOL(X4391) ),
inference(variable_rename,[status(thm)],[i_0_596]) ).
fof(i_0_1085,plain,
! [X3591,X3592] : c_HOL_OThe(X3592,hAPP(c_fequal,X3591)) = X3591,
inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial]) ).
fof(i_0_1086,plain,
! [X4345,X4346] :
( ~ class_Lattices_Obounded__lattice(X4346)
| class_Lattices_Obounded__lattice(tc_fun(X4345,X4346)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])]) ).
fof(i_0_1087,plain,
! [X4355,X4356] :
( ~ class_Orderings_Oorder(X4356)
| class_Orderings_Oorder(tc_fun(X4355,X4356)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1088,plain,
! [X4357,X4358] :
( ~ class_Orderings_Oord(X4358)
| class_Orderings_Oord(tc_fun(X4357,X4358)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1089,plain,
! [X4351,X4352] :
( ~ class_Orderings_Opreorder(X4352)
| class_Orderings_Opreorder(tc_fun(X4351,X4352)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1090,plain,
! [X4361,X4362] :
( ~ class_Groups_Ominus(X4362)
| class_Groups_Ominus(tc_fun(X4361,X4362)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).
fof(i_0_1091,plain,
! [X4359,X4360] :
( ~ class_Orderings_Obot(X4360)
| class_Orderings_Obot(tc_fun(X4359,X4360)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).
fof(i_0_1092,plain,
! [X4347,X4348] :
( ~ class_Lattices_Obounded__lattice(X4348)
| class_Lattices_Obounded__lattice__bot(tc_fun(X4347,X4348)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])]) ).
fof(i_0_1093,plain,
! [X4349,X4350] :
( ~ class_Lattices_Olattice(X4350)
| class_Lattices_Osemilattice__inf(tc_fun(X4349,X4350)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).
fof(i_0_1094,plain,
! [X4353,X4354] :
( ~ class_Lattices_Olattice(X4354)
| class_Lattices_Olattice(tc_fun(X4353,X4354)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).
fof(i_0_1095,plain,
! [X4392] :
( hBOOL(X4392)
| hBOOL(hAPP(c_fNot,X4392)) ),
inference(variable_rename,[status(thm)],[i_0_597]) ).
fof(i_0_1096,plain,
! [X4363,X4364] : hAPP(c_COMBI(X4364),X4363) = X4363,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
cnf(i_0_1097,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),esk38_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk39_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk40_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk41_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_598]),
[final] ).
cnf(i_0_1098,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),esk42_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk43_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk44_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk45_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_599]),
[final] ).
cnf(i_0_1099,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),esk44_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk45_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_599]),
[final] ).
cnf(i_0_1100,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),esk38_8(X5,X6,X7,X8,X4,X3,X2,X1)),esk39_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_598]),
[final] ).
cnf(i_0_1101,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),esk46_7(X3,X4,X5,X6,X7,X2,X1)),esk47_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_600]),
[final] ).
cnf(i_0_1102,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),esk46_7(X5,X6,X7,X4,X3,X2,X1)),esk47_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_600]),
[final] ).
cnf(i_0_1103,plain,
( hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(X1,esk40_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk41_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_598]),
[final] ).
cnf(i_0_1104,plain,
( hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(X1,esk42_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk43_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_599]),
[final] ).
cnf(i_0_1105,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(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(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,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(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(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,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_601]),
[final] ).
cnf(i_0_1106,plain,
( hBOOL(hAPP(hAPP(X1,esk38_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk39_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_598]),
[final] ).
cnf(i_0_1107,plain,
( hBOOL(hAPP(hAPP(X1,esk44_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk45_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_599]),
[final] ).
cnf(i_0_1108,plain,
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(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(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,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(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(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,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1109,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk67_7(X2,X3,X4,X1,X5,X6,X7)),X7)),X3))
| hAPP(hAPP(X2,X5),X7) = hAPP(hAPP(X2,X6),X7)
| ~ c_Recdef_Oadm__wf(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1110,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X5)),c_Relation_Oconverse(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),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(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,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),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1111,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2,c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X2,X1)))),c_Product__Type_OPair(X2,X1)))),X5)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Relation_Oconverse(X2,X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1112,plain,
( c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X5,hAPP(hAPP(c_Set_Oinsert(X1),esk82_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk83_7(X6,X7,X5,X4,X3,X2,X1))
| hAPP(hAPP(X3,X7),X6) = X4
| ~ c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X7),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1113,plain,
( c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X5,hAPP(hAPP(c_Set_Oinsert(X1),esk82_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk83_7(X6,X7,X5,X4,X3,X2,X1))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X7),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1114,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(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(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,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_605]),
[final] ).
cnf(i_0_1115,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(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(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,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_605]),
[final] ).
cnf(i_0_1116,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk82_7(X2,X3,X4,X5,X6,X7,X1)),X4))
| hAPP(hAPP(X6,X3),X2) = X5
| ~ c_Nitpick_Ofold__graph_H(X1,X7,X6,X5,X4,hAPP(hAPP(X6,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1117,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk82_7(X2,X3,X4,X5,X6,X7,X1)),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X1,X7,X6,X5,X4,hAPP(hAPP(X6,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1118,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(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(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,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(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(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,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_606]),
[final] ).
cnf(i_0_1119,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk59_6(X2,X3,X4,X5,X6,X1)),X3)),X4))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X6),X5),X4),X3) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X6),X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_607]),
[final] ).
cnf(i_0_1120,plain,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk82_7(X3,X2,X4,X5,X1,X6,X7)),esk83_7(X3,X2,X4,X5,X1,X6,X7))
| hAPP(hAPP(X1,X2),X3) = X5
| ~ c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1121,plain,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk82_7(X3,X2,X4,X5,X1,X6,X7)),esk83_7(X3,X2,X4,X5,X1,X6,X7))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1122,plain,
( hAPP(hAPP(X2,X1),X7) = hAPP(hAPP(X2,X6),X7)
| hAPP(X1,esk67_7(X2,X3,X4,X5,X1,X6,X7)) != hAPP(X6,esk67_7(X2,X3,X4,X5,X1,X6,X7))
| ~ c_Recdef_Oadm__wf(X5,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1123,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(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(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,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(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(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,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_606]),
[final] ).
cnf(i_0_1124,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),c_Relation_ODomain(X2,X1,c_Relation_Oconverse(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(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(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,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(rw,[status(thm)],[i_0_608,c_0_609]),
[final] ).
cnf(i_0_1125,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(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(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,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_610]),
[final] ).
cnf(i_0_1126,plain,
( X3 = X4
| hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),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(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,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(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(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,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_611]),
[final] ).
cnf(i_0_1127,plain,
c_Recdef_Oadm__wf(X1,X2,X3,hAPP(hAPP(c_COMBC(tc_fun(X1,X2),tc_fun(X1,X1),tc_fun(X1,X2)),hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X2)),tc_fun(tc_fun(X1,X1),tc_fun(X1,X2)),tc_fun(X1,X2),c_COMBS(X1,X1,X2)),hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X2)),tc_fun(X1,tc_fun(X1,X2)),tc_fun(X1,X2),c_COMBB(tc_fun(X1,X2),tc_fun(X1,X2),X1,X4)),hAPP(hAPP(c_COMBC(tc_fun(X1,X2),tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_fun(X1,X2))),c_Recdef_Ocut(X1,X2)),X3)))),c_COMBI(X1))),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1128,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(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(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,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_ODomain(X1,X3,c_Relation_Oconverse(X3,X1,X4)))) ),
inference(rw,[status(thm)],[i_0_613,c_0_609]),
[final] ).
cnf(i_0_1129,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(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(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,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_610]),
[final] ).
cnf(i_0_1130,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk79_6(X2,X3,X4,X5,X6,X1)),X6))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X3)),c_Fun_Ofun__upd(X1,X3,X5,X4,c_HOL_Oundefined(X3))),c_FuncSet_Oextensional__funcset(X1,X3,X6,c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X5,X4)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X3)),X5),c_FuncSet_Oextensional__funcset(X1,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),X6),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_1131,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk57_5(X2,X3,X4,X5,X1)),esk58_5(X2,X3,X4,X5,X1))),X3))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1132,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk62_5(X2,X3,X4,X5,X1)),esk63_5(X2,X3,X4,X5,X1))),X3))
| hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_616]),
[final] ).
cnf(i_0_1133,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X6),c_FuncSet_OPi(X1,X2,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),esk30_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_617]),
[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(X1),esk30_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_617]),
[final] ).
cnf(i_0_1135,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),c_FuncSet_Orestrict(X5,X1,X2,X4)),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk51_5(X3,X2,X1,X4,X5))),hAPP(X3,esk51_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1136,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,esk26_5(X3,X2,X1,X4,X5))),hAPP(X3,esk26_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1137,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,esk17_5(X3,X2,X1,X4,X5))),hAPP(X3,esk17_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1138,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk63_5(X2,X3,X4,X5,X1)),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
| hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_616]),
[final] ).
cnf(i_0_1139,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1,c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1,c_Relation_OImage(X1,X1,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1140,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,esk30_6(X5,X2,X3,X6,X4,X1)) != hAPP(X3,esk30_6(X5,X2,X3,X6,X4,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_617]),
[final] ).
cnf(i_0_1141,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,esk30_6(X5,X2,X6,X3,X4,X1)) != hAPP(X6,esk30_6(X5,X2,X6,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_617]),
[final] ).
cnf(i_0_1142,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk86_5(X3,X4,X1,X5,X2)),X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_622]),
[final] ).
cnf(i_0_1143,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk85_5(X3,X4,X1,X5,X2)),X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_623]),
[final] ).
cnf(i_0_1144,plain,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X1,hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot)),c_fequal)),X2),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[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(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,esk7_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,esk7_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_625]),
[final] ).
cnf(i_0_1146,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,esk7_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,esk7_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_625]),
[final] ).
cnf(i_0_1147,plain,
( hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X5),X1),X4),X3) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X5),X2),X4),X3)
| hAPP(X1,esk59_6(X2,X3,X4,X1,X5,X6)) != hAPP(X2,esk59_6(X2,X3,X4,X1,X5,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_607]),
[final] ).
cnf(i_0_1148,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),c_FuncSet_Orestrict(X5,X1,X2,X4)),c_FuncSet_OPi(X5,X1,X4,c_COMBK(tc_fun(X1,tc_HOL_Obool),X5,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk52_5(X3,X2,X1,X4,X5))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_626]),
[final] ).
cnf(i_0_1149,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X2) = c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2))
| ~ c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1,c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X2),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1150,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,esk24_5(X3,X2,X1,X4,X5))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_628]),
[final] ).
cnf(i_0_1151,plain,
( hAPP(X1,X2) = hAPP(X1,esk79_6(X3,X4,X2,X1,X5,X6))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X4)),c_Fun_Ofun__upd(X6,X4,X1,X2,c_HOL_Oundefined(X4))),c_FuncSet_Oextensional__funcset(X6,X4,X5,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X4)),X1),c_FuncSet_Oextensional__funcset(X6,X4,hAPP(hAPP(c_Set_Oinsert(X6),X2),X5),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_1152,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,esk7_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,esk7_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_625]),
[final] ).
cnf(i_0_1153,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,esk7_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,esk7_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_625]),
[final] ).
cnf(i_0_1154,plain,
( c_FuncSet_Orestrict(X1,X9,hAPP(c_COMBB(X6,X9,X1,X10),c_FuncSet_Orestrict(X1,X6,hAPP(c_COMBB(X2,X6,X1,X7),X3),X4)),X4) = c_FuncSet_Orestrict(X1,X9,hAPP(c_COMBB(X2,X9,X1,c_FuncSet_Orestrict(X2,X9,hAPP(c_COMBB(X6,X9,X2,X10),X7),X5)),X3),X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X9)),X10),c_FuncSet_OPi(X6,X9,X8,c_COMBK(tc_fun(X9,tc_HOL_Obool),X6,X11))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X6)),X7),c_FuncSet_OPi(X2,X6,X5,c_COMBK(tc_fun(X6,tc_HOL_Obool),X2,X8))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_629,c_0_630]),c_0_630]),c_0_630]),c_0_630]),
[final] ).
cnf(i_0_1155,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X3,X3,hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X3,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3,c_fNot)),c_fequal)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1156,plain,
hAPP(v_Q____,X1) = c_HOL_OLet(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),hAPP(hAPP(c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),hAPP(hAPP(c_fequal,v_a____),v_a_H____)),hAPP(v_P____,X1)),c_Arrow__Order__Mirabelle_Obelow(hAPP(v_P____,X1),v_a_H____,v_a____)),hAPP(hAPP(c_COMBS(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),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),hAPP(hAPP(c_fequal,v_b____),v_b_H____))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),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_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),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))),c_Arrow__Order__Mirabelle_Oabove),v_b____)),v_b_H____))),
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),esk57_5(X3,X4,X5,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X4)))
| hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(X3,X2))
| ~ 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))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1158,plain,
hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5) = c_HOL_OThe(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1,c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1,c_fequal),X4)),X5))),
inference(split_conjunct,[status(thm)],[i_0_632]),
[final] ).
cnf(i_0_1159,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X6)),c_FuncSet_Orestrict(X1,X6,hAPP(c_COMBB(X2,X6,X1,X7),X3),X4)),c_FuncSet_OPi(X1,X6,X4,c_COMBK(tc_fun(X6,tc_HOL_Obool),X1,X8))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X6)),X7),c_FuncSet_OPi(X2,X6,X5,c_COMBK(tc_fun(X6,tc_HOL_Obool),X2,X8))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)))) ),
inference(rw,[status(thm)],[i_0_633,c_0_630]),
[final] ).
cnf(i_0_1160,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X1)),c_Fun_Ofun__upd(X4,X1,X5,X7,X2)),c_FuncSet_Oextensional__funcset(X4,X1,hAPP(hAPP(c_Set_Oinsert(X4),X7),X6),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X1)),X5),c_FuncSet_Oextensional__funcset(X4,X1,X6,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))) ),
inference(split_conjunct,[status(thm)],[i_0_634]),
[final] ).
cnf(i_0_1161,plain,
( c_Nitpick_Ofold__graph_H(X6,X8,X1,X9,X7,hAPP(hAPP(X1,X2),X3))
| hAPP(hAPP(X1,X2),X3) != hAPP(hAPP(X1,X4),X5)
| ~ hBOOL(hAPP(hAPP(c_member(X6),X4),X7))
| ~ c_Nitpick_Ofold__graph_H(X6,X8,X1,X9,c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool),X7,hAPP(hAPP(c_Set_Oinsert(X6),X4),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X5) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1162,plain,
( c_Nitpick_Ofold__graph_H(X1,X4,X5,X6,X3,hAPP(hAPP(X5,X2),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Nitpick_Ofold__graph_H(X1,X4,X5,X6,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7) ),
inference(split_conjunct,[status(thm)],[i_0_635]),
[final] ).
cnf(i_0_1163,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_636]),
[final] ).
cnf(i_0_1164,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),esk5_2(X1,X2)),esk6_2(X1,X2))),hAPP(X2,esk4_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_637]),
[final] ).
cnf(i_0_1165,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_636]),
[final] ).
cnf(i_0_1166,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),esk5_2(X1,X2)),esk6_2(X1,X2))),hAPP(esk4_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_637]),
[final] ).
cnf(i_0_1167,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))),esk4_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_637]),
[final] ).
cnf(i_0_1168,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),c_Fun_Ofun__upd(X1,X4,X5,X2,c_HOL_Oundefined(X4))),c_FuncSet_Oextensional__funcset(X1,X4,X3,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X5),c_FuncSet_Oextensional__funcset(X1,X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_638]),
[final] ).
cnf(i_0_1169,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk18_4(X3,X4,X1,X2)),esk19_4(X3,X4,X1,X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),X4),c_Relation_Oconverse(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_639]),
[final] ).
cnf(i_0_1170,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk52_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),c_FuncSet_Orestrict(X1,X4,X3,X5)),c_FuncSet_OPi(X1,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_626]),
[final] ).
cnf(i_0_1171,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X1)),c_Fun_Ofun__upd(X4,X1,X5,X7,X2)),c_FuncSet_Oextensional__funcset(X4,X1,hAPP(hAPP(c_Set_Oinsert(X4),X7),X6),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X1)),X5),c_FuncSet_Oextensional__funcset(X4,X1,X6,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_640]),
[final] ).
cnf(i_0_1172,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk5_2(X1,X2) != esk6_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_637]),
[final] ).
cnf(i_0_1173,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk51_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),c_FuncSet_Orestrict(X1,X4,X3,X5)),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1174,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk73_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Otrancl(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1175,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk72_4(X2,X3,X4,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1176,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk24_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_628]),
[final] ).
cnf(i_0_1177,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk92_5(X2,X3,X4,X5,X1)),X4))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool),X4,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1178,plain,
( hBOOL(hAPP(hAPP(X1,esk92_5(X2,X1,X3,X4,X5)),X2))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X4,tc_HOL_Obool),X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1179,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk53_5(X2,X3,X4,X5,X1)),X3))
| X4 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X5)),X2),c_FuncSet_Oextensional(X1,X5,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X5)),X4),c_FuncSet_Oextensional(X1,X5,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_644]),
[final] ).
cnf(i_0_1180,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk26_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_619]),
[final] ).
cnf(i_0_1181,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk17_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_620]),
[final] ).
cnf(i_0_1182,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk61_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))
| X4 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Ortrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_1183,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk64_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_646]),
[final] ).
cnf(i_0_1184,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk86_5(X2,X3,X1,X4,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_622]),
[final] ).
cnf(i_0_1185,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk85_5(X2,X3,X1,X4,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_623]),
[final] ).
cnf(i_0_1186,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk60_4(X2,X3,X4,X1)),X3)),X2))
| X4 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Ortrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1187,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk65_4(X2,X3,X4,X1)),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1188,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_649]),
[final] ).
cnf(i_0_1189,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),c_FuncSet_Orestrict(X1,X2,hAPP(c_COMBB(X3,X2,X1,X5),X6),X4)),c_FuncSet_Oextensional(X1,X2,X4))),
inference(rw,[status(thm)],[i_0_650,c_0_630]),
[final] ).
cnf(i_0_1190,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_636]),
[final] ).
cnf(i_0_1191,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_636]),
[final] ).
cnf(i_0_1192,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk23_4(X4,X3,X2,X1)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ODomain(X1,X3,c_Relation_Oconverse(X3,X1,X4)))) ),
inference(rw,[status(thm)],[i_0_651,c_0_609]),
[final] ).
cnf(i_0_1193,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk21_4(X4,X3,X2,X1)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ODomain(X1,X3,c_Relation_Oconverse(X3,X1,X4)))) ),
inference(rw,[status(thm)],[i_0_652,c_0_609]),
[final] ).
cnf(i_0_1194,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1195,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_654]),
[final] ).
cnf(i_0_1196,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk58_5(X1,X2,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1197,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,esk62_5(X1,X2,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_616]),
[final] ).
cnf(i_0_1198,plain,
( X1 = X2
| hAPP(X1,esk53_5(X2,X3,X1,X4,X5)) != hAPP(X2,esk53_5(X2,X3,X1,X4,X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X2),c_FuncSet_Oextensional(X5,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X1),c_FuncSet_Oextensional(X5,X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_644]),
[final] ).
cnf(i_0_1199,plain,
( hAPP(esk68_4(X3,X4,X5,X1),X2) = hAPP(esk69_4(X3,X4,X5,X1),X2)
| c_Recdef_Oadm__wf(X1,X5,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk70_4(X3,X4,X5,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1200,plain,
( c_Fun_Oinj__on(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X7,X6),X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional__funcset(X1,X2,X4,c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X5,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_655]),
[final] ).
cnf(i_0_1201,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_1202,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X1)),c_FuncSet_Orestrict(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5)),c_FuncSet_OPi(X2,X1,X5,c_COMBK(tc_fun(X1,tc_HOL_Obool),X2,X4))))
| c_Set_Oimage(X1,X2,X3,X4) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1203,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk72_4(X3,X4,X2,X1))),c_Transitive__Closure_Otrancl(X1,X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1204,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk73_4(X3,X4,X2,X1))),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1205,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,esk12_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1206,plain,
( X1 = X2
| c_Fun_Ofun__upd(X3,X4,c_Fun_Ofun__upd(X3,X4,X5,X1,X6),X2,X7) = c_Fun_Ofun__upd(X3,X4,c_Fun_Ofun__upd(X3,X4,X5,X2,X7),X1,X6) ),
inference(split_conjunct,[status(thm)],[i_0_658]),
[final] ).
cnf(i_0_1207,plain,
( c_FuncSet_Orestrict(X1,X2,hAPP(c_COMBB(X2,X2,X1,c_FuncSet_Orestrict(X2,X2,c_COMBI(X2),X5)),X3),X4) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)))) ),
inference(rw,[status(thm)],[i_0_659,c_0_630]),
[final] ).
cnf(i_0_1208,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk60_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1209,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk65_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1210,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk61_4(X3,X4,X2,X1))),X3))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_1211,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk64_4(X3,X4,X2,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_646]),
[final] ).
cnf(i_0_1212,plain,
( hBOOL(hAPP(X1,esk57_5(X1,X2,X3,X4,X5)))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1213,plain,
( hBOOL(hAPP(X1,esk63_5(X1,X2,X3,X4,X5)))
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_616]),
[final] ).
cnf(i_0_1214,plain,
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_654]),
[final] ).
cnf(i_0_1215,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_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_660]),
[final] ).
cnf(i_0_1216,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)),X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),c_Set_Oimage(X1,X2,X3,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X6) ),
inference(split_conjunct,[status(thm)],[i_0_661]),
[final] ).
cnf(i_0_1217,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_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_662]),
[final] ).
cnf(i_0_1218,plain,
( c_Nitpick_Ofold__graph_H(X2,X7,X3,X6,X1,hAPP(hAPP(X3,X4),X5))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(X3,X4),X5) != X6 ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1219,plain,
( c_FuncSet_Orestrict(X1,X2,hAPP(c_COMBB(X1,X2,X1,X3),c_FuncSet_Orestrict(X1,X1,c_COMBI(X1),X4)),X4) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)))) ),
inference(rw,[status(thm)],[i_0_663,c_0_630]),
[final] ).
cnf(i_0_1220,plain,
c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1221,plain,
c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4),
inference(split_conjunct,[status(thm)],[i_0_665]),
[final] ).
cnf(i_0_1222,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool),X5,hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(X4,X1,X2,hAPP(hAPP(c_Set_Oinsert(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_666]),
[final] ).
cnf(i_0_1223,plain,
( hBOOL(hAPP(hAPP(c_member(X3),hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_667]),
[final] ).
cnf(i_0_1224,plain,
( c_Relation_Ototal__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk33_3(X2,X3,X1)),esk32_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1225,plain,
( c_Relation_Ototal__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk32_3(X2,X3,X1)),esk33_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1226,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_669]),
[final] ).
cnf(i_0_1227,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk29_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_670]),
[final] ).
cnf(i_0_1228,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk28_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_671]),
[final] ).
cnf(i_0_1229,plain,
( X5 = X6
| hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) != hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X6)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),c_Set_Oimage(X1,X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),c_Set_Oimage(X1,X2,X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_672]),
[final] ).
cnf(i_0_1230,plain,
( c_Recdef_Oadm__wf(X4,X3,X2,X1)
| hAPP(hAPP(X1,esk68_4(X1,X2,X3,X4)),esk70_4(X1,X2,X3,X4)) != hAPP(hAPP(X1,esk69_4(X1,X2,X3,X4)),esk70_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1231,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_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_660]),
[final] ).
cnf(i_0_1232,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_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_660]),
[final] ).
cnf(i_0_1233,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)),hAPP(hAPP(hAPP(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_660]),
[final] ).
cnf(i_0_1234,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)),hAPP(hAPP(hAPP(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_660]),
[final] ).
cnf(i_0_1235,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_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_662]),
[final] ).
cnf(i_0_1236,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_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_662]),
[final] ).
cnf(i_0_1237,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)),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_662]),
[final] ).
cnf(i_0_1238,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)),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_662]),
[final] ).
cnf(i_0_1239,plain,
( c_FuncSet_Orestrict(X2,X2,hAPP(c_COMBB(X1,X2,X2,X3),c_FuncSet_Orestrict(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5)),X5) = c_FuncSet_Orestrict(X2,X2,c_COMBI(X2),X5)
| c_Set_Oimage(X1,X2,X3,X4) != X5 ),
inference(rw,[status(thm)],[i_0_673,c_0_630]),
[final] ).
cnf(i_0_1240,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X6,X2)),hAPP(X6,X3))),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_Oinv__image(X4,X1,X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_674]),
[final] ).
cnf(i_0_1241,plain,
c_Fun_Ofun__upd(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4,X6) = c_Fun_Ofun__upd(X1,X2,X3,X4,X6),
inference(split_conjunct,[status(thm)],[i_0_675]),
[final] ).
cnf(i_0_1242,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X4)),c_Relation_Oinv__image(X1,X6,X5,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,X3)),hAPP(X2,X4))),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_674]),
[final] ).
cnf(i_0_1243,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_676]),
[final] ).
cnf(i_0_1244,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(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_Otrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_677]),
[final] ).
cnf(i_0_1245,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(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_678]),
[final] ).
cnf(i_0_1246,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_679]),
[final] ).
cnf(i_0_1247,plain,
( c_Set_Oimage(X1,X4,c_Fun_Ofun__upd(X1,X4,X5,X2,X6),X3) = hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Set_Oimage(X1,X4,X5,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_680]),
[final] ).
cnf(i_0_1248,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(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_Otrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_681]),
[final] ).
cnf(i_0_1249,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(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_682]),
[final] ).
cnf(i_0_1250,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(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_683]),
[final] ).
cnf(i_0_1251,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(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_684]),
[final] ).
cnf(i_0_1252,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_685]),
[final] ).
cnf(i_0_1253,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_686]),
[final] ).
cnf(i_0_1254,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(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)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_1255,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X5)),c_Set_Oimage(X1,X2,X3,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X4,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))))
| c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_666]),
[final] ).
cnf(i_0_1256,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X5),c_Set_Oimage(X1,X2,X3,X4)))
| c_Fun_Oinj__on(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X6,X5),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_1257,plain,
hAPP(c_Relation_OImage(X1,X2,X3),X4) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool),X4,hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1,c_Relation_OImage(X1,X2,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1258,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk84_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_690]),
[final] ).
cnf(i_0_1259,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)),hAPP(hAPP(hAPP(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_660]),
[final] ).
cnf(i_0_1260,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)),hAPP(hAPP(hAPP(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_660]),
[final] ).
cnf(i_0_1261,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)),hAPP(hAPP(hAPP(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_660]),
[final] ).
cnf(i_0_1262,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_691]),
[final] ).
cnf(i_0_1263,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_692]),
[final] ).
cnf(i_0_1264,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_Oconverse(X1,X1,c_Transitive__Closure_Otrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,c_Relation_Oconverse(X1,X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_693]),
[final] ).
cnf(i_0_1265,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk54_3(X3,X2,X1)),esk56_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_694]),
[final] ).
cnf(i_0_1266,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk54_3(X3,X2,X1)),esk55_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_694]),
[final] ).
cnf(i_0_1267,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk48_3(X3,X2,X1)),esk50_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_1268,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk48_3(X3,X2,X1)),esk49_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_1269,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,c_Relation_Oconverse(X1,X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_Oconverse(X1,X1,c_Transitive__Closure_Otrancl(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_696]),
[final] ).
cnf(i_0_1270,plain,
( X4 = X5
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X7),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X7)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_697]),
[final] ).
cnf(i_0_1271,plain,
( X5 = X6
| ~ 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(X1),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))
| ~ c_Equiv__Relations_Oequiv(X1,X7,X4) ),
inference(split_conjunct,[status(thm)],[i_0_698]),
[final] ).
cnf(i_0_1272,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_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_660]),
[final] ).
cnf(i_0_1273,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)),hAPP(hAPP(hAPP(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_660]),
[final] ).
cnf(i_0_1274,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)),hAPP(hAPP(hAPP(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_660]),
[final] ).
cnf(i_0_1275,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)),hAPP(hAPP(hAPP(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_660]),
[final] ).
cnf(i_0_1276,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_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_660]),
[final] ).
cnf(i_0_1277,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)),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_662]),
[final] ).
cnf(i_0_1278,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)),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_662]),
[final] ).
cnf(i_0_1279,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)),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_662]),
[final] ).
cnf(i_0_1280,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_699]),
[final] ).
cnf(i_0_1281,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk87_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_700]),
[final] ).
cnf(i_0_1282,plain,
( c_Set_Oimage(X1,X6,c_FuncSet_Orestrict(X1,X6,hAPP(c_COMBB(X2,X6,X1,X7),X3),X4),X4) = X8
| c_Set_Oimage(X2,X6,X7,X5) != X8
| c_Set_Oimage(X1,X2,X3,X4) != X5 ),
inference(rw,[status(thm)],[i_0_701,c_0_630]),
[final] ).
cnf(i_0_1283,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),esk10_1(X1)),esk11_1(X1))),hAPP(X1,esk8_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),esk10_1(X1)),esk11_1(X1))),hAPP(X1,esk9_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1284,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),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,c_Relation_Oconverse(X1,X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_1285,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)),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_662]),
[final] ).
cnf(i_0_1286,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)),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_662]),
[final] ).
cnf(i_0_1287,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)),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_662]),
[final] ).
cnf(i_0_1288,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)),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_662]),
[final] ).
cnf(i_0_1289,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_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_662]),
[final] ).
cnf(i_0_1290,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_703]),
[final] ).
cnf(i_0_1291,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_704]),
[final] ).
cnf(i_0_1292,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk87_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_700]),
[final] ).
cnf(i_0_1293,plain,
( ~ 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_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1294,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_1295,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_706]),
[final] ).
cnf(i_0_1296,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk88_4(X3,X2,X4,X1)),hAPP(X3,esk88_4(X3,X2,X4,X1)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1297,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_708]),
[final] ).
cnf(i_0_1298,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X3,X1,X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1299,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,c_Relation_Oconverse(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_710]),
[final] ).
cnf(i_0_1300,plain,
c_Set_Othe__elem(X1,X2) = c_HOL_OThe(X1,hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1,hAPP(c_fequal,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_1301,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_1302,plain,
( hAPP(X3,hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),c_Set_Oimage(X1,X2,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_713]),
[final] ).
cnf(i_0_1303,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_714]),
[final] ).
cnf(i_0_1304,plain,
( X1 = hAPP(c_Relation_OImage(X2,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),esk91_4(X3,X4,X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_1305,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_OImage(X1,X2,X5),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ 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_709]),
[final] ).
cnf(i_0_1306,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))
| ~ c_Equiv__Relations_Oequiv(X3,X7,X6) ),
inference(split_conjunct,[status(thm)],[i_0_698]),
[final] ).
cnf(i_0_1307,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Relation_Oconverse(X2,X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_716]),
[final] ).
cnf(i_0_1308,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Relation_Oconverse(X2,X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_1309,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Set_Oimage(X1,X4,c_Fun_Ofun__upd(X1,X4,X5,X2,X6),X3) = c_Set_Oimage(X1,X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_680]),
[final] ).
cnf(i_0_1310,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X3,X5)),c_Set_Oimage(X2,X1,X3,c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X4,X5))),
inference(split_conjunct,[status(thm)],[i_0_718]),
[final] ).
cnf(i_0_1311,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool),X4,X5)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X3,X5))),
inference(split_conjunct,[status(thm)],[i_0_719]),
[final] ).
cnf(i_0_1312,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),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(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_720]),
[final] ).
cnf(i_0_1313,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
| ~ c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_721]),
[final] ).
cnf(i_0_1314,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_720]),
[final] ).
cnf(i_0_1315,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk35_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_722]),
[final] ).
cnf(i_0_1316,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk34_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_723]),
[final] ).
cnf(i_0_1317,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk31_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_724]),
[final] ).
cnf(i_0_1318,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_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_660]),
[final] ).
cnf(i_0_1319,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),c_Relation_Oconverse(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_725]),
[final] ).
cnf(i_0_1320,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),c_Relation_Oconverse(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_717]),
[final] ).
cnf(i_0_1321,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),esk10_1(X1)),esk11_1(X1))),hAPP(esk9_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),esk10_1(X1)),esk11_1(X1))),hAPP(esk8_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1322,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X1)),esk11_1(X1))),hAPP(esk8_1(X1),X2)))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk10_1(X1)),esk11_1(X1))),hAPP(esk9_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1323,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,c_Relation_Oconverse(X2,X1,X3)),c_Relation_ODomain(X1,X2,c_Relation_Oconverse(X2,X1,X4))),c_Relation_ODomain(X1,X2,c_Relation_Oconverse(X2,X1,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3,X4)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_726,c_0_609]),c_0_609]),c_0_609]),
[final] ).
cnf(i_0_1324,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,c_Relation_Oconverse(X2,X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3,X4))),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,c_Relation_Oconverse(X2,X1,X3)),c_Relation_ODomain(X1,X2,c_Relation_Oconverse(X2,X1,X4)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_727,c_0_609]),c_0_609]),c_0_609]),
[final] ).
cnf(i_0_1325,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk91_4(X2,X3,X4,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_1326,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_721]),
[final] ).
cnf(i_0_1327,plain,
( X1 = X2
| 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(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Otrancl(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_728]),
[final] ).
cnf(i_0_1328,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
| X2 = X3
| ~ 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_729]),
[final] ).
cnf(i_0_1329,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
| X2 = X3
| ~ 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_728]),
[final] ).
cnf(i_0_1330,plain,
( 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),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_730]),
[final] ).
cnf(i_0_1331,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_731]),
[final] ).
cnf(i_0_1332,plain,
( hAPP(X4,hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_732]),
[final] ).
cnf(i_0_1333,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_691]),
[final] ).
cnf(i_0_1334,plain,
( hAPP(c_FuncSet_Orestrict(X1,X5,hAPP(c_COMBB(X4,X5,X1,X6),X7),X3),X2) = hAPP(X6,hAPP(X7,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_733,c_0_630]),
[final] ).
cnf(i_0_1335,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(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_734]),
[final] ).
cnf(i_0_1336,plain,
( hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ 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(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1337,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_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_662]),
[final] ).
cnf(i_0_1338,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk25_2(X2,X1)),esk25_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1339,plain,
c_Relation_ODomain(X2,X1,c_Relation_Oconverse(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))) = hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Relation_ODomain(X2,X1,c_Relation_Oconverse(X1,X2,X5))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_737,c_0_609]),c_0_609]),
[final] ).
cnf(i_0_1340,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk76_4(X2,X3,X4,X1)),X3))
| c_FuncSet_OPi(X1,X4,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X4),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_738]),
[final] ).
cnf(i_0_1341,plain,
hAPP(c_Relation_OImage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool),X5,X6)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool),X5,hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4,c_Relation_OImage(X1,X2,X3)),X6)),
inference(split_conjunct,[status(thm)],[i_0_739]),
[final] ).
cnf(i_0_1342,plain,
( X4 = X5
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X3))
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1343,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),c_FuncSet_Orestrict(X1,X2,X3,X4)),c_FuncSet_Oextensional(X1,X2,X4))),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_1344,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1345,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1346,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_742]),
[final] ).
cnf(i_0_1347,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_1348,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_744]),
[final] ).
cnf(i_0_1349,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_745]),
[final] ).
cnf(i_0_1350,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_746]),
[final] ).
cnf(i_0_1351,plain,
( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_745]),
[final] ).
cnf(i_0_1352,plain,
( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_746]),
[final] ).
cnf(i_0_1353,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional__funcset(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1354,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_731]),
[final] ).
cnf(i_0_1355,plain,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
inference(split_conjunct,[status(thm)],[i_0_748]),
[final] ).
cnf(i_0_1356,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_749]),
[final] ).
cnf(i_0_1357,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk19_4(X4,X1,X3,X2)),esk18_4(X4,X1,X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),c_Relation_Oconverse(X3,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_639]),
[final] ).
cnf(i_0_1358,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_Relation_OImage(X1,X4,X6),X3)))
| ~ 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)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_1359,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_Relation_OImage(X1,X4,X6),X3)))
| ~ 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)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_623]),
[final] ).
cnf(i_0_1360,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_751]),
[final] ).
cnf(i_0_1361,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_752]),
[final] ).
cnf(i_0_1362,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),c_Relation_ODomain(X2,X1,c_Relation_Oconverse(X1,X2,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_753,c_0_609]),
[final] ).
cnf(i_0_1363,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),c_Relation_ODomain(X2,X1,c_Relation_Oconverse(X1,X2,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_754,c_0_609]),
[final] ).
cnf(i_0_1364,plain,
( hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1365,plain,
( hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_755]),
[final] ).
cnf(i_0_1366,plain,
( X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omktop(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1367,plain,
( X1 = X2
| X2 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_751]),
[final] ).
cnf(i_0_1368,plain,
( X2 = X4
| X1 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omktop(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1369,plain,
( X1 = X4
| X2 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_751]),
[final] ).
cnf(i_0_1370,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk81_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1371,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk80_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1372,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_H____),v_b_H____)),hAPP(v_P_H____,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_757]),
[final] ).
cnf(i_0_1373,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_H____),v_b_H____)),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_757]),
[final] ).
cnf(i_0_1374,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ c_Equiv__Relations_Oequiv(X1,X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_758]),
[final] ).
cnf(i_0_1375,plain,
( hAPP(X3,X7) = hAPP(X6,X7)
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X3),X4),X5) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X6),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_607]),
[final] ).
cnf(i_0_1376,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Relation_Oconverse(X1,X1,X2),c_Transitive__Closure_Ortrancl(X1,X2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_759]),
[final] ).
cnf(i_0_1377,plain,
( c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X6)) = X6
| c_Set_Oimage(X1,X2,X3,X4) != X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X6,X5) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_1378,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),esk10_1(X1)),esk11_1(X1))),hAPP(X1,esk8_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),esk10_1(X1)),esk11_1(X1))),hAPP(X1,esk9_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1379,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_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_761]),
[final] ).
cnf(i_0_1380,plain,
( X1 = hAPP(X2,esk84_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_690]),
[final] ).
cnf(i_0_1381,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)),hAPP(hAPP(hAPP(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_660]),
[final] ).
cnf(i_0_1382,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_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_1383,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| c_Partial__Function_Oflat__lub(X1,X3,X2) = c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
inference(split_conjunct,[status(thm)],[i_0_763]),
[final] ).
cnf(i_0_1384,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| hAPP(X3,X6) = c_HOL_Oundefined(X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional__funcset(X1,X2,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_764]),
[final] ).
cnf(i_0_1385,plain,
( 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)))
| c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1386,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_765]),
[final] ).
cnf(i_0_1387,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_766]),
[final] ).
cnf(i_0_1388,plain,
( c_Set_Oimage(X1,X2,X3,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X5,X6)) = c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X5),c_Set_Oimage(X1,X2,X3,X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X5,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X6,X4) ),
inference(split_conjunct,[status(thm)],[i_0_767]),
[final] ).
cnf(i_0_1389,plain,
( c_Set_Oimage(X1,X2,X3,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X5,X6)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X5),c_Set_Oimage(X1,X2,X3,X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X5,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X6,X4) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[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_769]),
[final] ).
cnf(i_0_1391,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)),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_662]),
[final] ).
cnf(i_0_1392,plain,
( c_Set_Oimage(X2,X1,esk89_4(X5,X2,X1,X4),X5) = X4
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_770]),
[final] ).
cnf(i_0_1393,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_771]),
[final] ).
cnf(i_0_1394,plain,
( hAPP(X4,X5) = hAPP(X4,X6)
| ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_772]),
[final] ).
cnf(i_0_1395,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_773]),
[final] ).
cnf(i_0_1396,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_774]),
[final] ).
cnf(i_0_1397,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_775]),
[final] ).
cnf(i_0_1398,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_724]),
[final] ).
cnf(i_0_1399,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_776]),
[final] ).
cnf(i_0_1400,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_777]),
[final] ).
cnf(i_0_1401,plain,
c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X4,X1,X5,X6)) = c_Set_Oimage(X4,X2,hAPP(c_COMBB(X1,X2,X4,X3),X5),X6),
inference(split_conjunct,[status(thm)],[i_0_778]),
[final] ).
cnf(i_0_1402,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_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_779]),
[final] ).
cnf(i_0_1403,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk90_4(X3,X1,X2,X4),X4),X3)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X1,X2,X5,X3) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_770]),
[final] ).
cnf(i_0_1404,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1)),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_762]),
[final] ).
cnf(i_0_1405,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_671]),
[final] ).
cnf(i_0_1406,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_780]),
[final] ).
cnf(i_0_1407,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_781]),
[final] ).
cnf(i_0_1408,plain,
( hAPP(X3,X4) = X5
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_782]),
[final] ).
cnf(i_0_1409,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)),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1410,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),X4),X2)),X5))
| ~ c_Equiv__Relations_Oequiv(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1411,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_783]),
[final] ).
cnf(i_0_1412,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_784]),
[final] ).
cnf(i_0_1413,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_785]),
[final] ).
cnf(i_0_1414,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool)),X1,X6),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_786]),
[final] ).
cnf(i_0_1415,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool)),X6,X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_786]),
[final] ).
cnf(i_0_1416,plain,
( hBOOL(hAPP(hAPP(X3,X5),X6))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X3,X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1417,plain,
( hBOOL(hAPP(hAPP(X4,X5),X6))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X3,X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_1418,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),esk14_1(X1)),esk15_1(X1))),hAPP(X1,esk13_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1419,plain,
( X4 = X5
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X5) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_789]),
[final] ).
cnf(i_0_1420,plain,
( c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),c_Set_Oimage(X1,X2,X3,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_790]),
[final] ).
cnf(i_0_1421,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_791]),
[final] ).
cnf(i_0_1422,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Relation_OImage(X2,X1,X3),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool),X4,X5)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(c_Relation_OImage(X2,X1,X3),X4),hAPP(c_Relation_OImage(X2,X1,X3),X5))),
inference(split_conjunct,[status(thm)],[i_0_792]),
[final] ).
cnf(i_0_1423,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk71_2(X2,X1)),esk71_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_793]),
[final] ).
cnf(i_0_1424,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk66_2(X2,X1)),esk66_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_791]),
[final] ).
cnf(i_0_1425,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_785]),
[final] ).
cnf(i_0_1426,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk16_2(X2,X1)),esk16_2(X2,X1))),X2))
| c_Relation_Oirrefl(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_794]),
[final] ).
cnf(i_0_1427,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1428,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_795]),
[final] ).
cnf(i_0_1429,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_794]),
[final] ).
cnf(i_0_1430,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_796]),
[final] ).
cnf(i_0_1431,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_797]),
[final] ).
cnf(i_0_1432,plain,
( c_Fun_Oinj__on(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1433,plain,
( c_Set_Oimage(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),c_Set_Oimage(X1,X2,X3,X4)) = X4
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_799]),
[final] ).
cnf(i_0_1434,plain,
( c_Fun_Oinj__on(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),c_Set_Oimage(X1,X2,X3,X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_800]),
[final] ).
cnf(i_0_1435,plain,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X5) = hAPP(X5,X6)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_Equiv__Relations_Ocongruent(X1,tc_fun(X4,tc_HOL_Obool),X3,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_801]),
[final] ).
cnf(i_0_1436,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool),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_802]),
[final] ).
cnf(i_0_1437,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_749]),
[final] ).
cnf(i_0_1438,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_751]),
[final] ).
cnf(i_0_1439,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_752]),
[final] ).
cnf(i_0_1440,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_752]),
[final] ).
cnf(i_0_1441,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_751]),
[final] ).
cnf(i_0_1442,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_803]),
[final] ).
cnf(i_0_1443,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = c_HOL_Oundefined(X5) ),
inference(split_conjunct,[status(thm)],[i_0_775]),
[final] ).
cnf(i_0_1444,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_777]),
[final] ).
cnf(i_0_1445,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,c_FuncSet_Orestrict(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[i_0_804]),
[final] ).
cnf(i_0_1446,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))),esk3_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_769]),
[final] ).
cnf(i_0_1447,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool),X3,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1448,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool),X3,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_805]),
[final] ).
cnf(i_0_1449,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_806]),
[final] ).
cnf(i_0_1450,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_807]),
[final] ).
cnf(i_0_1451,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1452,plain,
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X6,tc_HOL_Obool)),X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_809]),
[final] ).
cnf(i_0_1453,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))),esk13_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1454,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))),esk9_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1455,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk8_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1456,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),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),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1457,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_810]),
[final] ).
cnf(i_0_1458,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_811]),
[final] ).
cnf(i_0_1459,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_690]),
[final] ).
cnf(i_0_1460,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_812]),
[final] ).
cnf(i_0_1461,plain,
c_FuncSet_Oextensional__funcset(X1,X2,X3,X4) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),c_FuncSet_OPi(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4)),c_FuncSet_Oextensional(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_813]),
[final] ).
cnf(i_0_1462,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_1463,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_1464,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_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(split_conjunct,[status(thm)],[fact__096Q_A_058_AProf_096]),
[final] ).
cnf(i_0_1465,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X1,X2,X4)),c_Relation_ODomain(X1,X2,c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4))),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1466,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X1,X2,X4))),
inference(split_conjunct,[status(thm)],[i_0_815]),
[final] ).
cnf(i_0_1467,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_785]),
[final] ).
cnf(i_0_1468,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_816]),
[final] ).
cnf(i_0_1469,plain,
( hAPP(X1,esk80_4(X2,X1,X3,X4)) = hAPP(X1,esk81_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1470,plain,
c_Relation_ODomain(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Relation_ODomain(X1,X2,X5)),
inference(split_conjunct,[status(thm)],[i_0_817]),
[final] ).
cnf(i_0_1471,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_818]),
[final] ).
cnf(i_0_1472,plain,
c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
inference(split_conjunct,[status(thm)],[i_0_819]),
[final] ).
cnf(i_0_1473,plain,
( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
| hAPP(X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_820]),
[final] ).
cnf(i_0_1474,plain,
( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
| hAPP(X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_782]),
[final] ).
cnf(i_0_1475,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_821]),
[final] ).
cnf(i_0_1476,plain,
( c_Fun_Oinj__on(X1,X2,X3,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_822]),
[final] ).
cnf(i_0_1477,plain,
( c_Fun_Oinj__on(X1,X2,esk90_4(X3,X2,X1,X4),X4)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Set_Oimage(X2,X1,X5,X3) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_770]),
[final] ).
cnf(i_0_1478,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_823]),
[final] ).
cnf(i_0_1479,plain,
( c_Fun_Oinj__on(X1,X2,c_FuncSet_Orestrict(X1,X2,X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_804]),
[final] ).
cnf(i_0_1480,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),esk14_1(X1)),esk15_1(X1))),hAPP(esk13_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1481,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk22_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_824]),
[final] ).
cnf(i_0_1482,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_825]),
[final] ).
cnf(i_0_1483,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)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_728]),
[final] ).
cnf(i_0_1484,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1485,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_826]),
[final] ).
cnf(i_0_1486,plain,
( hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_827]),
[final] ).
cnf(i_0_1487,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_1488,plain,
( hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X6) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(X3,X5) != X6
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1489,plain,
( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X6) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| hAPP(X3,X5) != X6 ),
inference(split_conjunct,[status(thm)],[i_0_830]),
[final] ).
cnf(i_0_1490,plain,
( hAPP(c_Relation_OImage(X2,X1,X3),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool),X4,X5)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(c_Relation_OImage(X2,X1,X3),X4),hAPP(c_Relation_OImage(X2,X1,X3),X5))
| ~ c_Relation_Osingle__valued(X1,X2,c_Relation_Oconverse(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1491,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_700]),
[final] ).
cnf(i_0_1492,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk35_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_722]),
[final] ).
cnf(i_0_1493,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk34_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_723]),
[final] ).
cnf(i_0_1494,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk31_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_724]),
[final] ).
cnf(i_0_1495,plain,
( c_FuncSet_Orestrict(X1,X2,X3,X4) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_832]),
[final] ).
cnf(i_0_1496,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_833]),
[final] ).
cnf(i_0_1497,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_834]),
[final] ).
cnf(i_0_1498,plain,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_835]),
[final] ).
cnf(i_0_1499,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_736]),
[final] ).
cnf(i_0_1500,plain,
( hAPP(X1,esk76_4(X1,X2,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| c_FuncSet_OPi(X4,X3,X2,X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,X3),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_738]),
[final] ).
cnf(i_0_1501,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk80_4(X1,X2,X3,X4) != esk81_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1502,plain,
( hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3)) = c_Set_Oimage(X1,X4,X5,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_836]),
[final] ).
cnf(i_0_1503,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk22_3(X3,X1,X2)),esk22_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_824]),
[final] ).
cnf(i_0_1504,plain,
c_Set_Oimage(X1,X2,c_FuncSet_Orestrict(X1,X2,X3,X4),X4) = c_Set_Oimage(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_837]),
[final] ).
cnf(i_0_1505,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| hAPP(X3,X5) = c_HOL_Oundefined(X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_838]),
[final] ).
cnf(i_0_1506,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_751]),
[final] ).
cnf(i_0_1507,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_752]),
[final] ).
cnf(i_0_1508,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),esk20_2(X2,X1)))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_839]),
[final] ).
cnf(i_0_1509,plain,
c_Set_Oimage(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X3,X4)),c_Set_Oimage(X1,X2,X3,X5)),
inference(split_conjunct,[status(thm)],[i_0_840]),
[final] ).
cnf(i_0_1510,plain,
c_Relation_Oconverse(X1,X1,c_Relation_Oinv__image(X2,X1,X3,X4)) = c_Relation_Oinv__image(X2,X1,c_Relation_Oconverse(X2,X2,X3),X4),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1511,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____))),
inference(split_conjunct,[status(thm)],[fact__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096]),
[final] ).
cnf(i_0_1512,plain,
( hBOOL(hAPP(hAPP(X3,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_842]),
[final] ).
cnf(i_0_1513,plain,
( hBOOL(hAPP(hAPP(X3,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_843]),
[final] ).
cnf(i_0_1514,plain,
( hBOOL(hAPP(hAPP(X3,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_844]),
[final] ).
cnf(i_0_1515,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),hAPP(c_Relation_OImage(X1,X2,X3),X5),hAPP(c_Relation_OImage(X1,X2,X4),X6))
| ~ 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_HOL_Obool),X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_845]),
[final] ).
cnf(i_0_1516,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_846]),
[final] ).
cnf(i_0_1517,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_847]),
[final] ).
cnf(i_0_1518,plain,
c_FuncSet_Oextensional__funcset(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X3) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,X2)),c_COMBK(X2,X1,c_HOL_Oundefined(X2))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_848]),
[final] ).
cnf(i_0_1519,plain,
c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4),
inference(split_conjunct,[status(thm)],[i_0_849]),
[final] ).
cnf(i_0_1520,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_850]),
[final] ).
cnf(i_0_1521,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_851]),
[final] ).
cnf(i_0_1522,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1523,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1524,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1525,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1526,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_853]),
[final] ).
cnf(i_0_1527,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_854]),
[final] ).
cnf(i_0_1528,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_855]),
[final] ).
cnf(i_0_1529,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_666]),
[final] ).
cnf(i_0_1530,plain,
( c_Fun_Oinj__on(X1,X2,X3,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X4,X5))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_856]),
[final] ).
cnf(i_0_1531,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_857]),
[final] ).
cnf(i_0_1532,plain,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),X5))
| ~ c_Fun_Oinj__on(X4,X6,X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_858]),
[final] ).
cnf(i_0_1533,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| hAPP(X3,X5) != hAPP(X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1534,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| hAPP(X3,X5) != hAPP(X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_859]),
[final] ).
cnf(i_0_1535,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(X3,X5) != hAPP(X3,X6)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_860]),
[final] ).
cnf(i_0_1536,plain,
( c_Fun_Oinj__on(X1,X2,X3,X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_861]),
[final] ).
cnf(i_0_1537,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_862]),
[final] ).
cnf(i_0_1538,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_853]),
[final] ).
cnf(i_0_1539,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_854]),
[final] ).
cnf(i_0_1540,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_1541,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_864]),
[final] ).
cnf(i_0_1542,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_865]),
[final] ).
cnf(i_0_1543,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_1544,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_865]),
[final] ).
cnf(i_0_1545,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_866]),
[final] ).
cnf(i_0_1546,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_1547,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_867]),
[final] ).
cnf(i_0_1548,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk20_2(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[i_0_839]),
[final] ).
cnf(i_0_1549,plain,
( hAPP(c_FuncSet_Orestrict(X1,X4,X5,X3),X2) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_868]),
[final] ).
cnf(i_0_1550,plain,
( hAPP(c_FuncSet_Orestrict(X1,X4,X5,X3),X2) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_869]),
[final] ).
cnf(i_0_1551,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_853]),
[final] ).
cnf(i_0_1552,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_870]),
[final] ).
cnf(i_0_1553,plain,
( hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,X2)),X3) = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Relation_OImage(X1,X1,X2),X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_871]),
[final] ).
cnf(i_0_1554,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_872]),
[final] ).
cnf(i_0_1555,plain,
c_FuncSet_Oextensional(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,X2)),c_COMBK(X2,X1,c_HOL_Oundefined(X2))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1556,plain,
c_Relation_Oconverse(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),c_Relation_Oconverse(X1,X2,X3),c_Relation_Oconverse(X1,X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_874]),
[final] ).
cnf(i_0_1557,plain,
c_Predicate_Oconversep(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_fun(X1,tc_HOL_Obool)),c_Predicate_Oconversep(X1,X2,X3),c_Predicate_Oconversep(X1,X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_875]),
[final] ).
cnf(i_0_1558,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_842]),
[final] ).
cnf(i_0_1559,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_843]),
[final] ).
cnf(i_0_1560,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_876]),
[final] ).
cnf(i_0_1561,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk78_3(X2,X3,X1)),X2))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_877]),
[final] ).
cnf(i_0_1562,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk77_3(X2,X3,X1)),X3))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_877]),
[final] ).
cnf(i_0_1563,plain,
( c_Relation_Orefl__on(X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X3,X5))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_878]),
[final] ).
cnf(i_0_1564,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,X5),c_Groups_Ominus__class_Ominus(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),X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_879]),
[final] ).
cnf(i_0_1565,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_880]),
[final] ).
cnf(i_0_1566,plain,
( c_Set_Oimage(X1,X4,c_COMBK(X4,X1,X5),X3) = hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_881]),
[final] ).
cnf(i_0_1567,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_FuncSet_Orestrict(X1,X4,X5,X3),X2) = c_HOL_Oundefined(X4) ),
inference(split_conjunct,[status(thm)],[i_0_868]),
[final] ).
cnf(i_0_1568,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_FuncSet_Orestrict(X1,X4,X5,X3),X2) = c_HOL_Oundefined(X4) ),
inference(split_conjunct,[status(thm)],[i_0_869]),
[final] ).
cnf(i_0_1569,plain,
c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_882]),
[final] ).
cnf(i_0_1570,plain,
c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X3)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X4),
inference(split_conjunct,[status(thm)],[i_0_883]),
[final] ).
cnf(i_0_1571,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,X3),X4) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_884]),
[final] ).
cnf(i_0_1572,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,X4)) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_885]),
[final] ).
cnf(i_0_1573,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_886]),
[final] ).
cnf(i_0_1574,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_1575,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk2_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_888]),
[final] ).
cnf(i_0_1576,plain,
( hBOOL(hAPP(hAPP(X1,esk37_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1577,plain,
( hBOOL(hAPP(hAPP(X1,esk36_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1578,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk33_3(X2,X3,X1)),X3))
| c_Relation_Ototal__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1579,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk32_3(X2,X3,X1)),X3))
| c_Relation_Ototal__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1580,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_891]),
[final] ).
cnf(i_0_1581,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| X2 = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_892]),
[final] ).
cnf(i_0_1582,plain,
( hBOOL(hAPP(hAPP(X3,esk27_2(X4,X3)),X4))
| ~ c_Predicate_ORangeP(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_893]),
[final] ).
cnf(i_0_1583,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_894]),
[final] ).
cnf(i_0_1584,plain,
( c_FuncSet_OPi(X1,X5,X3,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X5),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(X4,X2) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_738]),
[final] ).
cnf(i_0_1585,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool),X1,X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_895]),
[final] ).
cnf(i_0_1586,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool),X4,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_895]),
[final] ).
cnf(i_0_1587,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_896]),
[final] ).
cnf(i_0_1588,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1589,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_898]),
[final] ).
cnf(i_0_1590,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_899]),
[final] ).
cnf(i_0_1591,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1592,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_901]),
[final] ).
cnf(i_0_1593,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk37_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1594,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk36_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1595,plain,
( hAPP(hAPP(c_Set_Oinsert(X5),X1),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X5),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1596,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_850]),
[final] ).
cnf(i_0_1597,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
| X4 != X5 ),
inference(split_conjunct,[status(thm)],[i_0_877]),
[final] ).
cnf(i_0_1598,plain,
c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_902]),
[final] ).
cnf(i_0_1599,plain,
( c_Partial__Function_Oflat__lub(X1,X3,X2) = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_763]),
[final] ).
cnf(i_0_1600,plain,
c_Relation_ODomain(X2,X1,c_Relation_Oconverse(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(rw,[status(thm)],[i_0_903,c_0_609]),
[final] ).
cnf(i_0_1601,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_904]),
[final] ).
cnf(i_0_1602,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X3 ),
inference(split_conjunct,[status(thm)],[i_0_905]),
[final] ).
cnf(i_0_1603,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_906]),
[final] ).
cnf(i_0_1604,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X2,X3,c_COMBK(X3,X2,X4),X1) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_907]),
[final] ).
cnf(i_0_1605,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1606,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_909]),
[final] ).
cnf(i_0_1607,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_886]),
[final] ).
cnf(i_0_1608,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1609,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_911]),
[final] ).
cnf(i_0_1610,plain,
( c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X4,X2)) = X2
| ~ 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_912]),
[final] ).
cnf(i_0_1611,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1612,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1613,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4)
| hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1614,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1615,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_916]),
[final] ).
cnf(i_0_1616,plain,
c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X4) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_917]),
[final] ).
cnf(i_0_1617,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X4) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_918]),
[final] ).
cnf(i_0_1618,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_919]),
[final] ).
cnf(i_0_1619,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Set_Oimage(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_920]),
[final] ).
cnf(i_0_1620,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_921]),
[final] ).
cnf(i_0_1621,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4),c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X5))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_922]),
[final] ).
cnf(i_0_1622,plain,
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool),X1,X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_923]),
[final] ).
cnf(i_0_1623,plain,
c_Relation_ODomain(X2,X1,c_Relation_Oconverse(X1,X2,c_Relation_Oconverse(X2,X1,X3))) = c_Relation_ODomain(X2,X1,X3),
inference(rw,[status(thm)],[i_0_924,c_0_609]),
[final] ).
cnf(i_0_1624,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_925]),
[final] ).
cnf(i_0_1625,plain,
( c_Set_Oimage(X2,X3,c_COMBK(X3,X2,X4),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_907]),
[final] ).
cnf(i_0_1626,plain,
( c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X4,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_906]),
[final] ).
cnf(i_0_1627,plain,
( c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X4,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_926]),
[final] ).
cnf(i_0_1628,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_916]),
[final] ).
cnf(i_0_1629,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_927]),
[final] ).
cnf(i_0_1630,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_928]),
[final] ).
cnf(i_0_1631,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1632,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))
| hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1633,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_FuncSet_Oextensional__funcset(X2,X3,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,X3),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_929]),
[final] ).
cnf(i_0_1634,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1635,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_931]),
[final] ).
cnf(i_0_1636,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_932]),
[final] ).
cnf(i_0_1637,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_933]),
[final] ).
cnf(i_0_1638,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_934]),
[final] ).
cnf(i_0_1639,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_935]),
[final] ).
cnf(i_0_1640,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1641,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_936]),
[final] ).
cnf(i_0_1642,plain,
( X3 = X4
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_937]),
[final] ).
cnf(i_0_1643,plain,
( c_Predicate_ODomainP(X4,X5,X1,X2)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1644,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_893]),
[final] ).
cnf(i_0_1645,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_939]),
[final] ).
cnf(i_0_1646,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))
| c_Relation_ODomain(X2,X1,c_Relation_Oconverse(X1,X2,X3)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[i_0_940,c_0_609]),
[final] ).
cnf(i_0_1647,plain,
c_Relation_ODomain(X1,X1,c_Relation_Oconverse(X1,X1,c_Transitive__Closure_Otrancl(X1,X2))) = c_Relation_ODomain(X1,X1,c_Relation_Oconverse(X1,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_941,c_0_609]),c_0_609]),
[final] ).
cnf(i_0_1648,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_898]),
[final] ).
cnf(i_0_1649,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_942]),
[final] ).
cnf(i_0_1650,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1651,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_943]),
[final] ).
cnf(i_0_1652,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_Set_Oinsert(X1),X4),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1653,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_944]),
[final] ).
cnf(i_0_1654,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1655,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1656,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1657,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_889]),
[final] ).
cnf(i_0_1658,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_890]),
[final] ).
cnf(i_0_1659,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_948]),
[final] ).
cnf(i_0_1660,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_949]),
[final] ).
cnf(i_0_1661,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_950]),
[final] ).
cnf(i_0_1662,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_951]),
[final] ).
cnf(i_0_1663,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X4) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_952]),
[final] ).
cnf(i_0_1664,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X4) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_953]),
[final] ).
cnf(i_0_1665,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X4) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1666,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_1667,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1668,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_1669,plain,
( X2 = X3
| hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_958]),
[final] ).
cnf(i_0_1670,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_959]),
[final] ).
cnf(i_0_1671,plain,
c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_960]),
[final] ).
cnf(i_0_1672,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_961]),
[final] ).
cnf(i_0_1673,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_962]),
[final] ).
cnf(i_0_1674,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X4,X5) != c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_962]),
[final] ).
cnf(i_0_1675,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = c_Set_Oimage(X2,X3,X4,X1)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_920]),
[final] ).
cnf(i_0_1676,plain,
( c_Set_Oimage(X2,X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_921]),
[final] ).
cnf(i_0_1677,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1678,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1679,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X4,X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1680,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X4,X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1681,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_886]),
[final] ).
cnf(i_0_1682,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1683,plain,
( c_Relation_ODomain(X3,X2,c_Relation_Oconverse(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)) ),
inference(rw,[status(thm)],[i_0_964,c_0_609]),
[final] ).
cnf(i_0_1684,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
inference(split_conjunct,[status(thm)],[i_0_965]),
[final] ).
cnf(i_0_1685,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,X2,c_Relation_Oconverse(X1,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_1686,plain,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,X2,c_Relation_Oconverse(X1,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_967]),
[final] ).
cnf(i_0_1687,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_968]),
[final] ).
cnf(i_0_1688,plain,
c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,X3),X3) = c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,X3),
inference(split_conjunct,[status(thm)],[i_0_969]),
[final] ).
cnf(i_0_1689,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),
inference(split_conjunct,[status(thm)],[i_0_970]),
[final] ).
cnf(i_0_1690,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_971]),
[final] ).
cnf(i_0_1691,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_972]),
[final] ).
cnf(i_0_1692,plain,
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1),X3,X4),X5) = c_Groups_Ominus__class_Ominus(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_973]),
[final] ).
cnf(i_0_1693,plain,
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1),X3,X4),X5) = c_Groups_Ominus__class_Ominus(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_974]),
[final] ).
cnf(i_0_1694,plain,
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1),X3,X4),X5) = c_Lattices_Osemilattice__inf__class_Oinf(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_975]),
[final] ).
cnf(i_0_1695,plain,
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1),X3,X4),X5) = c_Lattices_Osemilattice__inf__class_Oinf(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_976]),
[final] ).
cnf(i_0_1696,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_931]),
[final] ).
cnf(i_0_1697,plain,
c_Relation_Orefl__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_977]),
[final] ).
cnf(i_0_1698,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X3,X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_978]),
[final] ).
cnf(i_0_1699,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X3)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_979]),
[final] ).
cnf(i_0_1700,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4),X3)
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_980]),
[final] ).
cnf(i_0_1701,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X4,X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_981]),
[final] ).
cnf(i_0_1702,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1703,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1704,plain,
hAPP(c_Relation_OImage(X1,X1,c_Relation_OId__on(X1,X2)),X3) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),
inference(split_conjunct,[status(thm)],[i_0_984]),
[final] ).
cnf(i_0_1705,plain,
c_Transitive__Closure_Otrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_985]),
[final] ).
cnf(i_0_1706,plain,
( c_Relation_Orefl__on(X1,X2,c_Relation_Oconverse(X1,X1,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_1707,plain,
( c_Relation_Ototal__on(X1,X2,c_Relation_Oconverse(X1,X1,X3))
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_967]),
[final] ).
cnf(i_0_1708,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_986]),
[final] ).
cnf(i_0_1709,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_987]),
[final] ).
cnf(i_0_1710,plain,
( c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,X3) = X2
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1711,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1712,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_990]),
[final] ).
cnf(i_0_1713,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_991]),
[final] ).
cnf(i_0_1714,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_707]),
[final] ).
cnf(i_0_1715,plain,
( c_Wellfounded_Oacyclic(X1,X3)
| ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_992]),
[final] ).
cnf(i_0_1716,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X2),esk75_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_993]),
[final] ).
cnf(i_0_1717,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk74_2(X2,X1)),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_994]),
[final] ).
cnf(i_0_1718,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_931]),
[final] ).
cnf(i_0_1719,plain,
c_Relation_ODomain(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_995]),
[final] ).
cnf(i_0_1720,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_996]),
[final] ).
cnf(i_0_1721,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_997]),
[final] ).
cnf(i_0_1722,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1723,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_1724,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1000]),
[final] ).
cnf(i_0_1725,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X3),
inference(split_conjunct,[status(thm)],[i_0_1001]),
[final] ).
cnf(i_0_1726,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1002]),
[final] ).
cnf(i_0_1727,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk55_3(X1,X2,X3) != esk56_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_694]),
[final] ).
cnf(i_0_1728,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk49_3(X1,X2,X3) != esk50_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_1729,plain,
( c_Relation_Ototal__on(X3,X2,X1)
| esk32_3(X1,X2,X3) != esk33_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1730,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_1731,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_1004]),
[final] ).
cnf(i_0_1732,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1005]),
[final] ).
cnf(i_0_1733,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1006]),
[final] ).
cnf(i_0_1734,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1007]),
[final] ).
cnf(i_0_1735,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1008]),
[final] ).
cnf(i_0_1736,plain,
c_Set_Othe__elem(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X2,
inference(split_conjunct,[status(thm)],[i_0_1009]),
[final] ).
cnf(i_0_1737,plain,
c_Relation_ODomain(X1,X1,c_Relation_Oconverse(X1,X1,c_Relation_OId__on(X1,X2))) = X2,
inference(rw,[status(thm)],[i_0_1010,c_0_609]),
[final] ).
cnf(i_0_1738,plain,
( esk77_3(X1,X2,X3) = esk78_3(X1,X2,X3)
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_877]),
[final] ).
cnf(i_0_1739,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1011]),
[final] ).
cnf(i_0_1740,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_994]),
[final] ).
cnf(i_0_1741,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_993]),
[final] ).
cnf(i_0_1742,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))
| c_Relation_ODomain(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_1012]),
[final] ).
cnf(i_0_1743,plain,
( c_Relation_ODomain(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_1012]),
[final] ).
cnf(i_0_1744,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1013]),
[final] ).
cnf(i_0_1745,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(X1,c_Relation_Oconverse(X1,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1014]),
[final] ).
cnf(i_0_1746,plain,
c_Transitive__Closure_Otrancl(X1,c_Relation_Oconverse(X1,X1,X2)) = c_Relation_Oconverse(X1,X1,c_Transitive__Closure_Otrancl(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1015]),
[final] ).
cnf(i_0_1747,plain,
c_Transitive__Closure_Ortrancl(X1,c_Relation_Oconverse(X1,X1,X2)) = c_Relation_Oconverse(X1,X1,c_Transitive__Closure_Ortrancl(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1016]),
[final] ).
cnf(i_0_1748,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1017]),
[final] ).
cnf(i_0_1749,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X2) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1750,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_1019]),
[final] ).
cnf(i_0_1751,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_1020]),
[final] ).
cnf(i_0_1752,plain,
hAPP(c_Relation_OImage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1021]),
[final] ).
cnf(i_0_1753,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1022]),
[final] ).
cnf(i_0_1754,plain,
( X3 = X4
| X1 != X2
| c_Groups_Ominus__class_Ominus(X5,X1,X2) != c_Groups_Ominus__class_Ominus(X5,X3,X4)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_1023]),
[final] ).
cnf(i_0_1755,plain,
( X3 = X4
| X1 != X2
| c_Groups_Ominus__class_Ominus(X5,X3,X4) != c_Groups_Ominus__class_Ominus(X5,X1,X2)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_1023]),
[final] ).
cnf(i_0_1756,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_1024]),
[final] ).
cnf(i_0_1757,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_1025]),
[final] ).
cnf(i_0_1758,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_1026]),
[final] ).
cnf(i_0_1759,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_1027]),
[final] ).
cnf(i_0_1760,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)),
inference(split_conjunct,[status(thm)],[i_0_1028]),
[final] ).
cnf(i_0_1761,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1762,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X1),X3)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_1763,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X1),X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_1004]),
[final] ).
cnf(i_0_1764,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1029]),
[final] ).
cnf(i_0_1765,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1766,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1031]),
[final] ).
cnf(i_0_1767,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1768,plain,
c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_1033]),
[final] ).
cnf(i_0_1769,plain,
c_Relation_Oconverse(X1,X2,c_Relation_Oconverse(X2,X1,X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_1034]),
[final] ).
cnf(i_0_1770,plain,
c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1035]),
[final] ).
cnf(i_0_1771,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1772,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1773,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1774,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X2),
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1775,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1022]),
[final] ).
cnf(i_0_1776,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) != X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1777,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1778,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = X2
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1779,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1780,plain,
c_Relation_OId__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1781,plain,
( c_Wellfounded_Oacyclic(X1,c_Relation_Oconverse(X1,X1,X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1014]),
[final] ).
cnf(i_0_1782,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk3_2(X2,X1)) != hAPP(esk3_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_769]),
[final] ).
cnf(i_0_1783,plain,
c_Relation_ODomain(X1,X1,c_Transitive__Closure_Otrancl(X1,X2)) = c_Relation_ODomain(X1,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1784,plain,
c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X2,
inference(split_conjunct,[status(thm)],[i_0_1044]),
[final] ).
cnf(i_0_1785,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2),
inference(split_conjunct,[status(thm)],[i_0_1045]),
[final] ).
cnf(i_0_1786,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1787,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1788,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1789,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1790,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1791,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1792,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_1052]),
[final] ).
cnf(i_0_1793,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_1053]),
[final] ).
cnf(i_0_1794,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_1054]),
[final] ).
cnf(i_0_1795,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1055]),
[final] ).
cnf(i_0_1796,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1056]),
[final] ).
cnf(i_0_1797,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1057]),
[final] ).
cnf(i_0_1798,plain,
c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2),
inference(split_conjunct,[status(thm)],[i_0_1058]),
[final] ).
cnf(i_0_1799,plain,
c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X2,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1059]),
[final] ).
cnf(i_0_1800,plain,
c_Relation_Oconverse(X1,X1,c_Relation_OId__on(X1,X2)) = c_Relation_OId__on(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1060]),
[final] ).
cnf(i_0_1801,plain,
( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1061]),
[final] ).
cnf(i_0_1802,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1062]),
[final] ).
cnf(i_0_1803,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1063]),
[final] ).
cnf(i_0_1804,plain,
c_Relation_ODomain(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1064]),
[final] ).
cnf(i_0_1805,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_986]),
[final] ).
cnf(i_0_1806,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_986]),
[final] ).
cnf(i_0_1807,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1065]),
[final] ).
cnf(i_0_1808,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1065]),
[final] ).
cnf(i_0_1809,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1066]),
[final] ).
cnf(i_0_1810,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1067]),
[final] ).
cnf(i_0_1811,plain,
c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1068]),
[final] ).
cnf(i_0_1812,plain,
c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1069]),
[final] ).
cnf(i_0_1813,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1070]),
[final] ).
cnf(i_0_1814,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1071]),
[final] ).
cnf(i_0_1815,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(split_conjunct,[status(thm)],[i_0_1072]),
[final] ).
cnf(i_0_1816,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,c_Orderings_Obot__class_Obot(X1),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1073]),
[final] ).
cnf(i_0_1817,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1074]),
[final] ).
cnf(i_0_1818,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Obot__class_Obot(X1),X2)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1075]),
[final] ).
cnf(i_0_1819,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1024]),
[final] ).
cnf(i_0_1820,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1024]),
[final] ).
cnf(i_0_1821,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1076]),
[final] ).
cnf(i_0_1822,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1077]),
[final] ).
cnf(i_0_1823,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1078]),
[final] ).
cnf(i_0_1824,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1079]),
[final] ).
cnf(i_0_1825,plain,
c_Transitive__Closure_Otrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1080]),
[final] ).
cnf(i_0_1826,plain,
c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1081]),
[final] ).
cnf(i_0_1827,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_1082]),
[final] ).
cnf(i_0_1828,plain,
c_Predicate_Oconversep(X1,X1,c_fequal) = c_fequal,
inference(split_conjunct,[status(thm)],[i_0_1083]),
[final] ).
cnf(i_0_1829,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1084]),
[final] ).
cnf(i_0_1830,plain,
c_HOL_OThe(X1,hAPP(c_fequal,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1085]),
[final] ).
cnf(i_0_1831,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1086]),
[final] ).
cnf(i_0_1832,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1087]),
[final] ).
cnf(i_0_1833,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1088]),
[final] ).
cnf(i_0_1834,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1089]),
[final] ).
cnf(i_0_1835,plain,
( class_Groups_Ominus(tc_fun(X2,X1))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1090]),
[final] ).
cnf(i_0_1836,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1091]),
[final] ).
cnf(i_0_1837,plain,
( class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1092]),
[final] ).
cnf(i_0_1838,plain,
( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1093]),
[final] ).
cnf(i_0_1839,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1094]),
[final] ).
cnf(i_0_1840,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1095]),
[final] ).
cnf(i_0_1841,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1096]),
[final] ).
cnf(i_0_1842,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]),
[final] ).
cnf(i_0_1843,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1844,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1845,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1846,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
[final] ).
cnf(i_0_1847,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]),
[final] ).
cnf(i_0_1848,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]),
[final] ).
cnf(i_0_1849,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_1850,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
[final] ).
cnf(i_0_1851,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1852,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1853,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact_d1_I1_J]),
[final] ).
cnf(i_0_1854,plain,
v_a____ != v_b_H____,
inference(split_conjunct,[status(thm)],[fact_d2_I1_J]),
[final] ).
cnf(i_0_1855,plain,
v_b____ != v_a_H____,
inference(split_conjunct,[status(thm)],[fact_d2_I2_J]),
[final] ).
cnf(i_0_1856,plain,
v_a_H____ != v_b_H____,
inference(split_conjunct,[status(thm)],[fact_d1_I2_J]),
[final] ).
cnf(i_0_1857,axiom,
X1 = X1 ).
cnf(i_0_1858,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1859,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1860,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1861,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1862,axiom,
( X1 != X2
| c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).
cnf(i_0_1863,axiom,
( X1 != X2
| c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).
cnf(i_0_1864,axiom,
( X1 != X2
| esk81_4(X1,X3,X4,X5) = esk81_4(X2,X3,X4,X5) ) ).
cnf(i_0_1865,axiom,
( X1 != X2
| esk81_4(X3,X1,X4,X5) = esk81_4(X3,X2,X4,X5) ) ).
cnf(i_0_1866,axiom,
( X1 != X2
| esk81_4(X3,X4,X1,X5) = esk81_4(X3,X4,X2,X5) ) ).
cnf(i_0_1867,axiom,
( X1 != X2
| esk81_4(X3,X4,X5,X1) = esk81_4(X3,X4,X5,X2) ) ).
cnf(i_0_1868,axiom,
( X1 != X2
| esk80_4(X1,X3,X4,X5) = esk80_4(X2,X3,X4,X5) ) ).
cnf(i_0_1869,axiom,
( X1 != X2
| esk80_4(X3,X1,X4,X5) = esk80_4(X3,X2,X4,X5) ) ).
cnf(i_0_1870,axiom,
( X1 != X2
| esk80_4(X3,X4,X1,X5) = esk80_4(X3,X4,X2,X5) ) ).
cnf(i_0_1871,axiom,
( X1 != X2
| esk80_4(X3,X4,X5,X1) = esk80_4(X3,X4,X5,X2) ) ).
cnf(i_0_1872,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).
cnf(i_0_1873,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).
cnf(i_0_1874,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| esk78_3(X1,X3,X4) = esk78_3(X2,X3,X4) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| esk78_3(X3,X1,X4) = esk78_3(X3,X2,X4) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| esk78_3(X3,X4,X1) = esk78_3(X3,X4,X2) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| esk77_3(X1,X3,X4) = esk77_3(X2,X3,X4) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| esk77_3(X3,X1,X4) = esk77_3(X3,X2,X4) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| esk77_3(X3,X4,X1) = esk77_3(X3,X4,X2) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4) = c_Lattices_Osemilattice__inf__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X3,X1,X4) = c_Lattices_Osemilattice__inf__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X3,X4,X1) = c_Lattices_Osemilattice__inf__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| c_Relation_Oconverse(X1,X3,X4) = c_Relation_Oconverse(X2,X3,X4) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X1,X4) = c_Relation_Oconverse(X3,X2,X4) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X4,X1) = c_Relation_Oconverse(X3,X4,X2) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| c_HOL_Oundefined(X1) = c_HOL_Oundefined(X2) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X1,X3,X4,X5) = c_FuncSet_Oextensional__funcset(X2,X3,X4,X5) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X1,X4,X5) = c_FuncSet_Oextensional__funcset(X3,X2,X4,X5) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X1,X5) = c_FuncSet_Oextensional__funcset(X3,X4,X2,X5) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X5,X1) = c_FuncSet_Oextensional__funcset(X3,X4,X5,X2) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1913,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X1,X3,X4,X5) = c_FuncSet_Orestrict(X2,X3,X4,X5) ) ).
cnf(i_0_1914,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X1,X4,X5) = c_FuncSet_Orestrict(X3,X2,X4,X5) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X1,X5) = c_FuncSet_Orestrict(X3,X4,X2,X5) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X5,X1) = c_FuncSet_Orestrict(X3,X4,X5,X2) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,X5) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X2,X4,X5) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X2,X5) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,X2) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| c_HOL_OLet(X1,X3,X4,X5) = c_HOL_OLet(X2,X3,X4,X5) ) ).
cnf(i_0_1922,axiom,
( X1 != X2
| c_HOL_OLet(X3,X1,X4,X5) = c_HOL_OLet(X3,X2,X4,X5) ) ).
cnf(i_0_1923,axiom,
( X1 != X2
| c_HOL_OLet(X3,X4,X1,X5) = c_HOL_OLet(X3,X4,X2,X5) ) ).
cnf(i_0_1924,axiom,
( X1 != X2
| c_HOL_OLet(X3,X4,X5,X1) = c_HOL_OLet(X3,X4,X5,X2) ) ).
cnf(i_0_1925,axiom,
( X1 != X2
| c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).
cnf(i_0_1926,axiom,
( X1 != X2
| c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).
cnf(i_0_1927,axiom,
( X1 != X2
| esk5_2(X1,X3) = esk5_2(X2,X3) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| esk5_2(X3,X1) = esk5_2(X3,X2) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| esk6_2(X1,X3) = esk6_2(X2,X3) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| esk6_2(X3,X1) = esk6_2(X3,X2) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| c_Transitive__Closure_Otrancl(X1,X3) = c_Transitive__Closure_Otrancl(X2,X3) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| c_Transitive__Closure_Otrancl(X3,X1) = c_Transitive__Closure_Otrancl(X3,X2) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X1,X3,X4) = c_FuncSet_Oextensional(X2,X3,X4) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X3,X1,X4) = c_FuncSet_Oextensional(X3,X2,X4) ) ).
cnf(i_0_1935,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X3,X4,X1) = c_FuncSet_Oextensional(X3,X4,X2) ) ).
cnf(i_0_1936,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1937,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1938,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1939,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1940,axiom,
( X1 != X2
| esk33_3(X1,X3,X4) = esk33_3(X2,X3,X4) ) ).
cnf(i_0_1941,axiom,
( X1 != X2
| esk33_3(X3,X1,X4) = esk33_3(X3,X2,X4) ) ).
cnf(i_0_1942,axiom,
( X1 != X2
| esk33_3(X3,X4,X1) = esk33_3(X3,X4,X2) ) ).
cnf(i_0_1943,axiom,
( X1 != X2
| esk32_3(X1,X3,X4) = esk32_3(X2,X3,X4) ) ).
cnf(i_0_1944,axiom,
( X1 != X2
| esk32_3(X3,X1,X4) = esk32_3(X3,X2,X4) ) ).
cnf(i_0_1945,axiom,
( X1 != X2
| esk32_3(X3,X4,X1) = esk32_3(X3,X4,X2) ) ).
cnf(i_0_1946,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_1947,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_1948,axiom,
( X1 != X2
| c_Relation_Oinv__image(X1,X3,X4,X5) = c_Relation_Oinv__image(X2,X3,X4,X5) ) ).
cnf(i_0_1949,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X1,X4,X5) = c_Relation_Oinv__image(X3,X2,X4,X5) ) ).
cnf(i_0_1950,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X1,X5) = c_Relation_Oinv__image(X3,X4,X2,X5) ) ).
cnf(i_0_1951,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X5,X1) = c_Relation_Oinv__image(X3,X4,X5,X2) ) ).
cnf(i_0_1952,axiom,
( X1 != X2
| esk56_3(X1,X3,X4) = esk56_3(X2,X3,X4) ) ).
cnf(i_0_1953,axiom,
( X1 != X2
| esk56_3(X3,X1,X4) = esk56_3(X3,X2,X4) ) ).
cnf(i_0_1954,axiom,
( X1 != X2
| esk56_3(X3,X4,X1) = esk56_3(X3,X4,X2) ) ).
cnf(i_0_1955,axiom,
( X1 != X2
| esk55_3(X1,X3,X4) = esk55_3(X2,X3,X4) ) ).
cnf(i_0_1956,axiom,
( X1 != X2
| esk55_3(X3,X1,X4) = esk55_3(X3,X2,X4) ) ).
cnf(i_0_1957,axiom,
( X1 != X2
| esk55_3(X3,X4,X1) = esk55_3(X3,X4,X2) ) ).
cnf(i_0_1958,axiom,
( X1 != X2
| esk50_3(X1,X3,X4) = esk50_3(X2,X3,X4) ) ).
cnf(i_0_1959,axiom,
( X1 != X2
| esk50_3(X3,X1,X4) = esk50_3(X3,X2,X4) ) ).
cnf(i_0_1960,axiom,
( X1 != X2
| esk50_3(X3,X4,X1) = esk50_3(X3,X4,X2) ) ).
cnf(i_0_1961,axiom,
( X1 != X2
| esk49_3(X1,X3,X4) = esk49_3(X2,X3,X4) ) ).
cnf(i_0_1962,axiom,
( X1 != X2
| esk49_3(X3,X1,X4) = esk49_3(X3,X2,X4) ) ).
cnf(i_0_1963,axiom,
( X1 != X2
| esk49_3(X3,X4,X1) = esk49_3(X3,X4,X2) ) ).
cnf(i_0_1964,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1965,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_1966,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_1967,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_1968,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1969,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_1970,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_1971,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_1972,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_1973,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_1974,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_1975,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_1976,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_1977,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1978,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1979,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1980,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1981,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1982,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1983,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1984,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1985,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_1986,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_1987,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_1988,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_1989,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_1990,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_1991,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_1992,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X1,X3,X4,X5)
| c_Recdef_Oadm__wf(X2,X3,X4,X5) ) ).
cnf(i_0_1993,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X1,X4,X5)
| c_Recdef_Oadm__wf(X3,X2,X4,X5) ) ).
cnf(i_0_1994,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X1,X5)
| c_Recdef_Oadm__wf(X3,X4,X2,X5) ) ).
cnf(i_0_1995,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X5,X1)
| c_Recdef_Oadm__wf(X3,X4,X5,X2) ) ).
cnf(i_0_1996,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_1997,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_1998,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_1999,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_2000,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_2001,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_2002,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2003,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2004,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_2005,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2006,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_2007,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_2008,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X1,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_2009,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X1,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_2010,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X1,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_2011,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X1,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_2012,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X1)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_2013,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__bot(X1)
| class_Lattices_Obounded__lattice__bot(X2) ) ).
cnf(i_0_2014,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_2015,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_2016,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_2017,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_2018,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X1,X3,X4,X5)
| c_Predicate_ORangeP(X2,X3,X4,X5) ) ).
cnf(i_0_2019,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X1,X4,X5)
| c_Predicate_ORangeP(X3,X2,X4,X5) ) ).
cnf(i_0_2020,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X1,X5)
| c_Predicate_ORangeP(X3,X4,X2,X5) ) ).
cnf(i_0_2021,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X5,X1)
| c_Predicate_ORangeP(X3,X4,X5,X2) ) ).
cnf(i_0_2022,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X1,X3,X4,X5)
| c_Predicate_ODomainP(X2,X3,X4,X5) ) ).
cnf(i_0_2023,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X1,X4,X5)
| c_Predicate_ODomainP(X3,X2,X4,X5) ) ).
cnf(i_0_2024,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X1,X5)
| c_Predicate_ODomainP(X3,X4,X2,X5) ) ).
cnf(i_0_2025,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X5,X1)
| c_Predicate_ODomainP(X3,X4,X5,X2) ) ).
cnf(i_0_2026,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_2027,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_2028,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_2029,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_2030,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_2031,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_2032,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1857_001,axiom,
X1 = X1 ).
cnf(i_0_1858_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1859_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1860_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1861_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1862_006,axiom,
( X1 != X2
| c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).
cnf(i_0_1863_007,axiom,
( X1 != X2
| c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).
cnf(i_0_1864_008,axiom,
( X1 != X2
| esk81_4(X1,X3,X4,X5) = esk81_4(X2,X3,X4,X5) ) ).
cnf(i_0_1865_009,axiom,
( X1 != X2
| esk81_4(X3,X1,X4,X5) = esk81_4(X3,X2,X4,X5) ) ).
cnf(i_0_1866_010,axiom,
( X1 != X2
| esk81_4(X3,X4,X1,X5) = esk81_4(X3,X4,X2,X5) ) ).
cnf(i_0_1867_011,axiom,
( X1 != X2
| esk81_4(X3,X4,X5,X1) = esk81_4(X3,X4,X5,X2) ) ).
cnf(i_0_1868_012,axiom,
( X1 != X2
| esk80_4(X1,X3,X4,X5) = esk80_4(X2,X3,X4,X5) ) ).
cnf(i_0_1869_013,axiom,
( X1 != X2
| esk80_4(X3,X1,X4,X5) = esk80_4(X3,X2,X4,X5) ) ).
cnf(i_0_1870_014,axiom,
( X1 != X2
| esk80_4(X3,X4,X1,X5) = esk80_4(X3,X4,X2,X5) ) ).
cnf(i_0_1871_015,axiom,
( X1 != X2
| esk80_4(X3,X4,X5,X1) = esk80_4(X3,X4,X5,X2) ) ).
cnf(i_0_1872_016,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).
cnf(i_0_1873_017,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).
cnf(i_0_1874_018,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).
cnf(i_0_1875_019,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_1876_020,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_1877_021,axiom,
( X1 != X2
| esk78_3(X1,X3,X4) = esk78_3(X2,X3,X4) ) ).
cnf(i_0_1878_022,axiom,
( X1 != X2
| esk78_3(X3,X1,X4) = esk78_3(X3,X2,X4) ) ).
cnf(i_0_1879_023,axiom,
( X1 != X2
| esk78_3(X3,X4,X1) = esk78_3(X3,X4,X2) ) ).
cnf(i_0_1880_024,axiom,
( X1 != X2
| esk77_3(X1,X3,X4) = esk77_3(X2,X3,X4) ) ).
cnf(i_0_1881_025,axiom,
( X1 != X2
| esk77_3(X3,X1,X4) = esk77_3(X3,X2,X4) ) ).
cnf(i_0_1882_026,axiom,
( X1 != X2
| esk77_3(X3,X4,X1) = esk77_3(X3,X4,X2) ) ).
cnf(i_0_1883_027,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4) = c_Lattices_Osemilattice__inf__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_1884_028,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X3,X1,X4) = c_Lattices_Osemilattice__inf__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_1885_029,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X3,X4,X1) = c_Lattices_Osemilattice__inf__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_1886_030,axiom,
( X1 != X2
| c_Relation_Oconverse(X1,X3,X4) = c_Relation_Oconverse(X2,X3,X4) ) ).
cnf(i_0_1887_031,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X1,X4) = c_Relation_Oconverse(X3,X2,X4) ) ).
cnf(i_0_1888_032,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X4,X1) = c_Relation_Oconverse(X3,X4,X2) ) ).
cnf(i_0_1889_033,axiom,
( X1 != X2
| c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).
cnf(i_0_1890_034,axiom,
( X1 != X2
| c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).
cnf(i_0_1891_035,axiom,
( X1 != X2
| c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).
cnf(i_0_1892_036,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_1893_037,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_1894_038,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_1895_039,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1896_040,axiom,
( X1 != X2
| c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).
cnf(i_0_1897_041,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).
cnf(i_0_1898_042,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).
cnf(i_0_1899_043,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1900_044,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1901_045,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1902_046,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1903_047,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1904_048,axiom,
( X1 != X2
| c_HOL_Oundefined(X1) = c_HOL_Oundefined(X2) ) ).
cnf(i_0_1905_049,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X1,X3,X4,X5) = c_FuncSet_Oextensional__funcset(X2,X3,X4,X5) ) ).
cnf(i_0_1906_050,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X1,X4,X5) = c_FuncSet_Oextensional__funcset(X3,X2,X4,X5) ) ).
cnf(i_0_1907_051,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X1,X5) = c_FuncSet_Oextensional__funcset(X3,X4,X2,X5) ) ).
cnf(i_0_1908_052,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X5,X1) = c_FuncSet_Oextensional__funcset(X3,X4,X5,X2) ) ).
cnf(i_0_1909_053,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1910_054,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1911_055,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1912_056,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1913_057,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X1,X3,X4,X5) = c_FuncSet_Orestrict(X2,X3,X4,X5) ) ).
cnf(i_0_1914_058,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X1,X4,X5) = c_FuncSet_Orestrict(X3,X2,X4,X5) ) ).
cnf(i_0_1915_059,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X1,X5) = c_FuncSet_Orestrict(X3,X4,X2,X5) ) ).
cnf(i_0_1916_060,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X5,X1) = c_FuncSet_Orestrict(X3,X4,X5,X2) ) ).
cnf(i_0_1917_061,axiom,
( X1 != X2
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,X5) ) ).
cnf(i_0_1918_062,axiom,
( X1 != X2
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X2,X4,X5) ) ).
cnf(i_0_1919_063,axiom,
( X1 != X2
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X2,X5) ) ).
cnf(i_0_1920_064,axiom,
( X1 != X2
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,X2) ) ).
cnf(i_0_1921_065,axiom,
( X1 != X2
| c_HOL_OLet(X1,X3,X4,X5) = c_HOL_OLet(X2,X3,X4,X5) ) ).
cnf(i_0_1922_066,axiom,
( X1 != X2
| c_HOL_OLet(X3,X1,X4,X5) = c_HOL_OLet(X3,X2,X4,X5) ) ).
cnf(i_0_1923_067,axiom,
( X1 != X2
| c_HOL_OLet(X3,X4,X1,X5) = c_HOL_OLet(X3,X4,X2,X5) ) ).
cnf(i_0_1924_068,axiom,
( X1 != X2
| c_HOL_OLet(X3,X4,X5,X1) = c_HOL_OLet(X3,X4,X5,X2) ) ).
cnf(i_0_1925_069,axiom,
( X1 != X2
| c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).
cnf(i_0_1926_070,axiom,
( X1 != X2
| c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).
cnf(i_0_1927_071,axiom,
( X1 != X2
| esk5_2(X1,X3) = esk5_2(X2,X3) ) ).
cnf(i_0_1928_072,axiom,
( X1 != X2
| esk5_2(X3,X1) = esk5_2(X3,X2) ) ).
cnf(i_0_1929_073,axiom,
( X1 != X2
| esk6_2(X1,X3) = esk6_2(X2,X3) ) ).
cnf(i_0_1930_074,axiom,
( X1 != X2
| esk6_2(X3,X1) = esk6_2(X3,X2) ) ).
cnf(i_0_1931_075,axiom,
( X1 != X2
| c_Transitive__Closure_Otrancl(X1,X3) = c_Transitive__Closure_Otrancl(X2,X3) ) ).
cnf(i_0_1932_076,axiom,
( X1 != X2
| c_Transitive__Closure_Otrancl(X3,X1) = c_Transitive__Closure_Otrancl(X3,X2) ) ).
cnf(i_0_1933_077,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X1,X3,X4) = c_FuncSet_Oextensional(X2,X3,X4) ) ).
cnf(i_0_1934_078,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X3,X1,X4) = c_FuncSet_Oextensional(X3,X2,X4) ) ).
cnf(i_0_1935_079,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X3,X4,X1) = c_FuncSet_Oextensional(X3,X4,X2) ) ).
cnf(i_0_1936_080,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1937_081,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1938_082,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1939_083,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1940_084,axiom,
( X1 != X2
| esk33_3(X1,X3,X4) = esk33_3(X2,X3,X4) ) ).
cnf(i_0_1941_085,axiom,
( X1 != X2
| esk33_3(X3,X1,X4) = esk33_3(X3,X2,X4) ) ).
cnf(i_0_1942_086,axiom,
( X1 != X2
| esk33_3(X3,X4,X1) = esk33_3(X3,X4,X2) ) ).
cnf(i_0_1943_087,axiom,
( X1 != X2
| esk32_3(X1,X3,X4) = esk32_3(X2,X3,X4) ) ).
cnf(i_0_1944_088,axiom,
( X1 != X2
| esk32_3(X3,X1,X4) = esk32_3(X3,X2,X4) ) ).
cnf(i_0_1945_089,axiom,
( X1 != X2
| esk32_3(X3,X4,X1) = esk32_3(X3,X4,X2) ) ).
cnf(i_0_1946_090,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_1947_091,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_1948_092,axiom,
( X1 != X2
| c_Relation_Oinv__image(X1,X3,X4,X5) = c_Relation_Oinv__image(X2,X3,X4,X5) ) ).
cnf(i_0_1949_093,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X1,X4,X5) = c_Relation_Oinv__image(X3,X2,X4,X5) ) ).
cnf(i_0_1950_094,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X1,X5) = c_Relation_Oinv__image(X3,X4,X2,X5) ) ).
cnf(i_0_1951_095,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X5,X1) = c_Relation_Oinv__image(X3,X4,X5,X2) ) ).
cnf(i_0_1952_096,axiom,
( X1 != X2
| esk56_3(X1,X3,X4) = esk56_3(X2,X3,X4) ) ).
cnf(i_0_1953_097,axiom,
( X1 != X2
| esk56_3(X3,X1,X4) = esk56_3(X3,X2,X4) ) ).
cnf(i_0_1954_098,axiom,
( X1 != X2
| esk56_3(X3,X4,X1) = esk56_3(X3,X4,X2) ) ).
cnf(i_0_1955_099,axiom,
( X1 != X2
| esk55_3(X1,X3,X4) = esk55_3(X2,X3,X4) ) ).
cnf(i_0_1956_100,axiom,
( X1 != X2
| esk55_3(X3,X1,X4) = esk55_3(X3,X2,X4) ) ).
cnf(i_0_1957_101,axiom,
( X1 != X2
| esk55_3(X3,X4,X1) = esk55_3(X3,X4,X2) ) ).
cnf(i_0_1958_102,axiom,
( X1 != X2
| esk50_3(X1,X3,X4) = esk50_3(X2,X3,X4) ) ).
cnf(i_0_1959_103,axiom,
( X1 != X2
| esk50_3(X3,X1,X4) = esk50_3(X3,X2,X4) ) ).
cnf(i_0_1960_104,axiom,
( X1 != X2
| esk50_3(X3,X4,X1) = esk50_3(X3,X4,X2) ) ).
cnf(i_0_1961_105,axiom,
( X1 != X2
| esk49_3(X1,X3,X4) = esk49_3(X2,X3,X4) ) ).
cnf(i_0_1962_106,axiom,
( X1 != X2
| esk49_3(X3,X1,X4) = esk49_3(X3,X2,X4) ) ).
cnf(i_0_1963_107,axiom,
( X1 != X2
| esk49_3(X3,X4,X1) = esk49_3(X3,X4,X2) ) ).
cnf(i_0_1964_108,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1965_109,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_1966_110,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_1967_111,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_1968_112,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1969_113,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_1970_114,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_1971_115,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_1972_116,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_1973_117,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_1974_118,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_1975_119,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_1976_120,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_1977_121,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1978_122,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1979_123,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1980_124,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1981_125,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1982_126,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1983_127,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1984_128,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1985_129,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_1986_130,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_1987_131,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_1988_132,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_1989_133,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_1990_134,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_1991_135,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_1992_136,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X1,X3,X4,X5)
| c_Recdef_Oadm__wf(X2,X3,X4,X5) ) ).
cnf(i_0_1993_137,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X1,X4,X5)
| c_Recdef_Oadm__wf(X3,X2,X4,X5) ) ).
cnf(i_0_1994_138,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X1,X5)
| c_Recdef_Oadm__wf(X3,X4,X2,X5) ) ).
cnf(i_0_1995_139,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X5,X1)
| c_Recdef_Oadm__wf(X3,X4,X5,X2) ) ).
cnf(i_0_1996_140,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_1997_141,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_1998_142,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_1999_143,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_2000_144,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_2001_145,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_2002_146,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2003_147,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2004_148,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_2005_149,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2006_150,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_2007_151,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_2008_152,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X1,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_2009_153,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X1,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_2010_154,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X1,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_2011_155,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X1,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_2012_156,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X1)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_2013_157,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__bot(X1)
| class_Lattices_Obounded__lattice__bot(X2) ) ).
cnf(i_0_2014_158,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_2015_159,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_2016_160,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_2017_161,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_2018_162,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X1,X3,X4,X5)
| c_Predicate_ORangeP(X2,X3,X4,X5) ) ).
cnf(i_0_2019_163,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X1,X4,X5)
| c_Predicate_ORangeP(X3,X2,X4,X5) ) ).
cnf(i_0_2020_164,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X1,X5)
| c_Predicate_ORangeP(X3,X4,X2,X5) ) ).
cnf(i_0_2021_165,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X5,X1)
| c_Predicate_ORangeP(X3,X4,X5,X2) ) ).
cnf(i_0_2022_166,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X1,X3,X4,X5)
| c_Predicate_ODomainP(X2,X3,X4,X5) ) ).
cnf(i_0_2023_167,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X1,X4,X5)
| c_Predicate_ODomainP(X3,X2,X4,X5) ) ).
cnf(i_0_2024_168,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X1,X5)
| c_Predicate_ODomainP(X3,X4,X2,X5) ) ).
cnf(i_0_2025_169,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X5,X1)
| c_Predicate_ODomainP(X3,X4,X5,X2) ) ).
cnf(i_0_2026_170,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_2027_171,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_2028_172,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_2029_173,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_2030_174,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_2031_175,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_2032_176,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_2033,plain,
( ~ c_Recdef_Oadm__wf(X1,X2,X3,X4)
| hAPP(hAPP(X4,X5),X6) = hAPP(hAPP(X4,X5),X6) ),
inference(equality_inference,[],[1122]) ).
cnf(i_0_2034,plain,
X1 = X1,
inference(equality_inference,[],[1126]) ).
cnf(i_0_2035,plain,
~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X1,hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot)),c_fequal)),X2),X2)),
inference(equality_inference,[],[1144]) ).
cnf(i_0_2036,plain,
hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X3),X4),X5) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X3),X4),X5),
inference(equality_inference,[],[1147]) ).
cnf(i_0_2037,plain,
( c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X6),X7))
| ~ c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool),X5,hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5)) ),
inference(equality_inference,[],[1161]) ).
cnf(i_0_2038,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),X3),X5))),c_Wellfounded_Olex__prod(X1,X2,X6,X7)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),X7)) ),
inference(equality_inference,[],[1190]) ).
cnf(i_0_2039,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),X1),c_FuncSet_Oextensional(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),X1),c_FuncSet_Oextensional(X2,X3,X4))) ),
inference(equality_inference,[],[1198]) ).
cnf(i_0_2040,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),c_FuncSet_Orestrict(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X4,X3))),c_FuncSet_OPi(X1,X2,c_Set_Oimage(X2,X1,X4,X3),c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X3)))),
inference(equality_inference,[],[1202]) ).
cnf(i_0_2041,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oimage(X3,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oimage(X3,X2,X4,X5))) ),
inference(equality_inference,[],[1229]) ).
cnf(i_0_2042,plain,
( X1 = X2
| 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),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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)),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)),X4))
| ~ 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(equality_inference,[],[1231]) ).
cnf(i_0_2043,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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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)),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)),X4))
| ~ 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(equality_inference,[],[1232]) ).
cnf(i_0_2044,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_Obelow(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),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),X2)),X4))
| ~ 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(equality_inference,[],[1235]) ).
cnf(i_0_2045,plain,
( X1 = X2
| 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),X2)),c_Arrow__Order__Mirabelle_Obelow(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),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),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)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1236]) ).
cnf(i_0_2046,plain,
c_FuncSet_Orestrict(X1,X1,hAPP(c_COMBB(X2,X1,X1,X3),c_FuncSet_Orestrict(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,X4,X3),c_Set_Oimage(X2,X1,X3,X4))),c_Set_Oimage(X2,X1,X3,X4)) = c_FuncSet_Orestrict(X1,X1,c_COMBI(X1),c_Set_Oimage(X2,X1,X3,X4)),
inference(equality_inference,[],[1239]) ).
cnf(i_0_2047,plain,
( X1 = X2
| 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),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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)),X4))
| ~ 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(equality_inference,[],[1259]) ).
cnf(i_0_2048,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),X2),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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)),X4))
| ~ 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(equality_inference,[],[1261]) ).
cnf(i_0_2049,plain,
( X1 = X2
| X3 = X2
| 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),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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)),X4))
| ~ 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(equality_inference,[],[1273]) ).
cnf(i_0_2050,plain,
( X1 = X2
| 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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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)),X4))
| ~ 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(equality_inference,[],[1274]) ).
cnf(i_0_2051,plain,
( X1 = X2
| 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),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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)),X4))
| ~ 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(equality_inference,[],[1276]) ).
cnf(i_0_2052,plain,
( X1 = X2
| 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),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(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),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)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1277]) ).
cnf(i_0_2053,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_Obelow(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),X2)),X4))
| ~ 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(equality_inference,[],[1279]) ).
cnf(i_0_2054,plain,
( X1 = X2
| X3 = X1
| 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_Obelow(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),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)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1286]) ).
cnf(i_0_2055,plain,
( X1 = X2
| X2 = 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),X2)),c_Arrow__Order__Mirabelle_Obelow(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),X2)),X4))
| ~ 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(equality_inference,[],[1287]) ).
cnf(i_0_2056,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_Obelow(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),X2)),X4))
| ~ 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(equality_inference,[],[1289]) ).
cnf(i_0_2057,plain,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X4)),X3)) ),
inference(equality_inference,[],[1306]) ).
cnf(i_0_2058,plain,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3)) ),
inference(equality_inference,[],[1314]) ).
cnf(i_0_2059,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),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X4),X1),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(equality_inference,[],[1318]) ).
cnf(i_0_2060,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),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,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(equality_inference,[],[1337]) ).
cnf(i_0_2061,plain,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
inference(equality_inference,[],[1352]) ).
cnf(i_0_2062,plain,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3)) ),
inference(equality_inference,[],[1374]) ).
cnf(i_0_2063,plain,
( hAPP(X1,X2) = hAPP(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X4)),X5)) ),
inference(equality_inference,[],[1375]) ).
cnf(i_0_2064,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oimage(X3,X1,X4,X5))
| c_Set_Oimage(X3,X1,X4,c_Set_Oimage(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2 ),
inference(equality_inference,[],[1377]) ).
cnf(i_0_2065,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk90_4(X3,X1,X2,c_Set_Oimage(X1,X2,X4,X3)),c_Set_Oimage(X1,X2,X4,X3)),X3)
| c_Set_Oimage(X1,X2,X4,X3) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(equality_inference,[],[1403]) ).
cnf(i_0_2066,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)),c_Arrow__Order__Mirabelle_Omktop(X3,X1))),
inference(equality_inference,[],[1440]) ).
cnf(i_0_2067,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)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))),
inference(equality_inference,[],[1441]) ).
cnf(i_0_2068,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
inference(equality_inference,[],[1460]) ).
cnf(i_0_2069,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Relation_OId__on(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(equality_inference,[],[1468]) ).
cnf(i_0_2070,plain,
c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
inference(equality_inference,[],[1474]) ).
cnf(i_0_2071,plain,
( c_Fun_Oinj__on(X1,X2,esk90_4(X3,X2,X1,c_Set_Oimage(X2,X1,X4,X3)),c_Set_Oimage(X2,X1,X4,X3))
| c_Set_Oimage(X2,X1,X4,X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(equality_inference,[],[1477]) ).
cnf(i_0_2072,plain,
X1 = X1,
inference(equality_inference,[],[1482]) ).
cnf(i_0_2073,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(equality_inference,[],[1483]) ).
cnf(i_0_2074,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(equality_inference,[],[1488]) ).
cnf(i_0_2075,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(equality_inference,[],[1489]) ).
cnf(i_0_2076,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X3,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X4,X5) ),
inference(equality_inference,[],[1491]) ).
cnf(i_0_2077,plain,
( X1 = X2
| 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)),c_Arrow__Order__Mirabelle_Omkbot(X3,X1))) ),
inference(equality_inference,[],[1506]) ).
cnf(i_0_2078,plain,
( X1 = 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),X2)),c_Arrow__Order__Mirabelle_Omktop(X3,X2))) ),
inference(equality_inference,[],[1507]) ).
cnf(i_0_2079,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1522]) ).
cnf(i_0_2080,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1523]) ).
cnf(i_0_2081,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1524]) ).
cnf(i_0_2082,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1525]) ).
cnf(i_0_2083,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5)) ),
inference(equality_inference,[],[1535]) ).
cnf(i_0_2084,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(equality_inference,[],[1642]) ).
cnf(i_0_2085,plain,
X1 = X1,
inference(equality_inference,[],[1669]) ).
cnf(i_0_2086,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(equality_inference,[],[1675]) ).
cnf(i_0_2087,plain,
c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[1676]) ).
cnf(i_0_2088,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
inference(equality_inference,[],[1682]) ).
cnf(i_0_2089,plain,
c_Relation_ODomain(X1,X2,c_Relation_Oconverse(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(equality_inference,[],[1683]) ).
cnf(i_0_2090,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),
inference(equality_inference,[],[1699]) ).
cnf(i_0_2091,plain,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
inference(equality_inference,[],[1718]) ).
cnf(i_0_2092,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(equality_inference,[],[1741]) ).
cnf(i_0_2093,plain,
c_Relation_ODomain(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(equality_inference,[],[1743]) ).
cnf(i_0_2094,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2),
inference(equality_inference,[],[1762]) ).
cnf(i_0_2095,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(equality_inference,[],[1763]) ).
cnf(i_0_2096,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1773]) ).
cnf(i_0_2097,plain,
X1 = X1,
inference(equality_inference,[],[1786]) ).
cnf(i_0_2098,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1809]) ).
cnf(i_0_2099,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1810]) ).
cnf(i_0_2100,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1813]) ).
cnf(i_0_2101,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1819]) ).
cnf(i_0_2102,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1820]) ).
cnf(i_0_2103,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1821]) ).
cnf(i_0_2104,plain,
$false,
inference(scs_inference,[],[i_0_1496,i_0_1201,i_0_1464,i_0_1291]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SCT126+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : 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 01:57:01 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 3.19/5.73 % Version : CSE_E---1.7
% 3.19/5.73 % Problem : theBenchmark.p
% 3.19/5.73 % SZS status Theorem for theBenchmark.p
% 3.19/5.73 % SZS output start CNFRefutation
% See solution above
% 3.38/5.84 % Total time : 5.389s
%------------------------------------------------------------------------------