%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT131+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:06:04 PM UTC 2026
% Result : Theorem 3.24s 5.73s
% Output : CNFRefutation 3.43s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_623)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Nitpick_Owfrec_H__def,axiom,
! [X12,X26,X15,X14,X6] :
( ( c_Wellfounded_Owf(X6,X14)
=> c_Nitpick_Owfrec_H(X6,X15,X14,X26,X12) = c_Nitpick_Owf__wfrec_H(X6,X15,X14,X26,X12) )
& ( ~ c_Wellfounded_Owf(X6,X14)
=> c_Nitpick_Owfrec_H(X6,X15,X14,X26,X12) = c_HOL_OThe(X15,c_Recdef_Owfrec__rel(X6,X15,X14,hAPP(hAPP(c_COMBC(tc_fun(X6,X15),tc_fun(X6,X6),tc_fun(X6,X15)),hAPP(c_COMBB(tc_fun(X6,tc_fun(X6,X15)),tc_fun(tc_fun(X6,X6),tc_fun(X6,X15)),tc_fun(X6,X15),c_COMBS(X6,X6,X15)),hAPP(c_COMBB(tc_fun(X6,tc_fun(X6,X15)),tc_fun(X6,tc_fun(X6,X15)),tc_fun(X6,X15),c_COMBB(tc_fun(X6,X15),tc_fun(X6,X15),X6,X26)),hAPP(hAPP(c_COMBC(tc_fun(X6,X15),tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_fun(X6,X15))),c_Recdef_Ocut(X6,X15)),X14)))),c_COMBI(X6)),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Owfrec_H__def) ).
fof(fact_converse__rtranclE2,axiom,
! [X18,X44,X45,X46,X47,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X47),X46)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X45),X44))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X15),X18)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X6,X15),X47),X46) != hAPP(hAPP(c_Product__Type_OPair(X6,X15),X45),X44)
=> ~ ! [X33,X34] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X47),X46)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X33),X34))),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X33),X34)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X45),X44))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X15),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
fof(fact_compose__assoc,axiom,
! [X40,X41,X42,X38,X1,X39,X7,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X15,X39)),X1),c_FuncSet_OPi(X15,X39,X7,c_COMBK(tc_fun(X39,tc_HOL_Obool),X15,X38))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X39,X42)),X41),c_FuncSet_OPi(X39,X42,X38,c_COMBK(tc_fun(X42,tc_HOL_Obool),X39,X40))))
=> c_FuncSet_Ocompose(X6,X39,X42,X8,X41,c_FuncSet_Ocompose(X6,X15,X39,X8,X1,X2)) = c_FuncSet_Ocompose(X6,X15,X42,X8,c_FuncSet_Ocompose(X15,X39,X42,X7,X41,X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__assoc) ).
fof(fact_compose__def,axiom,
! [X2,X1,X8,X15,X39,X6] : c_FuncSet_Ocompose(X6,X39,X15,X8,X1,X2) = c_FuncSet_Orestrict(X6,X15,hAPP(c_COMBB(X39,X15,X6,X1),X2),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__def) ).
fof(fact_funcset__compose,axiom,
! [X38,X1,X39,X7,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X15,X39)),X1),c_FuncSet_OPi(X15,X39,X7,c_COMBK(tc_fun(X39,tc_HOL_Obool),X15,X38))))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X39)),c_FuncSet_Ocompose(X6,X15,X39,X8,X1,X2)),c_FuncSet_OPi(X6,X39,X8,c_COMBK(tc_fun(X39,tc_HOL_Obool),X6,X38)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__compose) ).
fof(fact_irrefl__trancl__rD,axiom,
! [X11,X12,X18,X6] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X18))
=> X12 != X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__trancl__rD) ).
fof(fact_extensional__funcset__restrict__domain,axiom,
! [X36,X2,X15,X32,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X32))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional__funcset(X6,X15,c_Set_Oinsert(X6,X12,X32),X36)))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),c_Fun_Ofun__upd(X6,X15,X2,X12,c_HOL_Oundefined(X15))),c_FuncSet_Oextensional__funcset(X6,X15,X32,X36))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__restrict__domain) ).
fof(fact_converse__tranclE,axiom,
! [X18,X9,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X9)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X9)),X18))
=> ~ ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X29)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X9)),c_Transitive__Closure_Otrancl(X6,X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__tranclE) ).
fof(fact_tranclE,axiom,
! [X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),X18))
=> ~ ! [X60] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X60)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X60),X19)),X18)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclE) ).
fof(fact_converse__rtranclE,axiom,
! [X18,X9,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X9)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( X12 != X9
=> ~ ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X29)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X9)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE) ).
fof(fact_rtranclE,axiom,
! [X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( X20 != X19
=> ~ ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X29)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X19)),X18)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclE) ).
fof(fact_compose__extensional,axiom,
! [X1,X2,X8,X39,X15,X6] : hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),c_FuncSet_Ocompose(X6,X39,X15,X8,X2,X1)),c_FuncSet_Oextensional(X6,X15,X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__extensional) ).
fof(fact_Nitpick_Owf__wfrec_H__def,axiom,
! [X12,X26,X14,X6,X15] : c_Nitpick_Owf__wfrec_H(X15,X6,X14,X26,X12) = hAPP(hAPP(X26,hAPP(hAPP(hAPP(c_Recdef_Ocut(X15,X6),c_Nitpick_Owf__wfrec(X15,X6,X14,X26)),X14),X12)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Owf__wfrec_H__def) ).
fof(fact_RangeE,axiom,
! [X18,X15,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Relation_ORange(X15,X6,X18)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X15,X6)),hAPP(hAPP(c_Product__Type_OPair(X15,X6),X3),X19)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
fof(fact_Id__compose,axiom,
! [X7,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional(X6,X15,X8)))
=> c_FuncSet_Ocompose(X6,X15,X15,X8,c_FuncSet_Orestrict(X15,X15,c_COMBI(X15),X7),X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__compose) ).
fof(fact_compose__Id,axiom,
! [X7,X8,X1,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X1),c_FuncSet_OPi(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X1),c_FuncSet_Oextensional(X6,X15,X8)))
=> c_FuncSet_Ocompose(X6,X6,X15,X8,X1,c_FuncSet_Orestrict(X6,X6,c_COMBI(X6),X8)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__Id) ).
fof(fact_DomainE,axiom,
! [X18,X15,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),c_Relation_ODomain(X6,X15,X18)))
=> ~ ! [X29] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X29)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
fof(fact_inf2E,axiom,
! [X11,X12,X7,X8,X15,X6] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X15,tc_HOL_Obool))),X8),X7),X12),X11))
=> ~ ( hBOOL(hAPP(hAPP(X8,X12),X11))
=> ~ hBOOL(hAPP(hAPP(X7,X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
fof(fact_notin__Lin__iff,axiom,
! [X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> ( X12 != X11
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),X10))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11),X12)),X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X19,X20,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X19)),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),X19),X20)),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_SigmaE2,axiom,
! [X7,X8,X19,X20,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19)),c_Product__Type_OSigma(X6,X15,X8,X7)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> ~ hBOOL(hAPP(hAPP(c_member(X15),X19),hAPP(X7,X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE2) ).
fof(fact_wf__eq__minimal,axiom,
! [X18,X6] :
( c_Wellfounded_Owf(X6,X18)
<=> ! [X75] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X6),X3),X75))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X75))
& ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X3)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X29),X75)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
fof(fact_wf__asym,axiom,
! [X12,X20,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X12)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X20)),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).
fof(fact_wf__not__sym,axiom,
! [X12,X20,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X12)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X20)),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__sym) ).
fof(fact_not__acc__down,axiom,
! [X14,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X14)))
=> ~ ! [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X28),X12)),X14))
=> hBOOL(hAPP(hAPP(c_member(X6),X28),c_Wellfounded_Oacc(X6,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
fof(fact_compose__eq,axiom,
! [X2,X1,X15,X39,X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Ocompose(X6,X39,X15,X8,X1,X2),X12) = hAPP(X1,hAPP(X2,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__eq) ).
fof(fact_wf__insert,axiom,
! [X18,X12,X11,X6] :
( c_Wellfounded_Owf(X6,c_Set_Oinsert(tc_prod(X6,X6),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12),X18))
<=> ( c_Wellfounded_Owf(X6,X18)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).
fof(fact_acyclic__insert,axiom,
! [X18,X12,X11,X6] :
( c_Wellfounded_Oacyclic(X6,c_Set_Oinsert(tc_prod(X6,X6),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12),X18))
<=> ( c_Wellfounded_Oacyclic(X6,X18)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
fof(fact_PiE,axiom,
! [X12,X7,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,X7)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X12)),hAPP(X7,X12)))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiE) ).
fof(fact_extensional__funcset__arb,axiom,
! [X12,X36,X32,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional__funcset(X6,X15,X32,X36)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X32))
=> hAPP(X2,X12) = c_HOL_Oundefined(X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__arb) ).
fof(fact_cut__def,axiom,
! [X2,X15,X18,X12,X11,X6] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12)),X18))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),X2),X18),X12),X11) = hAPP(X2,X11) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12)),X18))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),X2),X18),X12),X11) = c_HOL_Oundefined(X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut__def) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [X11,X14,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Relation_ODomain(X6,X6,X14)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X14)))
<=> X12 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_acyclic__def,axiom,
! [X18,X6] :
( c_Wellfounded_Oacyclic(X6,X18)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),c_Transitive__Closure_Otrancl(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
fof(fact_acyclicI,axiom,
! [X18,X6] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),c_Transitive__Closure_Otrancl(X6,X18)))
=> c_Wellfounded_Oacyclic(X6,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
fof(fact_irrefl__def,axiom,
! [X18,X6] :
( c_Relation_Oirrefl(X6,X18)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(fact_wf__irrefl,axiom,
! [X20,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X20)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).
fof(fact_wf__not__refl,axiom,
! [X20,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X20)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__refl) ).
fof(fact_UnE,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).
fof(fact_IntE,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntE) ).
fof(fact_sup1E,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12))
=> ( ~ hBOOL(hAPP(X8,X12))
=> hBOOL(hAPP(X7,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
fof(fact_inf1E,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12))
=> ~ ( hBOOL(hAPP(X8,X12))
=> ~ hBOOL(hAPP(X7,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
fof(fact_extensional__arb,axiom,
! [X12,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional(X6,X15,X8)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(X2,X12) = c_HOL_Oundefined(X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__arb) ).
fof(fact_Int__insert__left,axiom,
! [X7,X38,X20,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X20),X38))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,X7)),X38) = c_Set_Oinsert(X6,X20,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X38))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,X7)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left) ).
fof(fact_UnCI,axiom,
! [X8,X7,X5,X6] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X6),X5),X7))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X8)) )
=> hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnCI) ).
fof(fact_Int__insert__right,axiom,
! [X7,X8,X20,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),c_Set_Oinsert(X6,X20,X7)) = c_Set_Oinsert(X6,X20,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),c_Set_Oinsert(X6,X20,X7)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right) ).
fof(fact_restrict__apply,axiom,
! [X2,X15,X8,X12,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X15,X2,X8),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X15,X2,X8),X12) = c_HOL_Oundefined(X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__apply) ).
fof(fact_restrict__def,axiom,
! [X2,X15,X8,X12,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X15,X2,X8),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X15,X2,X8),X12) = c_HOL_Oundefined(X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__def) ).
fof(fact_sup1CI,axiom,
! [X6,X8,X12,X7] :
( ( ~ hBOOL(hAPP(X7,X12))
=> hBOOL(hAPP(X8,X12)) )
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
fof(fact_Int__insert__left__if0,axiom,
! [X7,X38,X20,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X38))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,X7)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
fof(fact_Int__insert__right__if0,axiom,
! [X7,X8,X20,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),c_Set_Oinsert(X6,X20,X7)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
fof(fact_insertCI,axiom,
! [X19,X7,X20,X6] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X7))
=> X20 = X19 )
=> hBOOL(hAPP(hAPP(c_member(X6),X20),c_Set_Oinsert(X6,X19,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
fof(fact_subset__insert,axiom,
! [X7,X8,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,c_Set_Oinsert(X6,X12,X7))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
fof(fact_insert__ident,axiom,
! [X7,X8,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X7))
=> ( c_Set_Oinsert(X6,X12,X8) = c_Set_Oinsert(X6,X12,X7)
<=> X8 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(fact_empty__iff,axiom,
! [X5,X6] : ~ hBOOL(hAPP(hAPP(c_member(X6),X5),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
fof(fact_emptyE,axiom,
! [X20,X6] : ~ hBOOL(hAPP(hAPP(c_member(X6),X20),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
fof(fact_le__supE,axiom,
! [X56,X58,X59,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58),X56)
=> ~ ( c_Orderings_Oord__class_Oless__eq(X6,X59,X56)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,X58,X56) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supE) ).
fof(fact_le__infE,axiom,
! [X58,X59,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X6,X56,X59)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,X56,X58) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infE) ).
fof(fact_all__not__in__conv,axiom,
! [X8,X6] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
<=> X8 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_equals0D,axiom,
! [X20,X6,X8] :
( X8 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
fof(help_c__fconj__2,axiom,
! [X64,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X64))
| hBOOL(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [X64,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X64))
| hBOOL(X64) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).
fof(help_c__fequal__1,axiom,
! [X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X12),X11))
| X12 = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_linorder__le__cases,axiom,
! [X55,X56,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X56,X55)
=> c_Orderings_Oord__class_Oless__eq(X6,X55,X56) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(help_c__fconj__1,axiom,
! [X64,X17] :
( ~ hBOOL(X17)
| ~ hBOOL(X64)
| hBOOL(hAPP(hAPP(c_fconj,X17),X64)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(fact_equalityE,axiom,
! [X6,X7,X8] :
( X8 = X7
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
fof(fact_rtrancl__induct2,axiom,
! [X17,X18,X48,X49,X50,X51,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X51),X50)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X49),X48))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X15),X18)))
=> ( hBOOL(hAPP(hAPP(X17,X51),X50))
=> ( ! [X33,X34] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X51),X50)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X33),X34))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X15),X18)))
=> ! [X52,X53] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X33),X34)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X52),X53))),X18))
=> ( hBOOL(hAPP(hAPP(X17,X33),X34))
=> hBOOL(hAPP(hAPP(X17,X52),X53)) ) ) )
=> hBOOL(hAPP(hAPP(X17,X49),X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
fof(fact_converse__rtrancl__induct2,axiom,
! [X17,X18,X48,X49,X50,X51,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X51),X50)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X49),X48))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X15),X18)))
=> ( hBOOL(hAPP(hAPP(X17,X49),X48))
=> ( ! [X33,X34,X52,X53] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X33),X34)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X52),X53))),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X52),X53)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X49),X48))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X15),X18)))
=> ( hBOOL(hAPP(hAPP(X17,X52),X53))
=> hBOOL(hAPP(hAPP(X17,X33),X34)) ) ) )
=> hBOOL(hAPP(hAPP(X17,X51),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
fof(fact_inf__Int__eq2,axiom,
! [X11,X12,X32,X14,X15,X6] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X15,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_COMBC(X15,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X6,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X15),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X6,X15)))),c_Product__Type_OPair(X6,X15)))),X14)),hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_COMBC(X15,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X6,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X15),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X6,X15)))),c_Product__Type_OPair(X6,X15)))),X32)),X12),X11))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X12),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),X14),X32))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_wfrec__rel_Oequations,axiom,
! [X24,X25,X26,X14,X15,X6] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X15,X14,X26,X25),hAPP(hAPP(X26,X24),X25)))
<=> ? [X27] :
( hAPP(hAPP(X26,X24),X25) = hAPP(hAPP(X26,X27),X25)
& ! [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X28),X25)),X14))
=> hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X15,X14,X26,X28),hAPP(X27,X28))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Oequations) ).
fof(fact_wfrec__rel_Osimps,axiom,
! [X24,X25,X26,X14,X15,X6] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X15,X14,X26,X25),X24))
<=> ? [X27] :
( X24 = hAPP(hAPP(X26,X27),X25)
& ! [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X28),X25)),X14))
=> hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X15,X14,X26,X28),hAPP(X27,X28))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Osimps) ).
fof(fact_adm__wf__def,axiom,
! [X26,X14,X15,X6] :
( c_Recdef_Oadm__wf(X6,X15,X14,X26)
<=> ! [X30,X27,X3] :
( ! [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X28),X3)),X14))
=> hAPP(X30,X28) = hAPP(X27,X28) )
=> hAPP(hAPP(X26,X30),X3) = hAPP(hAPP(X26,X27),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adm__wf__def) ).
fof(fact_tranclp__trancl__eq,axiom,
! [X47,X12,X18,X6] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),X6,c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X6,tc_prod(X6,X6)),tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X6),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool),X6,c_member(tc_prod(X6,X6)))),c_Product__Type_OPair(X6,X6)))),X18)),X12),X47))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X47)),c_Transitive__Closure_Otrancl(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclp__trancl__eq) ).
fof(fact_accp__acc__eq,axiom,
! [X12,X18,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),X6,c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X6,tc_prod(X6,X6)),tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X6),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool),X6,c_member(tc_prod(X6,X6)))),c_Product__Type_OPair(X6,X6)))),X18)),X12))
<=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_pred__subset__eq2,axiom,
! [X32,X14,X15,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X15,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_COMBC(X15,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X6,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X15),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X6,X15)))),c_Product__Type_OPair(X6,X15)))),X14),hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_COMBC(X15,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X6,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X15),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X6,X15)))),c_Product__Type_OPair(X6,X15)))),X32))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),X14,X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_wfrec__rel_Ointros,axiom,
! [X1,X26,X15,X14,X12,X6] :
( ! [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X28),X12)),X14))
=> hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X15,X14,X26,X28),hAPP(X1,X28))) )
=> hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X15,X14,X26,X12),hAPP(hAPP(X26,X1),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Ointros) ).
fof(fact_cuts__eq,axiom,
! [X1,X12,X18,X2,X15,X6] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),X2),X18),X12) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),X1),X18),X12)
<=> ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X12)),X18))
=> hAPP(X2,X29) = hAPP(X1,X29) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cuts__eq) ).
fof(fact_wfrec__def,axiom,
! [X12,X26,X14,X6,X15] : hAPP(c_Recdef_Owfrec(X15,X6,X14,X26),X12) = c_HOL_OThe(X6,c_Recdef_Owfrec__rel(X15,X6,X14,hAPP(hAPP(c_COMBC(tc_fun(X15,X6),tc_fun(X15,X15),tc_fun(X15,X6)),hAPP(c_COMBB(tc_fun(X15,tc_fun(X15,X6)),tc_fun(tc_fun(X15,X15),tc_fun(X15,X6)),tc_fun(X15,X6),c_COMBS(X15,X15,X6)),hAPP(c_COMBB(tc_fun(X15,tc_fun(X15,X6)),tc_fun(X15,tc_fun(X15,X6)),tc_fun(X15,X6),c_COMBB(tc_fun(X15,X6),tc_fun(X15,X6),X15,X26)),hAPP(hAPP(c_COMBC(tc_fun(X15,X6),tc_fun(tc_prod(X15,X15),tc_HOL_Obool),tc_fun(X15,tc_fun(X15,X6))),c_Recdef_Ocut(X15,X6)),X14)))),c_COMBI(X15)),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__def) ).
fof(fact_DomainP__Domain__eq,axiom,
! [X12,X18,X15,X6] :
( c_Predicate_ODomainP(X6,X15,hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_COMBC(X15,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X6,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X15),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X6,X15)))),c_Product__Type_OPair(X6,X15)))),X18),X12)
<=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Relation_ODomain(X6,X15,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_RangeP__Range__eq,axiom,
! [X12,X18,X15,X6] :
( c_Predicate_ORangeP(X6,X15,hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_COMBC(X15,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X6,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X15),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X6,X15)))),c_Product__Type_OPair(X6,X15)))),X18),X12)
<=> hBOOL(hAPP(hAPP(c_member(X15),X12),c_Relation_ORange(X6,X15,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_wfP__wf__eq,axiom,
! [X18,X6] :
( c_Wellfounded_OwfP(X6,hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),X6,c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X6,tc_prod(X6,X6)),tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X6),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool),X6,c_member(tc_prod(X6,X6)))),c_Product__Type_OPair(X6,X6)))),X18))
<=> c_Wellfounded_Owf(X6,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [X32,X14,X15,X6] :
( hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_COMBC(X15,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X6,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X15),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X6,X15)))),c_Product__Type_OPair(X6,X15)))),X14) = hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_COMBC(X15,tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X6,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool)),X6,c_COMBB(tc_prod(X6,X15),tc_fun(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X6,X15)))),c_Product__Type_OPair(X6,X15)))),X32)
<=> X14 = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_Sigma__mono,axiom,
! [X40,X7,X15,X38,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X38)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),hAPP(X7,X3),hAPP(X40,X3)) )
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),c_Product__Type_OSigma(X6,X15,X8,X7),c_Product__Type_OSigma(X6,X15,X38,X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__mono) ).
fof(fact_adm__lemma,axiom,
! [X26,X14,X15,X6] : c_Recdef_Oadm__wf(X6,X15,X14,hAPP(hAPP(c_COMBC(tc_fun(X6,X15),tc_fun(X6,X6),tc_fun(X6,X15)),hAPP(c_COMBB(tc_fun(X6,tc_fun(X6,X15)),tc_fun(tc_fun(X6,X6),tc_fun(X6,X15)),tc_fun(X6,X15),c_COMBS(X6,X6,X15)),hAPP(c_COMBB(tc_fun(X6,tc_fun(X6,X15)),tc_fun(X6,tc_fun(X6,X15)),tc_fun(X6,X15),c_COMBB(tc_fun(X6,X15),tc_fun(X6,X15),X6,X26)),hAPP(hAPP(c_COMBC(tc_fun(X6,X15),tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_fun(X6,X15))),c_Recdef_Ocut(X6,X15)),X14)))),c_COMBI(X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adm__lemma) ).
fof(fact_rtrancl__Un__separator__converseE,axiom,
! [X64,X17,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X17),X64))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X19)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X3)),X64))
=> X29 = X3 ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
fof(fact_rtrancl__induct,axiom,
! [X17,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(X17,X20))
=> ( ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X29)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ! [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X28)),X18))
=> ( hBOOL(hAPP(X17,X29))
=> hBOOL(hAPP(X17,X28)) ) ) )
=> hBOOL(hAPP(X17,X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
fof(fact_converse__rtrancl__induct,axiom,
! [X17,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(X17,X19))
=> ( ! [X29,X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X28)),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X28),X19)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(X17,X28))
=> hBOOL(hAPP(X17,X29)) ) ) )
=> hBOOL(hAPP(X17,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
fof(fact_Pi__cong,axiom,
! [X7,X15,X1,X2,X8,X6] :
( ! [X37] :
( hBOOL(hAPP(hAPP(c_member(X6),X37),X8))
=> hAPP(X2,X37) = hAPP(X1,X37) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,X7)))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X1),c_FuncSet_OPi(X6,X15,X8,X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__cong) ).
fof(fact_restrictI,axiom,
! [X7,X2,X15,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X3)),hAPP(X7,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),c_FuncSet_Orestrict(X6,X15,X2,X8)),c_FuncSet_OPi(X6,X15,X8,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrictI) ).
fof(fact_Pi__I_H,axiom,
! [X7,X2,X15,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X3)),hAPP(X7,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I_H) ).
fof(fact_Pi__I,axiom,
! [X7,X2,X15,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X3)),hAPP(X7,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_IIA__def,axiom,
! [X26] :
( c_Arrow__Order__Mirabelle_OIIA(X26)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X35] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X35),c_Arrow__Order__Mirabelle_OProf))
=> ! [X33,X34] :
( ! [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),X33),X34)),hAPP(X3,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),X33),X34)),hAPP(X35,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),X33),X34)),hAPP(X26,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),X33),X34)),hAPP(X26,X35))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact_restrict__in__funcset,axiom,
! [X7,X2,X15,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X3)),X7)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),c_FuncSet_Orestrict(X6,X15,X2,X8)),c_FuncSet_OPi(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X7)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__in__funcset) ).
fof(fact_funcsetI,axiom,
! [X7,X2,X15,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X3)),X7)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X7)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcsetI) ).
fof(fact_Q__def,axiom,
! [X4] : hAPP(v_Q____,X4) = 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____,X4)),c_Arrow__Order__Mirabelle_Obelow(hAPP(v_P____,X4),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/sandbox/benchmark/theBenchmark.p',fact_Q__def) ).
fof(fact_SigmaE,axiom,
! [X7,X8,X5,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),X5),c_Product__Type_OSigma(X6,X15,X8,X7)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> ! [X29] :
( hBOOL(hAPP(hAPP(c_member(X15),X29),hAPP(X7,X3)))
=> X5 != hAPP(hAPP(c_Product__Type_OPair(X6,X15),X3),X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE) ).
fof(fact_the__inv__into__def,axiom,
! [X12,X2,X8,X15,X6] : c_Fun_Othe__inv__into(X6,X15,X8,X2,X12) = c_HOL_OThe(X6,hAPP(hAPP(c_COMBS(X6,tc_HOL_Obool,tc_HOL_Obool),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6,c_fconj),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8))),hAPP(hAPP(c_COMBC(X6,X15,tc_HOL_Obool),hAPP(c_COMBB(X15,tc_fun(X15,tc_HOL_Obool),X6,c_fequal),X2)),X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__def) ).
fof(fact_Pi__mono,axiom,
! [X38,X7,X15,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),hAPP(X7,X3),hAPP(X38,X3)) )
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X6,X15),tc_HOL_Obool),c_FuncSet_OPi(X6,X15,X8,X7),c_FuncSet_OPi(X6,X15,X8,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_in__lex__prod,axiom,
! [X21,X18,X22,X23,X19,X20,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X23),X22))),c_Wellfounded_Olex__prod(X6,X15,X18,X21)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X23)),X18))
| ( X20 = X23
& hBOOL(hAPP(hAPP(c_member(tc_prod(X15,X15)),hAPP(hAPP(c_Product__Type_OPair(X15,X15),X19),X22)),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact_dictatorI,axiom,
! [X4,X26] :
( 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))),X26),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))
=> ! [X33,X34] :
( X33 != X34
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X33),X34)),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),X33),X34)),hAPP(X26,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X26,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_sup__Un__eq,axiom,
! [X12,X32,X14,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X14)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X32)),X12))
<=> hBOOL(hAPP(hAPP(c_member(X6),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X14),X32))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq) ).
fof(fact_inf__Int__eq,axiom,
! [X12,X32,X14,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X14)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X32)),X12))
<=> hBOOL(hAPP(hAPP(c_member(X6),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X14),X32))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_extensional__funcset__extend__domainI,axiom,
! [X12,X32,X2,X15,X36,X11,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X11),X36))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X15,X6)),X2),c_FuncSet_Oextensional__funcset(X15,X6,X32,X36)))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X15,X6)),c_Fun_Ofun__upd(X15,X6,X2,X12,X11)),c_FuncSet_Oextensional__funcset(X15,X6,c_Set_Oinsert(X15,X12,X32),X36))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__extend__domainI) ).
fof(fact_extensionalityI,axiom,
! [X1,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional(X6,X15,X8)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X1),c_FuncSet_Oextensional(X6,X15,X8)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hAPP(X2,X3) = hAPP(X1,X3) )
=> X2 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensionalityI) ).
fof(fact_tranclD,axiom,
! [X14,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Otrancl(X6,X14)))
=> ? [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X28)),X14))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X28),X11)),c_Transitive__Closure_Ortrancl(X6,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).
fof(fact_tranclD2,axiom,
! [X14,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Otrancl(X6,X14)))
=> ? [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X28)),c_Transitive__Closure_Ortrancl(X6,X14)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X28),X11)),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).
fof(fact_same__fstI,axiom,
! [X6,X14,X11,X16,X15,X12,X17] :
( hBOOL(hAPP(X17,X12))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X15,X15)),hAPP(hAPP(c_Product__Type_OPair(X15,X15),X16),X11)),hAPP(X14,X12)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X12),X16)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X12),X11))),c_Recdef_Osame__fst(X6,X15,X17,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_Sigma__Un__distrib2,axiom,
! [X7,X8,X78,X15,X6] : c_Product__Type_OSigma(X6,X15,X78,hAPP(hAPP(c_COMBS(X6,tc_fun(X15,tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_HOL_Obool),tc_fun(tc_fun(X15,tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15,tc_HOL_Obool))),X8)),X7)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X15,X78,X8)),c_Product__Type_OSigma(X6,X15,X78,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).
fof(fact_Sigma__Int__distrib2,axiom,
! [X7,X8,X78,X15,X6] : c_Product__Type_OSigma(X6,X15,X78,hAPP(hAPP(c_COMBS(X6,tc_fun(X15,tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_HOL_Obool),tc_fun(tc_fun(X15,tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X6,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15,tc_HOL_Obool))),X8)),X7)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X15,X78,X8)),c_Product__Type_OSigma(X6,X15,X78,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
fof(fact_wfrec__unique,axiom,
! [X12,X26,X14,X15,X6] :
( c_Recdef_Oadm__wf(X6,X15,X14,X26)
=> ( c_Wellfounded_Owf(X6,X14)
=> ? [X3] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X15,X14,X26,X12),X3))
& ! [X29] :
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X15,X14,X26,X12),X29))
=> X29 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__unique) ).
fof(fact_Range__iff,axiom,
! [X18,X15,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),c_Relation_ORange(X15,X6,X18)))
<=> ? [X29] : hBOOL(hAPP(hAPP(c_member(tc_prod(X15,X6)),hAPP(hAPP(c_Product__Type_OPair(X15,X6),X29),X20)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
fof(fact_wfrec,axiom,
! [X20,X73,X15,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> hAPP(c_Recdef_Owfrec(X6,X15,X18,X73),X20) = hAPP(hAPP(X73,hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),c_Recdef_Owfrec(X6,X15,X18,X73)),X18),X20)),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec) ).
fof(fact_tfl__wfrec,axiom,
! [X15,X6,X72,X31] :
( c_Wellfounded_Owf(X6,X31)
=> ! [X3] : hAPP(c_Recdef_Owfrec(X6,X15,X31,X72),X3) = hAPP(hAPP(X72,hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),c_Recdef_Owfrec(X6,X15,X31,X72)),X31),X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__wfrec) ).
fof(fact_Un__Int__crazy,axiom,
! [X38,X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X38),X8)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X38))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X38),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).
fof(fact_insert__times__insert,axiom,
! [X7,X19,X8,X20,X15,X6] : c_Product__Type_OSigma(X6,X15,c_Set_Oinsert(X6,X20,X8),c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,c_Set_Oinsert(X15,X19,X7))) = c_Set_Oinsert(tc_prod(X6,X15),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,c_Set_Oinsert(X15,X19,X7)))),c_Product__Type_OSigma(X6,X15,c_Set_Oinsert(X6,X20,X8),c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X7)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__times__insert) ).
fof(fact_unanimity__def,axiom,
! [X26] :
( c_Arrow__Order__Mirabelle_Ounanimity(X26)
<=> ! [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))
=> ! [X33,X34] :
( ! [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),X33),X34)),hAPP(X3,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),X33),X34)),hAPP(X26,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_fun__upd__twist,axiom,
! [X70,X19,X71,X15,X6,X5,X20] :
( X20 != X5
=> c_Fun_Ofun__upd(X6,X15,c_Fun_Ofun__upd(X6,X15,X71,X20,X19),X5,X70) = c_Fun_Ofun__upd(X6,X15,c_Fun_Ofun__upd(X6,X15,X71,X5,X70),X20,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
fof(fact_refl__onI,axiom,
! [X8,X18,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X18,c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X18)) )
=> c_Relation_Orefl__on(X6,X8,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onI) ).
fof(fact_refl__on__def,axiom,
! [X18,X8,X6] :
( c_Relation_Orefl__on(X6,X8,X18)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X18,c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8)))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X18)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def) ).
fof(fact_in__above,axiom,
! [X11,X12,X10,X19,X20] :
( X20 != X19
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X10),X20),X19)))
<=> ( X12 != X11
& ( X12 = X19
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X11)),X10)) )
& ( X12 != X19
=> ( ( X11 = X19
=> ( X12 = 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),X12),X20)),X10)) ) )
& ( X11 != X19
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),X10)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_in__below,axiom,
! [X11,X12,X10,X19,X20] :
( X20 != X19
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),c_Arrow__Order__Mirabelle_Obelow(X10,X20,X19)))
<=> ( X12 != X11
& ( X11 = 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),X12),X19)),X10)) )
& ( X11 != X20
=> ( ( X12 = X20
=> ( X11 = X19
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X11)),X10)) ) )
& ( X12 != 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),X12),X11)),X10)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_total__on__def,axiom,
! [X18,X8,X6] :
( c_Relation_Ototal__on(X6,X8,X18)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> ! [X35] :
( hBOOL(hAPP(hAPP(c_member(X6),X35),X8))
=> ( X3 != X35
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X35)),X18))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X35),X3)),X18)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
fof(fact_single__valued__confluent,axiom,
! [X9,X11,X12,X18,X6] :
( c_Relation_Osingle__valued(X6,X6,X18)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X9)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X9)),c_Transitive__Closure_Ortrancl(X6,X18)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X9),X11)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_Domain__iff,axiom,
! [X18,X15,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),c_Relation_ODomain(X6,X15,X18)))
<=> ? [X29] : hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X29)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
fof(fact_bex__Un,axiom,
! [X17,X7,X8,X6] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
& hBOOL(hAPP(X17,X3)) )
<=> ( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
& hBOOL(hAPP(X17,X3)) )
| ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X7))
& hBOOL(hAPP(X17,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
fof(fact_ball__Un,axiom,
! [X17,X7,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
=> hBOOL(hAPP(X17,X3)) )
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(X17,X3)) )
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X7))
=> hBOOL(hAPP(X17,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
fof(fact_in__inv__image,axiom,
! [X2,X18,X15,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Relation_Oinv__image(X15,X6,X18,X2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X15,X15)),hAPP(hAPP(c_Product__Type_OPair(X15,X15),hAPP(X2,X12)),hAPP(X2,X11))),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).
fof(fact_fun__upd__upd,axiom,
! [X9,X11,X12,X2,X15,X6] : c_Fun_Ofun__upd(X6,X15,c_Fun_Ofun__upd(X6,X15,X2,X12,X11),X12,X9) = c_Fun_Ofun__upd(X6,X15,X2,X12,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
fof(fact_trancl__trans,axiom,
! [X5,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),c_Transitive__Closure_Otrancl(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Otrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [X9,X18,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X9)),c_Transitive__Closure_Otrancl(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X9)),c_Transitive__Closure_Otrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(fact_trancl__rtrancl__trancl,axiom,
! [X5,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Otrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(fact_rtrancl__trans,axiom,
! [X5,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_inf2D1,axiom,
! [X11,X12,X7,X8,X15,X6] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X15,tc_HOL_Obool))),X8),X7),X12),X11))
=> hBOOL(hAPP(hAPP(X8,X12),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
fof(fact_inf2D2,axiom,
! [X11,X12,X7,X8,X15,X6] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X15,tc_HOL_Obool))),X8),X7),X12),X11))
=> hBOOL(hAPP(hAPP(X7,X12),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
fof(fact_trancl__into__trancl2,axiom,
! [X5,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),c_Transitive__Closure_Otrancl(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Otrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
fof(fact_rtrancl__into__trancl2,axiom,
! [X5,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Otrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
! [X5,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),X18))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Otrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(fact_rtrancl__into__trancl1,axiom,
! [X5,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),X18))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Otrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [X5,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [X5,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),X18))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_r__r__into__trancl,axiom,
! [X5,X14,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),X14))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),X14))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X5)),c_Transitive__Closure_Otrancl(X6,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
fof(fact_in__rtrancl__UnI,axiom,
! [X32,X14,X12,X6] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X12),c_Transitive__Closure_Ortrancl(X6,X14)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X12),c_Transitive__Closure_Ortrancl(X6,X32))) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X12),c_Transitive__Closure_Ortrancl(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X14),X32)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
fof(fact_single__valuedI,axiom,
! [X18,X15,X6] :
( ! [X3,X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X3),X29)),X18))
=> ! [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X3),X28)),X18))
=> X29 = X28 ) )
=> c_Relation_Osingle__valued(X6,X15,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedI) ).
fof(fact_single__valued__def,axiom,
! [X18,X15,X6] :
( c_Relation_Osingle__valued(X6,X15,X18)
<=> ! [X3,X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X3),X29)),X18))
=> ! [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X3),X28)),X18))
=> X29 = X28 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(fact_Times__Un__distrib1,axiom,
! [X38,X7,X8,X15,X6] : c_Product__Type_OSigma(X6,X15,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X38)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X38))),c_Product__Type_OSigma(X6,X15,X7,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).
fof(fact_Times__Int__distrib1,axiom,
! [X38,X7,X8,X15,X6] : c_Product__Type_OSigma(X6,X15,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X38)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X38))),c_Product__Type_OSigma(X6,X15,X7,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).
fof(fact_funcset__mem,axiom,
! [X12,X7,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X12)),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_single__valuedD,axiom,
! [X9,X11,X12,X18,X15,X6] :
( c_Relation_Osingle__valued(X6,X15,X18)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X12),X11)),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X12),X9)),X18))
=> X11 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedD) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X6,X15] :
( class_Orderings_Oord(X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X15),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X15,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_mem__Sigma__iff,axiom,
! [X7,X8,X19,X20,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19)),c_Product__Type_OSigma(X6,X15,X8,X7)))
<=> ( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
& hBOOL(hAPP(hAPP(c_member(X15),X19),hAPP(X7,X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
fof(fact_SigmaD2,axiom,
! [X7,X8,X19,X20,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19)),c_Product__Type_OSigma(X6,X15,X8,X7)))
=> hBOOL(hAPP(hAPP(c_member(X15),X19),hAPP(X7,X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD2) ).
fof(fact_antisym__def,axiom,
! [X18,X6] :
( c_Relation_Oantisym(X6,X18)
<=> ! [X3,X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X29)),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X3)),X18))
=> X3 = X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__def) ).
fof(fact_antisymD,axiom,
! [X19,X20,X18,X6] :
( c_Relation_Oantisym(X6,X18)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X20)),X18))
=> X20 = X19 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisymD) ).
fof(fact_SigmaD1,axiom,
! [X7,X8,X19,X20,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19)),c_Product__Type_OSigma(X6,X15,X8,X7)))
=> hBOOL(hAPP(hAPP(c_member(X6),X20),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD1) ).
fof(fact_trancl__subset__Sigma__aux,axiom,
! [X8,X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X18,c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8)))
=> ( X20 = X19
| hBOOL(hAPP(hAPP(c_member(X6),X20),X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
fof(fact_const__Lin__Prof,axiom,
! [X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,X10)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_mlex__leq,axiom,
! [X14,X6,X11,X12,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X11))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X14))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Wellfounded_Omlex__prod(X6,X2,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_inf2I,axiom,
! [X15,X6,X7,X11,X12,X8] :
( hBOOL(hAPP(hAPP(X8,X12),X11))
=> ( hBOOL(hAPP(hAPP(X7,X12),X11))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X15,tc_HOL_Obool))),X8),X7),X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
fof(fact_Times__subset__cancel2,axiom,
! [X7,X8,X15,X38,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X38))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15,X6),tc_HOL_Obool),c_Product__Type_OSigma(X15,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X15,X38)),c_Product__Type_OSigma(X15,X6,X7,c_COMBK(tc_fun(X6,tc_HOL_Obool),X15,X38)))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).
fof(fact_acc_OaccI,axiom,
! [X18,X12,X6] :
( ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X12)),X18))
=> hBOOL(hAPP(hAPP(c_member(X6),X29),c_Wellfounded_Oacc(X6,X18))) )
=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
fof(fact_acc_Osimps,axiom,
! [X18,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),c_Wellfounded_Oacc(X6,X18)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X20)),X18))
=> hBOOL(hAPP(hAPP(c_member(X6),X3),c_Wellfounded_Oacc(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
fof(fact_rtrancl__eq__or__trancl,axiom,
! [X14,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X14)))
<=> ( X12 = X11
| ( X12 != X11
& hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Otrancl(X6,X14))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
fof(fact_rtranclD,axiom,
! [X14,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X14)))
=> ( X20 = X19
| ( X20 != X19
& hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Otrancl(X6,X14))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).
fof(fact_trancl__into__rtrancl,axiom,
! [X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Otrancl(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
fof(fact_trancl_Or__into__trancl,axiom,
! [X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),X18))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Otrancl(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
fof(fact_split__paired__All,axiom,
! [X15,X6,X17] :
( ! [X74] : hBOOL(hAPP(X17,X74))
<=> ! [X33,X34] : hBOOL(hAPP(X17,hAPP(hAPP(c_Product__Type_OPair(X6,X15),X33),X34))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [X18,X6] :
( c_Nitpick_Orefl_H(X6,X18)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_Pi__eq__empty,axiom,
! [X7,X8,X15,X6] :
( c_FuncSet_OPi(X6,X15,X8,X7) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X6,X15),tc_HOL_Obool))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
& hAPP(X7,X3) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__eq__empty) ).
fof(fact_Range__Int__subset,axiom,
! [X7,X8,X15,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Relation_ORange(X15,X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X15,X6),tc_HOL_Obool)),X8),X7)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Relation_ORange(X15,X6,X8)),c_Relation_ORange(X15,X6,X7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
fof(fact_Domain__Int__subset,axiom,
! [X7,X8,X15,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Relation_ODomain(X6,X15,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),X8),X7)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Relation_ODomain(X6,X15,X8)),c_Relation_ODomain(X6,X15,X7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_restrict__extensional,axiom,
! [X8,X2,X15,X6] : hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),c_FuncSet_Orestrict(X6,X15,X2,X8)),c_FuncSet_Oextensional(X6,X15,X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__extensional) ).
fof(fact_Pi__mem,axiom,
! [X12,X7,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,X7)))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X12)),hAPP(X7,X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_SigmaI,axiom,
! [X7,X19,X15,X8,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> ( hBOOL(hAPP(hAPP(c_member(X15),X19),hAPP(X7,X20)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19)),c_Product__Type_OSigma(X6,X15,X8,X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaI) ).
fof(fact_fun__upd__def,axiom,
! [X19,X2,X15,X6,X20,X12] :
( ( X12 = X20
=> hAPP(c_Fun_Ofun__upd(X6,X15,X2,X20,X19),X12) = X19 )
& ( X12 != X20
=> hAPP(c_Fun_Ofun__upd(X6,X15,X2,X20,X19),X12) = hAPP(X2,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
fof(fact_fun__upd__other,axiom,
! [X11,X2,X15,X6,X12,X9] :
( X9 != X12
=> hAPP(c_Fun_Ofun__upd(X6,X15,X2,X12,X11),X9) = hAPP(X2,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
fof(fact_fun__upd__apply,axiom,
! [X11,X2,X15,X6,X12,X9] :
( ( X9 = X12
=> hAPP(c_Fun_Ofun__upd(X6,X15,X2,X12,X11),X9) = X11 )
& ( X9 != X12
=> hAPP(c_Fun_Ofun__upd(X6,X15,X2,X12,X11),X9) = hAPP(X2,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
fof(fact_tranclp_Oequations_I1_J,axiom,
! [X24,X25,X18,X6] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X25),X24))
<=> ( hBOOL(hAPP(hAPP(X18,X25),X24))
| ? [X34] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X25),X34))
& hBOOL(hAPP(hAPP(X18,X34),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclp_Oequations_I1_J) ).
fof(fact_tranclp_Oequations_I2_J,axiom,
! [X61,X25,X18,X6] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X25),X61))
<=> ( hBOOL(hAPP(hAPP(X18,X25),X61))
| ? [X34] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X25),X34))
& hBOOL(hAPP(hAPP(X18,X34),X61)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclp_Oequations_I2_J) ).
fof(fact_extensional__funcset__mem,axiom,
! [X12,X36,X32,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional__funcset(X6,X15,X32,X36)))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X32))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X12)),X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__mem) ).
fof(fact_fun__upd__same,axiom,
! [X11,X12,X2,X6,X15] : hAPP(c_Fun_Ofun__upd(X15,X6,X2,X12,X11),X12) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
fof(fact_rtrancl__Un__subset,axiom,
! [X32,X14,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X6,X14)),c_Transitive__Closure_Ortrancl(X6,X32)),c_Transitive__Closure_Ortrancl(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X14),X32))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
fof(fact_trancl__subset__Sigma,axiom,
! [X8,X18,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X18,c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8)))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X6,X18),c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).
fof(fact_pred__subset__eq,axiom,
! [X32,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X14),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X32))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X14,X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_in__mkbot,axiom,
! [X9,X10,X11,X12] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),c_Arrow__Order__Mirabelle_Omkbot(X10,X9)))
<=> ( X11 != X9
& ( X12 = X9
=> X12 != X11 )
& ( X12 != X9
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [X9,X10,X11,X12] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),c_Arrow__Order__Mirabelle_Omktop(X10,X9)))
<=> ( X12 != X9
& ( X11 = X9
=> X12 != X11 )
& ( X11 != X9
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(fact_Sigma__Un__distrib1,axiom,
! [X38,X79,X78,X15,X6] : c_Product__Type_OSigma(X6,X15,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X78),X79),X38) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X15,X78,X38)),c_Product__Type_OSigma(X6,X15,X79,X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).
fof(fact_Sigma__Int__distrib1,axiom,
! [X38,X79,X78,X15,X6] : c_Product__Type_OSigma(X6,X15,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X78),X79),X38) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X15,X78,X38)),c_Product__Type_OSigma(X6,X15,X79,X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).
fof(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096,axiom,
! [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),v_a____),v_b____)),hAPP(v_P____,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),v_a____),v_b____)),hAPP(v_Q____,X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096) ).
fof(fact__C1_C,axiom,
! [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),v_a____),v_b____)),hAPP(v_P____,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),v_a_H____),v_b_H____)),hAPP(v_P_H____,X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_extensional__funcset__def,axiom,
! [X36,X32,X15,X6] : c_FuncSet_Oextensional__funcset(X6,X15,X32,X36) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X6,X15),tc_HOL_Obool)),c_FuncSet_OPi(X6,X15,X32,c_COMBK(tc_fun(X15,tc_HOL_Obool),X6,X36))),c_FuncSet_Oextensional(X6,X15,X32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__def) ).
fof(fact_above__Lin,axiom,
! [X10,X11,X12] :
( X12 != X11
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X10),X12),X11)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_wf__same__fst,axiom,
! [X6,X14,X15,X17] :
( ! [X3] :
( hBOOL(hAPP(X17,X3))
=> c_Wellfounded_Owf(X15,hAPP(X14,X3)) )
=> c_Wellfounded_Owf(tc_prod(X6,X15),c_Recdef_Osame__fst(X6,X15,X17,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__same__fst) ).
fof(fact_in__rel__def,axiom,
! [X11,X12,X14,X15,X6] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X6,X15,X14),X12),X11))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X12),X11)),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_acc__downwards__aux,axiom,
! [X18,X20,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X20)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X20),c_Wellfounded_Oacc(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(X6),X19),c_Wellfounded_Oacc(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_acc__downwards,axiom,
! [X19,X18,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),c_Wellfounded_Oacc(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X20)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> hBOOL(hAPP(hAPP(c_member(X6),X19),c_Wellfounded_Oacc(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
fof(fact_dictator__def,axiom,
! [X4,X26] :
( c_Arrow__Order__Mirabelle_Odictator(X26,X4)
<=> ! [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(X26,X3) = hAPP(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_tfl__cut__apply,axiom,
! [X15,X20,X12,X6,X30,X31] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X20)),X31))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),X30),X31),X20),X12) = hAPP(X30,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
fof(fact_cut__apply,axiom,
! [X2,X15,X18,X20,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X20)),X18))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),X2),X18),X20),X12) = hAPP(X2,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut__apply) ).
fof(fact_acc__downward,axiom,
! [X20,X18,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Wellfounded_Oacc(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),X18))
=> hBOOL(hAPP(hAPP(c_member(X6),X20),c_Wellfounded_Oacc(X6,X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).
fof(fact_below__Lin,axiom,
! [X10,X11,X12] :
( X12 != X11
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X10,X12,X11)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_DomainI,axiom,
! [X18,X19,X20,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19)),X18))
=> hBOOL(hAPP(hAPP(c_member(X6),X20),c_Relation_ODomain(X6,X15,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).
fof(fact_RangeI,axiom,
! [X18,X19,X20,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19)),X18))
=> hBOOL(hAPP(hAPP(c_member(X15),X19),c_Relation_ORange(X6,X15,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeI) ).
fof(fact_funcset__id,axiom,
! [X8,X6] : hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X6)),c_COMBI(X6)),c_FuncSet_OPi(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(fact_fun__upd__idem__iff,axiom,
! [X11,X12,X2,X15,X6] :
( c_Fun_Ofun__upd(X6,X15,X2,X12,X11) = X2
<=> hAPP(X2,X12) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
fof(fact_Un__Int__assoc__eq,axiom,
! [X38,X7,X8,X6] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X38))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X38,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
fof(fact_refl__onD1,axiom,
! [X11,X12,X18,X8,X6] :
( c_Relation_Orefl__on(X6,X8,X18)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X18))
=> hBOOL(hAPP(hAPP(c_member(X6),X12),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).
fof(fact_refl__onD2,axiom,
! [X11,X12,X18,X8,X6] :
( c_Relation_Orefl__on(X6,X8,X18)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X18))
=> hBOOL(hAPP(hAPP(c_member(X6),X11),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).
fof(fact_Id__on__iff,axiom,
! [X8,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Relation_OId__on(X6,X8)))
<=> ( X12 = X11
& hBOOL(hAPP(hAPP(c_member(X6),X12),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
fof(fact_Un__Int__distrib2,axiom,
! [X8,X38,X7,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38)),X8) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X38),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).
fof(fact_Int__Un__distrib2,axiom,
! [X8,X38,X7,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X38)),X8) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X38),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).
fof(fact_antisymI,axiom,
! [X18,X6] :
( ! [X3,X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X29)),X18))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X3)),X18))
=> X3 = X29 ) )
=> c_Relation_Oantisym(X6,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisymI) ).
fof(fact_mktop__Lin,axiom,
! [X12,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(X10,X12)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin) ).
fof(fact_mkbot__Lin,axiom,
! [X12,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(X10,X12)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_rtrancl__Un__rtrancl,axiom,
! [X32,X14,X6] : c_Transitive__Closure_Ortrancl(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X6,X14)),c_Transitive__Closure_Ortrancl(X6,X32))) = c_Transitive__Closure_Ortrancl(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X14),X32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
fof(fact_wf__Un,axiom,
! [X21,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ( c_Wellfounded_Owf(X6,X21)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Relation_ODomain(X6,X6,X18)),c_Relation_ORange(X6,X6,X21)) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> c_Wellfounded_Owf(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X18),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Un) ).
fof(fact_extensional__subset,axiom,
! [X7,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional(X6,X15,X8)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional(X6,X15,X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__subset) ).
fof(fact_Un__Int__distrib,axiom,
! [X38,X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).
fof(fact_Int__Un__distrib,axiom,
! [X38,X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).
fof(fact_Times__eq__cancel2,axiom,
! [X7,X8,X15,X38,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X38))
=> ( c_Product__Type_OSigma(X15,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X15,X38)) = c_Product__Type_OSigma(X15,X6,X7,c_COMBK(tc_fun(X6,tc_HOL_Obool),X15,X38))
<=> X8 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
fof(fact_internal__split__conv,axiom,
! [X19,X20,X5,X6,X39,X15] : c_Product__Type_Ointernal__split(X15,X39,X6,X5,hAPP(hAPP(c_Product__Type_OPair(X15,X39),X20),X19)) = hAPP(hAPP(X5,X20),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__conv) ).
fof(fact_prod_Orecs,axiom,
! [X19,X20,X80,X6,X39,X15] : c_Product__Type_Oprod_Oprod__rec(X15,X39,X6,X80,hAPP(hAPP(c_Product__Type_OPair(X15,X39),X20),X19)) = hAPP(hAPP(X80,X20),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
fof(conj_0,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_refl__onD,axiom,
! [X20,X18,X8,X6] :
( c_Relation_Orefl__on(X6,X8,X18)
=> ( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X20)),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).
fof(fact_Un__iff,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
<=> ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
| hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__iff) ).
fof(fact_Id__on__eqI,axiom,
! [X8,X6,X19,X20] :
( X20 = X19
=> ( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Relation_OId__on(X6,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_def__wfrec,axiom,
! [X20,X73,X18,X15,X6,X2] :
( X2 = c_Recdef_Owfrec(X6,X15,X18,X73)
=> ( c_Wellfounded_Owf(X6,X18)
=> hAPP(X2,X20) = hAPP(hAPP(X73,hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),X2),X18),X20)),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__wfrec) ).
fof(fact_Pi__anti__mono,axiom,
! [X7,X15,X8,X67,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X67,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X6,X15),tc_HOL_Obool),c_FuncSet_OPi(X6,X15,X8,X7),c_FuncSet_OPi(X6,X15,X67,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_fun__upd__triv,axiom,
! [X12,X2,X15,X6] : c_Fun_Ofun__upd(X6,X15,X2,X12,hAPP(X2,X12)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
fof(fact_fun__upd__idem,axiom,
! [X6,X15,X11,X12,X2] :
( hAPP(X2,X12) = X11
=> c_Fun_Ofun__upd(X15,X6,X2,X12,X11) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
fof(fact_Range__Un__eq,axiom,
! [X7,X8,X6,X15] : c_Relation_ORange(X15,X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15,X6),tc_HOL_Obool)),X8),X7)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),c_Relation_ORange(X15,X6,X8)),c_Relation_ORange(X15,X6,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Un__eq) ).
fof(fact_Domain__Un__eq,axiom,
! [X7,X8,X15,X6] : c_Relation_ODomain(X6,X15,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)),X8),X7)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),c_Relation_ODomain(X6,X15,X8)),c_Relation_ODomain(X6,X15,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).
fof(fact_refl__on__Un,axiom,
! [X21,X7,X18,X8,X6] :
( c_Relation_Orefl__on(X6,X8,X18)
=> ( c_Relation_Orefl__on(X6,X7,X21)
=> c_Relation_Orefl__on(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X18),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Un) ).
fof(fact_refl__on__Int,axiom,
! [X21,X7,X18,X8,X6] :
( c_Relation_Orefl__on(X6,X8,X18)
=> ( c_Relation_Orefl__on(X6,X7,X21)
=> c_Relation_Orefl__on(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X18),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Int) ).
fof(fact_Int__iff,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
<=> ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
& hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD1,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).
fof(fact_IntD2,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).
fof(fact_trancl__mono,axiom,
! [X21,X18,X43,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X43),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X18,X21)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X43),c_Transitive__Closure_Otrancl(X6,X21))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__mono) ).
fof(fact_Un__assoc,axiom,
! [X38,X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
fof(fact_Int__assoc,axiom,
! [X38,X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
fof(fact_Id__onE,axiom,
! [X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X5),c_Relation_OId__on(X6,X8)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> X5 != hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
fof(fact_pred__equals__eq,axiom,
! [X32,X14,X6] :
( hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X14) = hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X32)
<=> X14 = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [X18,X20,X6] : hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X20)),c_Transitive__Closure_Ortrancl(X6,X18))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_distrib__inf__le,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X54)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__inf__le) ).
fof(fact_distrib__sup__le,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X54)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__sup__le) ).
fof(fact_extensional__restrict,axiom,
! [X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional(X6,X15,X8)))
=> c_FuncSet_Orestrict(X6,X15,X2,X8) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__restrict) ).
fof(help_c__COMBB__1,axiom,
! [X14,X64,X17,X39,X6,X15] : hAPP(hAPP(c_COMBB(X15,X6,X39,X17),X64),X14) = hAPP(X17,hAPP(X64,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_IntI,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X5),X7))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).
fof(fact_inf1D1,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12))
=> hBOOL(hAPP(X8,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
fof(fact_inf1D2,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12))
=> hBOOL(hAPP(X7,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
fof(fact_Id__on__subset__Times,axiom,
! [X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),c_Relation_OId__on(X6,X8),c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).
fof(fact_complete__Lin,axiom,
! [X19,X20] :
( X20 != X19
=> ? [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),X20),X19)),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complete__Lin) ).
fof(fact__096_B_Bi_O_Ab_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_H_096,axiom,
! [X4] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_Q____,X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bi_O_Ab_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_H_096) ).
fof(fact_calculation_I2_J,axiom,
( v_a____ != v_a_H____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_a____)),hAPP(v_F,v_Q____))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_calculation_I2_J) ).
fof(fact_Un__mono,axiom,
! [X40,X7,X38,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X40)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X38),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
fof(fact_Int__mono,axiom,
! [X40,X7,X38,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X40)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X38),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
fof(fact_Int__insert__left__if1,axiom,
! [X7,X38,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),X38))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,X7)),X38) = c_Set_Oinsert(X6,X20,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
fof(fact_r__into__trancl_H,axiom,
! [X18,X43,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X43),X18))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X43),c_Transitive__Closure_Otrancl(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_r__into__rtrancl,axiom,
! [X18,X43,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X43),X18))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X43),c_Transitive__Closure_Ortrancl(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_Un__left__commute,axiom,
! [X38,X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
fof(fact_Int__left__commute,axiom,
! [X38,X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
fof(fact_UnI1,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).
fof(fact_UnI2,axiom,
! [X8,X7,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),X7))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).
fof(fact_doubleton__eq__iff,axiom,
! [X70,X5,X19,X20,X6] :
( c_Set_Oinsert(X6,X20,c_Set_Oinsert(X6,X19,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))) = c_Set_Oinsert(X6,X5,c_Set_Oinsert(X6,X70,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))))
<=> ( ( X20 = X5
& X19 = X70 )
| ( X20 = X70
& X19 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
fof(fact_singletonE,axiom,
! [X20,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Set_Oinsert(X6,X20,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))))
=> X19 = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
fof(fact_singleton__iff,axiom,
! [X20,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Set_Oinsert(X6,X20,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))))
<=> X19 = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
fof(fact_insert__inter__insert,axiom,
! [X7,X8,X20,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,X8)),c_Set_Oinsert(X6,X20,X7)) = c_Set_Oinsert(X6,X20,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
fof(fact_tranclp__trans,axiom,
! [X9,X11,X12,X18,X6] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X12),X11))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X11),X9))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X12),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclp__trans) ).
fof(fact_Int__insert__right__if1,axiom,
! [X7,X8,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),c_Set_Oinsert(X6,X20,X7)) = c_Set_Oinsert(X6,X20,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
fof(fact_Range__insert,axiom,
! [X18,X19,X20,X6,X15] : c_Relation_ORange(X15,X6,c_Set_Oinsert(tc_prod(X15,X6),hAPP(hAPP(c_Product__Type_OPair(X15,X6),X20),X19),X18)) = c_Set_Oinsert(X6,X19,c_Relation_ORange(X15,X6,X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).
fof(fact_Domain__insert,axiom,
! [X18,X19,X20,X15,X6] : c_Relation_ODomain(X6,X15,c_Set_Oinsert(tc_prod(X6,X15),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19),X18)) = c_Set_Oinsert(X6,X20,c_Relation_ODomain(X6,X15,X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).
fof(fact_wf__Int1,axiom,
! [X69,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> c_Wellfounded_Owf(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X18),X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int1) ).
fof(fact_wf__Int2,axiom,
! [X69,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> c_Wellfounded_Owf(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X69),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int2) ).
fof(fact_disjoint__iff__not__equal,axiom,
! [X7,X8,X6] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> ! [X35] :
( hBOOL(hAPP(hAPP(c_member(X6),X35),X7))
=> X3 != X35 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
fof(fact_Un__insert__left,axiom,
! [X38,X7,X20,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,X7)),X38) = c_Set_Oinsert(X6,X20,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
fof(fact_inf1I,axiom,
! [X6,X7,X12,X8] :
( hBOOL(hAPP(X8,X12))
=> ( hBOOL(hAPP(X7,X12))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
fof(fact_extensional__funcset__empty__domain,axiom,
! [X36,X15,X6] : c_FuncSet_Oextensional__funcset(X6,X15,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),X36) = c_Set_Oinsert(tc_fun(X6,X15),c_COMBK(X15,X6,c_HOL_Oundefined(X15)),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X6,X15),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__empty__domain) ).
fof(fact_sup1I1,axiom,
! [X7,X6,X12,X8] :
( hBOOL(hAPP(X8,X12))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
fof(fact_sup1I2,axiom,
! [X8,X6,X12,X7] :
( hBOOL(hAPP(X7,X12))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
fof(fact_sup__inf__distrib2,axiom,
! [X56,X54,X55,X6] :
( class_Lattices_Odistrib__lattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X54)),X56) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X56)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X54),X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).
fof(fact_inf__sup__distrib2,axiom,
! [X56,X54,X55,X6] :
( class_Lattices_Odistrib__lattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X54)),X56) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X56)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X54),X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).
fof(fact_insert__is__Un,axiom,
! [X8,X20,X6] : c_Set_Oinsert(X6,X20,X8) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
fof(fact_insert__iff,axiom,
! [X8,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),c_Set_Oinsert(X6,X19,X8)))
<=> ( X20 = X19
| hBOOL(hAPP(hAPP(c_member(X6),X20),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X8,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),c_Set_Oinsert(X6,X19,X8)))
=> ( X20 != X19
=> hBOOL(hAPP(hAPP(c_member(X6),X20),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_tranclp_Otrancl__into__trancl,axiom,
! [X5,X19,X20,X18,X6] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X20),X19))
=> ( hBOOL(hAPP(hAPP(X18,X19),X5))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X20),X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclp_Otrancl__into__trancl) ).
fof(fact_tranclp__into__tranclp2,axiom,
! [X5,X6,X19,X20,X18] :
( hBOOL(hAPP(hAPP(X18,X20),X19))
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X19),X5))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X20),X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclp__into__tranclp2) ).
fof(fact_Un__least,axiom,
! [X7,X38,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X38)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),X38) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
fof(fact_Int__greatest,axiom,
! [X7,X8,X38,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X38,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X38,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X38,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
fof(fact_accp_Oequations,axiom,
! [X20,X18,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X18),X20))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X18,X3),X20))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X18),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
fof(fact_accp_Osimps,axiom,
! [X20,X18,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X18),X20))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X18,X3),X20))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X18),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
fof(fact_Un__insert__right,axiom,
! [X7,X20,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),c_Set_Oinsert(X6,X20,X7)) = c_Set_Oinsert(X6,X20,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
fof(help_c__COMBS__1,axiom,
! [X14,X64,X17,X6,X39,X15] : hAPP(hAPP(hAPP(c_COMBS(X15,X39,X6),X17),X64),X14) = hAPP(hAPP(X17,X14),hAPP(X64,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_wf__lex__prod,axiom,
! [X62,X15,X63,X6] :
( c_Wellfounded_Owf(X6,X63)
=> ( c_Wellfounded_Owf(X15,X62)
=> c_Wellfounded_Owf(tc_prod(X6,X15),c_Wellfounded_Olex__prod(X6,X15,X63,X62)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
fof(fact_RangeP_Oequations,axiom,
! [X24,X18,X15,X6] :
( c_Predicate_ORangeP(X6,X15,X18,X24)
<=> ? [X33] : hBOOL(hAPP(hAPP(X18,X33),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
fof(fact_Un__left__absorb,axiom,
! [X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
fof(fact_Int__left__absorb,axiom,
! [X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
fof(help_c__COMBC__1,axiom,
! [X14,X64,X17,X6,X39,X15] : hAPP(hAPP(hAPP(c_COMBC(X15,X39,X6),X17),X64),X14) = hAPP(hAPP(X17,X14),X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_wf__inv__image,axiom,
! [X2,X15,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> c_Wellfounded_Owf(X15,c_Relation_Oinv__image(X6,X15,X18,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__inv__image) ).
fof(fact_sup__inf__distrib1,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Odistrib__lattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X54)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).
fof(fact_inf__sup__distrib1,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Odistrib__lattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X54)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).
fof(fact_the__eq__trivial,axiom,
! [X20,X6] : c_HOL_OThe(X6,hAPP(hAPP(c_COMBC(X6,X6,tc_HOL_Obool),c_fequal),X20)) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__eq__trivial) ).
fof(fact_Domain__mono,axiom,
! [X21,X18,X15,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),X18,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Relation_ODomain(X6,X15,X18),c_Relation_ODomain(X6,X15,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).
fof(fact_insertI2,axiom,
! [X19,X7,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),X7))
=> hBOOL(hAPP(hAPP(c_member(X6),X20),c_Set_Oinsert(X6,X19,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
fof(fact_rtrancl__subset,axiom,
! [X32,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X14,X32)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X32,c_Transitive__Closure_Ortrancl(X6,X14))
=> c_Transitive__Closure_Ortrancl(X6,X32) = c_Transitive__Closure_Ortrancl(X6,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_insert__subset,axiom,
! [X7,X8,X12,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Set_Oinsert(X6,X12,X8),X7)
<=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X7))
& c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_bot__empty__eq,axiom,
! [X12,X6] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),X12))
<=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
fof(fact_extensional__empty,axiom,
! [X15,X6] : c_FuncSet_Oextensional(X6,X15,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = c_Set_Oinsert(tc_fun(X6,X15),c_COMBK(X15,X6,c_HOL_Oundefined(X15)),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X6,X15),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__empty) ).
fof(fact_sup__fun__def,axiom,
! [X12,X1,X2,X15,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15,X6)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),hAPP(X2,X12)),hAPP(X1,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__fun__def) ).
fof(fact_sup__apply,axiom,
! [X12,X1,X2,X15,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15,X6)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),hAPP(X2,X12)),hAPP(X1,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__apply) ).
fof(fact_inf__apply,axiom,
! [X12,X1,X2,X15,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15,X6)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(X2,X12)),hAPP(X1,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__apply) ).
fof(fact_inf__fun__def,axiom,
! [X12,X1,X2,X15,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15,X6)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(X2,X12)),hAPP(X1,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__fun__def) ).
fof(fact_sup__mono,axiom,
! [X68,X58,X57,X59,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X59,X57)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X58,X68)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X57),X68)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__mono) ).
fof(fact_inf__mono,axiom,
! [X68,X58,X57,X59,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X59,X57)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X58,X68)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X57),X68)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__mono) ).
fof(fact_wf__acc__iff,axiom,
! [X18,X6] :
( c_Wellfounded_Owf(X6,X18)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(X6),X3),c_Wellfounded_Oacc(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [X21,X18,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X18,c_Transitive__Closure_Ortrancl(X6,X21))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X6,X18),c_Transitive__Closure_Ortrancl(X6,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_sup__assoc,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)),X54) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__assoc) ).
fof(fact_sup_Oassoc,axiom,
! [X57,X58,X59,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58)),X57) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X58),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oassoc) ).
fof(fact_inf__sup__aci_I6_J,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)),X54) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).
fof(fact_inf_Oassoc,axiom,
! [X57,X58,X59,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58)),X57) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X58),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
fof(fact_inf__assoc,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55)),X54) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__assoc) ).
fof(fact_inf__sup__aci_I2_J,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55)),X54) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
fof(fact_insert__code,axiom,
! [X12,X8,X11,X6] :
( hBOOL(hAPP(c_Set_Oinsert(X6,X11,X8),X12))
<=> ( X11 = X12
| hBOOL(hAPP(X8,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_insert__mono,axiom,
! [X20,X40,X38,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X38,X40)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Set_Oinsert(X6,X20,X38),c_Set_Oinsert(X6,X20,X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(fact_predicate2D,axiom,
! [X11,X12,X64,X17,X15,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X15,tc_HOL_Obool)),X17,X64)
=> ( hBOOL(hAPP(hAPP(X17,X12),X11))
=> hBOOL(hAPP(hAPP(X64,X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X64,X15,X6,X11,X12,X17] :
( hBOOL(hAPP(hAPP(X17,X12),X11))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X15,tc_HOL_Obool)),X17,X64)
=> hBOOL(hAPP(hAPP(X64,X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_extensional__funcset__empty__range,axiom,
! [X15,X6,X32] :
( X32 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> c_FuncSet_Oextensional__funcset(X6,X15,X32,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X6,X15),tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__empty__range) ).
fof(fact_set__rev__mp,axiom,
! [X7,X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> hBOOL(hAPP(hAPP(c_member(X6),X12),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_in__mono,axiom,
! [X12,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X12),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_set__mp,axiom,
! [X12,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X12),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_subsetD,axiom,
! [X5,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_rtrancl__mono,axiom,
! [X21,X18,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X18,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X6,X18),c_Transitive__Closure_Ortrancl(X6,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_RangeP_Ointros,axiom,
! [X15,X6,X19,X20,X18] :
( hBOOL(hAPP(hAPP(X18,X20),X19))
=> c_Predicate_ORangeP(X6,X15,X18,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_DomainP_Ointros,axiom,
! [X15,X6,X19,X20,X18] :
( hBOOL(hAPP(hAPP(X18,X20),X19))
=> c_Predicate_ODomainP(X6,X15,X18,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_wfP__empty,axiom,
! [X6] : c_Wellfounded_OwfP(X6,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,c_COMBK(tc_HOL_Obool,X6,c_fFalse))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__empty) ).
fof(fact_Int__lower1,axiom,
! [X7,X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
fof(fact_Int__lower2,axiom,
! [X7,X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
fof(fact_Un__upper1,axiom,
! [X7,X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
fof(fact_Un__upper2,axiom,
! [X8,X7,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
fof(fact_single__valued__subset,axiom,
! [X21,X18,X15,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X15),tc_HOL_Obool),X18,X21)
=> ( c_Relation_Osingle__valued(X6,X15,X21)
=> c_Relation_Osingle__valued(X6,X15,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).
fof(fact_accp__downward,axiom,
! [X20,X19,X18,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X18),X19))
=> ( hBOOL(hAPP(hAPP(X18,X20),X19))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X18),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
fof(fact_sup__least,axiom,
! [X54,X56,X55,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X55,X56)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X54,X56)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X54),X56) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__least) ).
fof(fact_le__supI,axiom,
! [X58,X56,X59,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X59,X56)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X58,X56)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58),X56) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI) ).
fof(fact_le__sup__iff,axiom,
! [X9,X11,X12,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X12),X11),X9)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X9)
& c_Orderings_Oord__class_Oless__eq(X6,X11,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__sup__iff) ).
fof(fact_le__inf__iff,axiom,
! [X9,X11,X12,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X11),X9))
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
& c_Orderings_Oord__class_Oless__eq(X6,X12,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__inf__iff) ).
fof(fact_le__infI,axiom,
! [X58,X59,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X59)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X58)
=> c_Orderings_Oord__class_Oless__eq(X6,X56,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI) ).
fof(fact_inf__greatest,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X55)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X54)
=> c_Orderings_Oord__class_Oless__eq(X6,X56,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X54)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__greatest) ).
fof(fact_singleton__inject,axiom,
! [X19,X20,X6] :
( c_Set_Oinsert(X6,X20,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = c_Set_Oinsert(X6,X19,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))
=> X20 = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
fof(fact_acc__subset,axiom,
! [X65,X66,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X66,X65)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Wellfounded_Oacc(X6,X65),c_Wellfounded_Oacc(X6,X66)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
fof(fact_accp__subset,axiom,
! [X65,X66,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X6,tc_HOL_Obool)),X66,X65)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Wellfounded_Oaccp(X6,X65),c_Wellfounded_Oaccp(X6,X66)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
fof(fact_insert__commute,axiom,
! [X8,X11,X12,X6] : c_Set_Oinsert(X6,X12,c_Set_Oinsert(X6,X11,X8)) = c_Set_Oinsert(X6,X11,c_Set_Oinsert(X6,X12,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_subset__trans,axiom,
! [X38,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X38)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X38) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_insertI1,axiom,
! [X7,X20,X6] : hBOOL(hAPP(hAPP(c_member(X6),X20),c_Set_Oinsert(X6,X20,X7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_sup__left__commute,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X54)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__commute) ).
fof(fact_sup_Oleft__commute,axiom,
! [X57,X59,X58,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X57)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X58),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).
fof(fact_inf__sup__aci_I7_J,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X54)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).
fof(fact_inf_Oleft__commute,axiom,
! [X57,X59,X58,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X57)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X58),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
fof(fact_inf__left__commute,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X54)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf__sup__aci_I3_J,axiom,
! [X54,X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X54)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
fof(fact_tranclp_Or__into__trancl,axiom,
! [X6,X19,X20,X18] :
( hBOOL(hAPP(hAPP(X18,X20),X19))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X6,X18),X20),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclp_Or__into__trancl) ).
fof(fact_subset__insertI2,axiom,
! [X19,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,c_Set_Oinsert(X6,X19,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_subset__Un__eq,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
fof(fact_Un__empty,axiom,
! [X7,X8,X6] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ( X8 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
& X7 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
fof(fact_Pair__eq,axiom,
! [X22,X23,X19,X20,X15,X6] :
( hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19) = hAPP(hAPP(c_Product__Type_OPair(X6,X15),X23),X22)
<=> ( X20 = X23
& X19 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
fof(fact_Pair__inject,axiom,
! [X76,X77,X58,X59,X15,X6] :
( hAPP(hAPP(c_Product__Type_OPair(X6,X15),X59),X58) = hAPP(hAPP(c_Product__Type_OPair(X6,X15),X77),X76)
=> ~ ( X59 = X77
=> X58 != X76 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
fof(fact_Un__commute,axiom,
! [X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
fof(fact_Int__commute,axiom,
! [X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
fof(fact_Int__empty__left,axiom,
! [X7,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),X7) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).
fof(fact_Un__absorb1,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
fof(fact_Un__absorb2,axiom,
! [X8,X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
fof(fact_Int__absorb2,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
fof(fact_Int__absorb1,axiom,
! [X8,X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
fof(fact_refl__on__empty,axiom,
! [X6] : c_Relation_Orefl__on(X6,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X6),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__empty) ).
fof(fact_le__infI1,axiom,
! [X58,X56,X59,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X59,X56)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58),X56) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI1) ).
fof(fact_le__infI2,axiom,
! [X59,X56,X58,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X58,X56)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58),X56) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI2) ).
fof(fact_le__supI1,axiom,
! [X58,X59,X56,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X59)
=> c_Orderings_Oord__class_Oless__eq(X6,X56,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI1) ).
fof(fact_le__supI2,axiom,
! [X59,X58,X56,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X58)
=> c_Orderings_Oord__class_Oless__eq(X6,X56,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI2) ).
fof(fact_trancl__empty,axiom,
! [X6] : c_Transitive__Closure_Otrancl(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X6),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__empty) ).
fof(fact_Un__empty__left,axiom,
! [X7,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),X7) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
fof(fact_set__eq__subset,axiom,
! [X6,X7,X8] :
( X8 = X7
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8)
=> X8 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_eq__mem,axiom,
! [X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),hAPP(c_fequal,X11)))
<=> X12 = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_le__funD,axiom,
! [X12,X1,X2,X6,X15] :
( class_Orderings_Oord(X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X15),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X15,hAPP(X2,X12),hAPP(X1,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X12,X1,X2,X6,X15] :
( class_Orderings_Oord(X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X15),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X15,hAPP(X2,X12),hAPP(X1,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_wf__subset,axiom,
! [X43,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X43,X18)
=> c_Wellfounded_Owf(X6,X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__subset) ).
fof(fact_antisym__subset,axiom,
! [X21,X18,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X18,X21)
=> ( c_Relation_Oantisym(X6,X21)
=> c_Relation_Oantisym(X6,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__subset) ).
fof(fact_acyclic__subset,axiom,
! [X18,X21,X6] :
( c_Wellfounded_Oacyclic(X6,X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X18,X21)
=> c_Wellfounded_Oacyclic(X6,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__subset) ).
fof(fact_ex__in__conv,axiom,
! [X8,X6] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
<=> X8 != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
fof(fact_Range__empty,axiom,
! [X6,X15] : c_Relation_ORange(X15,X6,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15,X6),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty) ).
fof(fact_Domain__empty,axiom,
! [X15,X6] : c_Relation_ODomain(X6,X15,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X15),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty) ).
fof(fact_wfP__subset,axiom,
! [X43,X18,X6] :
( c_Wellfounded_OwfP(X6,X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X6,tc_HOL_Obool)),X43,X18)
=> c_Wellfounded_OwfP(X6,X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
fof(fact_order__trans,axiom,
! [X54,X55,X56,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X55)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X55,X54)
=> c_Orderings_Oord__class_Oless__eq(X6,X56,X54) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X54,X56,X55,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X55,X56)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X54,X55)
=> c_Orderings_Oord__class_Oless__eq(X6,X54,X56) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_wfP__accp__iff,axiom,
! [X18,X6] :
( c_Wellfounded_OwfP(X6,X18)
<=> ! [X74] : hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X18),X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
fof(fact_insert__absorb,axiom,
! [X8,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> c_Set_Oinsert(X6,X20,X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_Int__empty__right,axiom,
! [X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).
fof(fact_insert__absorb2,axiom,
! [X8,X12,X6] : c_Set_Oinsert(X6,X12,c_Set_Oinsert(X6,X12,X8)) = c_Set_Oinsert(X6,X12,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(fact_sup__left__idem,axiom,
! [X55,X56,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__idem) ).
fof(fact_sup_Oleft__idem,axiom,
! [X58,X59,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).
fof(fact_inf__sup__aci_I8_J,axiom,
! [X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).
fof(fact_inf_Oleft__idem,axiom,
! [X58,X59,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
fof(fact_inf__left__idem,axiom,
! [X55,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__idem) ).
fof(fact_inf__sup__aci_I4_J,axiom,
! [X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
fof(fact_Range__empty__iff,axiom,
! [X18,X6,X15] :
( c_Relation_ORange(X15,X6,X18) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> X18 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15,X6),tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
fof(fact_Domain__empty__iff,axiom,
! [X18,X15,X6] :
( c_Relation_ODomain(X6,X15,X18) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> X18 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X15),tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
fof(fact_predicate1D,axiom,
! [X12,X64,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X17,X64)
=> ( hBOOL(hAPP(X17,X12))
=> hBOOL(hAPP(X64,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X64,X6,X12,X17] :
( hBOOL(hAPP(X17,X12))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X17,X64)
=> hBOOL(hAPP(X64,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_mem__def,axiom,
! [X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
<=> hBOOL(hAPP(X8,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_Un__empty__right,axiom,
! [X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
fof(fact_subset__insertI,axiom,
! [X20,X7,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,c_Set_Oinsert(X6,X20,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_xt1_I5_J,axiom,
! [X56,X55,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X55,X56)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X55)
=> X56 = X55 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__antisym,axiom,
! [X55,X56,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X55)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X55,X56)
=> X56 = X55 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_order__antisym__conv,axiom,
! [X12,X11,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X11,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> X12 = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__iff,axiom,
! [X11,X12,X6] :
( class_Orderings_Oorder(X6)
=> ( X12 = X11
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
& c_Orderings_Oord__class_Oless__eq(X6,X11,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_acc__wfD,axiom,
! [X12,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfD) ).
fof(fact_wf__empty,axiom,
! [X6] : c_Wellfounded_Owf(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X6),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).
fof(fact_antisym__empty,axiom,
! [X6] : c_Relation_Oantisym(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X6),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__empty) ).
fof(fact_inf__le1,axiom,
! [X55,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I1_J,axiom,
! [X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_inf__le2,axiom,
! [X55,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le2) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_sup__ge1,axiom,
! [X55,X56,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X56,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge1) ).
fof(fact_inf__sup__ord_I3_J,axiom,
! [X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X56,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).
fof(fact_sup__ge2,axiom,
! [X56,X55,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge2) ).
fof(fact_inf__sup__ord_I4_J,axiom,
! [X56,X55,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).
fof(fact_sup__inf__absorb,axiom,
! [X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55)) = X56 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).
fof(fact_inf__sup__absorb,axiom,
! [X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55)) = X56 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).
fof(fact_sup__absorb2,axiom,
! [X55,X56,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X55)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55) = X55 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb2) ).
fof(fact_le__iff__sup,axiom,
! [X11,X12,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X12),X11) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__sup) ).
fof(fact_sup__absorb1,axiom,
! [X56,X55,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X55,X56)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55) = X56 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb1) ).
fof(fact_le__iff__inf,axiom,
! [X11,X12,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X12),X11) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__inf) ).
fof(fact_inf__absorb1,axiom,
! [X55,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X55)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55) = X56 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb1) ).
fof(fact_inf__absorb2,axiom,
! [X56,X55,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X55,X56)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55) = X55 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb2) ).
fof(fact_Id__on__empty,axiom,
! [X6] : c_Relation_OId__on(X6,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__empty) ).
fof(fact_Un__absorb,axiom,
! [X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
fof(fact_Int__absorb,axiom,
! [X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(fact_wf__in__rel,axiom,
! [X14,X6] :
( c_Wellfounded_Owf(X6,X14)
=> c_Wellfounded_OwfP(X6,c_FunDef_Oin__rel(X6,X6,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__in__rel) ).
fof(fact_wf__mlex,axiom,
! [X2,X14,X6] :
( c_Wellfounded_Owf(X6,X14)
=> c_Wellfounded_Owf(X6,c_Wellfounded_Omlex__prod(X6,X2,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).
fof(fact_trancl__range,axiom,
! [X18,X6] : c_Relation_ORange(X6,X6,c_Transitive__Closure_Otrancl(X6,X18)) = c_Relation_ORange(X6,X6,X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).
fof(fact_trancl__domain,axiom,
! [X18,X6] : c_Relation_ODomain(X6,X6,c_Transitive__Closure_Otrancl(X6,X18)) = c_Relation_ODomain(X6,X6,X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).
fof(fact_empty__subsetI,axiom,
! [X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(fact_empty__not__insert,axiom,
! [X8,X20,X6] : c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) != c_Set_Oinsert(X6,X20,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
fof(fact_insert__not__empty,axiom,
! [X8,X20,X6] : c_Set_Oinsert(X6,X20,X8) != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(help_c__COMBK__1,axiom,
! [X84,X83,X15,X6] : hAPP(c_COMBK(X6,X15,X83),X84) = X83,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_linorder__linear,axiom,
! [X55,X56,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,X55)
| c_Orderings_Oord__class_Oless__eq(X6,X55,X56) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_sup__commute,axiom,
! [X55,X56,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__commute) ).
fof(fact_sup_Ocommute,axiom,
! [X58,X59,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X58),X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Ocommute) ).
fof(fact_inf__sup__aci_I5_J,axiom,
! [X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X55) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X55),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).
fof(fact_inf_Ocommute,axiom,
! [X58,X59,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X58),X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
fof(fact_inf__commute,axiom,
! [X55,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__commute) ).
fof(fact_inf__sup__aci_I1_J,axiom,
! [X55,X56,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X55) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X55),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
fof(fact_total__on__empty,axiom,
! [X18,X6] : c_Relation_Ototal__on(X6,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
fof(fact_accp__wfPD,axiom,
! [X12,X18,X6] :
( c_Wellfounded_OwfP(X6,X18)
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X18),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__wfPD) ).
fof(fact_sup__eq__bot__iff,axiom,
! [X11,X12,X6] :
( class_Lattices_Obounded__lattice__bot(X6)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X12),X11) = c_Orderings_Obot__class_Obot(X6)
<=> ( X12 = c_Orderings_Obot__class_Obot(X6)
& X11 = c_Orderings_Obot__class_Obot(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).
fof(fact_bot__apply,axiom,
! [X12,X15,X6] :
( class_Orderings_Obot(X6)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X15,X6)),X12) = c_Orderings_Obot__class_Obot(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(fact_bot__fun__def,axiom,
! [X12,X15,X6] :
( class_Orderings_Obot(X6)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X15,X6)),X12) = c_Orderings_Obot__class_Obot(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(fact_Range__Id__on,axiom,
! [X8,X6] : c_Relation_ORange(X6,X6,c_Relation_OId__on(X6,X8)) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).
fof(fact_Domain__Id__on,axiom,
! [X8,X6] : c_Relation_ODomain(X6,X6,c_Relation_OId__on(X6,X8)) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_equalityD1,axiom,
! [X6,X7,X8] :
( X8 = X7
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X6,X7,X8] :
( X8 = X7
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_refl__on__Id__on,axiom,
! [X8,X6] : c_Relation_Orefl__on(X6,X8,c_Relation_OId__on(X6,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
fof(fact_single__valued__Id__on,axiom,
! [X8,X6] : c_Relation_Osingle__valued(X6,X6,c_Relation_OId__on(X6,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
fof(help_c__fequal__2,axiom,
! [X11,X12] :
( X12 != X11
| hBOOL(hAPP(hAPP(c_fequal,X12),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_subset__refl,axiom,
! [X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_inf__bot__left,axiom,
! [X56,X6] :
( class_Lattices_Obounded__lattice__bot(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),c_Orderings_Obot__class_Obot(X6)),X56) = c_Orderings_Obot__class_Obot(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__left) ).
fof(fact_sup__bot__left,axiom,
! [X56,X6] :
( class_Lattices_Obounded__lattice__bot(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),c_Orderings_Obot__class_Obot(X6)),X56) = X56 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).
fof(fact_inf__bot__right,axiom,
! [X56,X6] :
( class_Lattices_Obounded__lattice__bot(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),c_Orderings_Obot__class_Obot(X6)) = c_Orderings_Obot__class_Obot(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__right) ).
fof(fact_sup__bot__right,axiom,
! [X56,X6] :
( class_Lattices_Obounded__lattice__bot(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),c_Orderings_Obot__class_Obot(X6)) = X56 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).
fof(fact_order__eq__refl,axiom,
! [X55,X56,X6] :
( class_Orderings_Opreorder(X6)
=> ( X56 = X55
=> c_Orderings_Oord__class_Oless__eq(X6,X56,X55) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_wfP__trancl,axiom,
! [X18,X6] :
( c_Wellfounded_OwfP(X6,X18)
=> c_Wellfounded_OwfP(X6,c_Transitive__Closure_Otranclp(X6,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__trancl) ).
fof(fact_wf__trancl,axiom,
! [X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> c_Wellfounded_Owf(X6,c_Transitive__Closure_Otrancl(X6,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__trancl) ).
fof(fact_acyclic__impl__antisym__rtrancl,axiom,
! [X18,X6] :
( c_Wellfounded_Oacyclic(X6,X18)
=> c_Relation_Oantisym(X6,c_Transitive__Closure_Ortrancl(X6,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
fof(fact_order__refl,axiom,
! [X56,X6] :
( class_Orderings_Opreorder(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X56,X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_sup__idem,axiom,
! [X56,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X56),X56) = X56 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__idem) ).
fof(fact_sup_Oidem,axiom,
! [X59,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X59) = X59 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).
fof(fact_inf_Oidem,axiom,
! [X59,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X59) = X59 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oidem) ).
fof(fact_inf__idem,axiom,
! [X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X56),X56) = X56 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
fof(fact_rtrancl__trancl__absorb,axiom,
! [X14,X6] : c_Transitive__Closure_Otrancl(X6,c_Transitive__Closure_Ortrancl(X6,X14)) = c_Transitive__Closure_Ortrancl(X6,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
fof(fact_trancl__rtrancl__absorb,axiom,
! [X14,X6] : c_Transitive__Closure_Ortrancl(X6,c_Transitive__Closure_Otrancl(X6,X14)) = c_Transitive__Closure_Ortrancl(X6,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(fact_rtrancl__idemp,axiom,
! [X18,X6] : c_Transitive__Closure_Ortrancl(X6,c_Transitive__Closure_Ortrancl(X6,X18)) = c_Transitive__Closure_Ortrancl(X6,X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_wf__measure,axiom,
! [X2,X6] : c_Wellfounded_Owf(X6,c_Wellfounded_Omeasure(X6,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
fof(fact_antisym__Id__on,axiom,
! [X8,X6] : c_Relation_Oantisym(X6,c_Relation_OId__on(X6,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id__on) ).
fof(fact_the__sym__eq__trivial,axiom,
! [X12,X6] : c_HOL_OThe(X6,hAPP(c_fequal,X12)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(arity_fun__Lattices_Obounded__lattice,axiom,
! [X81,X82] :
( class_Lattices_Obounded__lattice(X82)
=> class_Lattices_Obounded__lattice(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(arity_fun__Orderings_Obot,axiom,
! [X81,X82] :
( class_Orderings_Obot(X82)
=> class_Orderings_Obot(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
! [X81,X82] :
( class_Lattices_Obounded__lattice(X82)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(arity_fun__Lattices_Odistrib__lattice,axiom,
! [X81,X82] :
( class_Lattices_Odistrib__lattice(X82)
=> class_Lattices_Odistrib__lattice(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
fof(arity_fun__Lattices_Osemilattice__sup,axiom,
! [X81,X82] :
( class_Lattices_Olattice(X82)
=> class_Lattices_Osemilattice__sup(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X81,X82] :
( class_Orderings_Oorder(X82)
=> class_Orderings_Oorder(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X81,X82] :
( class_Orderings_Oord(X82)
=> class_Orderings_Oord(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X81,X82] :
( class_Orderings_Opreorder(X82)
=> class_Orderings_Opreorder(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Lattices_Osemilattice__inf,axiom,
! [X81,X82] :
( class_Lattices_Olattice(X82)
=> class_Lattices_Osemilattice__inf(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(arity_fun__Lattices_Olattice,axiom,
! [X81,X82] :
( class_Lattices_Olattice(X82)
=> class_Lattices_Olattice(tc_fun(X81,X82)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(fact_wf__acyclic,axiom,
! [X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> c_Wellfounded_Oacyclic(X6,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).
fof(help_c__COMBI__1,axiom,
! [X83,X6] : hAPP(c_COMBI(X6),X83) = X83,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(help_c__fFalse__1,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__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/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(fact__096P_H_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096P_H_A_058_AProf_096) ).
fof(fact__096P_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
fof(fact__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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) ).
fof(fact_calculation_I1_J,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_Q____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_calculation_I1_J) ).
fof(fact__096F_AQ_A_058_ALin_096,axiom,
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/sandbox/benchmark/theBenchmark.p',fact__096F_AQ_A_058_ALin_096) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(arity_Nat__Onat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(arity_Nat__Onat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(arity_HOL__Obool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
fof(fact_d2_I1_J,axiom,
v_a____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d2_I1_J) ).
fof(fact_d1_I1_J,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d1_I1_J) ).
fof(fact_d1_I2_J,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d1_I2_J) ).
fof(fact_d2_I2_J,axiom,
v_b____ != v_a_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d2_I2_J) ).
fof(fact__096b_A_126_061_Ab_H_096,axiom,
v_b____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096b_A_126_061_Ab_H_096) ).
fof(i_0_527,plain,
! [X12,X26,X15,X14,X6] :
( ( c_Wellfounded_Owf(X6,X14)
=> c_Nitpick_Owfrec_H(X6,X15,X14,X26,X12) = c_Nitpick_Owf__wfrec_H(X6,X15,X14,X26,X12) )
& ( ~ c_Wellfounded_Owf(X6,X14)
=> c_Nitpick_Owfrec_H(X6,X15,X14,X26,X12) = c_HOL_OThe(X15,c_Recdef_Owfrec__rel(X6,X15,X14,hAPP(hAPP(c_COMBC(tc_fun(X6,X15),tc_fun(X6,X6),tc_fun(X6,X15)),hAPP(c_COMBB(tc_fun(X6,tc_fun(X6,X15)),tc_fun(tc_fun(X6,X6),tc_fun(X6,X15)),tc_fun(X6,X15),c_COMBS(X6,X6,X15)),hAPP(c_COMBB(tc_fun(X6,tc_fun(X6,X15)),tc_fun(X6,tc_fun(X6,X15)),tc_fun(X6,X15),c_COMBB(tc_fun(X6,X15),tc_fun(X6,X15),X6,X26)),hAPP(hAPP(c_COMBC(tc_fun(X6,X15),tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_fun(X6,X15))),c_Recdef_Ocut(X6,X15)),X14)))),c_COMBI(X6)),X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_Nitpick_Owfrec_H__def]) ).
fof(i_0_528,plain,
! [X18,X44,X45,X46,X47,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X47),X46)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X45),X44))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X15),X18)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X6,X15),X47),X46) != hAPP(hAPP(c_Product__Type_OPair(X6,X15),X45),X44)
=> ~ ! [X33,X34] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X47),X46)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X33),X34))),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X15),tc_prod(X6,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X15),tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X33),X34)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X45),X44))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X15),X18))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_converse__rtranclE2]) ).
fof(i_0_529,plain,
! [X2420,X2421,X2422,X2423,X2424,X2425,X2426,X2427,X2428,X2429,X2430] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2430,X2429)),X2428),c_FuncSet_OPi(X2430,X2429,X2427,c_COMBK(tc_fun(X2429,tc_HOL_Obool),X2430,X2426))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2429,X2425)),X2424),c_FuncSet_OPi(X2429,X2425,X2426,c_COMBK(tc_fun(X2425,tc_HOL_Obool),X2429,X2423))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2425,X2422)),X2421),c_FuncSet_OPi(X2425,X2422,X2423,c_COMBK(tc_fun(X2422,tc_HOL_Obool),X2425,X2420))))
| c_FuncSet_Ocompose(X2430,X2425,X2422,X2427,X2421,c_FuncSet_Ocompose(X2430,X2429,X2425,X2427,X2424,X2428)) = c_FuncSet_Ocompose(X2430,X2429,X2422,X2427,c_FuncSet_Ocompose(X2429,X2425,X2422,X2426,X2421,X2424),X2428) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__assoc])]) ).
fof(i_0_530,plain,
! [X2495,X2496,X2497,X2498,X2499,X2500] : c_FuncSet_Ocompose(X2500,X2499,X2498,X2497,X2496,X2495) = c_FuncSet_Orestrict(X2500,X2498,hAPP(c_COMBB(X2499,X2498,X2500,X2496),X2495),X2497),
inference(variable_rename,[status(thm)],[fact_compose__def]) ).
fof(i_0_531,plain,
! [X2412,X2413,X2414,X2415,X2416,X2417,X2418,X2419] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2419,X2418)),X2417),c_FuncSet_OPi(X2419,X2418,X2416,c_COMBK(tc_fun(X2418,tc_HOL_Obool),X2419,X2415))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2418,X2414)),X2413),c_FuncSet_OPi(X2418,X2414,X2415,c_COMBK(tc_fun(X2414,tc_HOL_Obool),X2418,X2412))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2419,X2414)),c_FuncSet_Ocompose(X2419,X2418,X2414,X2416,X2413,X2417)),c_FuncSet_OPi(X2419,X2414,X2416,c_COMBK(tc_fun(X2414,tc_HOL_Obool),X2419,X2412)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__compose])]) ).
fof(i_0_532,plain,
! [X11,X12,X18,X6] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X18))
=> X12 != X11 ) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__trancl__rD]) ).
fof(i_0_533,plain,
! [X36,X2,X15,X32,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X32))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional__funcset(X6,X15,c_Set_Oinsert(X6,X12,X32),X36)))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),c_Fun_Ofun__upd(X6,X15,X2,X12,c_HOL_Oundefined(X15))),c_FuncSet_Oextensional__funcset(X6,X15,X32,X36))) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__funcset__restrict__domain]) ).
fof(i_0_534,plain,
! [X18,X9,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X9)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X9)),X18))
=> ~ ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X29)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X9)),c_Transitive__Closure_Otrancl(X6,X18))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_converse__tranclE]) ).
fof(i_0_535,plain,
! [X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),X18))
=> ~ ! [X60] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X60)),c_Transitive__Closure_Otrancl(X6,X18)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X60),X19)),X18)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_tranclE]) ).
fof(i_0_536,plain,
! [X18,X9,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X9)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( X12 != X9
=> ~ ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X29)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X9)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_converse__rtranclE]) ).
fof(i_0_537,plain,
! [X18,X19,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ( X20 != X19
=> ~ ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X29)),c_Transitive__Closure_Ortrancl(X6,X18)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X19)),X18)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_rtranclE]) ).
fof(i_0_538,plain,
! [X2435,X2436,X2437,X2438,X2439,X2440] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2440,X2439)),c_FuncSet_Ocompose(X2440,X2438,X2439,X2437,X2436,X2435)),c_FuncSet_Oextensional(X2440,X2439,X2437))),
inference(variable_rename,[status(thm)],[fact_compose__extensional]) ).
fof(i_0_539,plain,
! [X3563,X3564,X3565,X3566,X3567] :
( ( ~ c_Wellfounded_Owf(X3567,X3566)
| c_Nitpick_Owfrec_H(X3567,X3565,X3566,X3564,X3563) = c_Nitpick_Owf__wfrec_H(X3567,X3565,X3566,X3564,X3563) )
& ( c_Wellfounded_Owf(X3567,X3566)
| c_Nitpick_Owfrec_H(X3567,X3565,X3566,X3564,X3563) = c_HOL_OThe(X3565,c_Recdef_Owfrec__rel(X3567,X3565,X3566,hAPP(hAPP(c_COMBC(tc_fun(X3567,X3565),tc_fun(X3567,X3567),tc_fun(X3567,X3565)),hAPP(c_COMBB(tc_fun(X3567,tc_fun(X3567,X3565)),tc_fun(tc_fun(X3567,X3567),tc_fun(X3567,X3565)),tc_fun(X3567,X3565),c_COMBS(X3567,X3567,X3565)),hAPP(c_COMBB(tc_fun(X3567,tc_fun(X3567,X3565)),tc_fun(X3567,tc_fun(X3567,X3565)),tc_fun(X3567,X3565),c_COMBB(tc_fun(X3567,X3565),tc_fun(X3567,X3565),X3567,X3564)),hAPP(hAPP(c_COMBC(tc_fun(X3567,X3565),tc_fun(tc_prod(X3567,X3567),tc_HOL_Obool),tc_fun(X3567,tc_fun(X3567,X3565))),c_Recdef_Ocut(X3567,X3565)),X3566)))),c_COMBI(X3567)),X3563)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])]) ).
fof(i_0_540,plain,
! [X3572,X3573,X3574,X3575,X3576] : c_Nitpick_Owf__wfrec_H(X3576,X3575,X3574,X3573,X3572) = hAPP(hAPP(X3573,hAPP(hAPP(hAPP(c_Recdef_Ocut(X3576,X3575),c_Nitpick_Owf__wfrec(X3576,X3575,X3574,X3573)),X3574),X3572)),X3572),
inference(variable_rename,[status(thm)],[fact_Nitpick_Owf__wfrec_H__def]) ).
fof(i_0_541,plain,
! [X18,X15,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Relation_ORange(X15,X6,X18)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X15,X6)),hAPP(hAPP(c_Product__Type_OPair(X15,X6),X3),X19)),X18)) ),
inference(fof_simplification,[status(thm)],[fact_RangeE]) ).
fof(i_0_542,plain,
! [X2484,X2485,X2486,X2487,X2488] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2488,X2487)),X2486),c_FuncSet_OPi(X2488,X2487,X2485,c_COMBK(tc_fun(X2487,tc_HOL_Obool),X2488,X2484))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2488,X2487)),X2486),c_FuncSet_Oextensional(X2488,X2487,X2485)))
| c_FuncSet_Ocompose(X2488,X2487,X2487,X2485,c_FuncSet_Orestrict(X2487,X2487,c_COMBI(X2487),X2484),X2486) = X2486 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__compose])]) ).
fof(i_0_543,plain,
! [X2479,X2480,X2481,X2482,X2483] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2483,X2482)),X2481),c_FuncSet_OPi(X2483,X2482,X2480,c_COMBK(tc_fun(X2482,tc_HOL_Obool),X2483,X2479))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2483,X2482)),X2481),c_FuncSet_Oextensional(X2483,X2482,X2480)))
| c_FuncSet_Ocompose(X2483,X2483,X2482,X2480,X2481,c_FuncSet_Orestrict(X2483,X2483,c_COMBI(X2483),X2480)) = X2481 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__Id])]) ).
fof(i_0_544,plain,
! [X18,X15,X20,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X20),c_Relation_ODomain(X6,X15,X18)))
=> ~ ! [X29] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X29)),X18)) ),
inference(fof_simplification,[status(thm)],[fact_DomainE]) ).
fof(i_0_545,plain,
! [X11,X12,X7,X8,X15,X6] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X15,tc_HOL_Obool))),X8),X7),X12),X11))
=> ~ ( hBOOL(hAPP(hAPP(X8,X12),X11))
=> ~ hBOOL(hAPP(hAPP(X7,X12),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf2E]) ).
fof(i_0_546,plain,
! [X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> ( X12 != X11
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),X10))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11),X12)),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).
fof(i_0_547,plain,
! [X19,X20,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X19)),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),X19),X20)),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_548,plain,
! [X7,X8,X19,X20,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X15),X20),X19)),c_Product__Type_OSigma(X6,X15,X8,X7)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> ~ hBOOL(hAPP(hAPP(c_member(X15),X19),hAPP(X7,X20))) ) ),
inference(fof_simplification,[status(thm)],[fact_SigmaE2]) ).
fof(i_0_549,plain,
! [X18,X6] :
( c_Wellfounded_Owf(X6,X18)
<=> ! [X75] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X6),X3),X75))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X75))
& ! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X3)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X29),X75)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__eq__minimal]) ).
fof(i_0_550,plain,
! [X12,X20,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X12)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X20)),X18)) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__asym]) ).
fof(i_0_551,plain,
! [X12,X20,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X12)),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X20)),X18)) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__not__sym]) ).
fof(i_0_552,plain,
! [X14,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X14)))
=> ~ ! [X28] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X28),X12)),X14))
=> hBOOL(hAPP(hAPP(c_member(X6),X28),c_Wellfounded_Oacc(X6,X14))) ) ),
inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).
fof(i_0_553,plain,
! [X2441,X2442,X2443,X2444,X2445,X2446,X2447] :
( ~ hBOOL(hAPP(hAPP(c_member(X2447),X2446),X2445))
| hAPP(c_FuncSet_Ocompose(X2447,X2444,X2443,X2445,X2442,X2441),X2446) = hAPP(X2442,hAPP(X2441,X2446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__eq])]) ).
fof(i_0_554,plain,
! [X18,X12,X11,X6] :
( c_Wellfounded_Owf(X6,c_Set_Oinsert(tc_prod(X6,X6),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12),X18))
<=> ( c_Wellfounded_Owf(X6,X18)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__insert]) ).
fof(i_0_555,plain,
! [X18,X12,X11,X6] :
( c_Wellfounded_Oacyclic(X6,c_Set_Oinsert(tc_prod(X6,X6),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12),X18))
<=> ( c_Wellfounded_Oacyclic(X6,X18)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X18))) ) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__insert]) ).
fof(i_0_556,plain,
! [X12,X7,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_OPi(X6,X15,X8,X7)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X12)),hAPP(X7,X12)))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_PiE]) ).
fof(i_0_557,plain,
! [X12,X36,X32,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional__funcset(X6,X15,X32,X36)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X32))
=> hAPP(X2,X12) = c_HOL_Oundefined(X15) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__funcset__arb]) ).
fof(i_0_558,plain,
! [X2,X15,X18,X12,X11,X6] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12)),X18))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),X2),X18),X12),X11) = hAPP(X2,X11) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12)),X18))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X15),X2),X18),X12),X11) = c_HOL_Oundefined(X15) ) ),
inference(fof_simplification,[status(thm)],[fact_cut__def]) ).
fof(i_0_559,plain,
! [X11,X14,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Relation_ODomain(X6,X6,X14)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X14)))
<=> X12 = X11 ) ),
inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).
fof(i_0_560,plain,
! [X18,X6] :
( c_Wellfounded_Oacyclic(X6,X18)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),c_Transitive__Closure_Otrancl(X6,X18))) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).
fof(i_0_561,plain,
! [X18,X6] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),c_Transitive__Closure_Otrancl(X6,X18)))
=> c_Wellfounded_Oacyclic(X6,X18) ),
inference(fof_simplification,[status(thm)],[fact_acyclicI]) ).
fof(i_0_562,plain,
! [X18,X6] :
( c_Relation_Oirrefl(X6,X18)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X18)) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).
fof(i_0_563,plain,
! [X20,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X20)),X18)) ),
inference(fof_simplification,[status(thm)],[fact_wf__irrefl]) ).
fof(i_0_564,plain,
! [X20,X18,X6] :
( c_Wellfounded_Owf(X6,X18)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X20)),X18)) ),
inference(fof_simplification,[status(thm)],[fact_wf__not__refl]) ).
fof(i_0_565,plain,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_UnE]) ).
fof(i_0_566,plain,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_IntE]) ).
fof(i_0_567,plain,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12))
=> ( ~ hBOOL(hAPP(X8,X12))
=> hBOOL(hAPP(X7,X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_sup1E]) ).
fof(i_0_568,plain,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12))
=> ~ ( hBOOL(hAPP(X8,X12))
=> ~ hBOOL(hAPP(X7,X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf1E]) ).
fof(i_0_569,plain,
! [X12,X8,X2,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X15)),X2),c_FuncSet_Oextensional(X6,X15,X8)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(X2,X12) = c_HOL_Oundefined(X15) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__arb]) ).
fof(i_0_570,plain,
! [X7,X38,X20,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X20),X38))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,X7)),X38) = c_Set_Oinsert(X6,X20,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X38))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,X7)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38) ) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__left]) ).
fof(i_0_571,plain,
! [X8,X7,X5,X6] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X6),X5),X7))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X8)) )
=> hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7))) ),
inference(fof_simplification,[status(thm)],[fact_UnCI]) ).
fof(i_0_572,plain,
! [X7,X8,X20,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),c_Set_Oinsert(X6,X20,X7)) = c_Set_Oinsert(X6,X20,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),c_Set_Oinsert(X6,X20,X7)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) ) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__right]) ).
fof(i_0_573,plain,
! [X2,X15,X8,X12,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X15,X2,X8),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X15,X2,X8),X12) = c_HOL_Oundefined(X15) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__apply]) ).
fof(i_0_574,plain,
! [X2,X15,X8,X12,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X15,X2,X8),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X15,X2,X8),X12) = c_HOL_Oundefined(X15) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__def]) ).
fof(i_0_575,plain,
! [X6,X8,X12,X7] :
( ( ~ hBOOL(hAPP(X7,X12))
=> hBOOL(hAPP(X8,X12)) )
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12)) ),
inference(fof_simplification,[status(thm)],[fact_sup1CI]) ).
fof(i_0_576,plain,
! [X7,X38,X20,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X38))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),c_Set_Oinsert(X6,X20,X7)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X38) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__left__if0]) ).
fof(i_0_577,plain,
! [X7,X8,X20,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X8))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),c_Set_Oinsert(X6,X20,X7)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if0]) ).
fof(i_0_578,plain,
! [X19,X7,X20,X6] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X7))
=> X20 = X19 )
=> hBOOL(hAPP(hAPP(c_member(X6),X20),c_Set_Oinsert(X6,X19,X7))) ),
inference(fof_simplification,[status(thm)],[fact_insertCI]) ).
fof(i_0_579,plain,
! [X7,X8,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,c_Set_Oinsert(X6,X12,X7))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).
fof(i_0_580,plain,
! [X7,X8,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X7))
=> ( c_Set_Oinsert(X6,X12,X8) = c_Set_Oinsert(X6,X12,X7)
<=> X8 = X7 ) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).
fof(i_0_581,plain,
! [X5,X6] : ~ hBOOL(hAPP(hAPP(c_member(X6),X5),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).
fof(i_0_582,plain,
! [X20,X6] : ~ hBOOL(hAPP(hAPP(c_member(X6),X20),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_emptyE]) ).
fof(i_0_583,plain,
! [X56,X58,X59,X6] :
( class_Lattices_Osemilattice__sup(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6),X59),X58),X56)
=> ~ ( c_Orderings_Oord__class_Oless__eq(X6,X59,X56)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,X58,X56) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__supE]) ).
fof(i_0_584,plain,
! [X58,X59,X56,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X56,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X59),X58))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X6,X56,X59)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,X56,X58) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__infE]) ).
fof(i_0_585,plain,
! [X8,X6] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
<=> X8 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).
fof(i_0_586,plain,
! [X20,X6,X8] :
( X8 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X20),X8)) ),
inference(fof_simplification,[status(thm)],[fact_equals0D]) ).
fof(i_0_587,plain,
! [X64,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X64))
| hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(i_0_588,plain,
! [X64,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X64))
| hBOOL(X64) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).
fof(i_0_589,plain,
! [X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X12),X11))
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_590,plain,
! [X55,X56,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X56,X55)
=> c_Orderings_Oord__class_Oless__eq(X6,X55,X56) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_591,plain,
! [X64,X17] :
( ~ hBOOL(X17)
| ~ hBOOL(X64)
| hBOOL(hAPP(hAPP(c_fconj,X17),X64)) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).
fof(i_0_592,plain,
! [X6,X7,X8] :
( X8 = X7
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_593,plain,
! [X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2570,X2569),tc_prod(X2570,X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2570,X2569),tc_prod(X2570,X2569)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),X2568),X2567)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),esk45_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570)),esk46_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570)))),c_Transitive__Closure_Ortrancl(tc_prod(X2570,X2569),X2564)))
| hBOOL(hAPP(hAPP(X2563,X2566),X2565))
| ~ hBOOL(hAPP(hAPP(X2563,X2568),X2567))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2570,X2569),tc_prod(X2570,X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2570,X2569),tc_prod(X2570,X2569)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),X2568),X2567)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),X2566),X2565))),c_Transitive__Closure_Ortrancl(tc_prod(X2570,X2569),X2564))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2570,X2569),tc_prod(X2570,X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2570,X2569),tc_prod(X2570,X2569)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),esk45_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570)),esk46_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570))),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),esk47_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570)),esk48_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570)))),X2564))
| hBOOL(hAPP(hAPP(X2563,X2566),X2565))
| ~ hBOOL(hAPP(hAPP(X2563,X2568),X2567))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2570,X2569),tc_prod(X2570,X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2570,X2569),tc_prod(X2570,X2569)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),X2568),X2567)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),X2566),X2565))),c_Transitive__Closure_Ortrancl(tc_prod(X2570,X2569),X2564))) )
& ( hBOOL(hAPP(hAPP(X2563,esk45_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570)),esk46_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570)))
| hBOOL(hAPP(hAPP(X2563,X2566),X2565))
| ~ hBOOL(hAPP(hAPP(X2563,X2568),X2567))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2570,X2569),tc_prod(X2570,X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2570,X2569),tc_prod(X2570,X2569)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),X2568),X2567)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),X2566),X2565))),c_Transitive__Closure_Ortrancl(tc_prod(X2570,X2569),X2564))) )
& ( ~ hBOOL(hAPP(hAPP(X2563,esk47_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570)),esk48_8(X2563,X2564,X2565,X2566,X2567,X2568,X2569,X2570)))
| hBOOL(hAPP(hAPP(X2563,X2566),X2565))
| ~ hBOOL(hAPP(hAPP(X2563,X2568),X2567))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2570,X2569),tc_prod(X2570,X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2570,X2569),tc_prod(X2570,X2569)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),X2568),X2567)),hAPP(hAPP(c_Product__Type_OPair(X2570,X2569),X2566),X2565))),c_Transitive__Closure_Ortrancl(tc_prod(X2570,X2569),X2564))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__induct2])])])]) ).
fof(i_0_594,plain,
! [X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2558,X2557),tc_prod(X2558,X2557))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2558,X2557),tc_prod(X2558,X2557)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),esk41_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558)),esk42_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558))),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),esk43_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558)),esk44_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558)))),X2552))
| hBOOL(hAPP(hAPP(X2551,X2556),X2555))
| ~ hBOOL(hAPP(hAPP(X2551,X2554),X2553))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2558,X2557),tc_prod(X2558,X2557))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2558,X2557),tc_prod(X2558,X2557)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),X2556),X2555)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),X2554),X2553))),c_Transitive__Closure_Ortrancl(tc_prod(X2558,X2557),X2552))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2558,X2557),tc_prod(X2558,X2557))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2558,X2557),tc_prod(X2558,X2557)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),esk43_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558)),esk44_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558))),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),X2554),X2553))),c_Transitive__Closure_Ortrancl(tc_prod(X2558,X2557),X2552)))
| hBOOL(hAPP(hAPP(X2551,X2556),X2555))
| ~ hBOOL(hAPP(hAPP(X2551,X2554),X2553))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2558,X2557),tc_prod(X2558,X2557))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2558,X2557),tc_prod(X2558,X2557)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),X2556),X2555)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),X2554),X2553))),c_Transitive__Closure_Ortrancl(tc_prod(X2558,X2557),X2552))) )
& ( hBOOL(hAPP(hAPP(X2551,esk43_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558)),esk44_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558)))
| hBOOL(hAPP(hAPP(X2551,X2556),X2555))
| ~ hBOOL(hAPP(hAPP(X2551,X2554),X2553))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2558,X2557),tc_prod(X2558,X2557))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2558,X2557),tc_prod(X2558,X2557)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),X2556),X2555)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),X2554),X2553))),c_Transitive__Closure_Ortrancl(tc_prod(X2558,X2557),X2552))) )
& ( ~ hBOOL(hAPP(hAPP(X2551,esk41_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558)),esk42_8(X2551,X2552,X2553,X2554,X2555,X2556,X2557,X2558)))
| hBOOL(hAPP(hAPP(X2551,X2556),X2555))
| ~ hBOOL(hAPP(hAPP(X2551,X2554),X2553))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2558,X2557),tc_prod(X2558,X2557))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2558,X2557),tc_prod(X2558,X2557)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),X2556),X2555)),hAPP(hAPP(c_Product__Type_OPair(X2558,X2557),X2554),X2553))),c_Transitive__Closure_Ortrancl(tc_prod(X2558,X2557),X2552))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__induct2])])])]) ).
fof(i_0_595,plain,
! [X2542,X2543,X2544,X2545,X2546,X2547,X2548] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2548,X2547),tc_prod(X2548,X2547))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2548,X2547),tc_prod(X2548,X2547)),hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2546),X2545)),hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),esk39_7(X2542,X2543,X2544,X2545,X2546,X2547,X2548)),esk40_7(X2542,X2543,X2544,X2545,X2546,X2547,X2548)))),X2542))
| hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2546),X2545) = hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2544),X2543)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2548,X2547),tc_prod(X2548,X2547))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2548,X2547),tc_prod(X2548,X2547)),hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2546),X2545)),hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2544),X2543))),c_Transitive__Closure_Ortrancl(tc_prod(X2548,X2547),X2542))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2548,X2547),tc_prod(X2548,X2547))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2548,X2547),tc_prod(X2548,X2547)),hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),esk39_7(X2542,X2543,X2544,X2545,X2546,X2547,X2548)),esk40_7(X2542,X2543,X2544,X2545,X2546,X2547,X2548))),hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2544),X2543))),c_Transitive__Closure_Ortrancl(tc_prod(X2548,X2547),X2542)))
| hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2546),X2545) = hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2544),X2543)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2548,X2547),tc_prod(X2548,X2547))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2548,X2547),tc_prod(X2548,X2547)),hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2546),X2545)),hAPP(hAPP(c_Product__Type_OPair(X2548,X2547),X2544),X2543))),c_Transitive__Closure_Ortrancl(tc_prod(X2548,X2547),X2542))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])])]) ).
fof(i_0_596,plain,
! [X2687,X2688,X2689,X2690,X2691,X2692] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2692,tc_fun(X2691,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2692,tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_fun(X2691,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2691,tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_fun(X2691,tc_HOL_Obool)),X2692,c_COMBC(X2691,tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2691,tc_prod(X2692,X2691)),tc_fun(X2691,tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),X2692,c_COMBB(tc_prod(X2692,X2691),tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool),X2691,c_member(tc_prod(X2692,X2691)))),c_Product__Type_OPair(X2692,X2691)))),X2690)),hAPP(hAPP(c_COMBC(X2692,tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_fun(X2691,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2691,tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_fun(X2691,tc_HOL_Obool)),X2692,c_COMBC(X2691,tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2691,tc_prod(X2692,X2691)),tc_fun(X2691,tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),X2692,c_COMBB(tc_prod(X2692,X2691),tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool),X2691,c_member(tc_prod(X2692,X2691)))),c_Product__Type_OPair(X2692,X2691)))),X2689)),X2688),X2687))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2692,X2691)),hAPP(hAPP(c_Product__Type_OPair(X2692,X2691),X2688),X2687)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool)),X2690),X2689))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2692,X2691)),hAPP(hAPP(c_Product__Type_OPair(X2692,X2691),X2688),X2687)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool)),X2690),X2689)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2692,tc_fun(X2691,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2692,tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_fun(X2691,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2691,tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_fun(X2691,tc_HOL_Obool)),X2692,c_COMBC(X2691,tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2691,tc_prod(X2692,X2691)),tc_fun(X2691,tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),X2692,c_COMBB(tc_prod(X2692,X2691),tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool),X2691,c_member(tc_prod(X2692,X2691)))),c_Product__Type_OPair(X2692,X2691)))),X2690)),hAPP(hAPP(c_COMBC(X2692,tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_fun(X2691,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2691,tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_fun(X2691,tc_HOL_Obool)),X2692,c_COMBC(X2691,tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2691,tc_prod(X2692,X2691)),tc_fun(X2691,tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool)),X2692,c_COMBB(tc_prod(X2692,X2691),tc_fun(tc_fun(tc_prod(X2692,X2691),tc_HOL_Obool),tc_HOL_Obool),X2691,c_member(tc_prod(X2692,X2691)))),c_Product__Type_OPair(X2692,X2691)))),X2689)),X2688),X2687)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).
fof(i_0_597,plain,
! [X2177,X2178,X2179,X2180,X2181,X2182,X2184,X2185,X2186,X2187,X2188,X2189,X2190,X2191] :
( ( hAPP(hAPP(X2179,X2177),X2178) = hAPP(hAPP(X2179,esk4_6(X2177,X2178,X2179,X2180,X2181,X2182)),X2178)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X2182,X2181,X2180,X2179,X2178),hAPP(hAPP(X2179,X2177),X2178))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2182,X2182)),hAPP(hAPP(c_Product__Type_OPair(X2182,X2182),X2184),X2178)),X2180))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X2182,X2181,X2180,X2179,X2184),hAPP(esk4_6(X2177,X2178,X2179,X2180,X2181,X2182),X2184)))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X2182,X2181,X2180,X2179,X2178),hAPP(hAPP(X2179,X2177),X2178))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2190,X2190)),hAPP(hAPP(c_Product__Type_OPair(X2190,X2190),esk5_7(X2185,X2186,X2187,X2188,X2189,X2190,X2191)),X2186)),X2188))
| hAPP(hAPP(X2187,X2185),X2186) != hAPP(hAPP(X2187,X2191),X2186)
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X2190,X2189,X2188,X2187,X2186),hAPP(hAPP(X2187,X2185),X2186))) )
& ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X2190,X2189,X2188,X2187,esk5_7(X2185,X2186,X2187,X2188,X2189,X2190,X2191)),hAPP(X2191,esk5_7(X2185,X2186,X2187,X2188,X2189,X2190,X2191))))
| hAPP(hAPP(X2187,X2185),X2186) != hAPP(hAPP(X2187,X2191),X2186)
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X2190,X2189,X2188,X2187,X2186),hAPP(hAPP(X2187,X2185),X2186))) ) ),
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_wfrec__rel_Oequations])])])])])]) ).
fof(i_0_598,plain,
! [X2266,X2267,X2268,X2269,X2270,X2271,X2273,X2274,X2275,X2276,X2277,X2278,X2279,X2280] :
( ( X2266 = hAPP(hAPP(X2268,esk17_6(X2266,X2267,X2268,X2269,X2270,X2271)),X2267)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X2271,X2270,X2269,X2268,X2267),X2266)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2271,X2271)),hAPP(hAPP(c_Product__Type_OPair(X2271,X2271),X2273),X2267)),X2269))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X2271,X2270,X2269,X2268,X2273),hAPP(esk17_6(X2266,X2267,X2268,X2269,X2270,X2271),X2273)))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X2271,X2270,X2269,X2268,X2267),X2266)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2279,X2279)),hAPP(hAPP(c_Product__Type_OPair(X2279,X2279),esk18_7(X2274,X2275,X2276,X2277,X2278,X2279,X2280)),X2275)),X2277))
| X2274 != hAPP(hAPP(X2276,X2280),X2275)
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X2279,X2278,X2277,X2276,X2275),X2274)) )
& ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X2279,X2278,X2277,X2276,esk18_7(X2274,X2275,X2276,X2277,X2278,X2279,X2280)),hAPP(X2280,esk18_7(X2274,X2275,X2276,X2277,X2278,X2279,X2280))))
| X2274 != hAPP(hAPP(X2276,X2280),X2275)
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X2279,X2278,X2277,X2276,X2275),X2274)) ) ),
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_wfrec__rel_Osimps])])])])])]) ).
fof(i_0_599,plain,
! [X2340,X2341,X2342,X2343,X2344,X2345,X2346,X2348,X2349,X2350,X2351,X2355] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2343,X2343)),hAPP(hAPP(c_Product__Type_OPair(X2343,X2343),esk26_7(X2340,X2341,X2342,X2343,X2344,X2345,X2346)),X2346)),X2341))
| hAPP(hAPP(X2340,X2344),X2346) = hAPP(hAPP(X2340,X2345),X2346)
| ~ c_Recdef_Oadm__wf(X2343,X2342,X2341,X2340) )
& ( hAPP(X2344,esk26_7(X2340,X2341,X2342,X2343,X2344,X2345,X2346)) != hAPP(X2345,esk26_7(X2340,X2341,X2342,X2343,X2344,X2345,X2346))
| hAPP(hAPP(X2340,X2344),X2346) = hAPP(hAPP(X2340,X2345),X2346)
| ~ c_Recdef_Oadm__wf(X2343,X2342,X2341,X2340) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2351,X2351)),hAPP(hAPP(c_Product__Type_OPair(X2351,X2351),X2355),esk29_4(X2348,X2349,X2350,X2351))),X2349))
| hAPP(esk27_4(X2348,X2349,X2350,X2351),X2355) = hAPP(esk28_4(X2348,X2349,X2350,X2351),X2355)
| c_Recdef_Oadm__wf(X2351,X2350,X2349,X2348) )
& ( hAPP(hAPP(X2348,esk27_4(X2348,X2349,X2350,X2351)),esk29_4(X2348,X2349,X2350,X2351)) != hAPP(hAPP(X2348,esk28_4(X2348,X2349,X2350,X2351)),esk29_4(X2348,X2349,X2350,X2351))
| c_Recdef_Oadm__wf(X2351,X2350,X2349,X2348) ) ),
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_600,plain,
! [X3003,X3004,X3005,X3006] :
( ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3006,hAPP(hAPP(c_COMBC(X3006,tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_fun(X3006,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3006,tc_fun(tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_fun(X3006,tc_HOL_Obool)),X3006,c_COMBC(X3006,tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3006,tc_prod(X3006,X3006)),tc_fun(X3006,tc_fun(tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_HOL_Obool)),X3006,c_COMBB(tc_prod(X3006,X3006),tc_fun(tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_HOL_Obool),X3006,c_member(tc_prod(X3006,X3006)))),c_Product__Type_OPair(X3006,X3006)))),X3005)),X3004),X3003))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3006,X3006)),hAPP(hAPP(c_Product__Type_OPair(X3006,X3006),X3004),X3003)),c_Transitive__Closure_Otrancl(X3006,X3005))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3006,X3006)),hAPP(hAPP(c_Product__Type_OPair(X3006,X3006),X3004),X3003)),c_Transitive__Closure_Otrancl(X3006,X3005)))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3006,hAPP(hAPP(c_COMBC(X3006,tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_fun(X3006,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3006,tc_fun(tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_fun(X3006,tc_HOL_Obool)),X3006,c_COMBC(X3006,tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3006,tc_prod(X3006,X3006)),tc_fun(X3006,tc_fun(tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_HOL_Obool)),X3006,c_COMBB(tc_prod(X3006,X3006),tc_fun(tc_fun(tc_prod(X3006,X3006),tc_HOL_Obool),tc_HOL_Obool),X3006,c_member(tc_prod(X3006,X3006)))),c_Product__Type_OPair(X3006,X3006)))),X3005)),X3004),X3003)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclp__trancl__eq])]) ).
fof(i_0_601,plain,
! [X2329,X2330,X2331] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2331,hAPP(hAPP(c_COMBC(X2331,tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_fun(X2331,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2331,tc_fun(tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_fun(X2331,tc_HOL_Obool)),X2331,c_COMBC(X2331,tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2331,tc_prod(X2331,X2331)),tc_fun(X2331,tc_fun(tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_HOL_Obool)),X2331,c_COMBB(tc_prod(X2331,X2331),tc_fun(tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_HOL_Obool),X2331,c_member(tc_prod(X2331,X2331)))),c_Product__Type_OPair(X2331,X2331)))),X2330)),X2329))
| hBOOL(hAPP(hAPP(c_member(X2331),X2329),c_Wellfounded_Oacc(X2331,X2330))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2331),X2329),c_Wellfounded_Oacc(X2331,X2330)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2331,hAPP(hAPP(c_COMBC(X2331,tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_fun(X2331,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2331,tc_fun(tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_fun(X2331,tc_HOL_Obool)),X2331,c_COMBC(X2331,tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2331,tc_prod(X2331,X2331)),tc_fun(X2331,tc_fun(tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_HOL_Obool)),X2331,c_COMBB(tc_prod(X2331,X2331),tc_fun(tc_fun(tc_prod(X2331,X2331),tc_HOL_Obool),tc_HOL_Obool),X2331,c_member(tc_prod(X2331,X2331)))),c_Product__Type_OPair(X2331,X2331)))),X2330)),X2329)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).
fof(i_0_602,plain,
! [X3404,X3405,X3406,X3407] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3407,tc_fun(X3406,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3407,tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_fun(X3406,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3406,tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_fun(X3406,tc_HOL_Obool)),X3407,c_COMBC(X3406,tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3406,tc_prod(X3407,X3406)),tc_fun(X3406,tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),X3407,c_COMBB(tc_prod(X3407,X3406),tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool),X3406,c_member(tc_prod(X3407,X3406)))),c_Product__Type_OPair(X3407,X3406)))),X3405),hAPP(hAPP(c_COMBC(X3407,tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_fun(X3406,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3406,tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_fun(X3406,tc_HOL_Obool)),X3407,c_COMBC(X3406,tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3406,tc_prod(X3407,X3406)),tc_fun(X3406,tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),X3407,c_COMBB(tc_prod(X3407,X3406),tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool),X3406,c_member(tc_prod(X3407,X3406)))),c_Product__Type_OPair(X3407,X3406)))),X3404))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),X3405,X3404) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),X3405,X3404)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3407,tc_fun(X3406,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3407,tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_fun(X3406,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3406,tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_fun(X3406,tc_HOL_Obool)),X3407,c_COMBC(X3406,tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3406,tc_prod(X3407,X3406)),tc_fun(X3406,tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),X3407,c_COMBB(tc_prod(X3407,X3406),tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool),X3406,c_member(tc_prod(X3407,X3406)))),c_Product__Type_OPair(X3407,X3406)))),X3405),hAPP(hAPP(c_COMBC(X3407,tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_fun(X3406,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3406,tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_fun(X3406,tc_HOL_Obool)),X3407,c_COMBC(X3406,tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3406,tc_prod(X3407,X3406)),tc_fun(X3406,tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool)),X3407,c_COMBB(tc_prod(X3407,X3406),tc_fun(tc_fun(tc_prod(X3407,X3406),tc_HOL_Obool),tc_HOL_Obool),X3406,c_member(tc_prod(X3407,X3406)))),c_Product__Type_OPair(X3407,X3406)))),X3404)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_603,plain,
! [X2282,X2283,X2284,X2285,X2286,X2287] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2287,X2287)),hAPP(hAPP(c_Product__Type_OPair(X2287,X2287),esk19_6(X2282,X2283,X2284,X2285,X2286,X2287)),X2286)),X2285))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X2287,X2284,X2285,X2283,X2286),hAPP(hAPP(X2283,X2282),X2286))) )
& ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X2287,X2284,X2285,X2283,esk19_6(X2282,X2283,X2284,X2285,X2286,X2287)),hAPP(X2282,esk19_6(X2282,X2283,X2284,X2285,X2286,X2287))))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X2287,X2284,X2285,X2283,X2286),hAPP(hAPP(X2283,X2282),X2286))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfrec__rel_Ointros])])])]) ).
fof(i_0_604,plain,
! [X2199,X2200,X2201,X2202,X2203,X2204,X2205,X2206,X2207,X2208,X2209,X2210,X2211] :
( ( hAPP(hAPP(hAPP(c_Recdef_Ocut(X2204,X2203),X2202),X2201),X2200) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X2204,X2203),X2199),X2201),X2200)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2204,X2204)),hAPP(hAPP(c_Product__Type_OPair(X2204,X2204),X2205),X2200)),X2201))
| hAPP(X2202,X2205) = hAPP(X2199,X2205) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2211,X2211)),hAPP(hAPP(c_Product__Type_OPair(X2211,X2211),esk6_6(X2206,X2207,X2208,X2209,X2210,X2211)),X2207)),X2208))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X2211,X2210),X2209),X2208),X2207) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X2211,X2210),X2206),X2208),X2207) )
& ( hAPP(X2209,esk6_6(X2206,X2207,X2208,X2209,X2210,X2211)) != hAPP(X2206,esk6_6(X2206,X2207,X2208,X2209,X2210,X2211))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X2211,X2210),X2209),X2208),X2207) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X2211,X2210),X2206),X2208),X2207) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cuts__eq])])])])])]) ).
fof(i_0_605,plain,
! [X3543,X3544,X3545,X3546,X3547] : hAPP(c_Recdef_Owfrec(X3547,X3546,X3545,X3544),X3543) = c_HOL_OThe(X3546,c_Recdef_Owfrec__rel(X3547,X3546,X3545,hAPP(hAPP(c_COMBC(tc_fun(X3547,X3546),tc_fun(X3547,X3547),tc_fun(X3547,X3546)),hAPP(c_COMBB(tc_fun(X3547,tc_fun(X3547,X3546)),tc_fun(tc_fun(X3547,X3547),tc_fun(X3547,X3546)),tc_fun(X3547,X3546),c_COMBS(X3547,X3547,X3546)),hAPP(c_COMBB(tc_fun(X3547,tc_fun(X3547,X3546)),tc_fun(X3547,tc_fun(X3547,X3546)),tc_fun(X3547,X3546),c_COMBB(tc_fun(X3547,X3546),tc_fun(X3547,X3546),X3547,X3544)),hAPP(hAPP(c_COMBC(tc_fun(X3547,X3546),tc_fun(tc_prod(X3547,X3547),tc_HOL_Obool),tc_fun(X3547,tc_fun(X3547,X3546))),c_Recdef_Ocut(X3547,X3546)),X3545)))),c_COMBI(X3547)),X3543)),
inference(variable_rename,[status(thm)],[fact_wfrec__def]) ).
fof(i_0_606,plain,
! [X2668,X2669,X2670,X2671] :
( ( ~ c_Predicate_ODomainP(X2671,X2670,hAPP(hAPP(c_COMBC(X2671,tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_fun(X2670,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2670,tc_fun(tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_fun(X2670,tc_HOL_Obool)),X2671,c_COMBC(X2670,tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2670,tc_prod(X2671,X2670)),tc_fun(X2670,tc_fun(tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_HOL_Obool)),X2671,c_COMBB(tc_prod(X2671,X2670),tc_fun(tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_HOL_Obool),X2670,c_member(tc_prod(X2671,X2670)))),c_Product__Type_OPair(X2671,X2670)))),X2669),X2668)
| hBOOL(hAPP(hAPP(c_member(X2671),X2668),c_Relation_ODomain(X2671,X2670,X2669))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2671),X2668),c_Relation_ODomain(X2671,X2670,X2669)))
| c_Predicate_ODomainP(X2671,X2670,hAPP(hAPP(c_COMBC(X2671,tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_fun(X2670,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2670,tc_fun(tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_fun(X2670,tc_HOL_Obool)),X2671,c_COMBC(X2670,tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2670,tc_prod(X2671,X2670)),tc_fun(X2670,tc_fun(tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_HOL_Obool)),X2671,c_COMBB(tc_prod(X2671,X2670),tc_fun(tc_fun(tc_prod(X2671,X2670),tc_HOL_Obool),tc_HOL_Obool),X2670,c_member(tc_prod(X2671,X2670)))),c_Product__Type_OPair(X2671,X2670)))),X2669),X2668) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).
fof(i_0_607,plain,
! [X2816,X2817,X2818,X2819] :
( ( ~ c_Predicate_ORangeP(X2819,X2818,hAPP(hAPP(c_COMBC(X2819,tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_fun(X2818,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2818,tc_fun(tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_fun(X2818,tc_HOL_Obool)),X2819,c_COMBC(X2818,tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2818,tc_prod(X2819,X2818)),tc_fun(X2818,tc_fun(tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_HOL_Obool)),X2819,c_COMBB(tc_prod(X2819,X2818),tc_fun(tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_HOL_Obool),X2818,c_member(tc_prod(X2819,X2818)))),c_Product__Type_OPair(X2819,X2818)))),X2817),X2816)
| hBOOL(hAPP(hAPP(c_member(X2818),X2816),c_Relation_ORange(X2819,X2818,X2817))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2818),X2816),c_Relation_ORange(X2819,X2818,X2817)))
| c_Predicate_ORangeP(X2819,X2818,hAPP(hAPP(c_COMBC(X2819,tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_fun(X2818,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2818,tc_fun(tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_fun(X2818,tc_HOL_Obool)),X2819,c_COMBC(X2818,tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2818,tc_prod(X2819,X2818)),tc_fun(X2818,tc_fun(tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_HOL_Obool)),X2819,c_COMBB(tc_prod(X2819,X2818),tc_fun(tc_fun(tc_prod(X2819,X2818),tc_HOL_Obool),tc_HOL_Obool),X2818,c_member(tc_prod(X2819,X2818)))),c_Product__Type_OPair(X2819,X2818)))),X2817),X2816) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).
fof(i_0_608,plain,
! [X3583,X3584] :
( ( ~ c_Wellfounded_OwfP(X3584,hAPP(hAPP(c_COMBC(X3584,tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_fun(X3584,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3584,tc_fun(tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_fun(X3584,tc_HOL_Obool)),X3584,c_COMBC(X3584,tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3584,tc_prod(X3584,X3584)),tc_fun(X3584,tc_fun(tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_HOL_Obool)),X3584,c_COMBB(tc_prod(X3584,X3584),tc_fun(tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_HOL_Obool),X3584,c_member(tc_prod(X3584,X3584)))),c_Product__Type_OPair(X3584,X3584)))),X3583))
| c_Wellfounded_Owf(X3584,X3583) )
& ( ~ c_Wellfounded_Owf(X3584,X3583)
| c_Wellfounded_OwfP(X3584,hAPP(hAPP(c_COMBC(X3584,tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_fun(X3584,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3584,tc_fun(tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_fun(X3584,tc_HOL_Obool)),X3584,c_COMBC(X3584,tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3584,tc_prod(X3584,X3584)),tc_fun(X3584,tc_fun(tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_HOL_Obool)),X3584,c_COMBB(tc_prod(X3584,X3584),tc_fun(tc_fun(tc_prod(X3584,X3584),tc_HOL_Obool),tc_HOL_Obool),X3584,c_member(tc_prod(X3584,X3584)))),c_Product__Type_OPair(X3584,X3584)))),X3583)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])]) ).
fof(i_0_609,plain,
! [X2220,X2221,X2222,X2223] :
( ( hAPP(hAPP(c_COMBC(X2223,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),X2223,c_COMBC(X2222,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2222,tc_prod(X2223,X2222)),tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),X2223,c_COMBB(tc_prod(X2223,X2222),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool),X2222,c_member(tc_prod(X2223,X2222)))),c_Product__Type_OPair(X2223,X2222)))),X2221) != hAPP(hAPP(c_COMBC(X2223,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),X2223,c_COMBC(X2222,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2222,tc_prod(X2223,X2222)),tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),X2223,c_COMBB(tc_prod(X2223,X2222),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool),X2222,c_member(tc_prod(X2223,X2222)))),c_Product__Type_OPair(X2223,X2222)))),X2220)
| X2221 = X2220 )
& ( X2221 != X2220
| hAPP(hAPP(c_COMBC(X2223,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),X2223,c_COMBC(X2222,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2222,tc_prod(X2223,X2222)),tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),X2223,c_COMBB(tc_prod(X2223,X2222),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool),X2222,c_member(tc_prod(X2223,X2222)))),c_Product__Type_OPair(X2223,X2222)))),X2221) = hAPP(hAPP(c_COMBC(X2223,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),X2223,c_COMBC(X2222,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2222,tc_prod(X2223,X2222)),tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),X2223,c_COMBB(tc_prod(X2223,X2222),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool),X2222,c_member(tc_prod(X2223,X2222)))),c_Product__Type_OPair(X2223,X2222)))),X2220) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_610,plain,
! [X3735,X3736,X3737,X3738,X3739,X3740] :
( ( hBOOL(hAPP(hAPP(c_member(X3740),esk100_6(X3735,X3736,X3737,X3738,X3739,X3740)),X3739))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3740,X3737),tc_HOL_Obool),c_Product__Type_OSigma(X3740,X3737,X3739,X3736),c_Product__Type_OSigma(X3740,X3737,X3738,X3735))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3740,tc_HOL_Obool),X3739,X3738) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3737,tc_HOL_Obool),hAPP(X3736,esk100_6(X3735,X3736,X3737,X3738,X3739,X3740)),hAPP(X3735,esk100_6(X3735,X3736,X3737,X3738,X3739,X3740)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3740,X3737),tc_HOL_Obool),c_Product__Type_OSigma(X3740,X3737,X3739,X3736),c_Product__Type_OSigma(X3740,X3737,X3738,X3735))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3740,tc_HOL_Obool),X3739,X3738) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sigma__mono])])])]) ).
fof(i_0_611,plain,
! [X2247,X2248,X2249,X2250] : c_Recdef_Oadm__wf(X2250,X2249,X2248,hAPP(hAPP(c_COMBC(tc_fun(X2250,X2249),tc_fun(X2250,X2250),tc_fun(X2250,X2249)),hAPP(c_COMBB(tc_fun(X2250,tc_fun(X2250,X2249)),tc_fun(tc_fun(X2250,X2250),tc_fun(X2250,X2249)),tc_fun(X2250,X2249),c_COMBS(X2250,X2250,X2249)),hAPP(c_COMBB(tc_fun(X2250,tc_fun(X2250,X2249)),tc_fun(X2250,tc_fun(X2250,X2249)),tc_fun(X2250,X2249),c_COMBB(tc_fun(X2250,X2249),tc_fun(X2250,X2249),X2250,X2247)),hAPP(hAPP(c_COMBC(tc_fun(X2250,X2249),tc_fun(tc_prod(X2250,X2250),tc_HOL_Obool),tc_fun(X2250,tc_fun(X2250,X2249))),c_Recdef_Ocut(X2250,X2249)),X2248)))),c_COMBI(X2250))),
inference(variable_rename,[status(thm)],[fact_adm__lemma]) ).
fof(i_0_612,plain,
! [X4071,X4072,X4073,X4074,X4075] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4075,X4075)),hAPP(hAPP(c_Product__Type_OPair(X4075,X4075),esk107_5(X4071,X4072,X4073,X4074,X4075)),X4073)),c_Transitive__Closure_Ortrancl(X4075,X4072)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4075,X4075)),hAPP(hAPP(c_Product__Type_OPair(X4075,X4075),X4074),X4073)),c_Transitive__Closure_Ortrancl(X4075,X4072)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4075,X4075)),hAPP(hAPP(c_Product__Type_OPair(X4075,X4075),X4074),X4073)),c_Transitive__Closure_Ortrancl(X4075,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4075,X4075),tc_HOL_Obool)),X4072),X4071)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4075,X4075)),hAPP(hAPP(c_Product__Type_OPair(X4075,X4075),esk108_5(X4071,X4072,X4073,X4074,X4075)),esk107_5(X4071,X4072,X4073,X4074,X4075))),X4071))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4075,X4075)),hAPP(hAPP(c_Product__Type_OPair(X4075,X4075),X4074),X4073)),c_Transitive__Closure_Ortrancl(X4075,X4072)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4075,X4075)),hAPP(hAPP(c_Product__Type_OPair(X4075,X4075),X4074),X4073)),c_Transitive__Closure_Ortrancl(X4075,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4075,X4075),tc_HOL_Obool)),X4072),X4071)))) )
& ( esk108_5(X4071,X4072,X4073,X4074,X4075) != esk107_5(X4071,X4072,X4073,X4074,X4075)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4075,X4075)),hAPP(hAPP(c_Product__Type_OPair(X4075,X4075),X4074),X4073)),c_Transitive__Closure_Ortrancl(X4075,X4072)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4075,X4075)),hAPP(hAPP(c_Product__Type_OPair(X4075,X4075),X4074),X4073)),c_Transitive__Closure_Ortrancl(X4075,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4075,X4075),tc_HOL_Obool)),X4072),X4071)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE])])])]) ).
fof(i_0_613,plain,
! [X2769,X2770,X2771,X2772,X2773] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2772),esk58_5(X2769,X2770,X2771,X2772,X2773))),c_Transitive__Closure_Ortrancl(X2773,X2770)))
| hBOOL(hAPP(X2769,X2771))
| ~ hBOOL(hAPP(X2769,X2772))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2772),X2771)),c_Transitive__Closure_Ortrancl(X2773,X2770))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),esk58_5(X2769,X2770,X2771,X2772,X2773)),esk59_5(X2769,X2770,X2771,X2772,X2773))),X2770))
| hBOOL(hAPP(X2769,X2771))
| ~ hBOOL(hAPP(X2769,X2772))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2772),X2771)),c_Transitive__Closure_Ortrancl(X2773,X2770))) )
& ( hBOOL(hAPP(X2769,esk58_5(X2769,X2770,X2771,X2772,X2773)))
| hBOOL(hAPP(X2769,X2771))
| ~ hBOOL(hAPP(X2769,X2772))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2772),X2771)),c_Transitive__Closure_Ortrancl(X2773,X2770))) )
& ( ~ hBOOL(hAPP(X2769,esk59_5(X2769,X2770,X2771,X2772,X2773)))
| hBOOL(hAPP(X2769,X2771))
| ~ hBOOL(hAPP(X2769,X2772))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2772),X2771)),c_Transitive__Closure_Ortrancl(X2773,X2770))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__induct])])])]) ).
fof(i_0_614,plain,
! [X2839,X2840,X2841,X2842,X2843] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2843,X2843)),hAPP(hAPP(c_Product__Type_OPair(X2843,X2843),esk65_5(X2839,X2840,X2841,X2842,X2843)),esk66_5(X2839,X2840,X2841,X2842,X2843))),X2840))
| hBOOL(hAPP(X2839,X2842))
| ~ hBOOL(hAPP(X2839,X2841))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2843,X2843)),hAPP(hAPP(c_Product__Type_OPair(X2843,X2843),X2842),X2841)),c_Transitive__Closure_Ortrancl(X2843,X2840))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2843,X2843)),hAPP(hAPP(c_Product__Type_OPair(X2843,X2843),esk66_5(X2839,X2840,X2841,X2842,X2843)),X2841)),c_Transitive__Closure_Ortrancl(X2843,X2840)))
| hBOOL(hAPP(X2839,X2842))
| ~ hBOOL(hAPP(X2839,X2841))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2843,X2843)),hAPP(hAPP(c_Product__Type_OPair(X2843,X2843),X2842),X2841)),c_Transitive__Closure_Ortrancl(X2843,X2840))) )
& ( hBOOL(hAPP(X2839,esk66_5(X2839,X2840,X2841,X2842,X2843)))
| hBOOL(hAPP(X2839,X2842))
| ~ hBOOL(hAPP(X2839,X2841))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2843,X2843)),hAPP(hAPP(c_Product__Type_OPair(X2843,X2843),X2842),X2841)),c_Transitive__Closure_Ortrancl(X2843,X2840))) )
& ( ~ hBOOL(hAPP(X2839,esk65_5(X2839,X2840,X2841,X2842,X2843)))
| hBOOL(hAPP(X2839,X2842))
| ~ hBOOL(hAPP(X2839,X2841))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2843,X2843)),hAPP(hAPP(c_Product__Type_OPair(X2843,X2843),X2842),X2841)),c_Transitive__Closure_Ortrancl(X2843,X2840))) ) ),
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_615,plain,
! [X2399,X2400,X2401,X2402,X2403,X2404] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2404,X2400)),X2402),c_FuncSet_OPi(X2404,X2400,X2403,X2399)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2404,X2400)),X2401),c_FuncSet_OPi(X2404,X2400,X2403,X2399)))
| hBOOL(hAPP(hAPP(c_member(X2404),esk34_6(X2399,X2400,X2401,X2402,X2403,X2404)),X2403)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2404,X2400)),X2401),c_FuncSet_OPi(X2404,X2400,X2403,X2399)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2404,X2400)),X2402),c_FuncSet_OPi(X2404,X2400,X2403,X2399)))
| hBOOL(hAPP(hAPP(c_member(X2404),esk34_6(X2399,X2400,X2401,X2402,X2403,X2404)),X2403)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2404,X2400)),X2402),c_FuncSet_OPi(X2404,X2400,X2403,X2399)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2404,X2400)),X2401),c_FuncSet_OPi(X2404,X2400,X2403,X2399)))
| hAPP(X2402,esk34_6(X2399,X2400,X2401,X2402,X2403,X2404)) != hAPP(X2401,esk34_6(X2399,X2400,X2401,X2402,X2403,X2404)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2404,X2400)),X2401),c_FuncSet_OPi(X2404,X2400,X2403,X2399)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2404,X2400)),X2402),c_FuncSet_OPi(X2404,X2400,X2403,X2399)))
| hAPP(X2402,esk34_6(X2399,X2400,X2401,X2402,X2403,X2404)) != hAPP(X2401,esk34_6(X2399,X2400,X2401,X2402,X2403,X2404)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__cong])])])]) ).
fof(i_0_616,plain,
! [X2521,X2522,X2523,X2524,X2525] :
( ( hBOOL(hAPP(hAPP(c_member(X2525),esk37_5(X2521,X2522,X2523,X2524,X2525)),X2524))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2525,X2523)),c_FuncSet_Orestrict(X2525,X2523,X2522,X2524)),c_FuncSet_OPi(X2525,X2523,X2524,X2521))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2523),hAPP(X2522,esk37_5(X2521,X2522,X2523,X2524,X2525))),hAPP(X2521,esk37_5(X2521,X2522,X2523,X2524,X2525))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2525,X2523)),c_FuncSet_Orestrict(X2525,X2523,X2522,X2524)),c_FuncSet_OPi(X2525,X2523,X2524,X2521))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrictI])])])]) ).
fof(i_0_617,plain,
! [X2406,X2407,X2408,X2409,X2410] :
( ( hBOOL(hAPP(hAPP(c_member(X2410),esk35_5(X2406,X2407,X2408,X2409,X2410)),X2409))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2410,X2408)),X2407),c_FuncSet_OPi(X2410,X2408,X2409,X2406))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2408),hAPP(X2407,esk35_5(X2406,X2407,X2408,X2409,X2410))),hAPP(X2406,esk35_5(X2406,X2407,X2408,X2409,X2410))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2410,X2408)),X2407),c_FuncSet_OPi(X2410,X2408,X2409,X2406))) ) ),
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_618,plain,
! [X2381,X2382,X2383,X2384,X2385] :
( ( hBOOL(hAPP(hAPP(c_member(X2385),esk32_5(X2381,X2382,X2383,X2384,X2385)),X2384))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2385,X2383)),X2382),c_FuncSet_OPi(X2385,X2383,X2384,X2381))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2383),hAPP(X2382,esk32_5(X2381,X2382,X2383,X2384,X2385))),hAPP(X2381,esk32_5(X2381,X2382,X2383,X2384,X2385))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2385,X2383)),X2382),c_FuncSet_OPi(X2385,X2383,X2384,X2381))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_619,plain,
! [X2234,X2235,X2236,X2237,X2238,X2240,X2245,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),X2237),X2238)),hAPP(X2234,X2235)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2234,X2236)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2235,esk11_5(X2234,X2235,X2236,X2237,X2238))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2236,esk11_5(X2234,X2235,X2236,X2237,X2238))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2236),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))),X2235),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(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),X2237),X2238)),hAPP(X2234,X2236)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2234,X2235)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2235,esk11_5(X2234,X2235,X2236,X2237,X2238))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2236,esk11_5(X2234,X2235,X2236,X2237,X2238))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2236),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))),X2235),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(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),X2237),X2238)),hAPP(X2234,X2235)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2234,X2236)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2235,esk11_5(X2234,X2235,X2236,X2237,X2238))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2236,esk11_5(X2234,X2235,X2236,X2237,X2238))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2236),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))),X2235),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(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),X2237),X2238)),hAPP(X2234,X2236)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2234,X2235)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2235,esk11_5(X2234,X2235,X2236,X2237,X2238))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2238)),hAPP(X2236,esk11_5(X2234,X2235,X2236,X2237,X2238))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2236),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))),X2235),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2234) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk12_1(X2240)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2240) )
& ( hBOOL(hAPP(hAPP(c_member(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(X2240)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2240) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X2240)),esk15_1(X2240))),hAPP(esk12_1(X2240),X2245)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk14_1(X2240)),esk15_1(X2240))),hAPP(esk13_1(X2240),X2245)))
| c_Arrow__Order__Mirabelle_OIIA(X2240) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X2240)),esk15_1(X2240))),hAPP(esk13_1(X2240),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),esk14_1(X2240)),esk15_1(X2240))),hAPP(esk12_1(X2240),X2246)))
| c_Arrow__Order__Mirabelle_OIIA(X2240) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X2240)),esk15_1(X2240))),hAPP(X2240,esk12_1(X2240))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X2240)),esk15_1(X2240))),hAPP(X2240,esk13_1(X2240))))
| c_Arrow__Order__Mirabelle_OIIA(X2240) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X2240)),esk15_1(X2240))),hAPP(X2240,esk12_1(X2240))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X2240)),esk15_1(X2240))),hAPP(X2240,esk13_1(X2240))))
| c_Arrow__Order__Mirabelle_OIIA(X2240) ) ),
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_620,plain,
! [X2527,X2528,X2529,X2530,X2531] :
( ( hBOOL(hAPP(hAPP(c_member(X2531),esk38_5(X2527,X2528,X2529,X2530,X2531)),X2530))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2531,X2529)),c_FuncSet_Orestrict(X2531,X2529,X2528,X2530)),c_FuncSet_OPi(X2531,X2529,X2530,c_COMBK(tc_fun(X2529,tc_HOL_Obool),X2531,X2527)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2529),hAPP(X2528,esk38_5(X2527,X2528,X2529,X2530,X2531))),X2527))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2531,X2529)),c_FuncSet_Orestrict(X2531,X2529,X2528,X2530)),c_FuncSet_OPi(X2531,X2529,X2530,c_COMBK(tc_fun(X2529,tc_HOL_Obool),X2531,X2527)))) ) ),
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_621,plain,
! [X2387,X2388,X2389,X2390,X2391] :
( ( hBOOL(hAPP(hAPP(c_member(X2391),esk33_5(X2387,X2388,X2389,X2390,X2391)),X2390))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2391,X2389)),X2388),c_FuncSet_OPi(X2391,X2389,X2390,c_COMBK(tc_fun(X2389,tc_HOL_Obool),X2391,X2387)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2389),hAPP(X2388,esk33_5(X2387,X2388,X2389,X2390,X2391))),X2387))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2391,X2389)),X2388),c_FuncSet_OPi(X2391,X2389,X2390,c_COMBK(tc_fun(X2389,tc_HOL_Obool),X2391,X2387)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcsetI])])])]) ).
cnf(i_0_622,plain,
( c_FuncSet_Ocompose(X1,X6,X9,X4,X10,c_FuncSet_Ocompose(X1,X2,X6,X4,X7,X3)) = c_FuncSet_Ocompose(X1,X2,X9,X4,c_FuncSet_Ocompose(X2,X6,X9,X5,X10,X7),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X6)),X7),c_FuncSet_OPi(X2,X6,X5,c_COMBK(tc_fun(X6,tc_HOL_Obool),X2,X8))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X9)),X10),c_FuncSet_OPi(X6,X9,X8,c_COMBK(tc_fun(X9,tc_HOL_Obool),X6,X11)))) ),
inference(split_conjunct,[status(thm)],[i_0_529]) ).
cnf(i_0_623,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_530]) ).
fof(i_0_624,plain,
! [X2165] : hAPP(v_Q____,X2165) = 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____,X2165)),c_Arrow__Order__Mirabelle_Obelow(hAPP(v_P____,X2165),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_625,plain,
! [X3728,X3729,X3730,X3731,X3732] :
( ( hBOOL(hAPP(hAPP(c_member(X3732),esk98_5(X3728,X3729,X3730,X3731,X3732)),X3729))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3732,X3731)),X3730),c_Product__Type_OSigma(X3732,X3731,X3729,X3728))) )
& ( hBOOL(hAPP(hAPP(c_member(X3731),esk99_5(X3728,X3729,X3730,X3731,X3732)),hAPP(X3728,esk98_5(X3728,X3729,X3730,X3731,X3732))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3732,X3731)),X3730),c_Product__Type_OSigma(X3732,X3731,X3729,X3728))) )
& ( X3730 = hAPP(hAPP(c_Product__Type_OPair(X3732,X3731),esk98_5(X3728,X3729,X3730,X3731,X3732)),esk99_5(X3728,X3729,X3730,X3731,X3732))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3732,X3731)),X3730),c_Product__Type_OSigma(X3732,X3731,X3729,X3728))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaE])])])]) ).
fof(i_0_626,plain,
! [X3619,X3620,X3621,X3622,X3623] : c_Fun_Othe__inv__into(X3623,X3622,X3621,X3620,X3619) = c_HOL_OThe(X3623,hAPP(hAPP(c_COMBS(X3623,tc_HOL_Obool,tc_HOL_Obool),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3623,c_fconj),hAPP(hAPP(c_COMBC(X3623,tc_fun(X3623,tc_HOL_Obool),tc_HOL_Obool),c_member(X3623)),X3621))),hAPP(hAPP(c_COMBC(X3623,X3622,tc_HOL_Obool),hAPP(c_COMBB(X3622,tc_fun(X3622,tc_HOL_Obool),X3623,c_fequal),X3620)),X3619))),
inference(variable_rename,[status(thm)],[fact_the__inv__into__def]) ).
cnf(i_0_627,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_531]) ).
fof(i_0_628,plain,
! [X3577,X3578,X3579,X3580,X3581] :
( ( hBOOL(hAPP(hAPP(c_member(X3581),esk87_5(X3577,X3578,X3579,X3580,X3581)),X3580))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X3581,X3579),tc_HOL_Obool),c_FuncSet_OPi(X3581,X3579,X3580,X3578),c_FuncSet_OPi(X3581,X3579,X3580,X3577)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3579,tc_HOL_Obool),hAPP(X3578,esk87_5(X3577,X3578,X3579,X3580,X3581)),hAPP(X3577,esk87_5(X3577,X3578,X3579,X3580,X3581)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X3581,X3579),tc_HOL_Obool),c_FuncSet_OPi(X3581,X3579,X3580,X3578),c_FuncSet_OPi(X3581,X3579,X3580,X3577)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).
fof(i_0_629,plain,
! [X2166,X2167,X2168,X2169,X2170,X2171,X2172,X2173] :
( ( X2171 = X2169
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2173,X2173)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2173),X2171),X2169)),X2167))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2173,X2172),tc_prod(X2173,X2172))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2173,X2172),tc_prod(X2173,X2172)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2172),X2171),X2170)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2172),X2169),X2168))),c_Wellfounded_Olex__prod(X2173,X2172,X2167,X2166))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2172,X2172)),hAPP(hAPP(c_Product__Type_OPair(X2172,X2172),X2170),X2168)),X2166))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2173,X2173)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2173),X2171),X2169)),X2167))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2173,X2172),tc_prod(X2173,X2172))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2173,X2172),tc_prod(X2173,X2172)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2172),X2171),X2170)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2172),X2169),X2168))),c_Wellfounded_Olex__prod(X2173,X2172,X2167,X2166))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2173,X2173)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2173),X2171),X2169)),X2167))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2173,X2172),tc_prod(X2173,X2172))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2173,X2172),tc_prod(X2173,X2172)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2172),X2171),X2170)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2172),X2169),X2168))),c_Wellfounded_Olex__prod(X2173,X2172,X2167,X2166))) )
& ( X2171 != X2169
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2172,X2172)),hAPP(hAPP(c_Product__Type_OPair(X2172,X2172),X2170),X2168)),X2166))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2173,X2172),tc_prod(X2173,X2172))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2173,X2172),tc_prod(X2173,X2172)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2172),X2171),X2170)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2172),X2169),X2168))),c_Wellfounded_Olex__prod(X2173,X2172,X2167,X2166))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_630,plain,
! [X2310,X2311] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk21_2(X2310,X2311)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2311,X2310)
| ~ 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))),X2311),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)))) )
& ( esk22_2(X2310,X2311) != esk23_2(X2310,X2311)
| c_Arrow__Order__Mirabelle_Odictator(X2311,X2310)
| ~ 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))),X2311),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),esk22_2(X2310,X2311)),esk23_2(X2310,X2311))),hAPP(esk21_2(X2310,X2311),X2310)))
| c_Arrow__Order__Mirabelle_Odictator(X2311,X2310)
| ~ 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))),X2311),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),esk22_2(X2310,X2311)),esk23_2(X2310,X2311))),hAPP(X2311,esk21_2(X2310,X2311))))
| c_Arrow__Order__Mirabelle_Odictator(X2311,X2310)
| ~ 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))),X2311),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_631,plain,
! [X3870,X3871,X3872,X3873] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3873,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3873,tc_fun(X3873,tc_HOL_Obool),tc_HOL_Obool),c_member(X3873)),X3872)),hAPP(hAPP(c_COMBC(X3873,tc_fun(X3873,tc_HOL_Obool),tc_HOL_Obool),c_member(X3873)),X3871)),X3870))
| hBOOL(hAPP(hAPP(c_member(X3873),X3870),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3873,tc_HOL_Obool)),X3872),X3871))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3873),X3870),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3873,tc_HOL_Obool)),X3872),X3871)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3873,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3873,tc_fun(X3873,tc_HOL_Obool),tc_HOL_Obool),c_member(X3873)),X3872)),hAPP(hAPP(c_COMBC(X3873,tc_fun(X3873,tc_HOL_Obool),tc_HOL_Obool),c_member(X3873)),X3871)),X3870)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq])]) ).
fof(i_0_632,plain,
! [X2631,X2632,X2633,X2634] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2634,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2634,tc_fun(X2634,tc_HOL_Obool),tc_HOL_Obool),c_member(X2634)),X2633)),hAPP(hAPP(c_COMBC(X2634,tc_fun(X2634,tc_HOL_Obool),tc_HOL_Obool),c_member(X2634)),X2632)),X2631))
| hBOOL(hAPP(hAPP(c_member(X2634),X2631),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2634,tc_HOL_Obool)),X2633),X2632))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2634),X2631),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2634,tc_HOL_Obool)),X2633),X2632)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2634,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2634,tc_fun(X2634,tc_HOL_Obool),tc_HOL_Obool),c_member(X2634)),X2633)),hAPP(hAPP(c_COMBC(X2634,tc_fun(X2634,tc_HOL_Obool),tc_HOL_Obool),c_member(X2634)),X2632)),X2631)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).
fof(i_0_633,plain,
! [X2998,X2999,X3000,X3001] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3001,X3001)),hAPP(hAPP(c_Product__Type_OPair(X3001,X3001),esk76_4(X2998,X2999,X3000,X3001)),esk76_4(X2998,X2999,X3000,X3001))),c_Transitive__Closure_Otrancl(X3001,X3000)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3001,X3001)),hAPP(hAPP(c_Product__Type_OPair(X3001,X3001),X2999),X2998)),X3000))
| X2999 != X2998 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_532])])]) ).
fof(i_0_634,plain,
! [X3137,X3138,X3139,X3140,X3141,X3142] :
( hBOOL(hAPP(hAPP(c_member(X3142),X3141),X3140))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3142,X3139)),X3138),c_FuncSet_Oextensional__funcset(X3142,X3139,c_Set_Oinsert(X3142,X3141,X3140),X3137)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3142,X3139)),c_Fun_Ofun__upd(X3142,X3139,X3138,X3141,c_HOL_Oundefined(X3139))),c_FuncSet_Oextensional__funcset(X3142,X3139,X3140,X3137))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_533])]) ).
fof(i_0_635,plain,
! [X3143,X3144,X3145,X3146,X3147,X3148,X3149] :
( ~ hBOOL(hAPP(hAPP(c_member(X3149),X3148),X3147))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3146,X3149)),X3145),c_FuncSet_Oextensional__funcset(X3146,X3149,X3144,X3147)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3146,X3149)),c_Fun_Ofun__upd(X3146,X3149,X3145,X3143,X3148)),c_FuncSet_Oextensional__funcset(X3146,X3149,c_Set_Oinsert(X3146,X3143,X3144),X3147))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__extend__domainI])]) ).
fof(i_0_636,plain,
! [X2986,X2987,X2988,X2989] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2989,X2989)),hAPP(hAPP(c_Product__Type_OPair(X2989,X2989),X2988),esk74_4(X2986,X2987,X2988,X2989))),X2986))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2989,X2989)),hAPP(hAPP(c_Product__Type_OPair(X2989,X2989),X2988),X2987)),X2986))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2989,X2989)),hAPP(hAPP(c_Product__Type_OPair(X2989,X2989),X2988),X2987)),c_Transitive__Closure_Otrancl(X2989,X2986))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2989,X2989)),hAPP(hAPP(c_Product__Type_OPair(X2989,X2989),esk74_4(X2986,X2987,X2988,X2989)),X2987)),c_Transitive__Closure_Otrancl(X2989,X2986)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2989,X2989)),hAPP(hAPP(c_Product__Type_OPair(X2989,X2989),X2988),X2987)),X2986))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2989,X2989)),hAPP(hAPP(c_Product__Type_OPair(X2989,X2989),X2988),X2987)),c_Transitive__Closure_Otrancl(X2989,X2986))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_534])])])]) ).
fof(i_0_637,plain,
! [X2981,X2982,X2983,X2984] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2984,X2984)),hAPP(hAPP(c_Product__Type_OPair(X2984,X2984),X2983),esk73_4(X2981,X2982,X2983,X2984))),c_Transitive__Closure_Otrancl(X2984,X2981)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2984,X2984)),hAPP(hAPP(c_Product__Type_OPair(X2984,X2984),X2983),X2982)),X2981))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2984,X2984)),hAPP(hAPP(c_Product__Type_OPair(X2984,X2984),X2983),X2982)),c_Transitive__Closure_Otrancl(X2984,X2981))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2984,X2984)),hAPP(hAPP(c_Product__Type_OPair(X2984,X2984),esk73_4(X2981,X2982,X2983,X2984)),X2982)),X2981))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2984,X2984)),hAPP(hAPP(c_Product__Type_OPair(X2984,X2984),X2983),X2982)),X2981))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2984,X2984)),hAPP(hAPP(c_Product__Type_OPair(X2984,X2984),X2983),X2982)),c_Transitive__Closure_Otrancl(X2984,X2981))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_535])])])]) ).
fof(i_0_638,plain,
! [X2489,X2490,X2491,X2492,X2493] :
( ( hBOOL(hAPP(hAPP(c_member(X2493),esk36_5(X2489,X2490,X2491,X2492,X2493)),X2490))
| X2491 = X2489
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2493,X2492)),X2489),c_FuncSet_Oextensional(X2493,X2492,X2490)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2493,X2492)),X2491),c_FuncSet_Oextensional(X2493,X2492,X2490))) )
& ( hAPP(X2491,esk36_5(X2489,X2490,X2491,X2492,X2493)) != hAPP(X2489,esk36_5(X2489,X2490,X2491,X2492,X2493))
| X2491 = X2489
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2493,X2492)),X2489),c_FuncSet_Oextensional(X2493,X2492,X2490)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2493,X2492)),X2491),c_FuncSet_Oextensional(X2493,X2492,X2490))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensionalityI])])])]) ).
fof(i_0_639,plain,
! [X2834,X2835,X2836,X2837] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2837,X2837)),hAPP(hAPP(c_Product__Type_OPair(X2837,X2837),X2836),esk64_4(X2834,X2835,X2836,X2837))),X2834))
| X2836 = X2835
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2837,X2837)),hAPP(hAPP(c_Product__Type_OPair(X2837,X2837),X2836),X2835)),c_Transitive__Closure_Ortrancl(X2837,X2834))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2837,X2837)),hAPP(hAPP(c_Product__Type_OPair(X2837,X2837),esk64_4(X2834,X2835,X2836,X2837)),X2835)),c_Transitive__Closure_Ortrancl(X2837,X2834)))
| X2836 = X2835
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2837,X2837)),hAPP(hAPP(c_Product__Type_OPair(X2837,X2837),X2836),X2835)),c_Transitive__Closure_Ortrancl(X2837,X2834))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_536])])])]) ).
fof(i_0_640,plain,
! [X2970,X2971,X2972,X2973] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2973,X2973)),hAPP(hAPP(c_Product__Type_OPair(X2973,X2973),X2972),esk71_4(X2970,X2971,X2972,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))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2973,X2973)),hAPP(hAPP(c_Product__Type_OPair(X2973,X2973),esk71_4(X2970,X2971,X2972,X2973)),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))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD])])])]) ).
fof(i_0_641,plain,
! [X2829,X2830,X2831,X2832] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2832,X2832)),hAPP(hAPP(c_Product__Type_OPair(X2832,X2832),X2831),esk63_4(X2829,X2830,X2831,X2832))),c_Transitive__Closure_Ortrancl(X2832,X2829)))
| X2831 = X2830
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2832,X2832)),hAPP(hAPP(c_Product__Type_OPair(X2832,X2832),X2831),X2830)),c_Transitive__Closure_Ortrancl(X2832,X2829))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2832,X2832)),hAPP(hAPP(c_Product__Type_OPair(X2832,X2832),esk63_4(X2829,X2830,X2831,X2832)),X2830)),X2829))
| X2831 = X2830
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2832,X2832)),hAPP(hAPP(c_Product__Type_OPair(X2832,X2832),X2831),X2830)),c_Transitive__Closure_Ortrancl(X2832,X2829))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_537])])])]) ).
fof(i_0_642,plain,
! [X2965,X2966,X2967,X2968] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2968,X2968)),hAPP(hAPP(c_Product__Type_OPair(X2968,X2968),X2967),esk70_4(X2965,X2966,X2967,X2968))),c_Transitive__Closure_Ortrancl(X2968,X2965)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2968,X2968)),hAPP(hAPP(c_Product__Type_OPair(X2968,X2968),X2967),X2966)),c_Transitive__Closure_Otrancl(X2968,X2965))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2968,X2968)),hAPP(hAPP(c_Product__Type_OPair(X2968,X2968),esk70_4(X2965,X2966,X2967,X2968)),X2966)),X2965))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2968,X2968)),hAPP(hAPP(c_Product__Type_OPair(X2968,X2968),X2967),X2966)),c_Transitive__Closure_Otrancl(X2968,X2965))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD2])])])]) ).
fof(i_0_643,plain,
! [X2110,X2111,X2112,X2113,X2114,X2115,X2116] :
( ~ hBOOL(hAPP(X2116,X2115))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2114,X2114)),hAPP(hAPP(c_Product__Type_OPair(X2114,X2114),X2113),X2112)),hAPP(X2111,X2115)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2110,X2114),tc_prod(X2110,X2114))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2110,X2114),tc_prod(X2110,X2114)),hAPP(hAPP(c_Product__Type_OPair(X2110,X2114),X2115),X2113)),hAPP(hAPP(c_Product__Type_OPair(X2110,X2114),X2115),X2112))),c_Recdef_Osame__fst(X2110,X2114,X2116,X2111))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
cnf(i_0_644,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_538]) ).
fof(i_0_645,plain,
! [X3780,X3781,X3782,X3783,X3784] : c_Product__Type_OSigma(X3784,X3783,X3782,hAPP(hAPP(c_COMBS(X3784,tc_fun(X3783,tc_HOL_Obool),tc_fun(X3783,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3783,tc_HOL_Obool),tc_fun(tc_fun(X3783,tc_HOL_Obool),tc_fun(X3783,tc_HOL_Obool)),X3784,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3783,tc_HOL_Obool))),X3781)),X3780)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3784,X3783),tc_HOL_Obool)),c_Product__Type_OSigma(X3784,X3783,X3782,X3781)),c_Product__Type_OSigma(X3784,X3783,X3782,X3780)),
inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2]) ).
fof(i_0_646,plain,
! [X3685,X3686,X3687,X3688,X3689] : c_Product__Type_OSigma(X3689,X3688,X3687,hAPP(hAPP(c_COMBS(X3689,tc_fun(X3688,tc_HOL_Obool),tc_fun(X3688,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3688,tc_HOL_Obool),tc_fun(tc_fun(X3688,tc_HOL_Obool),tc_fun(X3688,tc_HOL_Obool)),X3689,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3688,tc_HOL_Obool))),X3686)),X3685)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3689,X3688),tc_HOL_Obool)),c_Product__Type_OSigma(X3689,X3688,X3687,X3686)),c_Product__Type_OSigma(X3689,X3688,X3687,X3685)),
inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2]) ).
fof(i_0_647,plain,
! [X3553,X3554,X3555,X3556,X3557,X3559] :
( ( hBOOL(hAPP(c_Recdef_Owfrec__rel(X3557,X3556,X3555,X3554,X3553),esk86_5(X3553,X3554,X3555,X3556,X3557)))
| ~ c_Wellfounded_Owf(X3557,X3555)
| ~ c_Recdef_Oadm__wf(X3557,X3556,X3555,X3554) )
& ( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X3557,X3556,X3555,X3554,X3553),X3559))
| X3559 = esk86_5(X3553,X3554,X3555,X3556,X3557)
| ~ c_Wellfounded_Owf(X3557,X3555)
| ~ c_Recdef_Oadm__wf(X3557,X3556,X3555,X3554) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfrec__unique])])])])]) ).
cnf(i_0_648,plain,
( c_Nitpick_Owfrec_H(X1,X3,X2,X4,X5) = c_Nitpick_Owf__wfrec_H(X1,X3,X2,X4,X5)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_539]) ).
cnf(i_0_649,plain,
c_Nitpick_Owf__wfrec_H(X1,X2,X3,X4,X5) = hAPP(hAPP(X4,hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),c_Nitpick_Owf__wfrec(X1,X2,X3,X4)),X3),X5)),X5),
inference(split_conjunct,[status(thm)],[i_0_540]) ).
fof(i_0_650,plain,
! [X2824,X2825,X2826,X2827] :
( ~ hBOOL(hAPP(hAPP(c_member(X2827),X2826),c_Relation_ORange(X2825,X2827,X2824)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2825,X2827)),hAPP(hAPP(c_Product__Type_OPair(X2825,X2827),esk62_4(X2824,X2825,X2826,X2827)),X2826)),X2824)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])])]) ).
fof(i_0_651,plain,
! [X2806,X2807,X2808,X2809,X2811,X2812,X2813,X2814,X2815] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2809),X2808),c_Relation_ORange(X2807,X2809,X2806)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2807,X2809)),hAPP(hAPP(c_Product__Type_OPair(X2807,X2809),esk60_4(X2806,X2807,X2808,X2809)),X2808)),X2806)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2812,X2814)),hAPP(hAPP(c_Product__Type_OPair(X2812,X2814),X2815),X2813)),X2811))
| hBOOL(hAPP(hAPP(c_member(X2814),X2813),c_Relation_ORange(X2812,X2814,X2811))) ) ),
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_652,plain,
! [X3520,X3521,X3522,X3523,X3524] :
( ~ c_Wellfounded_Owf(X3524,X3523)
| hAPP(c_Recdef_Owfrec(X3524,X3522,X3523,X3521),X3520) = hAPP(hAPP(X3521,hAPP(hAPP(hAPP(c_Recdef_Ocut(X3524,X3522),c_Recdef_Owfrec(X3524,X3522,X3523,X3521)),X3523),X3520)),X3520) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfrec])]) ).
fof(i_0_653,plain,
! [X3515,X3516,X3517,X3518,X3519] :
( ~ c_Wellfounded_Owf(X3516,X3518)
| hAPP(c_Recdef_Owfrec(X3516,X3515,X3518,X3517),X3519) = hAPP(hAPP(X3517,hAPP(hAPP(hAPP(c_Recdef_Ocut(X3516,X3515),c_Recdef_Owfrec(X3516,X3515,X3518,X3517)),X3518),X3519)),X3519) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__wfrec])])]) ).
fof(i_0_654,plain,
! [X4020,X4021,X4022,X4023] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4023,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4023,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4023,tc_HOL_Obool)),X4022),X4021)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4023,tc_HOL_Obool)),X4021),X4020))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4023,tc_HOL_Obool)),X4020),X4022)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4023,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4023,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4023,tc_HOL_Obool)),X4022),X4021)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4023,tc_HOL_Obool)),X4021),X4020))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4023,tc_HOL_Obool)),X4020),X4022)),
inference(variable_rename,[status(thm)],[fact_Un__Int__crazy]) ).
fof(i_0_655,plain,
! [X3748,X3749,X3750,X3751,X3752,X3753] : c_Product__Type_OSigma(X3753,X3752,c_Set_Oinsert(X3753,X3751,X3750),c_COMBK(tc_fun(X3752,tc_HOL_Obool),X3753,c_Set_Oinsert(X3752,X3749,X3748))) = c_Set_Oinsert(tc_prod(X3753,X3752),hAPP(hAPP(c_Product__Type_OPair(X3753,X3752),X3751),X3749),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3753,X3752),tc_HOL_Obool)),c_Product__Type_OSigma(X3753,X3752,X3750,c_COMBK(tc_fun(X3752,tc_HOL_Obool),X3753,c_Set_Oinsert(X3752,X3749,X3748)))),c_Product__Type_OSigma(X3753,X3752,c_Set_Oinsert(X3753,X3751,X3750),c_COMBK(tc_fun(X3752,tc_HOL_Obool),X3753,X3748)))),
inference(variable_rename,[status(thm)],[fact_insert__times__insert]) ).
fof(i_0_656,plain,
! [X2224,X2225,X2226,X2227,X2229,X2233] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2224)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2225),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),X2226),X2227)),hAPP(X2225,esk7_4(X2224,X2225,X2226,X2227))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2226),X2227)),hAPP(X2224,X2225))) )
& ( hBOOL(hAPP(hAPP(c_member(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(X2229)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(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),esk9_1(X2229)),esk10_1(X2229))),hAPP(esk8_1(X2229),X2233)))
| c_Arrow__Order__Mirabelle_Ounanimity(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),esk9_1(X2229)),esk10_1(X2229))),hAPP(X2229,esk8_1(X2229))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2229) ) ),
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_657,plain,
! [X3475,X3476,X3477,X3478,X3479,X3480,X3481] :
( X3481 = X3480
| c_Fun_Ofun__upd(X3479,X3478,c_Fun_Ofun__upd(X3479,X3478,X3477,X3481,X3476),X3480,X3475) = c_Fun_Ofun__upd(X3479,X3478,c_Fun_Ofun__upd(X3479,X3478,X3477,X3480,X3475),X3481,X3476) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__twist])]) ).
fof(i_0_658,plain,
! [X3718,X3719,X3720] :
( ( hBOOL(hAPP(hAPP(c_member(X3720),esk97_3(X3718,X3719,X3720)),X3718))
| c_Relation_Orefl__on(X3720,X3718,X3719)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3720,X3720),tc_HOL_Obool),X3719,c_Product__Type_OSigma(X3720,X3720,X3718,c_COMBK(tc_fun(X3720,tc_HOL_Obool),X3720,X3718))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3720,X3720)),hAPP(hAPP(c_Product__Type_OPair(X3720,X3720),esk97_3(X3718,X3719,X3720)),esk97_3(X3718,X3719,X3720))),X3719))
| c_Relation_Orefl__on(X3720,X3718,X3719)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3720,X3720),tc_HOL_Obool),X3719,c_Product__Type_OSigma(X3720,X3720,X3718,c_COMBK(tc_fun(X3720,tc_HOL_Obool),X3720,X3718))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onI])])])]) ).
fof(i_0_659,plain,
! [X3629,X3630,X3631,X3632,X3633,X3634,X3635] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3631,X3631),tc_HOL_Obool),X3629,c_Product__Type_OSigma(X3631,X3631,X3630,c_COMBK(tc_fun(X3631,tc_HOL_Obool),X3631,X3630)))
| ~ c_Relation_Orefl__on(X3631,X3630,X3629) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3631),X3632),X3630))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3631,X3631)),hAPP(hAPP(c_Product__Type_OPair(X3631,X3631),X3632),X3632)),X3629))
| ~ c_Relation_Orefl__on(X3631,X3630,X3629) )
& ( hBOOL(hAPP(hAPP(c_member(X3635),esk93_3(X3633,X3634,X3635)),X3634))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3635,X3635),tc_HOL_Obool),X3633,c_Product__Type_OSigma(X3635,X3635,X3634,c_COMBK(tc_fun(X3635,tc_HOL_Obool),X3635,X3634)))
| c_Relation_Orefl__on(X3635,X3634,X3633) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3635,X3635)),hAPP(hAPP(c_Product__Type_OPair(X3635,X3635),esk93_3(X3633,X3634,X3635)),esk93_3(X3633,X3634,X3635))),X3633))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3635,X3635),tc_HOL_Obool),X3633,c_Product__Type_OSigma(X3635,X3635,X3634,c_COMBK(tc_fun(X3635,tc_HOL_Obool),X3635,X3634)))
| c_Relation_Orefl__on(X3635,X3634,X3633) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__def])])])])])]) ).
cnf(i_0_660,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_542]) ).
fof(i_0_661,plain,
! [X2154,X2155,X2156,X2157,X2158] :
( ( X2155 != X2154
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2155 != X2157
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2158),X2154)),X2156))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2154 != X2157
| X2155 = X2158
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2158)),X2156))
| X2155 = X2157
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2154 = X2157
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),X2156))
| X2155 = X2157
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2155 != X2157
| X2155 = X2157
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2154 != X2157
| X2154 = X2157
| X2155 = X2157
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),X2156))
| X2154 = X2157
| X2155 = X2157
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2154 != X2157
| X2155 != X2158
| X2155 = X2157
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),X2156))
| X2155 != X2158
| X2155 = X2157
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2154 != X2157
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2158)),X2156))
| X2155 = X2157
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),X2156))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2158)),X2156))
| X2155 = X2157
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2155 != X2157
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2158),X2154)),X2156))
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2154 != X2157
| X2154 = X2157
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2158),X2154)),X2156))
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),X2156))
| X2154 = X2157
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2158),X2154)),X2156))
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2154 != X2157
| X2155 != X2158
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2158),X2154)),X2156))
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),X2156))
| X2155 != X2158
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2158),X2154)),X2156))
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( X2154 != X2157
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2158)),X2156))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2158),X2154)),X2156))
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),X2156))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2158)),X2156))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2158),X2154)),X2156))
| X2155 = X2154
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2155),X2154)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2156),X2158),X2157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2156),c_Arrow__Order__Mirabelle_OLin))
| X2158 = X2157 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_662,plain,
! [X2149,X2150,X2151,X2152,X2153] :
( ( X2150 != X2149
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2149 != X2153
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2152)),X2151))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2150 != X2153
| X2149 = X2152
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2149)),X2151))
| X2149 = X2153
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2150 = X2153
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),X2151))
| X2149 = X2153
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2149 != X2153
| X2149 = X2153
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2150 != X2153
| X2150 = X2153
| X2149 = X2153
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),X2151))
| X2150 = X2153
| X2149 = X2153
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2150 != X2153
| X2149 != X2152
| X2149 = X2153
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),X2151))
| X2149 != X2152
| X2149 = X2153
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2150 != X2153
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2149)),X2151))
| X2149 = X2153
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),X2151))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2149)),X2151))
| X2149 = X2153
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2149 != X2153
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2152)),X2151))
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2150 != X2153
| X2150 = X2153
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2152)),X2151))
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),X2151))
| X2150 = X2153
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2152)),X2151))
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2150 != X2153
| X2149 != X2152
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2152)),X2151))
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),X2151))
| X2149 != X2152
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2152)),X2151))
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( X2150 != X2153
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2149)),X2151))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2152)),X2151))
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),X2151))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2149)),X2151))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2152)),X2151))
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2150),X2149)),c_Arrow__Order__Mirabelle_Obelow(X2151,X2153,X2152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2151),c_Arrow__Order__Mirabelle_OLin))
| X2153 = X2152 ) ),
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_543]) ).
fof(i_0_664,plain,
! [X2861,X2862,X2863,X2864,X2865,X2866,X2867,X2868] :
( ( ~ c_Relation_Ototal__on(X2863,X2862,X2861)
| ~ hBOOL(hAPP(hAPP(c_member(X2863),X2864),X2862))
| ~ hBOOL(hAPP(hAPP(c_member(X2863),X2865),X2862))
| X2864 = X2865
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2863,X2863)),hAPP(hAPP(c_Product__Type_OPair(X2863,X2863),X2864),X2865)),X2861))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2863,X2863)),hAPP(hAPP(c_Product__Type_OPair(X2863,X2863),X2865),X2864)),X2861)) )
& ( hBOOL(hAPP(hAPP(c_member(X2868),esk68_3(X2866,X2867,X2868)),X2867))
| c_Relation_Ototal__on(X2868,X2867,X2866) )
& ( hBOOL(hAPP(hAPP(c_member(X2868),esk69_3(X2866,X2867,X2868)),X2867))
| c_Relation_Ototal__on(X2868,X2867,X2866) )
& ( esk68_3(X2866,X2867,X2868) != esk69_3(X2866,X2867,X2868)
| c_Relation_Ototal__on(X2868,X2867,X2866) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2868,X2868)),hAPP(hAPP(c_Product__Type_OPair(X2868,X2868),esk68_3(X2866,X2867,X2868)),esk69_3(X2866,X2867,X2868))),X2866))
| c_Relation_Ototal__on(X2868,X2867,X2866) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2868,X2868)),hAPP(hAPP(c_Product__Type_OPair(X2868,X2868),esk69_3(X2866,X2867,X2868)),esk68_3(X2866,X2867,X2868))),X2866))
| c_Relation_Ototal__on(X2868,X2867,X2866) ) ),
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_665,plain,
! [X2533,X2534,X2535,X2536,X2537] :
( ~ c_Relation_Osingle__valued(X2537,X2537,X2536)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2537,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2537,X2537),X2535),X2534)),c_Transitive__Closure_Ortrancl(X2537,X2536)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2537,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2537,X2537),X2535),X2533)),c_Transitive__Closure_Ortrancl(X2537,X2536)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2537,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2537,X2537),X2534),X2533)),c_Transitive__Closure_Ortrancl(X2537,X2536)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2537,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2537,X2537),X2533),X2534)),c_Transitive__Closure_Ortrancl(X2537,X2536))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).
fof(i_0_666,plain,
! [X2745,X2746,X2747,X2748] :
( ~ hBOOL(hAPP(hAPP(c_member(X2748),X2747),c_Relation_ODomain(X2748,X2746,X2745)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2748,X2746)),hAPP(hAPP(c_Product__Type_OPair(X2748,X2746),X2747),esk54_4(X2745,X2746,X2747,X2748))),X2745)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])])]) ).
fof(i_0_667,plain,
! [X2640,X2641,X2642,X2643,X2645,X2646,X2647,X2648,X2649] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2643),X2642),c_Relation_ODomain(X2643,X2641,X2640)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2643,X2641)),hAPP(hAPP(c_Product__Type_OPair(X2643,X2641),X2642),esk49_4(X2640,X2641,X2642,X2643))),X2640)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2648,X2646)),hAPP(hAPP(c_Product__Type_OPair(X2648,X2646),X2647),X2649)),X2645))
| hBOOL(hAPP(hAPP(c_member(X2648),X2647),c_Relation_ODomain(X2648,X2646,X2645))) ) ),
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_668,plain,
! [X3932,X3933,X3934,X3935,X3936,X3939,X3940,X3941,X3942,X3943,X3944] :
( ( hBOOL(hAPP(hAPP(c_member(X3935),esk102_4(X3932,X3933,X3934,X3935)),X3933))
| hBOOL(hAPP(hAPP(c_member(X3935),esk101_4(X3932,X3933,X3934,X3935)),X3934))
| ~ hBOOL(hAPP(hAPP(c_member(X3935),X3936),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3935,tc_HOL_Obool)),X3934),X3933)))
| ~ hBOOL(hAPP(X3932,X3936)) )
& ( hBOOL(hAPP(X3932,esk102_4(X3932,X3933,X3934,X3935)))
| hBOOL(hAPP(hAPP(c_member(X3935),esk101_4(X3932,X3933,X3934,X3935)),X3934))
| ~ hBOOL(hAPP(hAPP(c_member(X3935),X3936),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3935,tc_HOL_Obool)),X3934),X3933)))
| ~ hBOOL(hAPP(X3932,X3936)) )
& ( hBOOL(hAPP(hAPP(c_member(X3935),esk102_4(X3932,X3933,X3934,X3935)),X3933))
| hBOOL(hAPP(X3932,esk101_4(X3932,X3933,X3934,X3935)))
| ~ hBOOL(hAPP(hAPP(c_member(X3935),X3936),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3935,tc_HOL_Obool)),X3934),X3933)))
| ~ hBOOL(hAPP(X3932,X3936)) )
& ( hBOOL(hAPP(X3932,esk102_4(X3932,X3933,X3934,X3935)))
| hBOOL(hAPP(X3932,esk101_4(X3932,X3933,X3934,X3935)))
| ~ hBOOL(hAPP(hAPP(c_member(X3935),X3936),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3935,tc_HOL_Obool)),X3934),X3933)))
| ~ hBOOL(hAPP(X3932,X3936)) )
& ( hBOOL(hAPP(hAPP(c_member(X3942),esk103_4(X3939,X3940,X3941,X3942)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3942,tc_HOL_Obool)),X3941),X3940)))
| ~ hBOOL(hAPP(hAPP(c_member(X3942),X3943),X3941))
| ~ hBOOL(hAPP(X3939,X3943)) )
& ( hBOOL(hAPP(X3939,esk103_4(X3939,X3940,X3941,X3942)))
| ~ hBOOL(hAPP(hAPP(c_member(X3942),X3943),X3941))
| ~ hBOOL(hAPP(X3939,X3943)) )
& ( hBOOL(hAPP(hAPP(c_member(X3942),esk103_4(X3939,X3940,X3941,X3942)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3942,tc_HOL_Obool)),X3941),X3940)))
| ~ hBOOL(hAPP(hAPP(c_member(X3942),X3944),X3940))
| ~ hBOOL(hAPP(X3939,X3944)) )
& ( hBOOL(hAPP(X3939,esk103_4(X3939,X3940,X3941,X3942)))
| ~ hBOOL(hAPP(hAPP(c_member(X3942),X3944),X3940))
| ~ hBOOL(hAPP(X3939,X3944)) ) ),
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_bex__Un])])])])])]) ).
fof(i_0_669,plain,
! [X3946,X3947,X3948,X3949,X3951,X3952,X3953,X3954,X3955,X3956,X3959] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3949),X3951),X3948))
| hBOOL(hAPP(X3946,X3951))
| hBOOL(hAPP(hAPP(c_member(X3949),esk104_4(X3946,X3947,X3948,X3949)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3949,tc_HOL_Obool)),X3948),X3947))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3949),X3952),X3947))
| hBOOL(hAPP(X3946,X3952))
| hBOOL(hAPP(hAPP(c_member(X3949),esk104_4(X3946,X3947,X3948,X3949)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3949,tc_HOL_Obool)),X3948),X3947))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3949),X3951),X3948))
| hBOOL(hAPP(X3946,X3951))
| ~ hBOOL(hAPP(X3946,esk104_4(X3946,X3947,X3948,X3949))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3949),X3952),X3947))
| hBOOL(hAPP(X3946,X3952))
| ~ hBOOL(hAPP(X3946,esk104_4(X3946,X3947,X3948,X3949))) )
& ( hBOOL(hAPP(hAPP(c_member(X3956),esk106_4(X3953,X3954,X3955,X3956)),X3954))
| hBOOL(hAPP(hAPP(c_member(X3956),esk105_4(X3953,X3954,X3955,X3956)),X3955))
| ~ hBOOL(hAPP(hAPP(c_member(X3956),X3959),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3956,tc_HOL_Obool)),X3955),X3954)))
| hBOOL(hAPP(X3953,X3959)) )
& ( ~ hBOOL(hAPP(X3953,esk106_4(X3953,X3954,X3955,X3956)))
| hBOOL(hAPP(hAPP(c_member(X3956),esk105_4(X3953,X3954,X3955,X3956)),X3955))
| ~ hBOOL(hAPP(hAPP(c_member(X3956),X3959),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3956,tc_HOL_Obool)),X3955),X3954)))
| hBOOL(hAPP(X3953,X3959)) )
& ( hBOOL(hAPP(hAPP(c_member(X3956),esk106_4(X3953,X3954,X3955,X3956)),X3954))
| ~ hBOOL(hAPP(X3953,esk105_4(X3953,X3954,X3955,X3956)))
| ~ hBOOL(hAPP(hAPP(c_member(X3956),X3959),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3956,tc_HOL_Obool)),X3955),X3954)))
| hBOOL(hAPP(X3953,X3959)) )
& ( ~ hBOOL(hAPP(X3953,esk106_4(X3953,X3954,X3955,X3956)))
| ~ hBOOL(hAPP(X3953,esk105_4(X3953,X3954,X3955,X3956)))
| ~ hBOOL(hAPP(hAPP(c_member(X3956),X3959),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3956,tc_HOL_Obool)),X3955),X3954)))
| hBOOL(hAPP(X3953,X3959)) ) ),
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_ball__Un])])])])])]) ).
fof(i_0_670,plain,
! [X2871,X2872,X2873,X2874,X2875,X2876] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2876,X2876)),hAPP(hAPP(c_Product__Type_OPair(X2876,X2876),X2875),X2874)),c_Relation_Oinv__image(X2873,X2876,X2872,X2871)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2873,X2873)),hAPP(hAPP(c_Product__Type_OPair(X2873,X2873),hAPP(X2871,X2875)),hAPP(X2871,X2874))),X2872)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2873,X2873)),hAPP(hAPP(c_Product__Type_OPair(X2873,X2873),hAPP(X2871,X2875)),hAPP(X2871,X2874))),X2872))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2876,X2876)),hAPP(hAPP(c_Product__Type_OPair(X2876,X2876),X2875),X2874)),c_Relation_Oinv__image(X2873,X2876,X2872,X2871))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])]) ).
fof(i_0_671,plain,
! [X3458,X3459,X3460,X3461,X3462,X3463] : c_Fun_Ofun__upd(X3463,X3462,c_Fun_Ofun__upd(X3463,X3462,X3461,X3460,X3459),X3460,X3458) = c_Fun_Ofun__upd(X3463,X3462,X3461,X3460,X3458),
inference(variable_rename,[status(thm)],[fact_fun__upd__upd]) ).
fof(i_0_672,plain,
! [X2912,X2913,X2914,X2915,X2916] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2916,X2916)),hAPP(hAPP(c_Product__Type_OPair(X2916,X2916),X2915),X2914)),c_Transitive__Closure_Otrancl(X2916,X2913)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2916,X2916)),hAPP(hAPP(c_Product__Type_OPair(X2916,X2916),X2914),X2912)),c_Transitive__Closure_Otrancl(X2916,X2913)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2916,X2916)),hAPP(hAPP(c_Product__Type_OPair(X2916,X2916),X2915),X2912)),c_Transitive__Closure_Otrancl(X2916,X2913))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__trans])]) ).
fof(i_0_673,plain,
! [X2937,X2938,X2939,X2940,X2941] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2941,X2941)),hAPP(hAPP(c_Product__Type_OPair(X2941,X2941),X2940),X2939)),c_Transitive__Closure_Ortrancl(X2941,X2938)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2941,X2941)),hAPP(hAPP(c_Product__Type_OPair(X2941,X2941),X2939),X2937)),c_Transitive__Closure_Otrancl(X2941,X2938)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2941,X2941)),hAPP(hAPP(c_Product__Type_OPair(X2941,X2941),X2940),X2937)),c_Transitive__Closure_Otrancl(X2941,X2938))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl])]) ).
fof(i_0_674,plain,
! [X2942,X2943,X2944,X2945,X2946] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2946,X2946)),hAPP(hAPP(c_Product__Type_OPair(X2946,X2946),X2945),X2944)),c_Transitive__Closure_Otrancl(X2946,X2943)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2946,X2946)),hAPP(hAPP(c_Product__Type_OPair(X2946,X2946),X2944),X2942)),c_Transitive__Closure_Ortrancl(X2946,X2943)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2946,X2946)),hAPP(hAPP(c_Product__Type_OPair(X2946,X2946),X2945),X2942)),c_Transitive__Closure_Otrancl(X2946,X2943))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl])]) ).
fof(i_0_675,plain,
! [X2464,X2465,X2466,X2467,X2468] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2468,X2468)),hAPP(hAPP(c_Product__Type_OPair(X2468,X2468),X2467),X2466)),c_Transitive__Closure_Ortrancl(X2468,X2465)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2468,X2468)),hAPP(hAPP(c_Product__Type_OPair(X2468,X2468),X2466),X2464)),c_Transitive__Closure_Ortrancl(X2468,X2465)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2468,X2468)),hAPP(hAPP(c_Product__Type_OPair(X2468,X2468),X2467),X2464)),c_Transitive__Closure_Ortrancl(X2468,X2465))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).
fof(i_0_676,plain,
! [X2776,X2777,X2778,X2779,X2780,X2781] :
( ( hBOOL(hAPP(hAPP(X2779,X2777),X2776))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2781,tc_fun(X2780,tc_HOL_Obool))),X2779),X2778),X2777),X2776)) )
& ( hBOOL(hAPP(hAPP(X2778,X2777),X2776))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2781,tc_fun(X2780,tc_HOL_Obool))),X2779),X2778),X2777),X2776)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])])]) ).
fof(i_0_677,plain,
! [X2794,X2795,X2796,X2797,X2798,X2799] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2799,tc_fun(X2798,tc_HOL_Obool))),X2797),X2796),X2795),X2794))
| hBOOL(hAPP(hAPP(X2797,X2795),X2794)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).
fof(i_0_678,plain,
! [X2788,X2789,X2790,X2791,X2792,X2793] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2793,tc_fun(X2792,tc_HOL_Obool))),X2791),X2790),X2789),X2788))
| hBOOL(hAPP(hAPP(X2790,X2789),X2788)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).
fof(i_0_679,plain,
! [X2922,X2923,X2924,X2925,X2926] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2926,X2926)),hAPP(hAPP(c_Product__Type_OPair(X2926,X2926),X2925),X2924)),X2923))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2926,X2926)),hAPP(hAPP(c_Product__Type_OPair(X2926,X2926),X2924),X2922)),c_Transitive__Closure_Otrancl(X2926,X2923)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2926,X2926)),hAPP(hAPP(c_Product__Type_OPair(X2926,X2926),X2925),X2922)),c_Transitive__Closure_Otrancl(X2926,X2923))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])]) ).
fof(i_0_680,plain,
! [X2956,X2957,X2958,X2959,X2960] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2960,X2960)),hAPP(hAPP(c_Product__Type_OPair(X2960,X2960),X2959),X2958)),X2957))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2960,X2960)),hAPP(hAPP(c_Product__Type_OPair(X2960,X2960),X2958),X2956)),c_Transitive__Closure_Ortrancl(X2960,X2957)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2960,X2960)),hAPP(hAPP(c_Product__Type_OPair(X2960,X2960),X2959),X2956)),c_Transitive__Closure_Otrancl(X2960,X2957))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2])]) ).
fof(i_0_681,plain,
! [X2917,X2918,X2919,X2920,X2921] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2921,X2921)),hAPP(hAPP(c_Product__Type_OPair(X2921,X2921),X2920),X2919)),c_Transitive__Closure_Otrancl(X2921,X2918)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2921,X2921)),hAPP(hAPP(c_Product__Type_OPair(X2921,X2921),X2919),X2917)),X2918))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2921,X2921)),hAPP(hAPP(c_Product__Type_OPair(X2921,X2921),X2920),X2917)),c_Transitive__Closure_Otrancl(X2921,X2918))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])]) ).
fof(i_0_682,plain,
! [X2947,X2948,X2949,X2950,X2951] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2951,X2951)),hAPP(hAPP(c_Product__Type_OPair(X2951,X2951),X2950),X2949)),c_Transitive__Closure_Ortrancl(X2951,X2948)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2951,X2951)),hAPP(hAPP(c_Product__Type_OPair(X2951,X2951),X2949),X2947)),X2948))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2951,X2951)),hAPP(hAPP(c_Product__Type_OPair(X2951,X2951),X2950),X2947)),c_Transitive__Closure_Otrancl(X2951,X2948))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])]) ).
fof(i_0_683,plain,
! [X2474,X2475,X2476,X2477,X2478] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2478,X2478)),hAPP(hAPP(c_Product__Type_OPair(X2478,X2478),X2477),X2476)),X2475))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2478,X2478)),hAPP(hAPP(c_Product__Type_OPair(X2478,X2478),X2476),X2474)),c_Transitive__Closure_Ortrancl(X2478,X2475)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2478,X2478)),hAPP(hAPP(c_Product__Type_OPair(X2478,X2478),X2477),X2474)),c_Transitive__Closure_Ortrancl(X2478,X2475))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).
fof(i_0_684,plain,
! [X2469,X2470,X2471,X2472,X2473] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2473,X2473)),hAPP(hAPP(c_Product__Type_OPair(X2473,X2473),X2472),X2471)),c_Transitive__Closure_Ortrancl(X2473,X2470)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2473,X2473)),hAPP(hAPP(c_Product__Type_OPair(X2473,X2473),X2471),X2469)),X2470))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2473,X2473)),hAPP(hAPP(c_Product__Type_OPair(X2473,X2473),X2472),X2469)),c_Transitive__Closure_Ortrancl(X2473,X2470))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).
fof(i_0_685,plain,
! [X2927,X2928,X2929,X2930,X2931] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2931,X2931)),hAPP(hAPP(c_Product__Type_OPair(X2931,X2931),X2930),X2929)),X2928))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2931,X2931)),hAPP(hAPP(c_Product__Type_OPair(X2931,X2931),X2929),X2927)),X2928))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2931,X2931)),hAPP(hAPP(c_Product__Type_OPair(X2931,X2931),X2930),X2927)),c_Transitive__Closure_Otrancl(X2931,X2928))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
fof(i_0_686,plain,
! [X2131,X2132,X2133] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2132),X2131)),X2133))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2131),X2132)),X2133))
| X2132 = X2131
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2133),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),X2131),X2132)),X2133))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2132),X2131)),X2133))
| X2132 = X2131
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2133),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])])]) ).
fof(i_0_687,plain,
! [X2128,X2129,X2130] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2130),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),X2129),X2128)),X2130))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2128),X2129)),X2130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])]) ).
fof(i_0_688,plain,
! [X4064,X4065,X4066,X4067] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4067,X4067)),X4066),c_Transitive__Closure_Ortrancl(X4067,X4065)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4067,X4067)),X4066),c_Transitive__Closure_Ortrancl(X4067,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4067,X4067),tc_HOL_Obool)),X4065),X4064)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4067,X4067)),X4066),c_Transitive__Closure_Ortrancl(X4067,X4064)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4067,X4067)),X4066),c_Transitive__Closure_Ortrancl(X4067,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4067,X4067),tc_HOL_Obool)),X4065),X4064)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI])])]) ).
fof(i_0_689,plain,
! [X2763,X2764,X2765] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2765,X2764)),hAPP(hAPP(c_Product__Type_OPair(X2765,X2764),esk55_3(X2763,X2764,X2765)),esk56_3(X2763,X2764,X2765))),X2763))
| c_Relation_Osingle__valued(X2765,X2764,X2763) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2765,X2764)),hAPP(hAPP(c_Product__Type_OPair(X2765,X2764),esk55_3(X2763,X2764,X2765)),esk57_3(X2763,X2764,X2765))),X2763))
| c_Relation_Osingle__valued(X2765,X2764,X2763) )
& ( esk56_3(X2763,X2764,X2765) != esk57_3(X2763,X2764,X2765)
| c_Relation_Osingle__valued(X2765,X2764,X2763) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedI])])])]) ).
fof(i_0_690,plain,
! [X2656,X2657,X2658,X2659,X2660,X2661,X2662,X2663,X2664] :
( ( ~ c_Relation_Osingle__valued(X2658,X2657,X2656)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2658,X2657)),hAPP(hAPP(c_Product__Type_OPair(X2658,X2657),X2659),X2660)),X2656))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2658,X2657)),hAPP(hAPP(c_Product__Type_OPair(X2658,X2657),X2659),X2661)),X2656))
| X2660 = X2661 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2664,X2663)),hAPP(hAPP(c_Product__Type_OPair(X2664,X2663),esk50_3(X2662,X2663,X2664)),esk51_3(X2662,X2663,X2664))),X2662))
| c_Relation_Osingle__valued(X2664,X2663,X2662) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2664,X2663)),hAPP(hAPP(c_Product__Type_OPair(X2664,X2663),esk50_3(X2662,X2663,X2664)),esk52_3(X2662,X2663,X2664))),X2662))
| c_Relation_Osingle__valued(X2664,X2663,X2662) )
& ( esk51_3(X2662,X2663,X2664) != esk52_3(X2662,X2663,X2664)
| c_Relation_Osingle__valued(X2664,X2663,X2662) ) ),
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_691,plain,
! [X3775,X3776,X3777,X3778,X3779] : c_Product__Type_OSigma(X3779,X3778,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3779,tc_HOL_Obool)),X3777),X3776),c_COMBK(tc_fun(X3778,tc_HOL_Obool),X3779,X3775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3779,X3778),tc_HOL_Obool)),c_Product__Type_OSigma(X3779,X3778,X3777,c_COMBK(tc_fun(X3778,tc_HOL_Obool),X3779,X3775))),c_Product__Type_OSigma(X3779,X3778,X3776,c_COMBK(tc_fun(X3778,tc_HOL_Obool),X3779,X3775))),
inference(variable_rename,[status(thm)],[fact_Times__Un__distrib1]) ).
fof(i_0_692,plain,
! [X3690,X3691,X3692,X3693,X3694] : c_Product__Type_OSigma(X3694,X3693,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3694,tc_HOL_Obool)),X3692),X3691),c_COMBK(tc_fun(X3693,tc_HOL_Obool),X3694,X3690)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3694,X3693),tc_HOL_Obool)),c_Product__Type_OSigma(X3694,X3693,X3692,c_COMBK(tc_fun(X3693,tc_HOL_Obool),X3694,X3690))),c_Product__Type_OSigma(X3694,X3693,X3691,c_COMBK(tc_fun(X3693,tc_HOL_Obool),X3694,X3690))),
inference(variable_rename,[status(thm)],[fact_Times__Int__distrib1]) ).
fof(i_0_693,plain,
! [X2315,X2316,X2317,X2318,X2319,X2320] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2320,X2319)),X2318),c_FuncSet_OPi(X2320,X2319,X2317,c_COMBK(tc_fun(X2319,tc_HOL_Obool),X2320,X2316))))
| ~ hBOOL(hAPP(hAPP(c_member(X2320),X2315),X2317))
| hBOOL(hAPP(hAPP(c_member(X2319),hAPP(X2318,X2315)),X2316)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
fof(i_0_694,plain,
! [X2650,X2651,X2652,X2653,X2654,X2655] :
( ~ c_Relation_Osingle__valued(X2655,X2654,X2653)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2655,X2654)),hAPP(hAPP(c_Product__Type_OPair(X2655,X2654),X2652),X2651)),X2653))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2655,X2654)),hAPP(hAPP(c_Product__Type_OPair(X2655,X2654),X2652),X2650)),X2653))
| X2651 = X2650 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).
fof(i_0_695,plain,
! [X3499,X3500,X3501,X3502,X3503] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3501,X3502),X3500,X3499)
| c_Orderings_Oord__class_Oless__eq(X3502,hAPP(X3500,X3503),hAPP(X3499,X3503))
| ~ class_Orderings_Oord(X3502) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3502,hAPP(X3500,esk84_4(X3499,X3500,X3501,X3502)),hAPP(X3499,esk84_4(X3499,X3500,X3501,X3502)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3501,X3502),X3500,X3499)
| ~ class_Orderings_Oord(X3502) ) ),
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_696,plain,
! [X3700,X3701,X3702,X3703,X3704,X3705] :
( ( hBOOL(hAPP(hAPP(c_member(X3705),X3703),X3701))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3705,X3704)),hAPP(hAPP(c_Product__Type_OPair(X3705,X3704),X3703),X3702)),c_Product__Type_OSigma(X3705,X3704,X3701,X3700))) )
& ( hBOOL(hAPP(hAPP(c_member(X3704),X3702),hAPP(X3700,X3703)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3705,X3704)),hAPP(hAPP(c_Product__Type_OPair(X3705,X3704),X3703),X3702)),c_Product__Type_OSigma(X3705,X3704,X3701,X3700))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3705),X3703),X3701))
| ~ hBOOL(hAPP(hAPP(c_member(X3704),X3702),hAPP(X3700,X3703)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3705,X3704)),hAPP(hAPP(c_Product__Type_OPair(X3705,X3704),X3703),X3702)),c_Product__Type_OSigma(X3705,X3704,X3701,X3700))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])]) ).
fof(i_0_697,plain,
! [X3649,X3650,X3651,X3652,X3653,X3654] :
( ( hBOOL(hAPP(hAPP(c_member(X3654),X3652),X3650))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3654,X3653)),hAPP(hAPP(c_Product__Type_OPair(X3654,X3653),X3652),X3651)),c_Product__Type_OSigma(X3654,X3653,X3650,X3649))) )
& ( hBOOL(hAPP(hAPP(c_member(X3653),X3651),hAPP(X3649,X3652)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3654,X3653)),hAPP(hAPP(c_Product__Type_OPair(X3654,X3653),X3652),X3651)),c_Product__Type_OSigma(X3654,X3653,X3650,X3649))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])])]) ).
fof(i_0_698,plain,
! [X3712,X3713,X3714,X3715,X3716,X3717] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3717,X3716)),hAPP(hAPP(c_Product__Type_OPair(X3717,X3716),X3715),X3714)),c_Product__Type_OSigma(X3717,X3716,X3713,X3712)))
| hBOOL(hAPP(hAPP(c_member(X3716),X3714),hAPP(X3712,X3715))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])]) ).
fof(i_0_699,plain,
! [X3602,X3603,X3604,X3605,X3607,X3608,X3609,X3612] :
( ( hBOOL(hAPP(hAPP(c_member(X3603),esk89_3(X3602,X3603,X3604)),X3604))
| ~ hBOOL(hAPP(hAPP(c_member(X3603),X3605),X3604))
| ~ c_Wellfounded_Owf(X3603,X3602) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3603,X3603)),hAPP(hAPP(c_Product__Type_OPair(X3603,X3603),X3607),esk89_3(X3602,X3603,X3604))),X3602))
| ~ hBOOL(hAPP(hAPP(c_member(X3603),X3607),X3604))
| ~ hBOOL(hAPP(hAPP(c_member(X3603),X3605),X3604))
| ~ c_Wellfounded_Owf(X3603,X3602) )
& ( hBOOL(hAPP(hAPP(c_member(X3609),esk91_2(X3608,X3609)),esk90_2(X3608,X3609)))
| c_Wellfounded_Owf(X3609,X3608) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3609,X3609)),hAPP(hAPP(c_Product__Type_OPair(X3609,X3609),esk92_3(X3608,X3609,X3612)),X3612)),X3608))
| ~ hBOOL(hAPP(hAPP(c_member(X3609),X3612),esk90_2(X3608,X3609)))
| c_Wellfounded_Owf(X3609,X3608) )
& ( hBOOL(hAPP(hAPP(c_member(X3609),esk92_3(X3608,X3609,X3612)),esk90_2(X3608,X3609)))
| ~ hBOOL(hAPP(hAPP(c_member(X3609),X3612),esk90_2(X3608,X3609)))
| c_Wellfounded_Owf(X3609,X3608) ) ),
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)],[i_0_549])])])])])]) ).
fof(i_0_700,plain,
! [X3129,X3130,X3131,X3132,X3133,X3134] :
( ( ~ c_Relation_Oantisym(X3130,X3129)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3130,X3130)),hAPP(hAPP(c_Product__Type_OPair(X3130,X3130),X3131),X3132)),X3129))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3130,X3130)),hAPP(hAPP(c_Product__Type_OPair(X3130,X3130),X3132),X3131)),X3129))
| X3131 = X3132 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3134,X3134)),hAPP(hAPP(c_Product__Type_OPair(X3134,X3134),esk79_2(X3133,X3134)),esk80_2(X3133,X3134))),X3133))
| c_Relation_Oantisym(X3134,X3133) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3134,X3134)),hAPP(hAPP(c_Product__Type_OPair(X3134,X3134),esk80_2(X3133,X3134)),esk79_2(X3133,X3134))),X3133))
| c_Relation_Oantisym(X3134,X3133) )
& ( esk79_2(X3133,X3134) != esk80_2(X3133,X3134)
| c_Relation_Oantisym(X3134,X3133) ) ),
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_antisym__def])])])])])]) ).
fof(i_0_701,plain,
! [X3125,X3126,X3127,X3128] :
( ~ c_Relation_Oantisym(X3128,X3127)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3128,X3128)),hAPP(hAPP(c_Product__Type_OPair(X3128,X3128),X3126),X3125)),X3127))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3128,X3128)),hAPP(hAPP(c_Product__Type_OPair(X3128,X3128),X3125),X3126)),X3127))
| X3126 = X3125 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisymD])]) ).
fof(i_0_702,plain,
! [X3351,X3352,X3353,X3354] :
( ~ c_Wellfounded_Owf(X3354,X3353)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3354,X3354)),hAPP(hAPP(c_Product__Type_OPair(X3354,X3354),X3352),X3351)),X3353))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3354,X3354)),hAPP(hAPP(c_Product__Type_OPair(X3354,X3354),X3351),X3352)),X3353)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])]) ).
fof(i_0_703,plain,
! [X3347,X3348,X3349,X3350] :
( ~ c_Wellfounded_Owf(X3350,X3349)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3350,X3350)),hAPP(hAPP(c_Product__Type_OPair(X3350,X3350),X3348),X3347)),X3349))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3350,X3350)),hAPP(hAPP(c_Product__Type_OPair(X3350,X3350),X3347),X3348)),X3349)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])]) ).
fof(i_0_704,plain,
! [X3706,X3707,X3708,X3709,X3710,X3711] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3711,X3710)),hAPP(hAPP(c_Product__Type_OPair(X3711,X3710),X3709),X3708)),c_Product__Type_OSigma(X3711,X3710,X3707,X3706)))
| hBOOL(hAPP(hAPP(c_member(X3711),X3709),X3707)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])]) ).
fof(i_0_705,plain,
! [X3614,X3615,X3616,X3617,X3618] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3618,X3618)),hAPP(hAPP(c_Product__Type_OPair(X3618,X3618),X3617),X3616)),c_Transitive__Closure_Ortrancl(X3618,X3615)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3618,X3618),tc_HOL_Obool),X3615,c_Product__Type_OSigma(X3618,X3618,X3614,c_COMBK(tc_fun(X3618,tc_HOL_Obool),X3618,X3614)))
| X3617 = X3616
| hBOOL(hAPP(hAPP(c_member(X3618),X3617),X3614)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux])]) ).
fof(i_0_706,plain,
! [X2213] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2213),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,X2213)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_707,plain,
! [X3548,X3549,X3550,X3551,X3552] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X3552,X3551),hAPP(X3552,X3550))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3549,X3549)),hAPP(hAPP(c_Product__Type_OPair(X3549,X3549),X3551),X3550)),X3548))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3549,X3549)),hAPP(hAPP(c_Product__Type_OPair(X3549,X3549),X3551),X3550)),c_Wellfounded_Omlex__prod(X3549,X3552,X3548))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_708,plain,
! [X2782,X2783,X2784,X2785,X2786,X2787] :
( ~ hBOOL(hAPP(hAPP(X2787,X2786),X2785))
| ~ hBOOL(hAPP(hAPP(X2784,X2786),X2785))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2783,tc_fun(X2782,tc_HOL_Obool))),X2787),X2784),X2786),X2785)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).
fof(i_0_709,plain,
! [X3643,X3644,X3645,X3646,X3647,X3648] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3645,X3648),tc_HOL_Obool),c_Product__Type_OSigma(X3645,X3648,X3644,c_COMBK(tc_fun(X3648,tc_HOL_Obool),X3645,X3646)),c_Product__Type_OSigma(X3645,X3648,X3643,c_COMBK(tc_fun(X3648,tc_HOL_Obool),X3645,X3646)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3645,tc_HOL_Obool),X3644,X3643)
| ~ hBOOL(hAPP(hAPP(c_member(X3648),X3647),X3646)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3645,tc_HOL_Obool),X3644,X3643)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3645,X3648),tc_HOL_Obool),c_Product__Type_OSigma(X3645,X3648,X3644,c_COMBK(tc_fun(X3648,tc_HOL_Obool),X3645,X3646)),c_Product__Type_OSigma(X3645,X3648,X3643,c_COMBK(tc_fun(X3648,tc_HOL_Obool),X3645,X3646)))
| ~ hBOOL(hAPP(hAPP(c_member(X3648),X3647),X3646)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2])])]) ).
fof(i_0_710,plain,
! [X2336,X2337,X2338] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2338,X2338)),hAPP(hAPP(c_Product__Type_OPair(X2338,X2338),esk25_3(X2336,X2337,X2338)),X2337)),X2336))
| hBOOL(hAPP(hAPP(c_member(X2338),X2337),c_Wellfounded_Oacc(X2338,X2336))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2338),esk25_3(X2336,X2337,X2338)),c_Wellfounded_Oacc(X2338,X2336)))
| hBOOL(hAPP(hAPP(c_member(X2338),X2337),c_Wellfounded_Oacc(X2338,X2336))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).
fof(i_0_711,plain,
! [X2332,X2333,X2334] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2334,X2334)),hAPP(hAPP(c_Product__Type_OPair(X2334,X2334),esk24_3(X2332,X2333,X2334)),X2333)),X2332))
| hBOOL(hAPP(hAPP(c_member(X2334),X2333),c_Wellfounded_Oacc(X2334,X2332))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2334),esk24_3(X2332,X2333,X2334)),c_Wellfounded_Oacc(X2334,X2332)))
| hBOOL(hAPP(hAPP(c_member(X2334),X2333),c_Wellfounded_Oacc(X2334,X2332))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])])])]) ).
fof(i_0_712,plain,
! [X2289,X2290,X2291,X2292,X2293,X2294,X2295] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2291),X2290),c_Wellfounded_Oacc(X2291,X2289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2291,X2291)),hAPP(hAPP(c_Product__Type_OPair(X2291,X2291),X2292),X2290)),X2289))
| hBOOL(hAPP(hAPP(c_member(X2291),X2292),c_Wellfounded_Oacc(X2291,X2289))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2295,X2295)),hAPP(hAPP(c_Product__Type_OPair(X2295,X2295),esk20_3(X2293,X2294,X2295)),X2294)),X2293))
| hBOOL(hAPP(hAPP(c_member(X2295),X2294),c_Wellfounded_Oacc(X2295,X2293))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2295),esk20_3(X2293,X2294,X2295)),c_Wellfounded_Oacc(X2295,X2293)))
| hBOOL(hAPP(hAPP(c_member(X2295),X2294),c_Wellfounded_Oacc(X2295,X2293))) ) ),
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_713,plain,
! [X2961,X2962,X2963,X2964] :
( ( X2963 != X2962
| X2963 = X2962
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2964,X2964)),hAPP(hAPP(c_Product__Type_OPair(X2964,X2964),X2963),X2962)),c_Transitive__Closure_Ortrancl(X2964,X2961))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2964,X2964)),hAPP(hAPP(c_Product__Type_OPair(X2964,X2964),X2963),X2962)),c_Transitive__Closure_Otrancl(X2964,X2961)))
| X2963 = X2962
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2964,X2964)),hAPP(hAPP(c_Product__Type_OPair(X2964,X2964),X2963),X2962)),c_Transitive__Closure_Ortrancl(X2964,X2961))) )
& ( X2963 != X2962
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2964,X2964)),hAPP(hAPP(c_Product__Type_OPair(X2964,X2964),X2963),X2962)),c_Transitive__Closure_Ortrancl(X2964,X2961))) )
& ( X2963 = X2962
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2964,X2964)),hAPP(hAPP(c_Product__Type_OPair(X2964,X2964),X2963),X2962)),c_Transitive__Closure_Otrancl(X2964,X2961)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2964,X2964)),hAPP(hAPP(c_Product__Type_OPair(X2964,X2964),X2963),X2962)),c_Transitive__Closure_Ortrancl(X2964,X2961))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl])])]) ).
fof(i_0_714,plain,
! [X2952,X2953,X2954,X2955] :
( ( X2954 != X2953
| X2954 = X2953
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2955,X2955)),hAPP(hAPP(c_Product__Type_OPair(X2955,X2955),X2954),X2953)),c_Transitive__Closure_Ortrancl(X2955,X2952))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2955,X2955)),hAPP(hAPP(c_Product__Type_OPair(X2955,X2955),X2954),X2953)),c_Transitive__Closure_Otrancl(X2955,X2952)))
| X2954 = X2953
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2955,X2955)),hAPP(hAPP(c_Product__Type_OPair(X2955,X2955),X2954),X2953)),c_Transitive__Closure_Ortrancl(X2955,X2952))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtranclD])])]) ).
fof(i_0_715,plain,
! [X2891,X2892,X2893,X2894] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2894,X2894)),hAPP(hAPP(c_Product__Type_OPair(X2894,X2894),X2893),X2892)),c_Transitive__Closure_Otrancl(X2894,X2891)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2894,X2894)),hAPP(hAPP(c_Product__Type_OPair(X2894,X2894),X2893),X2892)),c_Transitive__Closure_Ortrancl(X2894,X2891))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl])]) ).
cnf(i_0_716,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_553]) ).
fof(i_0_717,plain,
! [X2895,X2896,X2897,X2898] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2898,X2898)),hAPP(hAPP(c_Product__Type_OPair(X2898,X2898),X2897),X2896)),X2895))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2898,X2898)),hAPP(hAPP(c_Product__Type_OPair(X2898,X2898),X2897),X2896)),c_Transitive__Closure_Otrancl(X2898,X2895))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl])]) ).
fof(i_0_718,plain,
! [X3667,X3668,X3669,X3671,X3672,X3673,X3674,X3675,X3678] :
( ( ~ hBOOL(hAPP(X3669,esk94_3(X3667,X3668,X3669)))
| hBOOL(hAPP(X3669,hAPP(hAPP(c_Product__Type_OPair(X3668,X3667),X3671),X3672))) )
& ( ~ hBOOL(hAPP(X3675,hAPP(hAPP(c_Product__Type_OPair(X3674,X3673),esk95_3(X3673,X3674,X3675)),esk96_3(X3673,X3674,X3675))))
| hBOOL(hAPP(X3675,X3678)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__paired__All])])])])]) ).
fof(i_0_719,plain,
! [X2118,X2119,X2120,X2121,X2122] :
( ( ~ c_Nitpick_Orefl_H(X2119,X2118)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2119,X2119)),hAPP(hAPP(c_Product__Type_OPair(X2119,X2119),X2120),X2120)),X2118)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2122,X2122)),hAPP(hAPP(c_Product__Type_OPair(X2122,X2122),esk2_2(X2121,X2122)),esk2_2(X2121,X2122))),X2121))
| c_Nitpick_Orefl_H(X2122,X2121) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def])])])])]) ).
fof(i_0_720,plain,
! [X4162,X4163,X4164,X4165,X4167,X4168,X4169,X4170,X4171] :
( ( hBOOL(hAPP(hAPP(c_member(X4165),esk113_4(X4162,X4163,X4164,X4165)),X4163))
| c_FuncSet_OPi(X4165,X4164,X4163,X4162) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4165,X4164),tc_HOL_Obool)) )
& ( hAPP(X4162,esk113_4(X4162,X4163,X4164,X4165)) = c_Orderings_Obot__class_Obot(tc_fun(X4164,tc_HOL_Obool))
| c_FuncSet_OPi(X4165,X4164,X4163,X4162) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4165,X4164),tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4170),X4171),X4168))
| hAPP(X4167,X4171) != c_Orderings_Obot__class_Obot(tc_fun(X4169,tc_HOL_Obool))
| c_FuncSet_OPi(X4170,X4169,X4168,X4167) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4170,X4169),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_721,plain,
! [X3150,X3151,X3152,X3153] :
( ( c_Wellfounded_Owf(X3153,X3150)
| ~ c_Wellfounded_Owf(X3153,c_Set_Oinsert(tc_prod(X3153,X3153),hAPP(hAPP(c_Product__Type_OPair(X3153,X3153),X3152),X3151),X3150)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3153,X3153)),hAPP(hAPP(c_Product__Type_OPair(X3153,X3153),X3151),X3152)),c_Transitive__Closure_Ortrancl(X3153,X3150)))
| ~ c_Wellfounded_Owf(X3153,c_Set_Oinsert(tc_prod(X3153,X3153),hAPP(hAPP(c_Product__Type_OPair(X3153,X3153),X3152),X3151),X3150)) )
& ( ~ c_Wellfounded_Owf(X3153,X3150)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3153,X3153)),hAPP(hAPP(c_Product__Type_OPair(X3153,X3153),X3151),X3152)),c_Transitive__Closure_Ortrancl(X3153,X3150)))
| c_Wellfounded_Owf(X3153,c_Set_Oinsert(tc_prod(X3153,X3153),hAPP(hAPP(c_Product__Type_OPair(X3153,X3153),X3152),X3151),X3150)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])])]) ).
fof(i_0_722,plain,
! [X2994,X2995,X2996,X2997] :
( ( c_Wellfounded_Oacyclic(X2997,X2994)
| ~ c_Wellfounded_Oacyclic(X2997,c_Set_Oinsert(tc_prod(X2997,X2997),hAPP(hAPP(c_Product__Type_OPair(X2997,X2997),X2996),X2995),X2994)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2997,X2997)),hAPP(hAPP(c_Product__Type_OPair(X2997,X2997),X2995),X2996)),c_Transitive__Closure_Ortrancl(X2997,X2994)))
| ~ c_Wellfounded_Oacyclic(X2997,c_Set_Oinsert(tc_prod(X2997,X2997),hAPP(hAPP(c_Product__Type_OPair(X2997,X2997),X2996),X2995),X2994)) )
& ( ~ c_Wellfounded_Oacyclic(X2997,X2994)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2997,X2997)),hAPP(hAPP(c_Product__Type_OPair(X2997,X2997),X2995),X2996)),c_Transitive__Closure_Ortrancl(X2997,X2994)))
| c_Wellfounded_Oacyclic(X2997,c_Set_Oinsert(tc_prod(X2997,X2997),hAPP(hAPP(c_Product__Type_OPair(X2997,X2997),X2996),X2995),X2994)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])])]) ).
fof(i_0_723,plain,
! [X3158,X3159,X3160,X3161] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3161,tc_HOL_Obool),c_Relation_ORange(X3160,X3161,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3160,X3161),tc_HOL_Obool)),X3159),X3158)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3161,tc_HOL_Obool)),c_Relation_ORange(X3160,X3161,X3159)),c_Relation_ORange(X3160,X3161,X3158))),
inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).
fof(i_0_724,plain,
! [X3384,X3385,X3386,X3387] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3387,tc_HOL_Obool),c_Relation_ODomain(X3387,X3386,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3387,X3386),tc_HOL_Obool)),X3385),X3384)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3387,tc_HOL_Obool)),c_Relation_ODomain(X3387,X3386,X3385)),c_Relation_ODomain(X3387,X3386,X3384))),
inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).
fof(i_0_725,plain,
! [X2501,X2502,X2503,X2504] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2504,X2503)),c_FuncSet_Orestrict(X2504,X2503,X2502,X2501)),c_FuncSet_Oextensional(X2504,X2503,X2501))),
inference(variable_rename,[status(thm)],[fact_restrict__extensional]) ).
fof(i_0_726,plain,
! [X2321,X2322,X2323,X2324,X2325,X2326] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2326,X2325)),X2324),c_FuncSet_OPi(X2326,X2325,X2323,X2322)))
| ~ hBOOL(hAPP(hAPP(c_member(X2326),X2321),X2323))
| hBOOL(hAPP(hAPP(c_member(X2325),hAPP(X2324,X2321)),hAPP(X2322,X2321))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_727,plain,
! [X2304,X2305,X2306,X2307,X2308,X2309] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2309,X2308)),X2307),c_FuncSet_OPi(X2309,X2308,X2306,X2305)))
| hBOOL(hAPP(hAPP(c_member(X2308),hAPP(X2307,X2304)),hAPP(X2305,X2304)))
| ~ hBOOL(hAPP(hAPP(c_member(X2309),X2304),X2306)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])]) ).
fof(i_0_728,plain,
! [X3637,X3638,X3639,X3640,X3641,X3642] :
( ~ hBOOL(hAPP(hAPP(c_member(X3642),X3641),X3640))
| ~ hBOOL(hAPP(hAPP(c_member(X3639),X3638),hAPP(X3637,X3641)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3642,X3639)),hAPP(hAPP(c_Product__Type_OPair(X3642,X3639),X3641),X3638)),c_Product__Type_OSigma(X3642,X3639,X3640,X3637))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaI])]) ).
fof(i_0_729,plain,
! [X3493,X3494,X3495,X3496,X3497,X3498] :
( ( X3498 != X3497
| hAPP(c_Fun_Ofun__upd(X3496,X3495,X3494,X3497,X3493),X3498) = X3493 )
& ( X3498 = X3497
| hAPP(c_Fun_Ofun__upd(X3496,X3495,X3494,X3497,X3493),X3498) = hAPP(X3494,X3498) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__def])]) ).
fof(i_0_730,plain,
! [X3482,X3483,X3484,X3485,X3486,X3487] :
( X3487 = X3486
| hAPP(c_Fun_Ofun__upd(X3485,X3484,X3483,X3486,X3482),X3487) = hAPP(X3483,X3487) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__other])]) ).
fof(i_0_731,plain,
! [X3469,X3470,X3471,X3472,X3473,X3474] :
( ( X3474 != X3473
| hAPP(c_Fun_Ofun__upd(X3472,X3471,X3470,X3473,X3469),X3474) = X3469 )
& ( X3474 = X3473
| hAPP(c_Fun_Ofun__upd(X3472,X3471,X3470,X3473,X3469),X3474) = hAPP(X3470,X3474) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__apply])]) ).
fof(i_0_732,plain,
! [X3078,X3079,X3080,X3081,X3083,X3084,X3085,X3086,X3087] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3081,X3080),X3079),esk78_4(X3078,X3079,X3080,X3081)))
| hBOOL(hAPP(hAPP(X3080,X3079),X3078))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3081,X3080),X3079),X3078)) )
& ( hBOOL(hAPP(hAPP(X3080,esk78_4(X3078,X3079,X3080,X3081)),X3078))
| hBOOL(hAPP(hAPP(X3080,X3079),X3078))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3081,X3080),X3079),X3078)) )
& ( ~ hBOOL(hAPP(hAPP(X3085,X3084),X3083))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3086,X3085),X3084),X3083)) )
& ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3086,X3085),X3084),X3087))
| ~ hBOOL(hAPP(hAPP(X3085,X3087),X3083))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3086,X3085),X3084),X3083)) ) ),
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_tranclp_Oequations_I1_J])])])])])]) ).
fof(i_0_733,plain,
! [X3068,X3069,X3070,X3071,X3073,X3074,X3075,X3076,X3077] :
( ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3071,X3070),X3069),esk77_4(X3068,X3069,X3070,X3071)))
| hBOOL(hAPP(hAPP(X3070,X3069),X3068))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3071,X3070),X3069),X3068)) )
& ( hBOOL(hAPP(hAPP(X3070,esk77_4(X3068,X3069,X3070,X3071)),X3068))
| hBOOL(hAPP(hAPP(X3070,X3069),X3068))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3071,X3070),X3069),X3068)) )
& ( ~ hBOOL(hAPP(hAPP(X3075,X3074),X3073))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3076,X3075),X3074),X3073)) )
& ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3076,X3075),X3074),X3077))
| ~ hBOOL(hAPP(hAPP(X3075,X3077),X3073))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3076,X3075),X3074),X3073)) ) ),
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_tranclp_Oequations_I2_J])])])])])]) ).
fof(i_0_734,plain,
! [X2448,X2449,X2450,X2451,X2452,X2453] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2453,X2452)),X2451),c_FuncSet_Oextensional__funcset(X2453,X2452,X2450,X2449)))
| ~ hBOOL(hAPP(hAPP(c_member(X2453),X2448),X2450))
| hBOOL(hAPP(hAPP(c_member(X2452),hAPP(X2451,X2448)),X2449)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__mem])]) ).
fof(i_0_735,plain,
! [X3464,X3465,X3466,X3467,X3468] : hAPP(c_Fun_Ofun__upd(X3468,X3467,X3466,X3465,X3464),X3465) = X3464,
inference(variable_rename,[status(thm)],[fact_fun__upd__same]) ).
fof(i_0_736,plain,
! [X3785,X3786,X3787] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3787,X3787),tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3787,X3787),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X3787,X3786)),c_Transitive__Closure_Ortrancl(X3787,X3785)),c_Transitive__Closure_Ortrancl(X3787,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3787,X3787),tc_HOL_Obool)),X3786),X3785))),
inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset]) ).
fof(i_0_737,plain,
! [X3624,X3625,X3626] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3626,X3626),tc_HOL_Obool),X3625,c_Product__Type_OSigma(X3626,X3626,X3624,c_COMBK(tc_fun(X3626,tc_HOL_Obool),X3626,X3624)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3626,X3626),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X3626,X3625),c_Product__Type_OSigma(X3626,X3626,X3624,c_COMBK(tc_fun(X3626,tc_HOL_Obool),X3626,X3624))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma])]) ).
fof(i_0_738,plain,
! [X3341,X3342,X3343] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3343,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3343,tc_fun(X3343,tc_HOL_Obool),tc_HOL_Obool),c_member(X3343)),X3342),hAPP(hAPP(c_COMBC(X3343,tc_fun(X3343,tc_HOL_Obool),tc_HOL_Obool),c_member(X3343)),X3341))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3343,tc_HOL_Obool),X3342,X3341) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3343,tc_HOL_Obool),X3342,X3341)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3343,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3343,tc_fun(X3343,tc_HOL_Obool),tc_HOL_Obool),c_member(X3343)),X3342),hAPP(hAPP(c_COMBC(X3343,tc_fun(X3343,tc_HOL_Obool),tc_HOL_Obool),c_member(X3343)),X3341)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_739,plain,
! [X2096,X2097,X2098,X2099] :
( ( X2098 != X2096
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),c_Arrow__Order__Mirabelle_Omkbot(X2097,X2096))) )
& ( X2099 != X2096
| X2099 != X2098
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),c_Arrow__Order__Mirabelle_Omkbot(X2097,X2096))) )
& ( X2099 = X2096
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),X2097))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),c_Arrow__Order__Mirabelle_Omkbot(X2097,X2096))) )
& ( X2099 != X2096
| X2099 = X2096
| X2098 = X2096
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),c_Arrow__Order__Mirabelle_Omkbot(X2097,X2096))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),X2097))
| X2099 = X2096
| X2098 = X2096
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),c_Arrow__Order__Mirabelle_Omkbot(X2097,X2096))) )
& ( X2099 != X2096
| X2099 = X2098
| X2098 = X2096
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),c_Arrow__Order__Mirabelle_Omkbot(X2097,X2096))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),X2097))
| X2099 = X2098
| X2098 = X2096
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2099),X2098)),c_Arrow__Order__Mirabelle_Omkbot(X2097,X2096))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_740,plain,
! [X2100,X2101,X2102,X2103] :
( ( X2103 != X2100
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),c_Arrow__Order__Mirabelle_Omktop(X2101,X2100))) )
& ( X2102 != X2100
| X2103 != X2102
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),c_Arrow__Order__Mirabelle_Omktop(X2101,X2100))) )
& ( X2102 = X2100
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),X2101))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),c_Arrow__Order__Mirabelle_Omktop(X2101,X2100))) )
& ( X2102 != X2100
| X2102 = X2100
| X2103 = X2100
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),c_Arrow__Order__Mirabelle_Omktop(X2101,X2100))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),X2101))
| X2102 = X2100
| X2103 = X2100
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),c_Arrow__Order__Mirabelle_Omktop(X2101,X2100))) )
& ( X2102 != X2100
| X2103 = X2102
| X2103 = X2100
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),c_Arrow__Order__Mirabelle_Omktop(X2101,X2100))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),X2101))
| X2103 = X2102
| X2103 = X2100
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2103),X2102)),c_Arrow__Order__Mirabelle_Omktop(X2101,X2100))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_741,plain,
! [X3770,X3771,X3772,X3773,X3774] : c_Product__Type_OSigma(X3774,X3773,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3774,tc_HOL_Obool)),X3772),X3771),X3770) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool)),c_Product__Type_OSigma(X3774,X3773,X3772,X3770)),c_Product__Type_OSigma(X3774,X3773,X3771,X3770)),
inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1]) ).
fof(i_0_742,plain,
! [X3695,X3696,X3697,X3698,X3699] : c_Product__Type_OSigma(X3699,X3698,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3699,tc_HOL_Obool)),X3697),X3696),X3695) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3699,X3698),tc_HOL_Obool)),c_Product__Type_OSigma(X3699,X3698,X3697,X3695)),c_Product__Type_OSigma(X3699,X3698,X3696,X3695)),
inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1]) ).
fof(i_0_743,plain,
! [X2104] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2104)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_Q____,X2104))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_Q____,X2104)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2104))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096])]) ).
fof(i_0_744,plain,
! [X2117] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X2117)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X2117))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X2117)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X2117))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])]) ).
fof(i_0_745,plain,
! [X2575,X2576,X2577,X2578] : c_FuncSet_Oextensional__funcset(X2578,X2577,X2576,X2575) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X2578,X2577),tc_HOL_Obool)),c_FuncSet_OPi(X2578,X2577,X2576,c_COMBK(tc_fun(X2577,tc_HOL_Obool),X2578,X2575))),c_FuncSet_Oextensional(X2578,X2577,X2576)),
inference(variable_rename,[status(thm)],[fact_extensional__funcset__def]) ).
fof(i_0_746,plain,
! [X2159,X2160,X2161] :
( X2161 = X2160
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2159),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,X2159),X2161),X2160)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_747,plain,
! [X2393,X2394,X2395,X2396,X2397,X2398] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2398,X2397)),X2396),c_FuncSet_Oextensional__funcset(X2398,X2397,X2395,X2394)))
| hBOOL(hAPP(hAPP(c_member(X2398),X2393),X2395))
| hAPP(X2396,X2393) = c_HOL_Oundefined(X2397) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])]) ).
fof(i_0_748,plain,
! [X3510,X3511,X3512,X3513] :
( ( hBOOL(hAPP(X3513,esk85_4(X3510,X3511,X3512,X3513)))
| c_Wellfounded_Owf(tc_prod(X3510,X3512),c_Recdef_Osame__fst(X3510,X3512,X3513,X3511)) )
& ( ~ c_Wellfounded_Owf(X3512,hAPP(X3511,esk85_4(X3510,X3511,X3512,X3513)))
| c_Wellfounded_Owf(tc_prod(X3510,X3512),c_Recdef_Osame__fst(X3510,X3512,X3513,X3511)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__same__fst])])])]) ).
fof(i_0_749,plain,
! [X2105,X2106,X2107,X2108,X2109] :
( ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X2109,X2108,X2107),X2106),X2105))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2109,X2108)),hAPP(hAPP(c_Product__Type_OPair(X2109,X2108),X2106),X2105)),X2107)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2109,X2108)),hAPP(hAPP(c_Product__Type_OPair(X2109,X2108),X2106),X2105)),X2107))
| hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X2109,X2108,X2107),X2106),X2105)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_750,plain,
! [X2454,X2455,X2456,X2457] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2457,X2457)),hAPP(hAPP(c_Product__Type_OPair(X2457,X2457),X2456),X2455)),c_Transitive__Closure_Ortrancl(X2457,X2454)))
| ~ hBOOL(hAPP(hAPP(c_member(X2457),X2455),c_Wellfounded_Oacc(X2457,X2454)))
| hBOOL(hAPP(hAPP(c_member(X2457),X2456),c_Wellfounded_Oacc(X2457,X2454))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).
fof(i_0_751,plain,
! [X2431,X2432,X2433,X2434] :
( ~ hBOOL(hAPP(hAPP(c_member(X2434),X2433),c_Wellfounded_Oacc(X2434,X2432)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2434,X2434)),hAPP(hAPP(c_Product__Type_OPair(X2434,X2434),X2431),X2433)),c_Transitive__Closure_Ortrancl(X2434,X2432)))
| hBOOL(hAPP(hAPP(c_member(X2434),X2431),c_Wellfounded_Oacc(X2434,X2432))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).
fof(i_0_752,plain,
! [X2251,X2252,X2253,X2254,X2255] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2252,X2251)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2253),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X2252,X2253) = hAPP(X2253,X2251) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk16_2(X2254,X2255)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2255,X2254) )
& ( hAPP(X2255,esk16_2(X2254,X2255)) != hAPP(esk16_2(X2254,X2255),X2254)
| c_Arrow__Order__Mirabelle_Odictator(X2255,X2254) ) ),
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_753,plain,
! [X2257,X2258,X2259,X2260,X2261,X2262] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2262,X2262)),hAPP(hAPP(c_Product__Type_OPair(X2262,X2262),X2261),X2260)),X2259))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X2262,X2258),X2257),X2259),X2260),X2261) = hAPP(X2257,X2261) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2262,X2262)),hAPP(hAPP(c_Product__Type_OPair(X2262,X2262),X2261),X2260)),X2259))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X2262,X2258),X2257),X2259),X2260),X2261) = c_HOL_Oundefined(X2258) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])]) ).
fof(i_0_754,plain,
! [X2214,X2215,X2216,X2217,X2218,X2219] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2217,X2217)),hAPP(hAPP(c_Product__Type_OPair(X2217,X2217),X2216),X2215)),X2219))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X2217,X2214),X2218),X2219),X2215),X2216) = hAPP(X2218,X2216) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__cut__apply])]) ).
fof(i_0_755,plain,
! [X2193,X2194,X2195,X2196,X2197,X2198] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2198,X2198)),hAPP(hAPP(c_Product__Type_OPair(X2198,X2198),X2197),X2196)),X2195))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X2198,X2194),X2193),X2195),X2196),X2197) = hAPP(X2193,X2197) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut__apply])]) ).
fof(i_0_756,plain,
! [X2300,X2301,X2302,X2303] :
( ~ hBOOL(hAPP(hAPP(c_member(X2303),X2302),c_Wellfounded_Oacc(X2303,X2301)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2303,X2303)),hAPP(hAPP(c_Product__Type_OPair(X2303,X2303),X2300),X2302)),X2301))
| hBOOL(hAPP(hAPP(c_member(X2303),X2300),c_Wellfounded_Oacc(X2303,X2301))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).
fof(i_0_757,plain,
! [X2538,X2539,X2540,X2541] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2541,X2541)),hAPP(hAPP(c_Product__Type_OPair(X2541,X2541),X2540),X2538)),c_Transitive__Closure_Ortrancl(X2541,X2539)))
| X2540 = X2538
| hBOOL(hAPP(hAPP(c_member(X2541),X2540),c_Relation_ODomain(X2541,X2541,X2539))) )
& ( X2540 != X2538
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2541,X2541)),hAPP(hAPP(c_Product__Type_OPair(X2541,X2541),X2540),X2538)),c_Transitive__Closure_Ortrancl(X2541,X2539)))
| hBOOL(hAPP(hAPP(c_member(X2541),X2540),c_Relation_ODomain(X2541,X2541,X2539))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])])]) ).
fof(i_0_758,plain,
! [X2162,X2163,X2164] :
( X2164 = X2163
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2162),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(X2162,X2164,X2163)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_759,plain,
! [X2635,X2636,X2637,X2638,X2639] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2639,X2638)),hAPP(hAPP(c_Product__Type_OPair(X2639,X2638),X2637),X2636)),X2635))
| hBOOL(hAPP(hAPP(c_member(X2639),X2637),c_Relation_ODomain(X2639,X2638,X2635))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).
fof(i_0_760,plain,
! [X2750,X2751,X2752,X2753,X2754] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2754,X2753)),hAPP(hAPP(c_Product__Type_OPair(X2754,X2753),X2752),X2751)),X2750))
| hBOOL(hAPP(hAPP(c_member(X2753),X2751),c_Relation_ORange(X2754,X2753,X2750))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).
fof(i_0_761,plain,
! [X2327,X2328] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2328,X2328)),c_COMBI(X2328)),c_FuncSet_OPi(X2328,X2328,X2327,c_COMBK(tc_fun(X2328,tc_HOL_Obool),X2328,X2327)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_762,plain,
! [X3453,X3454,X3455,X3456,X3457] :
( ( c_Fun_Ofun__upd(X3457,X3456,X3455,X3454,X3453) != X3455
| hAPP(X3455,X3454) = X3453 )
& ( hAPP(X3455,X3454) != X3453
| c_Fun_Ofun__upd(X3457,X3456,X3455,X3454,X3453) = X3455 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])]) ).
fof(i_0_763,plain,
! [X4060,X4061,X4062,X4063] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4063,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4063,tc_HOL_Obool)),X4062),X4061)),X4060) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4063,tc_HOL_Obool)),X4062),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4063,tc_HOL_Obool)),X4061),X4060))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4063,tc_HOL_Obool),X4060,X4062) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4063,tc_HOL_Obool),X4060,X4062)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4063,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4063,tc_HOL_Obool)),X4062),X4061)),X4060) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4063,tc_HOL_Obool)),X4062),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4063,tc_HOL_Obool)),X4061),X4060)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])]) ).
fof(i_0_764,plain,
! [X2877,X2878,X2879,X2880,X2881] :
( ~ c_Relation_Orefl__on(X2881,X2880,X2879)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2881,X2881)),hAPP(hAPP(c_Product__Type_OPair(X2881,X2881),X2878),X2877)),X2879))
| hBOOL(hAPP(hAPP(c_member(X2881),X2878),X2880)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD1])]) ).
fof(i_0_765,plain,
! [X2882,X2883,X2884,X2885,X2886] :
( ~ c_Relation_Orefl__on(X2886,X2885,X2884)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2886,X2886)),hAPP(hAPP(c_Product__Type_OPair(X2886,X2886),X2883),X2882)),X2884))
| hBOOL(hAPP(hAPP(c_member(X2886),X2882),X2885)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD2])]) ).
fof(i_0_766,plain,
! [X2755,X2756,X2757,X2758] :
( ( X2757 = X2756
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2758,X2758)),hAPP(hAPP(c_Product__Type_OPair(X2758,X2758),X2757),X2756)),c_Relation_OId__on(X2758,X2755))) )
& ( hBOOL(hAPP(hAPP(c_member(X2758),X2757),X2755))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2758,X2758)),hAPP(hAPP(c_Product__Type_OPair(X2758,X2758),X2757),X2756)),c_Relation_OId__on(X2758,X2755))) )
& ( X2757 != X2756
| ~ hBOOL(hAPP(hAPP(c_member(X2758),X2757),X2755))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2758,X2758)),hAPP(hAPP(c_Product__Type_OPair(X2758,X2758),X2757),X2756)),c_Relation_OId__on(X2758,X2755))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).
fof(i_0_767,plain,
! [X2975,X2976,X2977,X2978,X2979] :
( ( ~ c_Wellfounded_Oacyclic(X2976,X2975)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2976,X2976)),hAPP(hAPP(c_Product__Type_OPair(X2976,X2976),X2977),X2977)),c_Transitive__Closure_Otrancl(X2976,X2975))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2979,X2979)),hAPP(hAPP(c_Product__Type_OPair(X2979,X2979),esk72_2(X2978,X2979)),esk72_2(X2978,X2979))),c_Transitive__Closure_Otrancl(X2979,X2978)))
| c_Wellfounded_Oacyclic(X2979,X2978) ) ),
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_768,plain,
! [X2991,X2992] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2992,X2992)),hAPP(hAPP(c_Product__Type_OPair(X2992,X2992),esk75_2(X2991,X2992)),esk75_2(X2991,X2992))),c_Transitive__Closure_Otrancl(X2992,X2991)))
| c_Wellfounded_Oacyclic(X2992,X2991) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])])]) ).
fof(i_0_769,plain,
! [X4024,X4025,X4026,X4027] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4027,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4027,tc_HOL_Obool)),X4026),X4025)),X4024) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4027,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4027,tc_HOL_Obool)),X4026),X4024)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4027,tc_HOL_Obool)),X4025),X4024)),
inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2]) ).
fof(i_0_770,plain,
! [X4028,X4029,X4030,X4031] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4031,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4031,tc_HOL_Obool)),X4030),X4029)),X4028) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4031,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4031,tc_HOL_Obool)),X4030),X4028)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4031,tc_HOL_Obool)),X4029),X4028)),
inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2]) ).
fof(i_0_771,plain,
! [X3154,X3155] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3155,X3155)),hAPP(hAPP(c_Product__Type_OPair(X3155,X3155),esk81_2(X3154,X3155)),esk82_2(X3154,X3155))),X3154))
| c_Relation_Oantisym(X3155,X3154) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3155,X3155)),hAPP(hAPP(c_Product__Type_OPair(X3155,X3155),esk82_2(X3154,X3155)),esk81_2(X3154,X3155))),X3154))
| c_Relation_Oantisym(X3155,X3154) )
& ( esk81_2(X3154,X3155) != esk82_2(X3154,X3155)
| c_Relation_Oantisym(X3155,X3154) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisymI])])])]) ).
fof(i_0_772,plain,
! [X2739,X2740,X2741,X2742,X2743] :
( ( ~ c_Relation_Oirrefl(X2740,X2739)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2740,X2740)),hAPP(hAPP(c_Product__Type_OPair(X2740,X2740),X2741),X2741)),X2739)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2743,X2743)),hAPP(hAPP(c_Product__Type_OPair(X2743,X2743),esk53_2(X2742,X2743)),esk53_2(X2742,X2743))),X2742))
| c_Relation_Oirrefl(X2743,X2742) ) ),
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_562])])])])]) ).
fof(i_0_773,plain,
! [X3355,X3356,X3357] :
( ~ c_Wellfounded_Owf(X3357,X3356)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3357,X3357)),hAPP(hAPP(c_Product__Type_OPair(X3357,X3357),X3355),X3355)),X3356)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).
fof(i_0_774,plain,
! [X3344,X3345,X3346] :
( ~ c_Wellfounded_Owf(X3346,X3345)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3346,X3346)),hAPP(hAPP(c_Product__Type_OPair(X3346,X3346),X3344),X3344)),X3345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])]) ).
fof(i_0_775,plain,
! [X2126,X2127] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2127),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(X2127,X2126)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_776,plain,
! [X2124,X2125] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2125),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(X2125,X2124)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_777,plain,
! [X3874,X3875,X3876] : c_Transitive__Closure_Ortrancl(X3876,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3876,X3876),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X3876,X3875)),c_Transitive__Closure_Ortrancl(X3876,X3874))) = c_Transitive__Closure_Ortrancl(X3876,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3876,X3876),tc_HOL_Obool)),X3875),X3874)),
inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).
fof(i_0_778,plain,
! [X4068,X4069,X4070] :
( ~ c_Wellfounded_Owf(X4070,X4069)
| ~ c_Wellfounded_Owf(X4070,X4068)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4070,tc_HOL_Obool)),c_Relation_ODomain(X4070,X4070,X4069)),c_Relation_ORange(X4070,X4070,X4068)) != c_Orderings_Obot__class_Obot(tc_fun(X4070,tc_HOL_Obool))
| c_Wellfounded_Owf(X4070,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4070,X4070),tc_HOL_Obool)),X4069),X4068)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Un])]) ).
fof(i_0_779,plain,
! [X3379,X3380,X3381,X3382,X3383] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3383,X3382)),X3381),c_FuncSet_Oextensional(X3383,X3382,X3380)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3383,tc_HOL_Obool),X3380,X3379)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3383,X3382)),X3381),c_FuncSet_Oextensional(X3383,X3382,X3379))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__subset])]) ).
fof(i_0_780,plain,
! [X4032,X4033,X4034,X4035] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4035,tc_HOL_Obool)),X4034),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4035,tc_HOL_Obool)),X4033),X4032)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4035,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4035,tc_HOL_Obool)),X4034),X4033)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4035,tc_HOL_Obool)),X4034),X4032)),
inference(variable_rename,[status(thm)],[fact_Un__Int__distrib]) ).
fof(i_0_781,plain,
! [X4036,X4037,X4038,X4039] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4039,tc_HOL_Obool)),X4038),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4039,tc_HOL_Obool)),X4037),X4036)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4039,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4039,tc_HOL_Obool)),X4038),X4037)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4039,tc_HOL_Obool)),X4038),X4036)),
inference(variable_rename,[status(thm)],[fact_Int__Un__distrib]) ).
fof(i_0_782,plain,
! [X3679,X3680,X3681,X3682,X3683,X3684] :
( ( c_Product__Type_OSigma(X3681,X3684,X3680,c_COMBK(tc_fun(X3684,tc_HOL_Obool),X3681,X3682)) != c_Product__Type_OSigma(X3681,X3684,X3679,c_COMBK(tc_fun(X3684,tc_HOL_Obool),X3681,X3682))
| X3680 = X3679
| ~ hBOOL(hAPP(hAPP(c_member(X3684),X3683),X3682)) )
& ( X3680 != X3679
| c_Product__Type_OSigma(X3681,X3684,X3680,c_COMBK(tc_fun(X3684,tc_HOL_Obool),X3681,X3682)) = c_Product__Type_OSigma(X3681,X3684,X3679,c_COMBK(tc_fun(X3684,tc_HOL_Obool),X3681,X3682))
| ~ hBOOL(hAPP(hAPP(c_member(X3684),X3683),X3682)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2])])]) ).
fof(i_0_783,plain,
! [X3742,X3743,X3744,X3745,X3746,X3747] : c_Product__Type_Ointernal__split(X3747,X3746,X3745,X3744,hAPP(hAPP(c_Product__Type_OPair(X3747,X3746),X3743),X3742)) = hAPP(hAPP(X3744,X3743),X3742),
inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).
fof(i_0_784,plain,
! [X3722,X3723,X3724,X3725,X3726,X3727] : c_Product__Type_Oprod_Oprod__rec(X3727,X3726,X3725,X3724,hAPP(hAPP(c_Product__Type_OPair(X3727,X3726),X3723),X3722)) = hAPP(hAPP(X3724,X3723),X3722),
inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).
fof(i_0_785,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_786,plain,
! [X2887,X2888,X2889,X2890] :
( ~ c_Relation_Orefl__on(X2890,X2889,X2888)
| ~ hBOOL(hAPP(hAPP(c_member(X2890),X2887),X2889))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2890,X2890)),hAPP(hAPP(c_Product__Type_OPair(X2890,X2890),X2887),X2887)),X2888)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD])]) ).
fof(i_0_787,plain,
! [X4048,X4049,X4050,X4051] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X4051),X4050),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4051,tc_HOL_Obool)),X4049),X4048)))
| hBOOL(hAPP(hAPP(c_member(X4051),X4050),X4049))
| hBOOL(hAPP(hAPP(c_member(X4051),X4050),X4048)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4051),X4050),X4049))
| hBOOL(hAPP(hAPP(c_member(X4051),X4050),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4051,tc_HOL_Obool)),X4049),X4048))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4051),X4050),X4048))
| hBOOL(hAPP(hAPP(c_member(X4051),X4050),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4051,tc_HOL_Obool)),X4049),X4048))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__iff])])]) ).
fof(i_0_788,plain,
! [X3766,X3767,X3768,X3769] :
( ~ hBOOL(hAPP(hAPP(c_member(X3769),X3768),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3769,tc_HOL_Obool)),X3767),X3766)))
| hBOOL(hAPP(hAPP(c_member(X3769),X3768),X3767))
| hBOOL(hAPP(hAPP(c_member(X3769),X3768),X3766)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])]) ).
fof(i_0_789,plain,
! [X2759,X2760,X2761,X2762] :
( X2762 != X2761
| ~ hBOOL(hAPP(hAPP(c_member(X2760),X2762),X2759))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2760,X2760)),hAPP(hAPP(c_Product__Type_OPair(X2760,X2760),X2762),X2761)),c_Relation_OId__on(X2760,X2759))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).
fof(i_0_790,plain,
! [X3537,X3538,X3539,X3540,X3541,X3542] :
( X3542 != c_Recdef_Owfrec(X3541,X3540,X3539,X3538)
| ~ c_Wellfounded_Owf(X3541,X3539)
| hAPP(X3542,X3537) = hAPP(hAPP(X3538,hAPP(hAPP(hAPP(c_Recdef_Ocut(X3541,X3540),X3542),X3539),X3537)),X3537) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__wfrec])]) ).
fof(i_0_791,plain,
! [X3241,X3242,X3243,X3244,X3245] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3245,tc_HOL_Obool),X3244,X3243)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X3245,X3242),tc_HOL_Obool),c_FuncSet_OPi(X3245,X3242,X3243,X3241),c_FuncSet_OPi(X3245,X3242,X3244,X3241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_792,plain,
! [X3388,X3389,X3390,X3391] : c_Fun_Ofun__upd(X3391,X3390,X3389,X3388,hAPP(X3389,X3388)) = X3389,
inference(variable_rename,[status(thm)],[fact_fun__upd__triv]) ).
fof(i_0_793,plain,
! [X3488,X3489,X3490,X3491,X3492] :
( hAPP(X3492,X3491) != X3490
| c_Fun_Ofun__upd(X3489,X3488,X3492,X3491,X3490) = X3492 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem])]) ).
fof(i_0_794,plain,
! [X3904,X3905,X3906,X3907] : c_Relation_ORange(X3907,X3906,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3907,X3906),tc_HOL_Obool)),X3905),X3904)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3906,tc_HOL_Obool)),c_Relation_ORange(X3907,X3906,X3905)),c_Relation_ORange(X3907,X3906,X3904)),
inference(variable_rename,[status(thm)],[fact_Range__Un__eq]) ).
fof(i_0_795,plain,
! [X4016,X4017,X4018,X4019] : c_Relation_ODomain(X4019,X4018,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool)),X4017),X4016)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4019,tc_HOL_Obool)),c_Relation_ODomain(X4019,X4018,X4017)),c_Relation_ODomain(X4019,X4018,X4016)),
inference(variable_rename,[status(thm)],[fact_Domain__Un__eq]) ).
fof(i_0_796,plain,
! [X3877,X3878,X3879,X3880,X3881] :
( ~ c_Relation_Orefl__on(X3881,X3880,X3879)
| ~ c_Relation_Orefl__on(X3881,X3878,X3877)
| c_Relation_Orefl__on(X3881,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3881,tc_HOL_Obool)),X3880),X3878),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3881,X3881),tc_HOL_Obool)),X3879),X3877)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Un])]) ).
fof(i_0_797,plain,
! [X2932,X2933,X2934,X2935,X2936] :
( ~ c_Relation_Orefl__on(X2936,X2935,X2934)
| ~ c_Relation_Orefl__on(X2936,X2933,X2932)
| c_Relation_Orefl__on(X2936,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2936,tc_HOL_Obool)),X2935),X2933),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2936,X2936),tc_HOL_Obool)),X2934),X2932)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Int])]) ).
fof(i_0_798,plain,
! [X2627,X2628,X2629,X2630] :
( ( hBOOL(hAPP(hAPP(c_member(X2630),X2629),X2628))
| ~ hBOOL(hAPP(hAPP(c_member(X2630),X2629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2630,tc_HOL_Obool)),X2628),X2627))) )
& ( hBOOL(hAPP(hAPP(c_member(X2630),X2629),X2627))
| ~ hBOOL(hAPP(hAPP(c_member(X2630),X2629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2630,tc_HOL_Obool)),X2628),X2627))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2630),X2629),X2628))
| ~ hBOOL(hAPP(hAPP(c_member(X2630),X2629),X2627))
| hBOOL(hAPP(hAPP(c_member(X2630),X2629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2630,tc_HOL_Obool)),X2628),X2627))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).
fof(i_0_799,plain,
! [X2623,X2624,X2625,X2626] :
( ~ hBOOL(hAPP(hAPP(c_member(X2626),X2625),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2626,tc_HOL_Obool)),X2624),X2623)))
| hBOOL(hAPP(hAPP(c_member(X2626),X2625),X2624)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).
fof(i_0_800,plain,
! [X2587,X2588,X2589,X2590] :
( ( hBOOL(hAPP(hAPP(c_member(X2590),X2589),X2588))
| ~ hBOOL(hAPP(hAPP(c_member(X2590),X2589),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2590,tc_HOL_Obool)),X2588),X2587))) )
& ( hBOOL(hAPP(hAPP(c_member(X2590),X2589),X2587))
| ~ hBOOL(hAPP(hAPP(c_member(X2590),X2589),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2590,tc_HOL_Obool)),X2588),X2587))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])])]) ).
fof(i_0_801,plain,
! [X2619,X2620,X2621,X2622] :
( ~ hBOOL(hAPP(hAPP(c_member(X2622),X2621),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2622,tc_HOL_Obool)),X2620),X2619)))
| hBOOL(hAPP(hAPP(c_member(X2622),X2621),X2619)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).
fof(i_0_802,plain,
! [X3375,X3376,X3377,X3378] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3378,X3378)),X3377),c_Transitive__Closure_Otrancl(X3378,X3376)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3378,X3378),tc_HOL_Obool),X3376,X3375)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3378,X3378)),X3377),c_Transitive__Closure_Otrancl(X3378,X3375))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__mono])]) ).
fof(i_0_803,plain,
! [X3928,X3929,X3930,X3931] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3931,tc_HOL_Obool)),X3930),X3929)),X3928) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3931,tc_HOL_Obool)),X3930),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3931,tc_HOL_Obool)),X3929),X3928)),
inference(variable_rename,[status(thm)],[fact_Un__assoc]) ).
fof(i_0_804,plain,
! [X2595,X2596,X2597,X2598] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2598,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2598,tc_HOL_Obool)),X2597),X2596)),X2595) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2598,tc_HOL_Obool)),X2597),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2598,tc_HOL_Obool)),X2596),X2595)),
inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).
fof(i_0_805,plain,
! [X2820,X2821,X2822] :
( ( hBOOL(hAPP(hAPP(c_member(X2822),esk61_3(X2820,X2821,X2822)),X2820))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2822,X2822)),X2821),c_Relation_OId__on(X2822,X2820))) )
& ( X2821 = hAPP(hAPP(c_Product__Type_OPair(X2822,X2822),esk61_3(X2820,X2821,X2822)),esk61_3(X2820,X2821,X2822))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2822,X2822)),X2821),c_Relation_OId__on(X2822,X2820))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).
fof(i_0_806,plain,
! [X2263,X2264,X2265] :
( ( hAPP(hAPP(c_COMBC(X2265,tc_fun(X2265,tc_HOL_Obool),tc_HOL_Obool),c_member(X2265)),X2264) != hAPP(hAPP(c_COMBC(X2265,tc_fun(X2265,tc_HOL_Obool),tc_HOL_Obool),c_member(X2265)),X2263)
| X2264 = X2263 )
& ( X2264 != X2263
| hAPP(hAPP(c_COMBC(X2265,tc_fun(X2265,tc_HOL_Obool),tc_HOL_Obool),c_member(X2265)),X2264) = hAPP(hAPP(c_COMBC(X2265,tc_fun(X2265,tc_HOL_Obool),tc_HOL_Obool),c_member(X2265)),X2263) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_807,plain,
! [X2458,X2459,X2460] : hBOOL(hAPP(hAPP(c_member(tc_prod(X2460,X2460)),hAPP(hAPP(c_Product__Type_OPair(X2460,X2460),X2459),X2459)),c_Transitive__Closure_Ortrancl(X2460,X2458))),
inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
fof(i_0_808,plain,
! [X3866,X3867,X3868,X3869] :
( ~ class_Lattices_Olattice(X3869)
| c_Orderings_Oord__class_Oless__eq(X3869,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3869),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3869),X3868),X3867)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3869),X3868),X3866)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3869),X3868),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3869),X3867),X3866))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__inf__le])]) ).
fof(i_0_809,plain,
! [X3862,X3863,X3864,X3865] :
( ~ class_Lattices_Olattice(X3865)
| c_Orderings_Oord__class_Oless__eq(X3865,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3865),X3864),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3865),X3863),X3862)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3865),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3865),X3864),X3863)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3865),X3864),X3862))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__sup__le])]) ).
fof(i_0_810,plain,
! [X2505,X2506,X2507,X2508] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2508,X2507)),X2506),c_FuncSet_Oextensional(X2508,X2507,X2505)))
| c_FuncSet_Orestrict(X2508,X2507,X2506,X2505) = X2506 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__restrict])]) ).
fof(i_0_811,plain,
! [X4223,X4224,X4225,X4226,X4227,X4228] : hAPP(hAPP(c_COMBB(X4228,X4227,X4226,X4225),X4224),X4223) = hAPP(X4225,hAPP(X4224,X4223)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_812,plain,
! [X2591,X2592,X2593,X2594] :
( ~ hBOOL(hAPP(hAPP(c_member(X2594),X2593),X2592))
| ~ hBOOL(hAPP(hAPP(c_member(X2594),X2593),X2591))
| hBOOL(hAPP(hAPP(c_member(X2594),X2593),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2594,tc_HOL_Obool)),X2592),X2591))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).
fof(i_0_813,plain,
! [X3754,X3755,X3756,X3757] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3757,tc_HOL_Obool)),X3756),X3755),X3754))
| hBOOL(hAPP(X3756,X3754))
| hBOOL(hAPP(X3755,X3754)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_814,plain,
! [X2579,X2580,X2581,X2582] :
( ( hBOOL(hAPP(X2581,X2579))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2582,tc_HOL_Obool)),X2581),X2580),X2579)) )
& ( hBOOL(hAPP(X2580,X2579))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2582,tc_HOL_Obool)),X2581),X2580),X2579)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])])]) ).
fof(i_0_815,plain,
! [X2615,X2616,X2617,X2618] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2618,tc_HOL_Obool)),X2617),X2616),X2615))
| hBOOL(hAPP(X2617,X2615)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).
fof(i_0_816,plain,
! [X2611,X2612,X2613,X2614] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2614,tc_HOL_Obool)),X2613),X2612),X2611))
| hBOOL(hAPP(X2612,X2611)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).
fof(i_0_817,plain,
! [X2376,X2377,X2378,X2379,X2380] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2380,X2379)),X2378),c_FuncSet_Oextensional(X2380,X2379,X2377)))
| hBOOL(hAPP(hAPP(c_member(X2380),X2376),X2377))
| hAPP(X2378,X2376) = c_HOL_Oundefined(X2379) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).
fof(i_0_818,plain,
! [X3627,X3628] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3628,X3628),tc_HOL_Obool),c_Relation_OId__on(X3628,X3627),c_Product__Type_OSigma(X3628,X3628,X3627,c_COMBK(tc_fun(X3628,tc_HOL_Obool),X3628,X3627))),
inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times]) ).
fof(i_0_819,plain,
! [X2174,X2175] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk3_2(X2174,X2175)),c_Arrow__Order__Mirabelle_OLin))
| X2175 = X2174 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2175),X2174)),esk3_2(X2174,X2175)))
| X2175 = X2174 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_complete__Lin])])])]) ).
fof(i_0_820,plain,
! [X2091] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_Q____,X2091))),
inference(variable_rename,[status(thm)],[fact__096_B_Bi_O_Ab_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_H_096]) ).
fof(i_0_821,plain,
( v_a____ = v_a_H____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_a____)),hAPP(v_F,v_Q____))) ),
inference(fof_nnf,[status(thm)],[fact_calculation_I2_J]) ).
fof(i_0_822,plain,
! [X3807,X3808,X3809,X3810,X3811] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3811,tc_HOL_Obool),X3810,X3809)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3811,tc_HOL_Obool),X3808,X3807)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3811,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3811,tc_HOL_Obool)),X3810),X3808),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3811,tc_HOL_Obool)),X3809),X3807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__mono])]) ).
fof(i_0_823,plain,
! [X3188,X3189,X3190,X3191,X3192] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3192,tc_HOL_Obool),X3191,X3190)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3192,tc_HOL_Obool),X3189,X3188)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3192,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3192,tc_HOL_Obool)),X3191),X3189),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3192,tc_HOL_Obool)),X3190),X3188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).
fof(i_0_824,plain,
! [X3115,X3116,X3117,X3118] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3118),X3117),X3116))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3118,tc_HOL_Obool)),c_Set_Oinsert(X3118,X3117,X3115)),X3116) = c_Set_Oinsert(X3118,X3117,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3118,tc_HOL_Obool)),X3115),X3116)) )
& ( hBOOL(hAPP(hAPP(c_member(X3118),X3117),X3116))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3118,tc_HOL_Obool)),c_Set_Oinsert(X3118,X3117,X3115)),X3116) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3118,tc_HOL_Obool)),X3115),X3116) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])]) ).
fof(i_0_825,plain,
! [X3099,X3100,X3101,X3102] :
( ~ hBOOL(hAPP(hAPP(c_member(X3102),X3101),X3100))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3102,tc_HOL_Obool)),c_Set_Oinsert(X3102,X3101,X3099)),X3100) = c_Set_Oinsert(X3102,X3101,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3102,tc_HOL_Obool)),X3099),X3100)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1])]) ).
fof(i_0_826,plain,
! [X2899,X2900,X2901] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2901,X2901)),X2900),X2899))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2901,X2901)),X2900),c_Transitive__Closure_Otrancl(X2901,X2899))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])]) ).
fof(i_0_827,plain,
! [X2461,X2462,X2463] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2463,X2463)),X2462),X2461))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2463,X2463)),X2462),c_Transitive__Closure_Ortrancl(X2463,X2461))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).
fof(i_0_828,plain,
! [X3924,X3925,X3926,X3927] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3927,tc_HOL_Obool)),X3926),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3927,tc_HOL_Obool)),X3925),X3924)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3927,tc_HOL_Obool)),X3925),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3927,tc_HOL_Obool)),X3926),X3924)),
inference(variable_rename,[status(thm)],[fact_Un__left__commute]) ).
fof(i_0_829,plain,
! [X2599,X2600,X2601,X2602] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2602,tc_HOL_Obool)),X2601),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2602,tc_HOL_Obool)),X2600),X2599)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2602,tc_HOL_Obool)),X2600),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2602,tc_HOL_Obool)),X2601),X2599)),
inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).
fof(i_0_830,plain,
! [X4044,X4045,X4046,X4047] :
( ~ hBOOL(hAPP(hAPP(c_member(X4047),X4046),X4045))
| hBOOL(hAPP(hAPP(c_member(X4047),X4046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4047,tc_HOL_Obool)),X4045),X4044))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI1])]) ).
fof(i_0_831,plain,
! [X3762,X3763,X3764,X3765] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3765),X3764),X3763))
| hBOOL(hAPP(hAPP(c_member(X3765),X3764),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3765,tc_HOL_Obool)),X3762),X3763))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3765),X3764),X3762))
| hBOOL(hAPP(hAPP(c_member(X3765),X3764),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3765,tc_HOL_Obool)),X3762),X3763))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])])]) ).
fof(i_0_832,plain,
! [X4040,X4041,X4042,X4043] :
( ~ hBOOL(hAPP(hAPP(c_member(X4043),X4042),X4041))
| hBOOL(hAPP(hAPP(c_member(X4043),X4042),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4043,tc_HOL_Obool)),X4040),X4041))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI2])]) ).
fof(i_0_833,plain,
! [X4117,X4118,X4119,X4120,X4121] :
( ( X4120 = X4117
| X4120 = X4118
| c_Set_Oinsert(X4121,X4120,c_Set_Oinsert(X4121,X4119,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) != c_Set_Oinsert(X4121,X4118,c_Set_Oinsert(X4121,X4117,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) )
& ( X4119 = X4118
| X4120 = X4118
| c_Set_Oinsert(X4121,X4120,c_Set_Oinsert(X4121,X4119,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) != c_Set_Oinsert(X4121,X4118,c_Set_Oinsert(X4121,X4117,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) )
& ( X4120 = X4117
| X4119 = X4117
| c_Set_Oinsert(X4121,X4120,c_Set_Oinsert(X4121,X4119,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) != c_Set_Oinsert(X4121,X4118,c_Set_Oinsert(X4121,X4117,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) )
& ( X4119 = X4118
| X4119 = X4117
| c_Set_Oinsert(X4121,X4120,c_Set_Oinsert(X4121,X4119,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) != c_Set_Oinsert(X4121,X4118,c_Set_Oinsert(X4121,X4117,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) )
& ( X4120 != X4118
| X4119 != X4117
| c_Set_Oinsert(X4121,X4120,c_Set_Oinsert(X4121,X4119,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) = c_Set_Oinsert(X4121,X4118,c_Set_Oinsert(X4121,X4117,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) )
& ( X4120 != X4117
| X4119 != X4118
| c_Set_Oinsert(X4121,X4120,c_Set_Oinsert(X4121,X4119,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) = c_Set_Oinsert(X4121,X4118,c_Set_Oinsert(X4121,X4117,c_Orderings_Obot__class_Obot(tc_fun(X4121,tc_HOL_Obool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])]) ).
fof(i_0_834,plain,
! [X4103,X4104,X4105] :
( ~ hBOOL(hAPP(hAPP(c_member(X4105),X4104),c_Set_Oinsert(X4105,X4103,c_Orderings_Obot__class_Obot(tc_fun(X4105,tc_HOL_Obool)))))
| X4104 = X4103 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singletonE])]) ).
fof(i_0_835,plain,
! [X4100,X4101,X4102] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X4102),X4101),c_Set_Oinsert(X4102,X4100,c_Orderings_Obot__class_Obot(tc_fun(X4102,tc_HOL_Obool)))))
| X4101 = X4100 )
& ( X4101 != X4100
| hBOOL(hAPP(hAPP(c_member(X4102),X4101),c_Set_Oinsert(X4102,X4100,c_Orderings_Obot__class_Obot(tc_fun(X4102,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])]) ).
fof(i_0_836,plain,
! [X3039,X3040,X3041,X3042] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3042,tc_HOL_Obool)),c_Set_Oinsert(X3042,X3041,X3040)),c_Set_Oinsert(X3042,X3041,X3039)) = c_Set_Oinsert(X3042,X3041,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3042,tc_HOL_Obool)),X3040),X3039)),
inference(variable_rename,[status(thm)],[fact_insert__inter__insert]) ).
fof(i_0_837,plain,
! [X3053,X3054,X3055,X3056,X3057] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3057,X3056),X3055),X3054))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3057,X3056),X3054),X3053))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3057,X3056),X3055),X3053)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclp__trans])]) ).
fof(i_0_838,plain,
! [X3119,X3120,X3121,X3122] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3122),X3121),X3120))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3122,tc_HOL_Obool)),X3120),c_Set_Oinsert(X3122,X3121,X3119)) = c_Set_Oinsert(X3122,X3121,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3122,tc_HOL_Obool)),X3120),X3119)) )
& ( hBOOL(hAPP(hAPP(c_member(X3122),X3121),X3120))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3122,tc_HOL_Obool)),X3120),c_Set_Oinsert(X3122,X3121,X3119)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3122,tc_HOL_Obool)),X3120),X3119) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).
fof(i_0_839,plain,
! [X3103,X3104,X3105,X3106] :
( ~ hBOOL(hAPP(hAPP(c_member(X3106),X3105),X3104))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3106,tc_HOL_Obool)),X3104),c_Set_Oinsert(X3106,X3105,X3103)) = c_Set_Oinsert(X3106,X3105,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3106,tc_HOL_Obool)),X3104),X3103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1])]) ).
fof(i_0_840,plain,
! [X3048,X3049,X3050,X3051,X3052] : c_Relation_ORange(X3052,X3051,c_Set_Oinsert(tc_prod(X3052,X3051),hAPP(hAPP(c_Product__Type_OPair(X3052,X3051),X3050),X3049),X3048)) = c_Set_Oinsert(X3051,X3049,c_Relation_ORange(X3052,X3051,X3048)),
inference(variable_rename,[status(thm)],[fact_Range__insert]) ).
fof(i_0_841,plain,
! [X3043,X3044,X3045,X3046,X3047] : c_Relation_ODomain(X3047,X3046,c_Set_Oinsert(tc_prod(X3047,X3046),hAPP(hAPP(c_Product__Type_OPair(X3047,X3046),X3045),X3044),X3043)) = c_Set_Oinsert(X3047,X3045,c_Relation_ODomain(X3047,X3046,X3043)),
inference(variable_rename,[status(thm)],[fact_Domain__insert]) ).
fof(i_0_842,plain,
! [X3323,X3324,X3325] :
( ~ c_Wellfounded_Owf(X3325,X3324)
| c_Wellfounded_Owf(X3325,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3325,X3325),tc_HOL_Obool)),X3324),X3323)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int1])]) ).
fof(i_0_843,plain,
! [X3326,X3327,X3328] :
( ~ c_Wellfounded_Owf(X3328,X3327)
| c_Wellfounded_Owf(X3328,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3328,X3328),tc_HOL_Obool)),X3326),X3327)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int2])]) ).
fof(i_0_844,plain,
! [X4129,X4130,X4131,X4132,X4133,X4134,X4135,X4136] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4131,tc_HOL_Obool)),X4130),X4129) != c_Orderings_Obot__class_Obot(tc_fun(X4131,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X4131),X4132),X4130))
| ~ hBOOL(hAPP(hAPP(c_member(X4131),X4133),X4129))
| X4132 != X4133 )
& ( hBOOL(hAPP(hAPP(c_member(X4136),esk109_3(X4134,X4135,X4136)),X4135))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4136,tc_HOL_Obool)),X4135),X4134) = c_Orderings_Obot__class_Obot(tc_fun(X4136,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X4136),esk110_3(X4134,X4135,X4136)),X4134))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4136,tc_HOL_Obool)),X4135),X4134) = c_Orderings_Obot__class_Obot(tc_fun(X4136,tc_HOL_Obool)) )
& ( esk109_3(X4134,X4135,X4136) = esk110_3(X4134,X4135,X4136)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4136,tc_HOL_Obool)),X4135),X4134) = c_Orderings_Obot__class_Obot(tc_fun(X4136,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_845,plain,
! [X4056,X4057,X4058,X4059] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4059,tc_HOL_Obool)),c_Set_Oinsert(X4059,X4058,X4057)),X4056) = c_Set_Oinsert(X4059,X4058,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4059,tc_HOL_Obool)),X4057),X4056)),
inference(variable_rename,[status(thm)],[fact_Un__insert__left]) ).
fof(i_0_846,plain,
! [X2583,X2584,X2585,X2586] :
( ~ hBOOL(hAPP(X2586,X2585))
| ~ hBOOL(hAPP(X2584,X2585))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2583,tc_HOL_Obool)),X2586),X2584),X2585)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).
fof(i_0_847,plain,
! [X2514,X2515,X2516,X2517,X2518] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2518),X2517),X2516))
| hAPP(c_FuncSet_Orestrict(X2518,X2515,X2514,X2516),X2517) = hAPP(X2514,X2517) )
& ( hBOOL(hAPP(hAPP(c_member(X2518),X2517),X2516))
| hAPP(c_FuncSet_Orestrict(X2518,X2515,X2514,X2516),X2517) = c_HOL_Oundefined(X2515) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_573])]) ).
fof(i_0_848,plain,
! [X2509,X2510,X2511,X2512,X2513] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2513),X2512),X2511))
| hAPP(c_FuncSet_Orestrict(X2513,X2510,X2509,X2511),X2512) = hAPP(X2509,X2512) )
& ( hBOOL(hAPP(hAPP(c_member(X2513),X2512),X2511))
| hAPP(c_FuncSet_Orestrict(X2513,X2510,X2509,X2511),X2512) = c_HOL_Oundefined(X2510) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_574])]) ).
fof(i_0_849,plain,
! [X4106,X4107,X4108] : c_FuncSet_Oextensional__funcset(X4108,X4107,c_Orderings_Obot__class_Obot(tc_fun(X4108,tc_HOL_Obool)),X4106) = c_Set_Oinsert(tc_fun(X4108,X4107),c_COMBK(X4107,X4108,c_HOL_Oundefined(X4107)),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4108,X4107),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_extensional__funcset__empty__domain]) ).
fof(i_0_850,plain,
! [X3908,X3909,X3910,X3911] :
( ~ hBOOL(hAPP(X3911,X3910))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3909,tc_HOL_Obool)),X3911),X3908),X3910)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I1])]) ).
fof(i_0_851,plain,
! [X3758,X3759,X3760,X3761] :
( ( ~ hBOOL(hAPP(X3761,X3760))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3758,tc_HOL_Obool)),X3759),X3761),X3760)) )
& ( ~ hBOOL(hAPP(X3759,X3760))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3758,tc_HOL_Obool)),X3759),X3761),X3760)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_575])])]) ).
fof(i_0_852,plain,
! [X3912,X3913,X3914,X3915] :
( ~ hBOOL(hAPP(X3915,X3914))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3913,tc_HOL_Obool)),X3912),X3915),X3914)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I2])]) ).
fof(i_0_853,plain,
! [X3882,X3883,X3884,X3885] :
( ~ class_Lattices_Odistrib__lattice(X3885)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3885),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3885),X3884),X3883)),X3882) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3885),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3885),X3884),X3882)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3885),X3883),X3882)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2])]) ).
fof(i_0_854,plain,
! [X3886,X3887,X3888,X3889] :
( ~ class_Lattices_Odistrib__lattice(X3889)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3889),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3889),X3888),X3887)),X3886) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3889),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3889),X3888),X3886)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3889),X3887),X3886)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2])]) ).
fof(i_0_855,plain,
! [X4097,X4098,X4099] : c_Set_Oinsert(X4099,X4098,X4097) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4099,tc_HOL_Obool)),c_Set_Oinsert(X4099,X4098,c_Orderings_Obot__class_Obot(tc_fun(X4099,tc_HOL_Obool)))),X4097),
inference(variable_rename,[status(thm)],[fact_insert__is__Un]) ).
fof(i_0_856,plain,
! [X3024,X3025,X3026,X3027] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3027),X3026),c_Set_Oinsert(X3027,X3025,X3024)))
| X3026 = X3025
| hBOOL(hAPP(hAPP(c_member(X3027),X3026),X3024)) )
& ( X3026 != X3025
| hBOOL(hAPP(hAPP(c_member(X3027),X3026),c_Set_Oinsert(X3027,X3025,X3024))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3027),X3026),X3024))
| hBOOL(hAPP(hAPP(c_member(X3027),X3026),c_Set_Oinsert(X3027,X3025,X3024))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_857,plain,
! [X3017,X3018,X3019,X3020] :
( ~ hBOOL(hAPP(hAPP(c_member(X3020),X3019),c_Set_Oinsert(X3020,X3018,X3017)))
| X3019 = X3018
| hBOOL(hAPP(hAPP(c_member(X3020),X3019),X3017)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).
fof(i_0_858,plain,
! [X3058,X3059,X3060,X3061,X3062] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3062,X3061),X3060),X3059))
| ~ hBOOL(hAPP(hAPP(X3061,X3059),X3058))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3062,X3061),X3060),X3058)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclp_Otrancl__into__trancl])]) ).
fof(i_0_859,plain,
! [X3063,X3064,X3065,X3066,X3067] :
( ~ hBOOL(hAPP(hAPP(X3067,X3066),X3065))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3064,X3067),X3065),X3063))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3064,X3067),X3066),X3063)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclp__into__tranclp2])]) ).
fof(i_0_860,plain,
! [X3107,X3108,X3109,X3110] :
( hBOOL(hAPP(hAPP(c_member(X3110),X3109),X3108))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3110,tc_HOL_Obool)),c_Set_Oinsert(X3110,X3109,X3107)),X3108) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3110,tc_HOL_Obool)),X3107),X3108) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_576])]) ).
fof(i_0_861,plain,
! [X3803,X3804,X3805,X3806] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3806,tc_HOL_Obool),X3805,X3804)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3806,tc_HOL_Obool),X3803,X3804)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3806,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3806,tc_HOL_Obool)),X3805),X3803),X3804) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__least])]) ).
fof(i_0_862,plain,
! [X3193,X3194,X3195,X3196] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3196,tc_HOL_Obool),X3195,X3194)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3196,tc_HOL_Obool),X3195,X3193)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3196,tc_HOL_Obool),X3195,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3196,tc_HOL_Obool)),X3194),X3193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).
fof(i_0_863,plain,
! [X2364,X2365,X2366,X2367,X2368,X2369,X2370] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2366,X2365),X2364))
| ~ hBOOL(hAPP(hAPP(X2365,X2367),X2364))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2366,X2365),X2367)) )
& ( hBOOL(hAPP(hAPP(X2369,esk31_3(X2368,X2369,X2370)),X2368))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2370,X2369),X2368)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2370,X2369),esk31_3(X2368,X2369,X2370)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2370,X2369),X2368)) ) ),
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_864,plain,
! [X2356,X2357,X2358,X2359,X2360,X2361,X2362] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2358,X2357),X2356))
| ~ hBOOL(hAPP(hAPP(X2357,X2359),X2356))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2358,X2357),X2359)) )
& ( hBOOL(hAPP(hAPP(X2361,esk30_3(X2360,X2361,X2362)),X2360))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2362,X2361),X2360)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2362,X2361),esk30_3(X2360,X2361,X2362)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2362,X2361),X2360)) ) ),
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_865,plain,
! [X4052,X4053,X4054,X4055] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4055,tc_HOL_Obool)),X4054),c_Set_Oinsert(X4055,X4053,X4052)) = c_Set_Oinsert(X4055,X4053,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4055,tc_HOL_Obool)),X4054),X4052)),
inference(variable_rename,[status(thm)],[fact_Un__insert__right]) ).
fof(i_0_866,plain,
! [X4235,X4236,X4237,X4238,X4239,X4240] : hAPP(hAPP(hAPP(c_COMBS(X4240,X4239,X4238),X4237),X4236),X4235) = hAPP(hAPP(X4237,X4235),hAPP(X4236,X4235)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_867,plain,
! [X3173,X3174,X3175,X3176] :
( ~ c_Wellfounded_Owf(X3176,X3175)
| ~ c_Wellfounded_Owf(X3174,X3173)
| c_Wellfounded_Owf(tc_prod(X3176,X3174),c_Wellfounded_Olex__prod(X3176,X3174,X3175,X3173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex__prod])]) ).
fof(i_0_868,plain,
! [X2851,X2852,X2853,X2854,X2856,X2857,X2858,X2859,X2860] :
( ( ~ c_Predicate_ORangeP(X2854,X2853,X2852,X2851)
| hBOOL(hAPP(hAPP(X2852,esk67_2(X2851,X2852)),X2851)) )
& ( ~ hBOOL(hAPP(hAPP(X2857,X2858),X2856))
| c_Predicate_ORangeP(X2860,X2859,X2857,X2856) ) ),
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_869,plain,
! [X3921,X3922,X3923] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3923,tc_HOL_Obool)),X3922),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3923,tc_HOL_Obool)),X3922),X3921)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3923,tc_HOL_Obool)),X3922),X3921),
inference(variable_rename,[status(thm)],[fact_Un__left__absorb]) ).
fof(i_0_870,plain,
! [X2603,X2604,X2605] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2605,tc_HOL_Obool)),X2604),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2605,tc_HOL_Obool)),X2604),X2603)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2605,tc_HOL_Obool)),X2604),X2603),
inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).
fof(i_0_871,plain,
! [X4229,X4230,X4231,X4232,X4233,X4234] : hAPP(hAPP(hAPP(c_COMBC(X4234,X4233,X4232),X4231),X4230),X4229) = hAPP(hAPP(X4231,X4229),X4230),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_872,plain,
! [X3169,X3170,X3171,X3172] :
( ~ c_Wellfounded_Owf(X3172,X3171)
| c_Wellfounded_Owf(X3170,c_Relation_Oinv__image(X3172,X3170,X3171,X3169)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])]) ).
fof(i_0_873,plain,
! [X3890,X3891,X3892,X3893] :
( ~ class_Lattices_Odistrib__lattice(X3893)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3893),X3892),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3893),X3891),X3890)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3893),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3893),X3892),X3891)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3893),X3892),X3890)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1])]) ).
fof(i_0_874,plain,
! [X3894,X3895,X3896,X3897] :
( ~ class_Lattices_Odistrib__lattice(X3897)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3897),X3896),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3897),X3895),X3894)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3897),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3897),X3896),X3895)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3897),X3896),X3894)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1])]) ).
fof(i_0_875,plain,
! [X3570,X3571] : c_HOL_OThe(X3571,hAPP(hAPP(c_COMBC(X3571,X3571,tc_HOL_Obool),c_fequal),X3570)) = X3570,
inference(variable_rename,[status(thm)],[fact_the__eq__trivial]) ).
fof(i_0_876,plain,
! [X3111,X3112,X3113,X3114] :
( hBOOL(hAPP(hAPP(c_member(X3114),X3113),X3112))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3114,tc_HOL_Obool)),X3112),c_Set_Oinsert(X3114,X3113,X3111)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3114,tc_HOL_Obool)),X3112),X3111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_577])]) ).
fof(i_0_877,plain,
! [X3246,X3247,X3248,X3249] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3249,X3248),tc_HOL_Obool),X3247,X3246)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3249,tc_HOL_Obool),c_Relation_ODomain(X3249,X3248,X3247),c_Relation_ODomain(X3249,X3248,X3246)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).
fof(i_0_878,plain,
! [X3032,X3033,X3034,X3035] :
( ~ hBOOL(hAPP(hAPP(c_member(X3035),X3034),X3033))
| hBOOL(hAPP(hAPP(c_member(X3035),X3034),c_Set_Oinsert(X3035,X3032,X3033))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_879,plain,
! [X3013,X3014,X3015,X3016] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3016),X3015),X3014))
| hBOOL(hAPP(hAPP(c_member(X3016),X3015),c_Set_Oinsert(X3016,X3013,X3014))) )
& ( X3015 != X3013
| hBOOL(hAPP(hAPP(c_member(X3016),X3015),c_Set_Oinsert(X3016,X3013,X3014))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_578])])]) ).
fof(i_0_880,plain,
! [X3317,X3318,X3319] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3319,X3319),tc_HOL_Obool),X3318,X3317)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3319,X3319),tc_HOL_Obool),X3317,c_Transitive__Closure_Ortrancl(X3319,X3318))
| c_Transitive__Closure_Ortrancl(X3319,X3317) = c_Transitive__Closure_Ortrancl(X3319,X3318) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).
fof(i_0_881,plain,
! [X3358,X3359,X3360,X3361] :
( ( hBOOL(hAPP(hAPP(c_member(X3361),X3360),X3358))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3361,tc_HOL_Obool),c_Set_Oinsert(X3361,X3360,X3359),X3358) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3361,tc_HOL_Obool),X3359,X3358)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3361,tc_HOL_Obool),c_Set_Oinsert(X3361,X3360,X3359),X3358) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3361),X3360),X3358))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3361,tc_HOL_Obool),X3359,X3358)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3361,tc_HOL_Obool),c_Set_Oinsert(X3361,X3360,X3359),X3358) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_882,plain,
! [X3362,X3363,X3364,X3365] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3365,tc_HOL_Obool),X3363,c_Set_Oinsert(X3365,X3364,X3362))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3365,tc_HOL_Obool),X3363,X3362)
| hBOOL(hAPP(hAPP(c_member(X3365),X3364),X3363)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3365,tc_HOL_Obool),X3363,X3362)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3365,tc_HOL_Obool),X3363,c_Set_Oinsert(X3365,X3364,X3362))
| hBOOL(hAPP(hAPP(c_member(X3365),X3364),X3363)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_579])])]) ).
fof(i_0_883,plain,
! [X4188,X4189] :
( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4189,tc_HOL_Obool)),X4188))
| hBOOL(hAPP(hAPP(c_member(X4189),X4188),c_Orderings_Obot__class_Obot(tc_fun(X4189,tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4189),X4188),c_Orderings_Obot__class_Obot(tc_fun(X4189,tc_HOL_Obool))))
| hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4189,tc_HOL_Obool)),X4188)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])]) ).
fof(i_0_884,plain,
! [X4109,X4110] : c_FuncSet_Oextensional(X4110,X4109,c_Orderings_Obot__class_Obot(tc_fun(X4110,tc_HOL_Obool))) = c_Set_Oinsert(tc_fun(X4110,X4109),c_COMBK(X4109,X4110,c_HOL_Oundefined(X4109)),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4110,X4109),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_extensional__empty]) ).
fof(i_0_885,plain,
! [X4011,X4012,X4013,X4014,X4015] :
( ~ class_Lattices_Olattice(X4015)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4014,X4015)),X4013),X4012),X4011) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4015),hAPP(X4013,X4011)),hAPP(X4012,X4011)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__fun__def])]) ).
fof(i_0_886,plain,
! [X4006,X4007,X4008,X4009,X4010] :
( ~ class_Lattices_Olattice(X4010)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4009,X4010)),X4008),X4007),X4006) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4010),hAPP(X4008,X4006)),hAPP(X4007,X4006)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__apply])]) ).
fof(i_0_887,plain,
! [X2677,X2678,X2679,X2680,X2681] :
( ~ class_Lattices_Olattice(X2681)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2680,X2681)),X2679),X2678),X2677) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2681),hAPP(X2679,X2677)),hAPP(X2678,X2677)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).
fof(i_0_888,plain,
! [X2672,X2673,X2674,X2675,X2676] :
( ~ class_Lattices_Olattice(X2676)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2675,X2676)),X2674),X2673),X2672) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2676),hAPP(X2674,X2672)),hAPP(X2673,X2672)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).
fof(i_0_889,plain,
! [X3853,X3854,X3855,X3856,X3857] :
( ~ class_Lattices_Osemilattice__sup(X3857)
| ~ c_Orderings_Oord__class_Oless__eq(X3857,X3856,X3855)
| ~ c_Orderings_Oord__class_Oless__eq(X3857,X3854,X3853)
| c_Orderings_Oord__class_Oless__eq(X3857,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3857),X3856),X3854),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3857),X3855),X3853)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__mono])]) ).
fof(i_0_890,plain,
! [X3254,X3255,X3256,X3257,X3258] :
( ~ class_Lattices_Osemilattice__inf(X3258)
| ~ c_Orderings_Oord__class_Oless__eq(X3258,X3257,X3256)
| ~ c_Orderings_Oord__class_Oless__eq(X3258,X3255,X3254)
| c_Orderings_Oord__class_Oless__eq(X3258,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3258),X3257),X3255),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3258),X3256),X3254)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).
fof(i_0_891,plain,
! [X3366,X3367,X3368,X3369,X3370] :
( ( ~ c_Wellfounded_Owf(X3367,X3366)
| hBOOL(hAPP(hAPP(c_member(X3367),X3368),c_Wellfounded_Oacc(X3367,X3366))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3370),esk83_2(X3369,X3370)),c_Wellfounded_Oacc(X3370,X3369)))
| c_Wellfounded_Owf(X3370,X3369) ) ),
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_wf__acc__iff])])])])]) ).
fof(i_0_892,plain,
! [X3320,X3321,X3322] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3322,X3322),tc_HOL_Obool),X3321,c_Transitive__Closure_Ortrancl(X3322,X3320))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3322,X3322),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X3322,X3321),c_Transitive__Closure_Ortrancl(X3322,X3320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).
fof(i_0_893,plain,
! [X4002,X4003,X4004,X4005] :
( ~ class_Lattices_Osemilattice__sup(X4005)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4005),X4004),X4003)),X4002) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4005),X4004),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4005),X4003),X4002)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__assoc])]) ).
fof(i_0_894,plain,
! [X3994,X3995,X3996,X3997] :
( ~ class_Lattices_Osemilattice__sup(X3997)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3997),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3997),X3996),X3995)),X3994) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3997),X3996),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3997),X3995),X3994)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oassoc])]) ).
fof(i_0_895,plain,
! [X3998,X3999,X4000,X4001] :
( ~ class_Lattices_Olattice(X4001)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4001),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4001),X4000),X3999)),X3998) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4001),X4000),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4001),X3999),X3998)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J])]) ).
fof(i_0_896,plain,
! [X2701,X2702,X2703,X2704] :
( ~ class_Lattices_Osemilattice__inf(X2704)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2704),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2704),X2703),X2702)),X2701) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2704),X2703),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2704),X2702),X2701)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).
fof(i_0_897,plain,
! [X2693,X2694,X2695,X2696] :
( ~ class_Lattices_Osemilattice__inf(X2696)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2696),X2695),X2694)),X2693) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2696),X2695),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2696),X2694),X2693)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).
fof(i_0_898,plain,
! [X2697,X2698,X2699,X2700] :
( ~ class_Lattices_Olattice(X2700)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2700),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2700),X2699),X2698)),X2697) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2700),X2699),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2700),X2698),X2697)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).
fof(i_0_899,plain,
! [X3088,X3089,X3090,X3091] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X3091,X3090,X3089),X3088))
| X3090 = X3088
| hBOOL(hAPP(X3089,X3088)) )
& ( X3090 != X3088
| hBOOL(hAPP(c_Set_Oinsert(X3091,X3090,X3089),X3088)) )
& ( ~ hBOOL(hAPP(X3089,X3088))
| hBOOL(hAPP(c_Set_Oinsert(X3091,X3090,X3089),X3088)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_900,plain,
! [X3177,X3178,X3179,X3180] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3180,tc_HOL_Obool),X3179,X3178)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3180,tc_HOL_Obool),c_Set_Oinsert(X3180,X3177,X3179),c_Set_Oinsert(X3180,X3177,X3178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
fof(i_0_901,plain,
! [X3525,X3526,X3527,X3528,X3529,X3530] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3530,tc_fun(X3529,tc_HOL_Obool)),X3528,X3527)
| ~ hBOOL(hAPP(hAPP(X3528,X3526),X3525))
| hBOOL(hAPP(hAPP(X3527,X3526),X3525)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_902,plain,
! [X3531,X3532,X3533,X3534,X3535,X3536] :
( ~ hBOOL(hAPP(hAPP(X3536,X3535),X3534))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3533,tc_fun(X3532,tc_HOL_Obool)),X3536,X3531)
| hBOOL(hAPP(hAPP(X3531,X3535),X3534)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_903,plain,
! [X4172,X4173,X4174] :
( X4174 = c_Orderings_Obot__class_Obot(tc_fun(X4173,tc_HOL_Obool))
| c_FuncSet_Oextensional__funcset(X4173,X4172,X4174,c_Orderings_Obot__class_Obot(tc_fun(X4172,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4173,X4172),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__empty__range])]) ).
fof(i_0_904,plain,
! [X3304,X3305,X3306,X3307] :
( ~ hBOOL(hAPP(hAPP(c_member(X3307),X3306),X3305))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3307,tc_HOL_Obool),X3305,X3304)
| hBOOL(hAPP(hAPP(c_member(X3307),X3306),X3304)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_905,plain,
! [X3308,X3309,X3310,X3311] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3311,tc_HOL_Obool),X3310,X3309)
| ~ hBOOL(hAPP(hAPP(c_member(X3311),X3308),X3310))
| hBOOL(hAPP(hAPP(c_member(X3311),X3308),X3309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_906,plain,
! [X3300,X3301,X3302,X3303] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3303,tc_HOL_Obool),X3302,X3301)
| ~ hBOOL(hAPP(hAPP(c_member(X3303),X3300),X3302))
| hBOOL(hAPP(hAPP(c_member(X3303),X3300),X3301)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_907,plain,
! [X3165,X3166,X3167,X3168] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3168,tc_HOL_Obool),X3167,X3166)
| ~ hBOOL(hAPP(hAPP(c_member(X3168),X3165),X3167))
| hBOOL(hAPP(hAPP(c_member(X3168),X3165),X3166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_908,plain,
! [X3028,X3029,X3030,X3031] :
( ( c_Set_Oinsert(X3031,X3030,X3029) != c_Set_Oinsert(X3031,X3030,X3028)
| X3029 = X3028
| hBOOL(hAPP(hAPP(c_member(X3031),X3030),X3028))
| hBOOL(hAPP(hAPP(c_member(X3031),X3030),X3029)) )
& ( X3029 != X3028
| c_Set_Oinsert(X3031,X3030,X3029) = c_Set_Oinsert(X3031,X3030,X3028)
| hBOOL(hAPP(hAPP(c_member(X3031),X3030),X3028))
| hBOOL(hAPP(hAPP(c_member(X3031),X3030),X3029)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_580])])]) ).
fof(i_0_909,plain,
! [X3314,X3315,X3316] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3316,X3316),tc_HOL_Obool),X3315,X3314)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3316,X3316),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X3316,X3315),c_Transitive__Closure_Ortrancl(X3316,X3314)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).
fof(i_0_910,plain,
! [X2846,X2847,X2848,X2849,X2850] :
( ~ hBOOL(hAPP(hAPP(X2850,X2849),X2848))
| c_Predicate_ORangeP(X2847,X2846,X2850,X2848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).
fof(i_0_911,plain,
! [X2682,X2683,X2684,X2685,X2686] :
( ~ hBOOL(hAPP(hAPP(X2686,X2685),X2684))
| c_Predicate_ODomainP(X2683,X2682,X2686,X2685) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).
fof(i_0_912,plain,
! [X3585] : c_Wellfounded_OwfP(X3585,c_COMBK(tc_fun(X3585,tc_HOL_Obool),X3585,c_COMBK(tc_HOL_Obool,X3585,c_fFalse))),
inference(variable_rename,[status(thm)],[fact_wfP__empty]) ).
fof(i_0_913,plain,
! [X3206,X3207,X3208] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3208,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3208,tc_HOL_Obool)),X3207),X3206),X3207),
inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).
fof(i_0_914,plain,
! [X3203,X3204,X3205] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3205,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3205,tc_HOL_Obool)),X3204),X3203),X3203),
inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).
fof(i_0_915,plain,
! [X3788,X3789,X3790] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3790,tc_HOL_Obool),X3789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3790,tc_HOL_Obool)),X3789),X3788)),
inference(variable_rename,[status(thm)],[fact_Un__upper1]) ).
fof(i_0_916,plain,
! [X3791,X3792,X3793] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3793,tc_HOL_Obool),X3792,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3793,tc_HOL_Obool)),X3791),X3792)),
inference(variable_rename,[status(thm)],[fact_Un__upper2]) ).
fof(i_0_917,plain,
! [X3337,X3338,X3339,X3340] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3340,X3339),tc_HOL_Obool),X3338,X3337)
| ~ c_Relation_Osingle__valued(X3340,X3339,X3337)
| c_Relation_Osingle__valued(X3340,X3339,X3338) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).
fof(i_0_918,plain,
! [X2372,X2373,X2374,X2375] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2375,X2374),X2373))
| ~ hBOOL(hAPP(hAPP(X2374,X2372),X2373))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2375,X2374),X2372)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).
fof(i_0_919,plain,
! [X3849,X3850,X3851,X3852] :
( ~ class_Lattices_Osemilattice__sup(X3852)
| ~ c_Orderings_Oord__class_Oless__eq(X3852,X3851,X3850)
| ~ c_Orderings_Oord__class_Oless__eq(X3852,X3849,X3850)
| c_Orderings_Oord__class_Oless__eq(X3852,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3852),X3851),X3849),X3850) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__least])]) ).
fof(i_0_920,plain,
! [X3845,X3846,X3847,X3848] :
( ~ class_Lattices_Osemilattice__sup(X3848)
| ~ c_Orderings_Oord__class_Oless__eq(X3848,X3847,X3846)
| ~ c_Orderings_Oord__class_Oless__eq(X3848,X3845,X3846)
| c_Orderings_Oord__class_Oless__eq(X3848,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3848),X3847),X3845),X3846) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI])]) ).
fof(i_0_921,plain,
! [X3827,X3828,X3829,X3830] :
( ( c_Orderings_Oord__class_Oless__eq(X3830,X3829,X3827)
| ~ c_Orderings_Oord__class_Oless__eq(X3830,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3830),X3829),X3828),X3827)
| ~ class_Lattices_Osemilattice__sup(X3830) )
& ( c_Orderings_Oord__class_Oless__eq(X3830,X3828,X3827)
| ~ c_Orderings_Oord__class_Oless__eq(X3830,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3830),X3829),X3828),X3827)
| ~ class_Lattices_Osemilattice__sup(X3830) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3830,X3829,X3827)
| ~ c_Orderings_Oord__class_Oless__eq(X3830,X3828,X3827)
| c_Orderings_Oord__class_Oless__eq(X3830,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3830),X3829),X3828),X3827)
| ~ class_Lattices_Osemilattice__sup(X3830) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__sup__iff])])]) ).
fof(i_0_922,plain,
! [X3281,X3282,X3283,X3284] :
( ( c_Orderings_Oord__class_Oless__eq(X3284,X3283,X3282)
| ~ c_Orderings_Oord__class_Oless__eq(X3284,X3283,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3284),X3282),X3281))
| ~ class_Lattices_Osemilattice__inf(X3284) )
& ( c_Orderings_Oord__class_Oless__eq(X3284,X3283,X3281)
| ~ c_Orderings_Oord__class_Oless__eq(X3284,X3283,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3284),X3282),X3281))
| ~ class_Lattices_Osemilattice__inf(X3284) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3284,X3283,X3282)
| ~ c_Orderings_Oord__class_Oless__eq(X3284,X3283,X3281)
| c_Orderings_Oord__class_Oless__eq(X3284,X3283,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3284),X3282),X3281))
| ~ class_Lattices_Osemilattice__inf(X3284) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).
fof(i_0_923,plain,
! [X3263,X3264,X3265,X3266] :
( ~ class_Lattices_Osemilattice__inf(X3266)
| ~ c_Orderings_Oord__class_Oless__eq(X3266,X3265,X3264)
| ~ c_Orderings_Oord__class_Oless__eq(X3266,X3265,X3263)
| c_Orderings_Oord__class_Oless__eq(X3266,X3265,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3266),X3264),X3263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).
fof(i_0_924,plain,
! [X3259,X3260,X3261,X3262] :
( ~ class_Lattices_Osemilattice__inf(X3262)
| ~ c_Orderings_Oord__class_Oless__eq(X3262,X3261,X3260)
| ~ c_Orderings_Oord__class_Oless__eq(X3262,X3261,X3259)
| c_Orderings_Oord__class_Oless__eq(X3262,X3261,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3262),X3260),X3259)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).
fof(i_0_925,plain,
! [X4122,X4123,X4124] :
( c_Set_Oinsert(X4124,X4123,c_Orderings_Obot__class_Obot(tc_fun(X4124,tc_HOL_Obool))) != c_Set_Oinsert(X4124,X4122,c_Orderings_Obot__class_Obot(tc_fun(X4124,tc_HOL_Obool)))
| X4123 = X4122 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])]) ).
fof(i_0_926,plain,
! [X3238,X3239,X3240] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3240,X3240),tc_HOL_Obool),X3239,X3238)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3240,tc_HOL_Obool),c_Wellfounded_Oacc(X3240,X3238),c_Wellfounded_Oacc(X3240,X3239)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).
fof(i_0_927,plain,
! [X4152,X4153] : ~ hBOOL(hAPP(hAPP(c_member(X4153),X4152),c_Orderings_Obot__class_Obot(tc_fun(X4153,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_581]) ).
fof(i_0_928,plain,
! [X4079,X4080] : ~ hBOOL(hAPP(hAPP(c_member(X4080),X4079),c_Orderings_Obot__class_Obot(tc_fun(X4080,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_582]) ).
fof(i_0_929,plain,
! [X3401,X3402,X3403] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3403,tc_fun(X3403,tc_HOL_Obool)),X3402,X3401)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3403,tc_HOL_Obool),c_Wellfounded_Oaccp(X3403,X3401),c_Wellfounded_Oaccp(X3403,X3402)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).
fof(i_0_930,plain,
! [X3092,X3093,X3094,X3095] : c_Set_Oinsert(X3095,X3094,c_Set_Oinsert(X3095,X3093,X3092)) = c_Set_Oinsert(X3095,X3093,c_Set_Oinsert(X3095,X3094,X3092)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_931,plain,
! [X3228,X3229,X3230,X3231] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3231,tc_HOL_Obool),X3230,X3229)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3231,tc_HOL_Obool),X3229,X3228)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3231,tc_HOL_Obool),X3230,X3228) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_932,plain,
! [X3021,X3022,X3023] : hBOOL(hAPP(hAPP(c_member(X3023),X3022),c_Set_Oinsert(X3023,X3022,X3021))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_933,plain,
! [X3990,X3991,X3992,X3993] :
( ~ class_Lattices_Osemilattice__sup(X3993)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3993),X3992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3993),X3991),X3990)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3993),X3991),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3993),X3992),X3990)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__commute])]) ).
fof(i_0_934,plain,
! [X3982,X3983,X3984,X3985] :
( ~ class_Lattices_Osemilattice__sup(X3985)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3985),X3984),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3985),X3983),X3982)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3985),X3983),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3985),X3984),X3982)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute])]) ).
fof(i_0_935,plain,
! [X3986,X3987,X3988,X3989] :
( ~ class_Lattices_Olattice(X3989)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3989),X3988),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3989),X3987),X3986)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3989),X3987),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3989),X3988),X3986)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J])]) ).
fof(i_0_936,plain,
! [X2713,X2714,X2715,X2716] :
( ~ class_Lattices_Osemilattice__inf(X2716)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2716),X2715),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2716),X2714),X2713)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2716),X2714),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2716),X2715),X2713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).
fof(i_0_937,plain,
! [X2705,X2706,X2707,X2708] :
( ~ class_Lattices_Osemilattice__inf(X2708)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2708),X2707),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2708),X2706),X2705)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2708),X2706),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2708),X2707),X2705)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).
fof(i_0_938,plain,
! [X2709,X2710,X2711,X2712] :
( ~ class_Lattices_Olattice(X2712)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2712),X2711),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2712),X2710),X2709)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2712),X2710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2712),X2711),X2709)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).
fof(i_0_939,plain,
! [X3009,X3010,X3011,X3012] :
( ~ hBOOL(hAPP(hAPP(X3012,X3011),X3010))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X3009,X3012),X3011),X3010)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclp_Or__into__trancl])]) ).
fof(i_0_940,plain,
! [X3858,X3859,X3860,X3861] :
( ( c_Orderings_Oord__class_Oless__eq(X3861,X3860,X3858)
| ~ c_Orderings_Oord__class_Oless__eq(X3861,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3861),X3860),X3859),X3858)
| ~ class_Lattices_Osemilattice__sup(X3861) )
& ( c_Orderings_Oord__class_Oless__eq(X3861,X3859,X3858)
| ~ c_Orderings_Oord__class_Oless__eq(X3861,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3861),X3860),X3859),X3858)
| ~ class_Lattices_Osemilattice__sup(X3861) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_583])])]) ).
fof(i_0_941,plain,
! [X3250,X3251,X3252,X3253] :
( ( c_Orderings_Oord__class_Oless__eq(X3253,X3252,X3251)
| ~ c_Orderings_Oord__class_Oless__eq(X3253,X3252,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3253),X3251),X3250))
| ~ class_Lattices_Osemilattice__inf(X3253) )
& ( c_Orderings_Oord__class_Oless__eq(X3253,X3252,X3250)
| ~ c_Orderings_Oord__class_Oless__eq(X3253,X3252,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3253),X3251),X3250))
| ~ class_Lattices_Osemilattice__inf(X3253) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_584])])]) ).
fof(i_0_942,plain,
! [X3181,X3182,X3183,X3184] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3184,tc_HOL_Obool),X3183,X3182)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3184,tc_HOL_Obool),X3183,c_Set_Oinsert(X3184,X3181,X3182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_943,plain,
! [X3794,X3795,X3796] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3796,tc_HOL_Obool),X3795,X3794)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3796,tc_HOL_Obool)),X3795),X3794) = X3794 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3796,tc_HOL_Obool)),X3795),X3794) != X3794
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3796,tc_HOL_Obool),X3795,X3794) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])]) ).
fof(i_0_944,plain,
! [X4087,X4088,X4089] :
( ( X4088 = c_Orderings_Obot__class_Obot(tc_fun(X4089,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4089,tc_HOL_Obool)),X4088),X4087) != c_Orderings_Obot__class_Obot(tc_fun(X4089,tc_HOL_Obool)) )
& ( X4087 = c_Orderings_Obot__class_Obot(tc_fun(X4089,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4089,tc_HOL_Obool)),X4088),X4087) != c_Orderings_Obot__class_Obot(tc_fun(X4089,tc_HOL_Obool)) )
& ( X4088 != c_Orderings_Obot__class_Obot(tc_fun(X4089,tc_HOL_Obool))
| X4087 != c_Orderings_Obot__class_Obot(tc_fun(X4089,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4089,tc_HOL_Obool)),X4088),X4087) = c_Orderings_Obot__class_Obot(tc_fun(X4089,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])]) ).
fof(i_0_945,plain,
! [X3661,X3662,X3663,X3664,X3665,X3666] :
( ( X3664 = X3662
| hAPP(hAPP(c_Product__Type_OPair(X3666,X3665),X3664),X3663) != hAPP(hAPP(c_Product__Type_OPair(X3666,X3665),X3662),X3661) )
& ( X3663 = X3661
| hAPP(hAPP(c_Product__Type_OPair(X3666,X3665),X3664),X3663) != hAPP(hAPP(c_Product__Type_OPair(X3666,X3665),X3662),X3661) )
& ( X3664 != X3662
| X3663 != X3661
| hAPP(hAPP(c_Product__Type_OPair(X3666,X3665),X3664),X3663) = hAPP(hAPP(c_Product__Type_OPair(X3666,X3665),X3662),X3661) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).
fof(i_0_946,plain,
! [X3655,X3656,X3657,X3658,X3659,X3660] :
( ( X3658 = X3656
| hAPP(hAPP(c_Product__Type_OPair(X3660,X3659),X3658),X3657) != hAPP(hAPP(c_Product__Type_OPair(X3660,X3659),X3656),X3655) )
& ( X3657 = X3655
| hAPP(hAPP(c_Product__Type_OPair(X3660,X3659),X3658),X3657) != hAPP(hAPP(c_Product__Type_OPair(X3660,X3659),X3656),X3655) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).
fof(i_0_947,plain,
! [X3918,X3919,X3920] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3920,tc_HOL_Obool)),X3919),X3918) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3920,tc_HOL_Obool)),X3918),X3919),
inference(variable_rename,[status(thm)],[fact_Un__commute]) ).
fof(i_0_948,plain,
! [X2606,X2607,X2608] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2608,tc_HOL_Obool)),X2607),X2606) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2608,tc_HOL_Obool)),X2606),X2607),
inference(variable_rename,[status(thm)],[fact_Int__commute]) ).
fof(i_0_949,plain,
! [X4125,X4126] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4126,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4126,tc_HOL_Obool))),X4125) = c_Orderings_Obot__class_Obot(tc_fun(X4126,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Int__empty__left]) ).
fof(i_0_950,plain,
! [X3797,X3798,X3799] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3799,tc_HOL_Obool),X3798,X3797)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3799,tc_HOL_Obool)),X3798),X3797) = X3797 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb1])]) ).
fof(i_0_951,plain,
! [X3800,X3801,X3802] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3802,tc_HOL_Obool),X3801,X3800)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3802,tc_HOL_Obool)),X3800),X3801) = X3800 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])]) ).
fof(i_0_952,plain,
! [X3200,X3201,X3202] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3202,tc_HOL_Obool),X3201,X3200)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3202,tc_HOL_Obool)),X3201),X3200) = X3201 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).
fof(i_0_953,plain,
! [X3197,X3198,X3199] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3199,tc_HOL_Obool),X3198,X3197)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3199,tc_HOL_Obool)),X3197),X3198) = X3198 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).
fof(i_0_954,plain,
! [X4181] : c_Relation_Orefl__on(X4181,c_Orderings_Obot__class_Obot(tc_fun(X4181,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4181,X4181),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_refl__on__empty]) ).
fof(i_0_955,plain,
! [X3277,X3278,X3279,X3280] :
( ~ class_Lattices_Osemilattice__inf(X3280)
| ~ c_Orderings_Oord__class_Oless__eq(X3280,X3279,X3278)
| c_Orderings_Oord__class_Oless__eq(X3280,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3280),X3279),X3277),X3278) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).
fof(i_0_956,plain,
! [X3273,X3274,X3275,X3276] :
( ~ class_Lattices_Osemilattice__inf(X3276)
| ~ c_Orderings_Oord__class_Oless__eq(X3276,X3275,X3274)
| c_Orderings_Oord__class_Oless__eq(X3276,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3276),X3273),X3275),X3274) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).
fof(i_0_957,plain,
! [X3831,X3832,X3833,X3834] :
( ~ class_Lattices_Osemilattice__sup(X3834)
| ~ c_Orderings_Oord__class_Oless__eq(X3834,X3833,X3832)
| c_Orderings_Oord__class_Oless__eq(X3834,X3833,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3834),X3832),X3831)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI1])]) ).
fof(i_0_958,plain,
! [X3835,X3836,X3837,X3838] :
( ~ class_Lattices_Osemilattice__sup(X3838)
| ~ c_Orderings_Oord__class_Oless__eq(X3838,X3837,X3836)
| c_Orderings_Oord__class_Oless__eq(X3838,X3837,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3838),X3835),X3836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI2])]) ).
fof(i_0_959,plain,
! [X4139] : c_Transitive__Closure_Otrancl(X4139,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4139,X4139),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4139,X4139),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_trancl__empty]) ).
fof(i_0_960,plain,
! [X4083,X4084] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4084,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4084,tc_HOL_Obool))),X4083) = X4083,
inference(variable_rename,[status(thm)],[fact_Un__empty__left]) ).
fof(i_0_961,plain,
! [X3219,X3220,X3221] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3219,tc_HOL_Obool),X3221,X3220)
| X3221 != X3220 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3219,tc_HOL_Obool),X3220,X3221)
| X3221 != X3220 )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3219,tc_HOL_Obool),X3221,X3220)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3219,tc_HOL_Obool),X3220,X3221)
| X3221 = X3220 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_962,plain,
! [X3162,X3163,X3164] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3164,tc_HOL_Obool),X3163,X3162)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3164,tc_HOL_Obool),X3162,X3163)
| X3163 = X3162 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_963,plain,
! [X2297,X2298,X2299] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2299),X2298),hAPP(c_fequal,X2297)))
| X2298 = X2297 )
& ( X2298 != X2297
| hBOOL(hAPP(hAPP(c_member(X2299),X2298),hAPP(c_fequal,X2297))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_964,plain,
! [X3505,X3506,X3507,X3508,X3509] :
( ~ class_Orderings_Oord(X3509)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3508,X3509),X3507,X3506)
| c_Orderings_Oord__class_Oless__eq(X3509,hAPP(X3507,X3505),hAPP(X3506,X3505)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_965,plain,
! [X3396,X3397,X3398,X3399,X3400] :
( ~ class_Orderings_Oord(X3400)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3399,X3400),X3398,X3397)
| c_Orderings_Oord__class_Oless__eq(X3400,hAPP(X3398,X3396),hAPP(X3397,X3396)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_966,plain,
! [X3235,X3236,X3237] :
( ~ c_Wellfounded_Owf(X3237,X3236)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3237,X3237),tc_HOL_Obool),X3235,X3236)
| c_Wellfounded_Owf(X3237,X3235) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__subset])]) ).
fof(i_0_967,plain,
! [X3331,X3332,X3333] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3333,X3333),tc_HOL_Obool),X3332,X3331)
| ~ c_Relation_Oantisym(X3333,X3331)
| c_Relation_Oantisym(X3333,X3332) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__subset])]) ).
fof(i_0_968,plain,
! [X3334,X3335,X3336] :
( ~ c_Wellfounded_Oacyclic(X3336,X3335)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3336,X3336),tc_HOL_Obool),X3334,X3335)
| c_Wellfounded_Oacyclic(X3336,X3334) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__subset])]) ).
fof(i_0_969,plain,
! [X4146,X4147,X4148,X4149,X4150] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X4147),X4148),X4146))
| X4146 != c_Orderings_Obot__class_Obot(tc_fun(X4147,tc_HOL_Obool)) )
& ( X4149 = c_Orderings_Obot__class_Obot(tc_fun(X4150,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X4150),esk112_2(X4149,X4150)),X4149)) ) ),
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_970,plain,
! [X4140,X4141,X4143,X4144,X4145] :
( ( hBOOL(hAPP(hAPP(c_member(X4141),esk111_2(X4140,X4141)),X4140))
| X4140 = c_Orderings_Obot__class_Obot(tc_fun(X4141,tc_HOL_Obool)) )
& ( X4143 != c_Orderings_Obot__class_Obot(tc_fun(X4144,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X4144),X4145),X4143)) ) ),
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_585])])])])]) ).
fof(i_0_971,plain,
! [X4176,X4177] : c_Relation_ORange(X4177,X4176,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4177,X4176),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X4176,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Range__empty]) ).
fof(i_0_972,plain,
! [X4157,X4158] : c_Relation_ODomain(X4158,X4157,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4158,X4157),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X4158,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Domain__empty]) ).
fof(i_0_973,plain,
! [X3597,X3598,X3599] :
( ~ c_Wellfounded_OwfP(X3599,X3598)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3599,tc_fun(X3599,tc_HOL_Obool)),X3597,X3598)
| c_Wellfounded_OwfP(X3599,X3597) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__subset])]) ).
fof(i_0_974,plain,
! [X3439,X3440,X3441,X3442] :
( ~ class_Orderings_Opreorder(X3442)
| ~ c_Orderings_Oord__class_Oless__eq(X3442,X3441,X3440)
| ~ c_Orderings_Oord__class_Oless__eq(X3442,X3440,X3439)
| c_Orderings_Oord__class_Oless__eq(X3442,X3441,X3439) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_975,plain,
! [X3446,X3447,X3448,X3449] :
( ~ class_Orderings_Oorder(X3449)
| ~ c_Orderings_Oord__class_Oless__eq(X3449,X3448,X3447)
| ~ c_Orderings_Oord__class_Oless__eq(X3449,X3446,X3448)
| c_Orderings_Oord__class_Oless__eq(X3449,X3446,X3447) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_976,plain,
! [X3586,X3587,X3588,X3589,X3590] :
( ( ~ c_Wellfounded_OwfP(X3587,X3586)
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3587,X3586),X3588)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X3590,X3589),esk88_2(X3589,X3590)))
| c_Wellfounded_OwfP(X3590,X3589) ) ),
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_wfP__accp__iff])])])])]) ).
fof(i_0_977,plain,
! [X3036,X3037,X3038] :
( ~ hBOOL(hAPP(hAPP(c_member(X3038),X3037),X3036))
| c_Set_Oinsert(X3038,X3037,X3036) = X3036 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_978,plain,
! [X4127,X4128] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4128,tc_HOL_Obool)),X4127),c_Orderings_Obot__class_Obot(tc_fun(X4128,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X4128,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Int__empty__right]) ).
fof(i_0_979,plain,
! [X3096,X3097,X3098] : c_Set_Oinsert(X3098,X3097,c_Set_Oinsert(X3098,X3097,X3096)) = c_Set_Oinsert(X3098,X3097,X3096),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
fof(i_0_980,plain,
! [X3979,X3980,X3981] :
( ~ class_Lattices_Osemilattice__sup(X3981)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3981),X3980),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3981),X3980),X3979)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3981),X3980),X3979) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__idem])]) ).
fof(i_0_981,plain,
! [X3973,X3974,X3975] :
( ~ class_Lattices_Osemilattice__sup(X3975)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3975),X3974),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3975),X3974),X3973)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3975),X3974),X3973) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem])]) ).
fof(i_0_982,plain,
! [X3976,X3977,X3978] :
( ~ class_Lattices_Olattice(X3978)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3978),X3977),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3978),X3977),X3976)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3978),X3977),X3976) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])]) ).
fof(i_0_983,plain,
! [X2723,X2724,X2725] :
( ~ class_Lattices_Osemilattice__inf(X2725)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2725),X2724),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2725),X2724),X2723)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2725),X2724),X2723) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).
fof(i_0_984,plain,
! [X2717,X2718,X2719] :
( ~ class_Lattices_Osemilattice__inf(X2719)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2719),X2718),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2719),X2718),X2717)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2719),X2718),X2717) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).
fof(i_0_985,plain,
! [X2720,X2721,X2722] :
( ~ class_Lattices_Olattice(X2722)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2722),X2721),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2722),X2721),X2720)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2722),X2721),X2720) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).
fof(i_0_986,plain,
! [X4154,X4155,X4156] :
( X4156 != c_Orderings_Obot__class_Obot(tc_fun(X4155,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X4155),X4154),X4156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_586])]) ).
fof(i_0_987,plain,
! [X4178,X4179,X4180] :
( ( c_Relation_ORange(X4180,X4179,X4178) != c_Orderings_Obot__class_Obot(tc_fun(X4179,tc_HOL_Obool))
| X4178 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4180,X4179),tc_HOL_Obool)) )
& ( X4178 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4180,X4179),tc_HOL_Obool))
| c_Relation_ORange(X4180,X4179,X4178) = c_Orderings_Obot__class_Obot(tc_fun(X4179,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])]) ).
fof(i_0_988,plain,
! [X4159,X4160,X4161] :
( ( c_Relation_ODomain(X4161,X4160,X4159) != c_Orderings_Obot__class_Obot(tc_fun(X4161,tc_HOL_Obool))
| X4159 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4161,X4160),tc_HOL_Obool)) )
& ( X4159 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4161,X4160),tc_HOL_Obool))
| c_Relation_ODomain(X4161,X4160,X4159) = c_Orderings_Obot__class_Obot(tc_fun(X4161,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])]) ).
fof(i_0_989,plain,
! [X3213,X3214,X3215,X3216] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3216,tc_HOL_Obool),X3215,X3214)
| ~ hBOOL(hAPP(X3215,X3213))
| hBOOL(hAPP(X3214,X3213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_990,plain,
! [X3209,X3210,X3211,X3212] :
( ~ hBOOL(hAPP(X3212,X3211))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3210,tc_HOL_Obool),X3212,X3209)
| hBOOL(hAPP(X3209,X3211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_991,plain,
! [X2146,X2147,X2148] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2148),X2147),X2146))
| hBOOL(hAPP(X2146,X2147)) )
& ( ~ hBOOL(hAPP(X2146,X2147))
| hBOOL(hAPP(hAPP(c_member(X2148),X2147),X2146)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_992,plain,
! [X4085,X4086] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4086,tc_HOL_Obool)),X4085),c_Orderings_Obot__class_Obot(tc_fun(X4086,tc_HOL_Obool))) = X4085,
inference(variable_rename,[status(thm)],[fact_Un__empty__right]) ).
fof(i_0_993,plain,
! [X3185,X3186,X3187] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3187,tc_HOL_Obool),X3186,c_Set_Oinsert(X3187,X3185,X3186)),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_994,plain,
! [X3443,X3444,X3445] :
( ~ class_Orderings_Oorder(X3445)
| ~ c_Orderings_Oord__class_Oless__eq(X3445,X3444,X3443)
| ~ c_Orderings_Oord__class_Oless__eq(X3445,X3443,X3444)
| X3443 = X3444 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_995,plain,
! [X3436,X3437,X3438] :
( ~ class_Orderings_Oorder(X3438)
| ~ c_Orderings_Oord__class_Oless__eq(X3438,X3437,X3436)
| ~ c_Orderings_Oord__class_Oless__eq(X3438,X3436,X3437)
| X3437 = X3436 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_996,plain,
! [X3417,X3418,X3419] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3419,X3417,X3418)
| X3417 = X3418
| ~ c_Orderings_Oord__class_Oless__eq(X3419,X3418,X3417)
| ~ class_Orderings_Oorder(X3419) )
& ( X3417 != X3418
| c_Orderings_Oord__class_Oless__eq(X3419,X3417,X3418)
| ~ c_Orderings_Oord__class_Oless__eq(X3419,X3418,X3417)
| ~ class_Orderings_Oorder(X3419) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_997,plain,
! [X3411,X3412,X3413] :
( ( c_Orderings_Oord__class_Oless__eq(X3413,X3412,X3411)
| X3412 != X3411
| ~ class_Orderings_Oorder(X3413) )
& ( c_Orderings_Oord__class_Oless__eq(X3413,X3411,X3412)
| X3412 != X3411
| ~ class_Orderings_Oorder(X3413) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3413,X3412,X3411)
| ~ c_Orderings_Oord__class_Oless__eq(X3413,X3411,X3412)
| X3412 = X3411
| ~ class_Orderings_Oorder(X3413) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_998,plain,
! [X3372,X3373,X3374] :
( ~ c_Wellfounded_Owf(X3374,X3373)
| hBOOL(hAPP(hAPP(c_member(X3374),X3372),c_Wellfounded_Oacc(X3374,X3373))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__wfD])]) ).
fof(i_0_999,plain,
! [X4078] : c_Wellfounded_Owf(X4078,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4078,X4078),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_wf__empty]) ).
fof(i_0_1000,plain,
! [X4190] : c_Relation_Oantisym(X4190,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4190,X4190),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_antisym__empty]) ).
fof(i_0_1001,plain,
! [X3294,X3295,X3296] :
( ~ class_Lattices_Osemilattice__inf(X3296)
| c_Orderings_Oord__class_Oless__eq(X3296,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3296),X3295),X3294),X3295) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).
fof(i_0_1002,plain,
! [X3297,X3298,X3299] :
( ~ class_Lattices_Olattice(X3299)
| c_Orderings_Oord__class_Oless__eq(X3299,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3299),X3298),X3297),X3298) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).
fof(i_0_1003,plain,
! [X3288,X3289,X3290] :
( ~ class_Lattices_Osemilattice__inf(X3290)
| c_Orderings_Oord__class_Oless__eq(X3290,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3290),X3289),X3288),X3288) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).
fof(i_0_1004,plain,
! [X3291,X3292,X3293] :
( ~ class_Lattices_Olattice(X3293)
| c_Orderings_Oord__class_Oless__eq(X3293,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3293),X3292),X3291),X3291) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).
fof(i_0_1005,plain,
! [X3815,X3816,X3817] :
( ~ class_Lattices_Osemilattice__sup(X3817)
| c_Orderings_Oord__class_Oless__eq(X3817,X3816,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3817),X3816),X3815)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge1])]) ).
fof(i_0_1006,plain,
! [X3812,X3813,X3814] :
( ~ class_Lattices_Olattice(X3814)
| c_Orderings_Oord__class_Oless__eq(X3814,X3813,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3814),X3813),X3812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J])]) ).
fof(i_0_1007,plain,
! [X3821,X3822,X3823] :
( ~ class_Lattices_Osemilattice__sup(X3823)
| c_Orderings_Oord__class_Oless__eq(X3823,X3822,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3823),X3821),X3822)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge2])]) ).
fof(i_0_1008,plain,
! [X3818,X3819,X3820] :
( ~ class_Lattices_Olattice(X3820)
| c_Orderings_Oord__class_Oless__eq(X3820,X3819,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3820),X3818),X3819)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J])]) ).
fof(i_0_1009,plain,
! [X3898,X3899,X3900] :
( ~ class_Lattices_Olattice(X3900)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3900),X3899),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3900),X3899),X3898)) = X3899 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb])]) ).
fof(i_0_1010,plain,
! [X3901,X3902,X3903] :
( ~ class_Lattices_Olattice(X3903)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3903),X3902),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3903),X3902),X3901)) = X3902 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb])]) ).
fof(i_0_1011,plain,
! [X3839,X3840,X3841] :
( ~ class_Lattices_Osemilattice__sup(X3841)
| ~ c_Orderings_Oord__class_Oless__eq(X3841,X3840,X3839)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3841),X3840),X3839) = X3839 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb2])]) ).
fof(i_0_1012,plain,
! [X3824,X3825,X3826] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3826,X3825,X3824)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3826),X3825),X3824) = X3824
| ~ class_Lattices_Osemilattice__sup(X3826) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3826),X3825),X3824) != X3824
| c_Orderings_Oord__class_Oless__eq(X3826,X3825,X3824)
| ~ class_Lattices_Osemilattice__sup(X3826) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__sup])])]) ).
fof(i_0_1013,plain,
! [X3842,X3843,X3844] :
( ~ class_Lattices_Osemilattice__sup(X3844)
| ~ c_Orderings_Oord__class_Oless__eq(X3844,X3843,X3842)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3844),X3842),X3843) = X3842 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb1])]) ).
fof(i_0_1014,plain,
! [X3285,X3286,X3287] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3287,X3286,X3285)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3287),X3286),X3285) = X3286
| ~ class_Lattices_Osemilattice__inf(X3287) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3287),X3286),X3285) != X3286
| c_Orderings_Oord__class_Oless__eq(X3287,X3286,X3285)
| ~ class_Lattices_Osemilattice__inf(X3287) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).
fof(i_0_1015,plain,
! [X3270,X3271,X3272] :
( ~ class_Lattices_Osemilattice__inf(X3272)
| ~ c_Orderings_Oord__class_Oless__eq(X3272,X3271,X3270)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3272),X3271),X3270) = X3271 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).
fof(i_0_1016,plain,
! [X3267,X3268,X3269] :
( ~ class_Lattices_Osemilattice__inf(X3269)
| ~ c_Orderings_Oord__class_Oless__eq(X3269,X3268,X3267)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3269),X3267),X3268) = X3268 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).
fof(i_0_1017,plain,
! [X4175] : c_Relation_OId__on(X4175,c_Orderings_Obot__class_Obot(tc_fun(X4175,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4175,X4175),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Id__on__empty]) ).
fof(i_0_1018,plain,
! [X3916,X3917] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3917,tc_HOL_Obool)),X3916),X3916) = X3916,
inference(variable_rename,[status(thm)],[fact_Un__absorb]) ).
fof(i_0_1019,plain,
! [X2609,X2610] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2610,tc_HOL_Obool)),X2609),X2609) = X2609,
inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).
fof(i_0_1020,plain,
! [X3600,X3601] :
( ~ c_Wellfounded_Owf(X3601,X3600)
| c_Wellfounded_OwfP(X3601,c_FunDef_Oin__rel(X3601,X3601,X3600)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__in__rel])]) ).
fof(i_0_1021,plain,
! [X3560,X3561,X3562] :
( ~ c_Wellfounded_Owf(X3562,X3561)
| c_Wellfounded_Owf(X3562,c_Wellfounded_Omlex__prod(X3562,X3560,X3561)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__mlex])]) ).
fof(i_0_1022,plain,
! [X2908,X2909] : c_Relation_ORange(X2909,X2909,c_Transitive__Closure_Otrancl(X2909,X2908)) = c_Relation_ORange(X2909,X2909,X2908),
inference(variable_rename,[status(thm)],[fact_trancl__range]) ).
fof(i_0_1023,plain,
! [X2906,X2907] : c_Relation_ODomain(X2907,X2907,c_Transitive__Closure_Otrancl(X2907,X2906)) = c_Relation_ODomain(X2907,X2907,X2906),
inference(variable_rename,[status(thm)],[fact_trancl__domain]) ).
fof(i_0_1024,plain,
! [X4081,X4082] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4082,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X4082,tc_HOL_Obool)),X4081),
inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).
fof(i_0_1025,plain,
! [X4111,X4112,X4113] : c_Orderings_Obot__class_Obot(tc_fun(X4113,tc_HOL_Obool)) != c_Set_Oinsert(X4113,X4112,X4111),
inference(variable_rename,[status(thm)],[fact_empty__not__insert]) ).
fof(i_0_1026,plain,
! [X4114,X4115,X4116] : c_Set_Oinsert(X4116,X4115,X4114) != c_Orderings_Obot__class_Obot(tc_fun(X4116,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_insert__not__empty]) ).
fof(i_0_1027,plain,
! [X2088,X2089] :
( hAPP(X2089,esk1_2(X2088,X2089)) != hAPP(X2088,esk1_2(X2088,X2089))
| X2089 = X2088 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_1028,plain,
! [X4247,X4248] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4248),X4247))
| hBOOL(X4248) ),
inference(variable_rename,[status(thm)],[i_0_587]) ).
fof(i_0_1029,plain,
! [X4249,X4250] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4250),X4249))
| hBOOL(X4249) ),
inference(variable_rename,[status(thm)],[i_0_588]) ).
fof(i_0_1030,plain,
! [X4241,X4242] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X4242),X4241))
| X4242 = X4241 ),
inference(variable_rename,[status(thm)],[i_0_589]) ).
fof(i_0_1031,plain,
! [X4219,X4220,X4221,X4222] : hAPP(c_COMBK(X4222,X4221,X4220),X4219) = X4220,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_1032,plain,
! [X3450,X3451,X3452] :
( ~ class_Orderings_Olinorder(X3452)
| c_Orderings_Oord__class_Oless__eq(X3452,X3451,X3450)
| c_Orderings_Oord__class_Oless__eq(X3452,X3450,X3451) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_590])]) ).
fof(i_0_1033,plain,
! [X3408,X3409,X3410] :
( ~ class_Orderings_Olinorder(X3410)
| c_Orderings_Oord__class_Oless__eq(X3410,X3409,X3408)
| c_Orderings_Oord__class_Oless__eq(X3410,X3408,X3409) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_1034,plain,
! [X3970,X3971,X3972] :
( ~ class_Lattices_Osemilattice__sup(X3972)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3972),X3971),X3970) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3972),X3970),X3971) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__commute])]) ).
fof(i_0_1035,plain,
! [X3964,X3965,X3966] :
( ~ class_Lattices_Osemilattice__sup(X3966)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3966),X3965),X3964) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3966),X3964),X3965) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Ocommute])]) ).
fof(i_0_1036,plain,
! [X3967,X3968,X3969] :
( ~ class_Lattices_Olattice(X3969)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3969),X3968),X3967) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3969),X3967),X3968) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J])]) ).
fof(i_0_1037,plain,
! [X2732,X2733,X2734] :
( ~ class_Lattices_Osemilattice__inf(X2734)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2734),X2733),X2732) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2734),X2732),X2733) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).
fof(i_0_1038,plain,
! [X2726,X2727,X2728] :
( ~ class_Lattices_Osemilattice__inf(X2728)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2728),X2727),X2726) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2728),X2726),X2727) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).
fof(i_0_1039,plain,
! [X2729,X2730,X2731] :
( ~ class_Lattices_Olattice(X2731)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2731),X2730),X2729) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2731),X2729),X2730) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).
fof(i_0_1040,plain,
! [X4186,X4187] : c_Relation_Ototal__on(X4187,c_Orderings_Obot__class_Obot(tc_fun(X4187,tc_HOL_Obool)),X4186),
inference(variable_rename,[status(thm)],[fact_total__on__empty]) ).
fof(i_0_1041,plain,
! [X3592,X3593,X3594] :
( ~ c_Wellfounded_OwfP(X3594,X3593)
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3594,X3593),X3592)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__wfPD])]) ).
fof(i_0_1042,plain,
! [X4094,X4095,X4096] :
( ( X4095 = c_Orderings_Obot__class_Obot(X4096)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4096),X4095),X4094) != c_Orderings_Obot__class_Obot(X4096)
| ~ class_Lattices_Obounded__lattice__bot(X4096) )
& ( X4094 = c_Orderings_Obot__class_Obot(X4096)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4096),X4095),X4094) != c_Orderings_Obot__class_Obot(X4096)
| ~ class_Lattices_Obounded__lattice__bot(X4096) )
& ( X4095 != c_Orderings_Obot__class_Obot(X4096)
| X4094 != c_Orderings_Obot__class_Obot(X4096)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4096),X4095),X4094) = c_Orderings_Obot__class_Obot(X4096)
| ~ class_Lattices_Obounded__lattice__bot(X4096) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff])])]) ).
fof(i_0_1043,plain,
! [X4245,X4246] :
( ~ hBOOL(X4246)
| ~ hBOOL(X4245)
| hBOOL(hAPP(hAPP(c_fconj,X4246),X4245)) ),
inference(variable_rename,[status(thm)],[i_0_591]) ).
fof(i_0_1044,plain,
! [X4194,X4195,X4196] :
( ~ class_Orderings_Obot(X4196)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4195,X4196)),X4194) = c_Orderings_Obot__class_Obot(X4196) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).
fof(i_0_1045,plain,
! [X4191,X4192,X4193] :
( ~ class_Orderings_Obot(X4193)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4192,X4193)),X4191) = c_Orderings_Obot__class_Obot(X4193) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).
fof(i_0_1046,plain,
! [X2800,X2801] : c_Relation_ORange(X2801,X2801,c_Relation_OId__on(X2801,X2800)) = X2800,
inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).
fof(i_0_1047,plain,
! [X2802,X2803] : c_Relation_ODomain(X2803,X2803,c_Relation_OId__on(X2803,X2802)) = X2802,
inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).
fof(i_0_1048,plain,
! [X3232,X3233,X3234] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3232,tc_HOL_Obool),X3234,X3233)
| X3234 != X3233 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3232,tc_HOL_Obool),X3233,X3234)
| X3234 != X3233 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_592])])]) ).
fof(i_0_1049,plain,
! [X3222,X3223,X3224] :
( X3224 != X3223
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3222,tc_HOL_Obool),X3224,X3223) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_1050,plain,
! [X3225,X3226,X3227] :
( X3227 != X3226
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3225,tc_HOL_Obool),X3226,X3227) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_1051,plain,
! [X2910,X2911] : c_Relation_Orefl__on(X2911,X2910,c_Relation_OId__on(X2911,X2910)),
inference(variable_rename,[status(thm)],[fact_refl__on__Id__on]) ).
fof(i_0_1052,plain,
! [X2804,X2805] : c_Relation_Osingle__valued(X2805,X2805,c_Relation_OId__on(X2805,X2804)),
inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).
fof(i_0_1053,plain,
! [X4243,X4244] :
( X4244 != X4243
| hBOOL(hAPP(hAPP(c_fequal,X4244),X4243)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1054,plain,
! [X3217,X3218] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3218,tc_HOL_Obool),X3217,X3217),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_1055,plain,
! [X4184,X4185] :
( ~ class_Lattices_Obounded__lattice__bot(X4185)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4185),c_Orderings_Obot__class_Obot(X4185)),X4184) = c_Orderings_Obot__class_Obot(X4185) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])]) ).
fof(i_0_1056,plain,
! [X4090,X4091] :
( ~ class_Lattices_Obounded__lattice__bot(X4091)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4091),c_Orderings_Obot__class_Obot(X4091)),X4090) = X4090 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__left])]) ).
fof(i_0_1057,plain,
! [X4182,X4183] :
( ~ class_Lattices_Obounded__lattice__bot(X4183)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4183),X4182),c_Orderings_Obot__class_Obot(X4183)) = c_Orderings_Obot__class_Obot(X4183) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__right])]) ).
fof(i_0_1058,plain,
! [X4092,X4093] :
( ~ class_Lattices_Obounded__lattice__bot(X4093)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4093),X4092),c_Orderings_Obot__class_Obot(X4093)) = X4092 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__right])]) ).
fof(i_0_1059,plain,
! [X3414,X3415,X3416] :
( ~ class_Orderings_Opreorder(X3416)
| X3415 != X3414
| c_Orderings_Oord__class_Oless__eq(X3416,X3415,X3414) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1060,plain,
! [X3595,X3596] :
( ~ c_Wellfounded_OwfP(X3596,X3595)
| c_Wellfounded_OwfP(X3596,c_Transitive__Closure_Otranclp(X3596,X3595)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__trancl])]) ).
fof(i_0_1061,plain,
! [X3312,X3313] :
( ~ c_Wellfounded_Owf(X3313,X3312)
| c_Wellfounded_Owf(X3313,c_Transitive__Closure_Otrancl(X3313,X3312)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__trancl])]) ).
fof(i_0_1062,plain,
! [X3007,X3008] :
( ~ c_Wellfounded_Oacyclic(X3008,X3007)
| c_Relation_Oantisym(X3008,c_Transitive__Closure_Ortrancl(X3008,X3007)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__impl__antisym__rtrancl])]) ).
fof(i_0_1063,plain,
! [X3392,X3393] :
( ~ class_Orderings_Opreorder(X3393)
| c_Orderings_Oord__class_Oless__eq(X3393,X3392,X3392) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1064,plain,
! [X3962,X3963] :
( ~ class_Lattices_Osemilattice__sup(X3963)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3963),X3962),X3962) = X3962 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__idem])]) ).
fof(i_0_1065,plain,
! [X3960,X3961] :
( ~ class_Lattices_Osemilattice__sup(X3961)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3961),X3960),X3960) = X3960 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oidem])]) ).
fof(i_0_1066,plain,
! [X2737,X2738] :
( ~ class_Lattices_Osemilattice__inf(X2738)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2738),X2737),X2737) = X2737 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).
fof(i_0_1067,plain,
! [X2735,X2736] :
( ~ class_Lattices_Osemilattice__inf(X2736)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2736),X2735),X2735) = X2735 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).
fof(i_0_1068,plain,
! [X2904,X2905] : c_Transitive__Closure_Otrancl(X2905,c_Transitive__Closure_Ortrancl(X2905,X2904)) = c_Transitive__Closure_Ortrancl(X2905,X2904),
inference(variable_rename,[status(thm)],[fact_rtrancl__trancl__absorb]) ).
fof(i_0_1069,plain,
! [X2902,X2903] : c_Transitive__Closure_Ortrancl(X2903,c_Transitive__Closure_Otrancl(X2903,X2902)) = c_Transitive__Closure_Ortrancl(X2903,X2902),
inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb]) ).
fof(i_0_1070,plain,
! [X2519,X2520] : c_Transitive__Closure_Ortrancl(X2520,c_Transitive__Closure_Ortrancl(X2520,X2519)) = c_Transitive__Closure_Ortrancl(X2520,X2519),
inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).
fof(i_0_1071,plain,
! [X3394,X3395] : c_Wellfounded_Owf(X3395,c_Wellfounded_Omeasure(X3395,X3394)),
inference(variable_rename,[status(thm)],[fact_wf__measure]) ).
fof(i_0_1072,plain,
! [X3123,X3124] : c_Relation_Oantisym(X3124,c_Relation_OId__on(X3124,X3123)),
inference(variable_rename,[status(thm)],[fact_antisym__Id__on]) ).
fof(i_0_1073,plain,
! [X3568,X3569] : c_HOL_OThe(X3569,hAPP(c_fequal,X3568)) = X3568,
inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial]) ).
fof(i_0_1074,plain,
! [X4197,X4198] :
( ~ class_Lattices_Obounded__lattice(X4198)
| class_Lattices_Obounded__lattice(tc_fun(X4197,X4198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])]) ).
fof(i_0_1075,plain,
! [X4215,X4216] :
( ~ class_Orderings_Obot(X4216)
| class_Orderings_Obot(tc_fun(X4215,X4216)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).
fof(i_0_1076,plain,
! [X4199,X4200] :
( ~ class_Lattices_Obounded__lattice(X4200)
| class_Lattices_Obounded__lattice__bot(tc_fun(X4199,X4200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])]) ).
fof(i_0_1077,plain,
! [X4205,X4206] :
( ~ class_Lattices_Odistrib__lattice(X4206)
| class_Lattices_Odistrib__lattice(tc_fun(X4205,X4206)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])]) ).
fof(i_0_1078,plain,
! [X4201,X4202] :
( ~ class_Lattices_Olattice(X4202)
| class_Lattices_Osemilattice__sup(tc_fun(X4201,X4202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])]) ).
fof(i_0_1079,plain,
! [X4211,X4212] :
( ~ class_Orderings_Oorder(X4212)
| class_Orderings_Oorder(tc_fun(X4211,X4212)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1080,plain,
! [X4213,X4214] :
( ~ class_Orderings_Oord(X4214)
| class_Orderings_Oord(tc_fun(X4213,X4214)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1081,plain,
! [X4207,X4208] :
( ~ class_Orderings_Opreorder(X4208)
| class_Orderings_Opreorder(tc_fun(X4207,X4208)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1082,plain,
! [X4203,X4204] :
( ~ class_Lattices_Olattice(X4204)
| class_Lattices_Osemilattice__inf(tc_fun(X4203,X4204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).
fof(i_0_1083,plain,
! [X4209,X4210] :
( ~ class_Lattices_Olattice(X4210)
| class_Lattices_Olattice(tc_fun(X4209,X4210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).
fof(i_0_1084,plain,
! [X3329,X3330] :
( ~ c_Wellfounded_Owf(X3330,X3329)
| c_Wellfounded_Oacyclic(X3330,X3329) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acyclic])]) ).
fof(i_0_1085,plain,
! [X4217,X4218] : hAPP(c_COMBI(X4218),X4217) = X4217,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1086,plain,
~ hBOOL(c_fFalse),
inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).
cnf(i_0_1087,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk45_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk46_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk47_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk48_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))
| hBOOL(hAPP(hAPP(X3,X6),X5))
| ~ hBOOL(hAPP(hAPP(X3,X8),X7))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1088,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),esk41_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk42_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk43_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk44_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))
| hBOOL(hAPP(hAPP(X3,X8),X7))
| ~ hBOOL(hAPP(hAPP(X3,X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1089,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk43_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk44_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))
| hBOOL(hAPP(hAPP(X3,X8),X7))
| ~ hBOOL(hAPP(hAPP(X3,X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1090,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),esk45_8(X5,X6,X7,X8,X4,X3,X2,X1)),esk46_8(X5,X6,X7,X8,X4,X3,X2,X1)))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6)))
| hBOOL(hAPP(hAPP(X5,X8),X7))
| ~ hBOOL(hAPP(hAPP(X5,X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1091,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk39_7(X3,X4,X5,X6,X7,X2,X1)),esk40_7(X3,X4,X5,X6,X7,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3)))
| hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_595]),
[final] ).
cnf(i_0_1092,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),esk39_7(X5,X6,X7,X4,X3,X2,X1)),esk40_7(X5,X6,X7,X4,X3,X2,X1)))),X5))
| hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_595]),
[final] ).
cnf(i_0_1093,plain,
( hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(X1,esk47_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk48_8(X1,X2,X3,X4,X5,X6,X7,X8)))
| ~ hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1094,plain,
( hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(X1,esk41_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk42_8(X1,X2,X3,X4,X5,X6,X7,X8)))
| ~ hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1095,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(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_596]),
[final] ).
cnf(i_0_1096,plain,
( hBOOL(hAPP(hAPP(X1,esk45_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk46_8(X1,X2,X3,X4,X5,X6,X7,X8)))
| hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1097,plain,
( hBOOL(hAPP(hAPP(X1,esk43_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk44_8(X1,X2,X3,X4,X5,X6,X7,X8)))
| hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1098,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1099,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk5_7(X2,X3,X4,X5,X6,X1,X7)),X3)),X5))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X6,X5,X4,X3),hAPP(hAPP(X4,X2),X3)))
| hAPP(hAPP(X4,X2),X3) != hAPP(hAPP(X4,X7),X3) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1100,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk18_7(X2,X3,X4,X5,X6,X1,X7)),X3)),X5))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X6,X5,X4,X3),X2))
| X2 != hAPP(hAPP(X4,X7),X3) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1101,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk26_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_599]),
[final] ).
cnf(i_0_1102,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Otrancl(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(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),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_600]),
[final] ).
cnf(i_0_1103,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,X6),hAPP(hAPP(X4,X5),X6)))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,esk5_7(X5,X6,X4,X3,X2,X1,X7)),hAPP(X7,esk5_7(X5,X6,X4,X3,X2,X1,X7))))
| hAPP(hAPP(X4,X5),X6) != hAPP(hAPP(X4,X7),X6) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1104,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,X6),X5))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,esk18_7(X5,X6,X4,X3,X2,X1,X7)),hAPP(X7,esk18_7(X5,X6,X4,X3,X2,X1,X7))))
| X5 != hAPP(hAPP(X4,X7),X6) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1105,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(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)))),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_Otrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_600]),
[final] ).
cnf(i_0_1106,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_601]),
[final] ).
cnf(i_0_1107,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_601]),
[final] ).
cnf(i_0_1108,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_602]),
[final] ).
cnf(i_0_1109,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk19_6(X2,X3,X4,X5,X6,X1)),X6)),X5))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X4,X5,X3,X6),hAPP(hAPP(X3,X2),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1110,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk6_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_604]),
[final] ).
cnf(i_0_1111,plain,
( hAPP(hAPP(X2,X1),X7) = hAPP(hAPP(X2,X6),X7)
| hAPP(X1,esk26_7(X2,X3,X4,X5,X1,X6,X7)) != hAPP(X6,esk26_7(X2,X3,X4,X5,X1,X6,X7))
| ~ c_Recdef_Oadm__wf(X5,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1112,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,X6),hAPP(hAPP(X4,X5),X6)))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,esk19_6(X5,X4,X2,X3,X6,X1)),hAPP(X5,esk19_6(X5,X4,X2,X3,X6,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1113,plain,
( c_Wellfounded_Owf(X1,X2)
| c_Nitpick_Owfrec_H(X1,X3,X2,X4,X5) = c_HOL_OThe(X3,c_Recdef_Owfrec__rel(X1,X3,X2,hAPP(hAPP(c_COMBC(tc_fun(X1,X3),tc_fun(X1,X1),tc_fun(X1,X3)),hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X3)),tc_fun(tc_fun(X1,X1),tc_fun(X1,X3)),tc_fun(X1,X3),c_COMBS(X1,X1,X3)),hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X3)),tc_fun(X1,tc_fun(X1,X3)),tc_fun(X1,X3),c_COMBB(tc_fun(X1,X3),tc_fun(X1,X3),X1,X4)),hAPP(hAPP(c_COMBC(tc_fun(X1,X3),tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_fun(X1,X3))),c_Recdef_Ocut(X1,X3)),X2)))),c_COMBI(X1)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_539]),
[final] ).
cnf(i_0_1114,plain,
hAPP(c_Recdef_Owfrec(X1,X2,X3,X4),X5) = c_HOL_OThe(X2,c_Recdef_Owfrec__rel(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)),X5)),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1115,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_602]),
[final] ).
cnf(i_0_1116,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_606]),
[final] ).
cnf(i_0_1117,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_607]),
[final] ).
cnf(i_0_1118,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_OwfP(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)) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1119,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_609]),
[final] ).
cnf(i_0_1120,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X1),tc_HOL_Obool),c_Product__Type_OSigma(X6,X1,X5,X2),c_Product__Type_OSigma(X6,X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(X2,esk100_6(X3,X2,X1,X4,X5,X6)),hAPP(X3,esk100_6(X3,X2,X1,X4,X5,X6)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1121,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_611]),
[final] ).
cnf(i_0_1122,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_607]),
[final] ).
cnf(i_0_1123,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_606]),
[final] ).
cnf(i_0_1124,plain,
( c_Wellfounded_OwfP(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))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1125,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk108_5(X2,X3,X4,X5,X1)),esk107_5(X2,X3,X4,X5,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,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1126,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X5,X4,X6,X2),hAPP(esk4_6(X7,X3,X6,X4,X5,X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X5,X4,X6,X3),hAPP(hAPP(X6,X7),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1127,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X5,X4,X6,X2),hAPP(esk17_6(X7,X3,X6,X4,X5,X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X5,X4,X6,X3),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1128,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk58_5(X2,X3,X4,X5,X1)),esk59_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_613]),
[final] ).
cnf(i_0_1129,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk65_5(X2,X3,X4,X5,X1)),esk66_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_614]),
[final] ).
cnf(i_0_1130,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X6),c_FuncSet_OPi(X1,X2,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),esk34_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_615]),
[final] ).
cnf(i_0_1131,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X6),c_FuncSet_OPi(X1,X2,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),esk34_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_615]),
[final] ).
cnf(i_0_1132,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk100_6(X2,X3,X4,X5,X6,X1)),X6))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool),c_Product__Type_OSigma(X1,X4,X6,X3),c_Product__Type_OSigma(X1,X4,X5,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X6,X5) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1133,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,esk37_5(X3,X2,X1,X4,X5))),hAPP(X3,esk37_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_616]),
[final] ).
cnf(i_0_1134,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,esk35_5(X3,X2,X1,X4,X5))),hAPP(X3,esk35_5(X3,X2,X1,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)),X2),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk32_5(X3,X2,X1,X4,X5))),hAPP(X3,esk32_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_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk107_5(X2,X3,X4,X5,X1)),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))
| 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)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1137,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk66_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_614]),
[final] ).
cnf(i_0_1138,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,esk34_6(X5,X2,X3,X6,X4,X1)) != hAPP(X3,esk34_6(X5,X2,X3,X6,X4,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1139,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,esk34_6(X5,X2,X6,X3,X4,X1)) != hAPP(X6,esk34_6(X5,X2,X6,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1140,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,esk11_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,esk11_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_619]),
[final] ).
cnf(i_0_1141,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(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,esk11_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,esk11_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_619]),
[final] ).
cnf(i_0_1142,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,esk6_6(X2,X3,X4,X1,X5,X6)) != hAPP(X2,esk6_6(X2,X3,X4,X1,X5,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1143,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,esk38_5(X3,X2,X1,X4,X5))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1144,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,esk33_5(X3,X2,X1,X4,X5))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1145,plain,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk4_6(X2,X3,X1,X4,X5,X6)),X3)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X5,X4,X1,X3),hAPP(hAPP(X1,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1146,plain,
( X1 = hAPP(hAPP(X2,esk17_6(X1,X3,X2,X4,X5,X6)),X3)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X6,X5,X4,X2,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1147,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,esk11_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,esk11_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_619]),
[final] ).
cnf(i_0_1148,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,esk11_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,esk11_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_619]),
[final] ).
cnf(i_0_1149,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_622,c_0_623]),c_0_623]),c_0_623]),c_0_623]),
[final] ).
cnf(i_0_1150,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_624]),
[final] ).
cnf(i_0_1151,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk58_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_613]),
[final] ).
cnf(i_0_1152,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk99_5(X2,X3,X4,X1,X5)),hAPP(X2,esk98_5(X2,X3,X4,X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),X4),c_Product__Type_OSigma(X5,X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1153,plain,
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_626]),
[final] ).
cnf(i_0_1154,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_627,c_0_623]),
[final] ).
cnf(i_0_1155,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X1),tc_HOL_Obool),c_FuncSet_OPi(X5,X1,X4,X2),c_FuncSet_OPi(X5,X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(X2,esk87_5(X3,X2,X1,X4,X5)),hAPP(X3,esk87_5(X3,X2,X1,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_628]),
[final] ).
cnf(i_0_1156,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| 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_629]),
[final] ).
cnf(i_0_1157,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),esk22_2(X1,X2)),esk23_2(X1,X2))),hAPP(X2,esk21_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_630]),
[final] ).
cnf(i_0_1158,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_629]),
[final] ).
cnf(i_0_1159,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_631]),
[final] ).
cnf(i_0_1160,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_632]),
[final] ).
cnf(i_0_1161,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),esk22_2(X1,X2)),esk23_2(X1,X2))),hAPP(esk21_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_630]),
[final] ).
cnf(i_0_1162,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk76_4(X2,X3,X4,X1)),esk76_4(X2,X3,X4,X1))),c_Transitive__Closure_Otrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4))
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1163,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))),esk21_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_630]),
[final] ).
cnf(i_0_1164,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,c_Set_Oinsert(X1,X2,X3),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_634]),
[final] ).
cnf(i_0_1165,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk38_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_620]),
[final] ).
cnf(i_0_1166,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,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_635]),
[final] ).
cnf(i_0_1167,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk22_2(X1,X2) != esk23_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_630]),
[final] ).
cnf(i_0_1168,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk37_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_616]),
[final] ).
cnf(i_0_1169,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk98_5(X2,X3,X4,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X5)),X4),c_Product__Type_OSigma(X1,X5,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1170,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk74_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_636]),
[final] ).
cnf(i_0_1171,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)),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_637]),
[final] ).
cnf(i_0_1172,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk33_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_621]),
[final] ).
cnf(i_0_1173,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk36_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_638]),
[final] ).
cnf(i_0_1174,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk35_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_617]),
[final] ).
cnf(i_0_1175,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk32_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_618]),
[final] ).
cnf(i_0_1176,plain,
( 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)))
| esk108_5(X1,X2,X3,X4,X5) != esk107_5(X1,X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1177,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk87_5(X2,X3,X4,X5,X1)),X5))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X5,X3),c_FuncSet_OPi(X1,X4,X5,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_628]),
[final] ).
cnf(i_0_1178,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)))
| 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_639]),
[final] ).
cnf(i_0_1179,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk71_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_640]),
[final] ).
cnf(i_0_1180,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk63_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_641]),
[final] ).
cnf(i_0_1181,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk70_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_642]),
[final] ).
cnf(i_0_1182,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_643]),
[final] ).
cnf(i_0_1183,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_644,c_0_623]),
[final] ).
cnf(i_0_1184,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Wellfounded_Olex__prod(X7,X3,X8,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_629]),
[final] ).
cnf(i_0_1185,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X5),tc_prod(X1,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X5),tc_prod(X1,X5)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X2),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X3),X7))),c_Wellfounded_Olex__prod(X1,X5,X4,X8)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_629]),
[final] ).
cnf(i_0_1186,plain,
c_Product__Type_OSigma(X1,X2,X3,hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X3,X4)),c_Product__Type_OSigma(X1,X2,X3,X5)),
inference(split_conjunct,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_1187,plain,
c_Product__Type_OSigma(X1,X2,X3,hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X3,X4)),c_Product__Type_OSigma(X1,X2,X3,X5)),
inference(split_conjunct,[status(thm)],[i_0_646]),
[final] ).
cnf(i_0_1188,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_631]),
[final] ).
cnf(i_0_1189,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_632]),
[final] ).
cnf(i_0_1190,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,X5),esk86_5(X5,X4,X3,X2,X1)))
| ~ c_Wellfounded_Owf(X1,X3)
| ~ c_Recdef_Oadm__wf(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1191,plain,
( hAPP(hAPP(X4,hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X3),c_Nitpick_Owf__wfrec(X1,X3,X2,X4)),X2),X5)),X5) = c_Nitpick_Owfrec_H(X1,X3,X2,X4,X5)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(rw,[status(thm)],[i_0_648,c_0_649]),
[final] ).
cnf(i_0_1192,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk62_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_650]),
[final] ).
cnf(i_0_1193,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk60_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_651]),
[final] ).
cnf(i_0_1194,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk59_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_613]),
[final] ).
cnf(i_0_1195,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,esk65_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_614]),
[final] ).
cnf(i_0_1196,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk98_5(X4,X5,X1,X3,X2)),esk99_5(X4,X5,X1,X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),c_Product__Type_OSigma(X2,X3,X5,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1197,plain,
( X1 = X2
| hAPP(X1,esk36_5(X2,X3,X1,X4,X5)) != hAPP(X2,esk36_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_638]),
[final] ).
cnf(i_0_1198,plain,
( hAPP(c_Recdef_Owfrec(X1,X3,X2,X4),X5) = hAPP(hAPP(X4,hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X3),c_Recdef_Owfrec(X1,X3,X2,X4)),X2),X5)),X5)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1199,plain,
( hAPP(c_Recdef_Owfrec(X1,X3,X2,X4),X5) = hAPP(hAPP(X4,hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X3),c_Recdef_Owfrec(X1,X3,X2,X4)),X2),X5)),X5)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1200,plain,
( X6 = esk86_5(X5,X4,X3,X2,X1)
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,X5),X6))
| ~ c_Wellfounded_Owf(X1,X3)
| ~ c_Recdef_Oadm__wf(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1201,plain,
( hAPP(esk27_4(X3,X4,X5,X1),X2) = hAPP(esk28_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),esk29_4(X3,X4,X5,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1202,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2)),
inference(split_conjunct,[status(thm)],[i_0_654]),
[final] ).
cnf(i_0_1203,plain,
c_Product__Type_OSigma(X1,X2,c_Set_Oinsert(X1,X3,X4),c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X5,X6))) = c_Set_Oinsert(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X5,X6)))),c_Product__Type_OSigma(X1,X2,c_Set_Oinsert(X1,X3,X4),c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X6)))),
inference(split_conjunct,[status(thm)],[i_0_655]),
[final] ).
cnf(i_0_1204,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_1205,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))),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_637]),
[final] ).
cnf(i_0_1206,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk74_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_636]),
[final] ).
cnf(i_0_1207,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,esk7_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1208,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_657]),
[final] ).
cnf(i_0_1209,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk97_3(X2,X3,X1)),esk97_3(X2,X3,X1))),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X3,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_658]),
[final] ).
cnf(i_0_1210,plain,
( c_Relation_Orefl__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk93_3(X2,X3,X1)),esk93_3(X2,X3,X1))),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Product__Type_OSigma(X1,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_659]),
[final] ).
cnf(i_0_1211,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_660,c_0_623]),
[final] ).
cnf(i_0_1212,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk63_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_641]),
[final] ).
cnf(i_0_1213,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk70_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_642]),
[final] ).
cnf(i_0_1214,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))
| 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_639]),
[final] ).
cnf(i_0_1215,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk71_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_640]),
[final] ).
cnf(i_0_1216,plain,
( hBOOL(hAPP(X1,esk58_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_613]),
[final] ).
cnf(i_0_1217,plain,
( hBOOL(hAPP(X1,esk66_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_614]),
[final] ).
cnf(i_0_1218,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_661]),
[final] ).
cnf(i_0_1219,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_1220,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_623]),
[final] ).
cnf(i_0_1221,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),esk69_3(X2,X3,X1)),esk68_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1222,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),esk68_3(X2,X3,X1)),esk69_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1223,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),c_Transitive__Closure_Ortrancl(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ c_Relation_Osingle__valued(X1,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_665]),
[final] ).
cnf(i_0_1224,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk54_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_666]),
[final] ).
cnf(i_0_1225,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk49_4(X4,X3,X2,X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ODomain(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_667]),
[final] ).
cnf(i_0_1226,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk102_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(hAPP(c_member(X1),esk101_4(X2,X3,X4,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1227,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk106_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(hAPP(c_member(X1),esk105_4(X2,X3,X4,X1)),X4))
| hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1228,plain,
( c_Recdef_Oadm__wf(X4,X3,X2,X1)
| hAPP(hAPP(X1,esk27_4(X1,X2,X3,X4)),esk29_4(X1,X2,X3,X4)) != hAPP(hAPP(X1,esk28_4(X1,X2,X3,X4)),esk29_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1229,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_661]),
[final] ).
cnf(i_0_1230,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_661]),
[final] ).
cnf(i_0_1231,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_661]),
[final] ).
cnf(i_0_1232,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_661]),
[final] ).
cnf(i_0_1233,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_1234,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_1235,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_1236,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_1237,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_670]),
[final] ).
cnf(i_0_1238,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_671]),
[final] ).
cnf(i_0_1239,plain,
( hBOOL(hAPP(hAPP(c_member(X4),esk105_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,esk106_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1240,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk106_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(X2,esk105_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1241,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_670]),
[final] ).
cnf(i_0_1242,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_672]),
[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_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_673]),
[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_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_674]),
[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_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_675]),
[final] ).
cnf(i_0_1246,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_676]),
[final] ).
cnf(i_0_1247,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_676]),
[final] ).
cnf(i_0_1248,plain,
( hBOOL(hAPP(hAPP(X3,X5),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_677]),
[final] ).
cnf(i_0_1249,plain,
( hBOOL(hAPP(hAPP(X4,X5),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_678]),
[final] ).
cnf(i_0_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)),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_679]),
[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)),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_680]),
[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_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_681]),
[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_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_682]),
[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_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_683]),
[final] ).
cnf(i_0_1255,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_1256,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_685]),
[final] ).
cnf(i_0_1257,plain,
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,esk106_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(X1,esk105_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1258,plain,
( hBOOL(hAPP(X1,esk102_4(X1,X2,X3,X4)))
| hBOOL(hAPP(hAPP(c_member(X4),esk101_4(X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))
| ~ hBOOL(hAPP(X1,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1259,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk102_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(X2,esk101_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1260,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_661]),
[final] ).
cnf(i_0_1261,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_661]),
[final] ).
cnf(i_0_1262,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_661]),
[final] ).
cnf(i_0_1263,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_686]),
[final] ).
cnf(i_0_1264,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_687]),
[final] ).
cnf(i_0_1265,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_1266,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_1267,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk55_3(X3,X2,X1)),esk57_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1268,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk55_3(X3,X2,X1)),esk56_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1269,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk50_3(X3,X2,X1)),esk52_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_1270,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk50_3(X3,X2,X1)),esk51_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_1271,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_661]),
[final] ).
cnf(i_0_1272,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_661]),
[final] ).
cnf(i_0_1273,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_661]),
[final] ).
cnf(i_0_1274,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_661]),
[final] ).
cnf(i_0_1275,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_661]),
[final] ).
cnf(i_0_1276,plain,
( X3 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X5))
| X3 = X2
| X2 = X4
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),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_1277,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| X3 = X2
| X2 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),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_1278,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| X2 = X4
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),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_1279,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),esk14_1(X1)),esk15_1(X1))),hAPP(X1,esk12_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),esk14_1(X1)),esk15_1(X1))),hAPP(X1,esk13_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1280,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_1281,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_1282,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_1283,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_1284,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_1285,plain,
c_Product__Type_OSigma(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4),c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))),c_Product__Type_OSigma(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_1286,plain,
c_Product__Type_OSigma(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4),c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))),c_Product__Type_OSigma(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))),
inference(split_conjunct,[status(thm)],[i_0_692]),
[final] ).
cnf(i_0_1287,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_693]),
[final] ).
cnf(i_0_1288,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_690]),
[final] ).
cnf(i_0_1289,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_694]),
[final] ).
cnf(i_0_1290,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk84_4(X3,X2,X4,X1)),hAPP(X3,esk84_4(X3,X2,X4,X1)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_1291,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),c_Product__Type_OSigma(X5,X1,X6,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_696]),
[final] ).
cnf(i_0_1292,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),c_Product__Type_OSigma(X5,X1,X6,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_697]),
[final] ).
cnf(i_0_1293,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(X6,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Product__Type_OSigma(X1,X2,X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_698]),
[final] ).
cnf(i_0_1294,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk89_3(X3,X1,X4))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ c_Wellfounded_Owf(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_699]),
[final] ).
cnf(i_0_1295,plain,
( X3 = X4
| ~ c_Relation_Oantisym(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_700]),
[final] ).
cnf(i_0_1296,plain,
( X3 = X4
| ~ c_Relation_Oantisym(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_1297,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_1298,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_703]),
[final] ).
cnf(i_0_1299,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),c_Product__Type_OSigma(X1,X4,X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_696]),
[final] ).
cnf(i_0_1300,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),c_Product__Type_OSigma(X1,X4,X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_697]),
[final] ).
cnf(i_0_1301,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Product__Type_OSigma(X1,X2,X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_704]),
[final] ).
cnf(i_0_1302,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X4,c_Product__Type_OSigma(X1,X1,X5,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1303,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_706]),
[final] ).
cnf(i_0_1304,plain,
( hBOOL(hAPP(X1,esk102_4(X1,X2,X3,X4)))
| hBOOL(hAPP(X1,esk101_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))
| ~ hBOOL(hAPP(X1,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1305,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1306,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X6,tc_HOL_Obool))),X1),X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_708]),
[final] ).
cnf(i_0_1307,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk92_3(X2,X1,X3)),X3)),X2))
| c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk90_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_699]),
[final] ).
cnf(i_0_1308,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),c_Product__Type_OSigma(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4)),c_Product__Type_OSigma(X1,X2,X5,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1309,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk25_3(X2,X3,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_710]),
[final] ).
cnf(i_0_1310,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk24_3(X2,X3,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_1311,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk20_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_712]),
[final] ).
cnf(i_0_1312,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_661]),
[final] ).
cnf(i_0_1313,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk14_1(X1)),esk15_1(X1))),hAPP(esk13_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),esk14_1(X1)),esk15_1(X1))),hAPP(esk12_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1314,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk14_1(X1)),esk15_1(X1))),hAPP(esk12_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),esk14_1(X1)),esk15_1(X1))),hAPP(esk13_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1315,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk103_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
| ~ hBOOL(hAPP(X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1316,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk103_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(X2,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1317,plain,
( hBOOL(hAPP(X4,X2))
| hBOOL(hAPP(hAPP(c_member(X1),esk104_4(X4,X3,X5,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1318,plain,
( hBOOL(hAPP(X4,X2))
| hBOOL(hAPP(hAPP(c_member(X1),esk104_4(X4,X5,X3,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1319,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_713]),
[final] ).
cnf(i_0_1320,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_713]),
[final] ).
cnf(i_0_1321,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_714]),
[final] ).
cnf(i_0_1322,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_715]),
[final] ).
cnf(i_0_1323,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_686]),
[final] ).
cnf(i_0_1324,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_716,c_0_623]),
[final] ).
cnf(i_0_1325,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_717]),
[final] ).
cnf(i_0_1326,plain,
( X4 = X5
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),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_1327,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk95_3(X3,X2,X1)),esk96_3(X3,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_718]),
[final] ).
cnf(i_0_1328,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk2_2(X2,X1)),esk2_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_719]),
[final] ).
cnf(i_0_1329,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk113_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_720]),
[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)))
| ~ c_Wellfounded_Owf(X1,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_721]),
[final] ).
cnf(i_0_1331,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,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_722]),
[final] ).
cnf(i_0_1332,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ORange(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Relation_ORange(X2,X1,X3)),c_Relation_ORange(X2,X1,X4))),
inference(split_conjunct,[status(thm)],[i_0_723]),
[final] ).
cnf(i_0_1333,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Relation_ODomain(X1,X2,X3)),c_Relation_ODomain(X1,X2,X4))),
inference(split_conjunct,[status(thm)],[i_0_724]),
[final] ).
cnf(i_0_1334,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_664]),
[final] ).
cnf(i_0_1335,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_725]),
[final] ).
cnf(i_0_1336,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_726]),
[final] ).
cnf(i_0_1337,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_727]),
[final] ).
cnf(i_0_1338,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),c_Product__Type_OSigma(X1,X4,X3,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_696]),
[final] ).
cnf(i_0_1339,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),c_Product__Type_OSigma(X1,X4,X3,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_728]),
[final] ).
cnf(i_0_1340,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_729]),
[final] ).
cnf(i_0_1341,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_730]),
[final] ).
cnf(i_0_1342,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_731]),
[final] ).
cnf(i_0_1343,plain,
( hBOOL(hAPP(hAPP(X1,esk78_4(X2,X3,X1,X4)),X2))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X4,X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_732]),
[final] ).
cnf(i_0_1344,plain,
( hBOOL(hAPP(hAPP(X1,esk77_4(X2,X3,X1,X4)),X2))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X4,X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_733]),
[final] ).
cnf(i_0_1345,plain,
( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_729]),
[final] ).
cnf(i_0_1346,plain,
( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_731]),
[final] ).
cnf(i_0_1347,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional__funcset(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_734]),
[final] ).
cnf(i_0_1348,plain,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1349,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1350,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X2),c_Product__Type_OSigma(X1,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Product__Type_OSigma(X1,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_737]),
[final] ).
cnf(i_0_1351,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_738]),
[final] ).
cnf(i_0_1352,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_739]),
[final] ).
cnf(i_0_1353,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_740]),
[final] ).
cnf(i_0_1354,plain,
c_Product__Type_OSigma(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X3,X5)),c_Product__Type_OSigma(X1,X2,X4,X5)),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1355,plain,
c_Product__Type_OSigma(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X3,X5)),c_Product__Type_OSigma(X1,X2,X4,X5)),
inference(split_conjunct,[status(thm)],[i_0_742]),
[final] ).
cnf(i_0_1356,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_740]),
[final] ).
cnf(i_0_1357,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_739]),
[final] ).
cnf(i_0_1358,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_740]),
[final] ).
cnf(i_0_1359,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_739]),
[final] ).
cnf(i_0_1360,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_743]),
[final] ).
cnf(i_0_1361,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_744]),
[final] ).
cnf(i_0_1362,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_Q____,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_743]),
[final] ).
cnf(i_0_1363,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_744]),
[final] ).
cnf(i_0_1364,plain,
c_FuncSet_Oextensional__funcset(X1,X2,X3,X4) = hAPP(hAPP(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_745]),
[final] ).
cnf(i_0_1365,plain,
( hAPP(X3,X7) = hAPP(X6,X7)
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X3),X4),X5) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X6),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1366,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(X1,esk12_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),esk14_1(X1)),esk15_1(X1))),hAPP(X1,esk13_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1367,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_746]),
[final] ).
cnf(i_0_1368,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_661]),
[final] ).
cnf(i_0_1369,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_747]),
[final] ).
cnf(i_0_1370,plain,
( c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))
| ~ c_Wellfounded_Owf(X1,hAPP(X2,esk85_4(X3,X2,X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_748]),
[final] ).
cnf(i_0_1371,plain,
( hBOOL(hAPP(hAPP(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_749]),
[final] ).
cnf(i_0_1372,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_1373,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_751]),
[final] ).
cnf(i_0_1374,plain,
( hAPP(X1,X3) = hAPP(X3,X2)
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1375,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_1376,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_753]),
[final] ).
cnf(i_0_1377,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_754]),
[final] ).
cnf(i_0_1378,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_755]),
[final] ).
cnf(i_0_1379,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk97_3(X2,X3,X1)),X2))
| c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X3,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_658]),
[final] ).
cnf(i_0_1380,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk93_3(X2,X3,X1)),X3))
| c_Relation_Orefl__on(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Product__Type_OSigma(X1,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_659]),
[final] ).
cnf(i_0_1381,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1382,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_712]),
[final] ).
cnf(i_0_1383,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_757]),
[final] ).
cnf(i_0_1384,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool),c_Product__Type_OSigma(X1,X4,X2,c_COMBK(tc_fun(X4,tc_HOL_Obool),X1,X5)),c_Product__Type_OSigma(X1,X4,X3,c_COMBK(tc_fun(X4,tc_HOL_Obool),X1,X5)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1385,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),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_758]),
[final] ).
cnf(i_0_1386,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_667]),
[final] ).
cnf(i_0_1387,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_759]),
[final] ).
cnf(i_0_1388,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_651]),
[final] ).
cnf(i_0_1389,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_760]),
[final] ).
cnf(i_0_1390,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_761]),
[final] ).
cnf(i_0_1391,plain,
( hAPP(X3,X4) = X5
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_1392,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X2)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_763]),
[final] ).
cnf(i_0_1393,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_749]),
[final] ).
cnf(i_0_1394,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_764]),
[final] ).
cnf(i_0_1395,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_765]),
[final] ).
cnf(i_0_1396,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_766]),
[final] ).
cnf(i_0_1397,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X4,esk104_4(X4,X3,X5,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1398,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X4,esk104_4(X4,X5,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1399,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),esk9_1(X1)),esk10_1(X1))),hAPP(X1,esk8_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1400,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_767]),
[final] ).
cnf(i_0_1401,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk75_2(X2,X1)),esk75_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[final] ).
cnf(i_0_1402,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk72_2(X2,X1)),esk72_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_767]),
[final] ).
cnf(i_0_1403,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_766]),
[final] ).
cnf(i_0_1404,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_769]),
[final] ).
cnf(i_0_1405,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_770]),
[final] ).
cnf(i_0_1406,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk82_2(X2,X1)),esk81_2(X2,X1))),X2))
| c_Relation_Oantisym(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_771]),
[final] ).
cnf(i_0_1407,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk81_2(X2,X1)),esk82_2(X2,X1))),X2))
| c_Relation_Oantisym(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_771]),
[final] ).
cnf(i_0_1408,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk80_2(X2,X1)),esk79_2(X2,X1))),X2))
| c_Relation_Oantisym(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_700]),
[final] ).
cnf(i_0_1409,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk79_2(X2,X1)),esk80_2(X2,X1))),X2))
| c_Relation_Oantisym(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_700]),
[final] ).
cnf(i_0_1410,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk53_2(X2,X1)),esk53_2(X2,X1))),X2))
| c_Relation_Oirrefl(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_772]),
[final] ).
cnf(i_0_1411,plain,
( ~ c_Wellfounded_Owf(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_773]),
[final] ).
cnf(i_0_1412,plain,
( ~ c_Wellfounded_Owf(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_774]),
[final] ).
cnf(i_0_1413,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_772]),
[final] ).
cnf(i_0_1414,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_775]),
[final] ).
cnf(i_0_1415,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_776]),
[final] ).
cnf(i_0_1416,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_Owf(X1,c_Set_Oinsert(tc_prod(X1,X1),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3),X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_721]),
[final] ).
cnf(i_0_1417,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,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_722]),
[final] ).
cnf(i_0_1418,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_738]),
[final] ).
cnf(i_0_1419,plain,
c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3))) = c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_777]),
[final] ).
cnf(i_0_1420,plain,
( hBOOL(hAPP(X1,esk85_4(X2,X3,X4,X1)))
| c_Wellfounded_Owf(tc_prod(X2,X4),c_Recdef_Osame__fst(X2,X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_748]),
[final] ).
cnf(i_0_1421,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),esk78_4(X4,X3,X2,X1)))
| hBOOL(hAPP(hAPP(X2,X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_732]),
[final] ).
cnf(i_0_1422,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),esk77_4(X4,X3,X2,X1)))
| hBOOL(hAPP(hAPP(X2,X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_733]),
[final] ).
cnf(i_0_1423,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X1,X3)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Relation_ODomain(X1,X1,X2)),c_Relation_ORange(X1,X1,X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_778]),
[final] ).
cnf(i_0_1424,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_739]),
[final] ).
cnf(i_0_1425,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_740]),
[final] ).
cnf(i_0_1426,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_1427,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_739]),
[final] ).
cnf(i_0_1428,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_779]),
[final] ).
cnf(i_0_1429,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_753]),
[final] ).
cnf(i_0_1430,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1431,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_781]),
[final] ).
cnf(i_0_1432,plain,
( X3 = X5
| c_Product__Type_OSigma(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4)) != c_Product__Type_OSigma(X1,X2,X5,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_782]),
[final] ).
cnf(i_0_1433,plain,
c_Product__Type_Ointernal__split(X1,X2,X3,X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_783]),
[final] ).
cnf(i_0_1434,plain,
c_Product__Type_Oprod_Oprod__rec(X1,X2,X3,X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_784]),
[final] ).
cnf(i_0_1435,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_757]),
[final] ).
cnf(i_0_1436,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_F,v_Q____))),
inference(split_conjunct,[status(thm)],[i_0_785]),
[final] ).
cnf(i_0_1437,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk16_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1438,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk13_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1439,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk12_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1440,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_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1441,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Relation_Orefl__on(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_659]),
[final] ).
cnf(i_0_1442,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_786]),
[final] ).
cnf(i_0_1443,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_1444,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
inference(split_conjunct,[status(thm)],[fact__096P_A_058_AProf_096]),
[final] ).
cnf(i_0_1445,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(split_conjunct,[status(thm)],[fact__096Q_A_058_AProf_096]),
[final] ).
cnf(i_0_1446,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1447,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_1448,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_763]),
[final] ).
cnf(i_0_1449,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_789]),
[final] ).
cnf(i_0_1450,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_766]),
[final] ).
cnf(i_0_1451,plain,
( hAPP(X1,X6) = hAPP(hAPP(X5,hAPP(hAPP(hAPP(c_Recdef_Ocut(X2,X3),X1),X4),X6)),X6)
| X1 != c_Recdef_Owfrec(X2,X3,X4,X5)
| ~ c_Wellfounded_Owf(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_790]),
[final] ).
cnf(i_0_1452,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_791]),
[final] ).
cnf(i_0_1453,plain,
( hBOOL(hAPP(X1,esk103_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X2))
| ~ hBOOL(hAPP(X1,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1454,plain,
( hBOOL(hAPP(X1,esk103_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X3))
| ~ hBOOL(hAPP(X1,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1455,plain,
c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
inference(split_conjunct,[status(thm)],[i_0_792]),
[final] ).
cnf(i_0_1456,plain,
( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
| hAPP(X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_793]),
[final] ).
cnf(i_0_1457,plain,
( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
| hAPP(X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_1458,plain,
c_Relation_ORange(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),c_Relation_ORange(X1,X2,X3)),c_Relation_ORange(X1,X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_794]),
[final] ).
cnf(i_0_1459,plain,
c_Relation_ODomain(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_795]),
[final] ).
cnf(i_0_1460,plain,
( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_796]),
[final] ).
cnf(i_0_1461,plain,
( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(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_797]),
[final] ).
cnf(i_0_1462,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1463,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_799]),
[final] ).
cnf(i_0_1464,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_800]),
[final] ).
cnf(i_0_1465,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1466,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_800]),
[final] ).
cnf(i_0_1467,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_801]),
[final] ).
cnf(i_0_1468,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_802]),
[final] ).
cnf(i_0_1469,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_803]),
[final] ).
cnf(i_0_1470,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_804]),
[final] ).
cnf(i_0_1471,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk9_1(X1)),esk10_1(X1))),hAPP(esk8_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1472,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk61_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_805]),
[final] ).
cnf(i_0_1473,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_806]),
[final] ).
cnf(i_0_1474,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_713]),
[final] ).
cnf(i_0_1475,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_807]),
[final] ).
cnf(i_0_1476,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1477,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_809]),
[final] ).
cnf(i_0_1478,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk25_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_710]),
[final] ).
cnf(i_0_1479,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk24_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_1480,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk20_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_1481,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_810]),
[final] ).
cnf(i_0_1482,plain,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_811]),
[final] ).
cnf(i_0_1483,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_719]),
[final] ).
cnf(i_0_1484,plain,
( hAPP(X1,esk113_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_720]),
[final] ).
cnf(i_0_1485,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Product__Type_OSigma(X1,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X3)))
| ~ c_Relation_Orefl__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_659]),
[final] ).
cnf(i_0_1486,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1487,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_812]),
[final] ).
cnf(i_0_1488,plain,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_813]),
[final] ).
cnf(i_0_1489,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk61_3(X3,X1,X2)),esk61_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_805]),
[final] ).
cnf(i_0_1490,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1491,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1492,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_815]),
[final] ).
cnf(i_0_1493,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_816]),
[final] ).
cnf(i_0_1494,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_817]),
[final] ).
cnf(i_0_1495,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_739]),
[final] ).
cnf(i_0_1496,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_740]),
[final] ).
cnf(i_0_1497,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Relation_OId__on(X1,X2),c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_818]),
[final] ).
cnf(i_0_1498,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)),esk3_2(X2,X1)))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_819]),
[final] ).
cnf(i_0_1499,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_b_H____)),hAPP(v_Q____,X1))),
inference(split_conjunct,[status(thm)],[i_0_820]),
[final] ).
cnf(i_0_1500,plain,
( v_a____ = v_a_H____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_a____)),hAPP(v_F,v_Q____))) ),
inference(split_conjunct,[status(thm)],[i_0_821]),
[final] ).
cnf(i_0_1501,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_1502,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_Q____))),
inference(split_conjunct,[status(thm)],[fact_calculation_I1_J]),
[final] ).
cnf(i_0_1503,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_822]),
[final] ).
cnf(i_0_1504,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_823]),
[final] ).
cnf(i_0_1505,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X4)),X3) = c_Set_Oinsert(X1,X2,hAPP(hAPP(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_824]),
[final] ).
cnf(i_0_1506,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X4)),X3) = c_Set_Oinsert(X1,X2,hAPP(hAPP(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_825]),
[final] ).
cnf(i_0_1507,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_826]),
[final] ).
cnf(i_0_1508,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_827]),
[final] ).
cnf(i_0_1509,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_1510,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1511,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X1,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_721]),
[final] ).
cnf(i_0_1512,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(X1,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_722]),
[final] ).
cnf(i_0_1513,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk92_3(X2,X1,X3)),esk90_2(X2,X1)))
| c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk90_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_699]),
[final] ).
cnf(i_0_1514,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1515,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_830]),
[final] ).
cnf(i_0_1516,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1517,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1518,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_832]),
[final] ).
cnf(i_0_1519,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1520,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_833]),
[final] ).
cnf(i_0_1521,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,X5,c_Set_Oinsert(X4,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X2,c_Set_Oinsert(X4,X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_833]),
[final] ).
cnf(i_0_1522,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X4,X1,c_Set_Oinsert(X4,X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X5,c_Set_Oinsert(X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_833]),
[final] ).
cnf(i_0_1523,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X4,X3,c_Set_Oinsert(X4,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != c_Set_Oinsert(X4,X2,c_Set_Oinsert(X4,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_833]),
[final] ).
cnf(i_0_1524,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_834]),
[final] ).
cnf(i_0_1525,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[i_0_835]),
[final] ).
cnf(i_0_1526,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X3)),c_Set_Oinsert(X1,X2,X4)) = c_Set_Oinsert(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_836]),
[final] ).
cnf(i_0_1527,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))
| ~ hBOOL(hAPP(X1,esk94_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_718]),
[final] ).
cnf(i_0_1528,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_837]),
[final] ).
cnf(i_0_1529,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Set_Oinsert(X1,X2,X4)) = c_Set_Oinsert(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_838]),
[final] ).
cnf(i_0_1530,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Set_Oinsert(X1,X2,X4)) = c_Set_Oinsert(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_839]),
[final] ).
cnf(i_0_1531,plain,
c_Relation_ORange(X1,X2,c_Set_Oinsert(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4),X5)) = c_Set_Oinsert(X2,X4,c_Relation_ORange(X1,X2,X5)),
inference(split_conjunct,[status(thm)],[i_0_840]),
[final] ).
cnf(i_0_1532,plain,
c_Relation_ODomain(X1,X2,c_Set_Oinsert(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4),X5)) = c_Set_Oinsert(X1,X3,c_Relation_ODomain(X1,X2,X5)),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1533,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_842]),
[final] ).
cnf(i_0_1534,plain,
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_843]),
[final] ).
cnf(i_0_1535,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk89_3(X2,X1,X3)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_699]),
[final] ).
cnf(i_0_1536,plain,
( hBOOL(hAPP(hAPP(c_member(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_OLin))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[i_0_819]),
[final] ).
cnf(i_0_1537,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk110_3(X2,X3,X1)),X2))
| hAPP(hAPP(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_844]),
[final] ).
cnf(i_0_1538,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk109_3(X2,X3,X1)),X3))
| hAPP(hAPP(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_844]),
[final] ).
cnf(i_0_1539,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X3)),X4) = c_Set_Oinsert(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_845]),
[final] ).
cnf(i_0_1540,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_846]),
[final] ).
cnf(i_0_1541,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_847]),
[final] ).
cnf(i_0_1542,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_848]),
[final] ).
cnf(i_0_1543,plain,
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)],[fact__096F_AQ_A_058_ALin_096]),
[final] ).
cnf(i_0_1544,plain,
c_FuncSet_Oextensional__funcset(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X3) = 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_849]),
[final] ).
cnf(i_0_1545,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_850]),
[final] ).
cnf(i_0_1546,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_851]),
[final] ).
cnf(i_0_1547,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1548,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_851]),
[final] ).
cnf(i_0_1549,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_853]),
[final] ).
cnf(i_0_1550,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_854]),
[final] ).
cnf(i_0_1551,plain,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3),
inference(split_conjunct,[status(thm)],[i_0_855]),
[final] ).
cnf(i_0_1552,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_847]),
[final] ).
cnf(i_0_1553,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_848]),
[final] ).
cnf(i_0_1554,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_856]),
[final] ).
cnf(i_0_1555,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_857]),
[final] ).
cnf(i_0_1556,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_732]),
[final] ).
cnf(i_0_1557,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_733]),
[final] ).
cnf(i_0_1558,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_858]),
[final] ).
cnf(i_0_1559,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X4,X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X4,X1),X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_859]),
[final] ).
cnf(i_0_1560,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X4)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_824]),
[final] ).
cnf(i_0_1561,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X4)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_860]),
[final] ).
cnf(i_0_1562,plain,
( hAPP(hAPP(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_844]),
[final] ).
cnf(i_0_1563,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),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),X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_861]),
[final] ).
cnf(i_0_1564,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_862]),
[final] ).
cnf(i_0_1565,plain,
( hBOOL(hAPP(hAPP(X1,esk31_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_1566,plain,
( hBOOL(hAPP(hAPP(X1,esk30_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_864]),
[final] ).
cnf(i_0_1567,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Set_Oinsert(X1,X3,X4)) = c_Set_Oinsert(X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_865]),
[final] ).
cnf(i_0_1568,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk69_3(X2,X3,X1)),X3))
| c_Relation_Ototal__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1569,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk68_3(X2,X3,X1)),X3))
| c_Relation_Ototal__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1570,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_866]),
[final] ).
cnf(i_0_1571,plain,
( c_Wellfounded_Owf(tc_prod(X1,X3),c_Wellfounded_Olex__prod(X1,X3,X2,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_867]),
[final] ).
cnf(i_0_1572,plain,
( hBOOL(hAPP(hAPP(X3,esk67_2(X4,X3)),X4))
| ~ c_Predicate_ORangeP(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_868]),
[final] ).
cnf(i_0_1573,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_869]),
[final] ).
cnf(i_0_1574,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_870]),
[final] ).
cnf(i_0_1575,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_871]),
[final] ).
cnf(i_0_1576,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_720]),
[final] ).
cnf(i_0_1577,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk31_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_1578,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk30_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_864]),
[final] ).
cnf(i_0_1579,plain,
( c_Set_Oinsert(X5,X1,c_Set_Oinsert(X5,X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Set_Oinsert(X5,X4,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_833]),
[final] ).
cnf(i_0_1580,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),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_835]),
[final] ).
cnf(i_0_1581,plain,
( c_Wellfounded_Owf(X3,c_Relation_Oinv__image(X1,X3,X2,X4))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_872]),
[final] ).
cnf(i_0_1582,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1583,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_874]),
[final] ).
cnf(i_0_1584,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_875]),
[final] ).
cnf(i_0_1585,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Set_Oinsert(X1,X2,X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_838]),
[final] ).
cnf(i_0_1586,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Set_Oinsert(X1,X2,X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_876]),
[final] ).
cnf(i_0_1587,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_877]),
[final] ).
cnf(i_0_1588,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_878]),
[final] ).
cnf(i_0_1589,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_856]),
[final] ).
cnf(i_0_1590,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_879]),
[final] ).
cnf(i_0_1591,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_880]),
[final] ).
cnf(i_0_1592,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),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_881]),
[final] ).
cnf(i_0_1593,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,c_Set_Oinsert(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_882]),
[final] ).
cnf(i_0_1594,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_883]),
[final] ).
cnf(i_0_1595,plain,
c_FuncSet_Oextensional(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = 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_884]),
[final] ).
cnf(i_0_1596,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_885]),
[final] ).
cnf(i_0_1597,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_886]),
[final] ).
cnf(i_0_1598,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_1599,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_888]),
[final] ).
cnf(i_0_1600,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X5))
| ~ class_Lattices_Osemilattice__sup(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_889]),
[final] ).
cnf(i_0_1601,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X5))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1602,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk83_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1603,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_892]),
[final] ).
cnf(i_0_1604,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_883]),
[final] ).
cnf(i_0_1605,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_893]),
[final] ).
cnf(i_0_1606,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_894]),
[final] ).
cnf(i_0_1607,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_895]),
[final] ).
cnf(i_0_1608,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_896]),
[final] ).
cnf(i_0_1609,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1610,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_898]),
[final] ).
cnf(i_0_1611,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_899]),
[final] ).
cnf(i_0_1612,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,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_882]),
[final] ).
cnf(i_0_1613,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X4,X2),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_900]),
[final] ).
cnf(i_0_1614,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_901]),
[final] ).
cnf(i_0_1615,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_902]),
[final] ).
cnf(i_0_1616,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_903]),
[final] ).
cnf(i_0_1617,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_904]),
[final] ).
cnf(i_0_1618,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_905]),
[final] ).
cnf(i_0_1619,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_906]),
[final] ).
cnf(i_0_1620,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_907]),
[final] ).
cnf(i_0_1621,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X2,X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_881]),
[final] ).
cnf(i_0_1622,plain,
( X3 = X4
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1623,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_909]),
[final] ).
cnf(i_0_1624,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_868]),
[final] ).
cnf(i_0_1625,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1626,plain,
( c_Predicate_ODomainP(X4,X5,X1,X2)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_911]),
[final] ).
cnf(i_0_1627,plain,
c_Wellfounded_OwfP(X1,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,c_COMBK(tc_HOL_Obool,X1,c_fFalse))),
inference(split_conjunct,[status(thm)],[i_0_912]),
[final] ).
cnf(i_0_1628,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),c_Set_Oinsert(X1,X4,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_881]),
[final] ).
cnf(i_0_1629,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1630,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X3),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1631,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1632,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)),
inference(split_conjunct,[status(thm)],[i_0_916]),
[final] ).
cnf(i_0_1633,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_917]),
[final] ).
cnf(i_0_1634,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_918]),
[final] ).
cnf(i_0_1635,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_863]),
[final] ).
cnf(i_0_1636,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_864]),
[final] ).
cnf(i_0_1637,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4),X3)
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_919]),
[final] ).
cnf(i_0_1638,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4),X3)
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_920]),
[final] ).
cnf(i_0_1639,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_921]),
[final] ).
cnf(i_0_1640,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_922]),
[final] ).
cnf(i_0_1641,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_923]),
[final] ).
cnf(i_0_1642,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_924]),
[final] ).
cnf(i_0_1643,plain,
( X2 = X3
| c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) != c_Set_Oinsert(X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1644,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_926]),
[final] ).
cnf(i_0_1645,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_927]),
[final] ).
cnf(i_0_1646,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_928]),
[final] ).
cnf(i_0_1647,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_929]),
[final] ).
cnf(i_0_1648,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_856]),
[final] ).
cnf(i_0_1649,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_879]),
[final] ).
cnf(i_0_1650,plain,
c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X3,X4)) = c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1651,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_931]),
[final] ).
cnf(i_0_1652,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_932]),
[final] ).
cnf(i_0_1653,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1654,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_934]),
[final] ).
cnf(i_0_1655,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_935]),
[final] ).
cnf(i_0_1656,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_936]),
[final] ).
cnf(i_0_1657,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_937]),
[final] ).
cnf(i_0_1658,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1659,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X4,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_732]),
[final] ).
cnf(i_0_1660,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X4,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_733]),
[final] ).
cnf(i_0_1661,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(X4,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_939]),
[final] ).
cnf(i_0_1662,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4),X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1663,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4),X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_921]),
[final] ).
cnf(i_0_1664,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2),X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1665,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2),X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_921]),
[final] ).
cnf(i_0_1666,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_922]),
[final] ).
cnf(i_0_1667,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_941]),
[final] ).
cnf(i_0_1668,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_922]),
[final] ).
cnf(i_0_1669,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_941]),
[final] ).
cnf(i_0_1670,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,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_942]),
[final] ).
cnf(i_0_1671,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_943]),
[final] ).
cnf(i_0_1672,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_944]),
[final] ).
cnf(i_0_1673,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_944]),
[final] ).
cnf(i_0_1674,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_899]),
[final] ).
cnf(i_0_1675,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1676,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1677,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1678,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1679,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1680,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_948]),
[final] ).
cnf(i_0_1681,plain,
( esk109_3(X1,X2,X3) = esk110_3(X1,X2,X3)
| hAPP(hAPP(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_844]),
[final] ).
cnf(i_0_1682,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk91_2(X2,X1)),esk90_2(X2,X1)))
| c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_699]),
[final] ).
cnf(i_0_1683,plain,
hAPP(hAPP(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_949]),
[final] ).
cnf(i_0_1684,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_950]),
[final] ).
cnf(i_0_1685,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_943]),
[final] ).
cnf(i_0_1686,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2) = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_951]),
[final] ).
cnf(i_0_1687,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_952]),
[final] ).
cnf(i_0_1688,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_953]),
[final] ).
cnf(i_0_1689,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_954]),
[final] ).
cnf(i_0_1690,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_944]),
[final] ).
cnf(i_0_1691,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4),X3)
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_1692,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1693,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_1694,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3))
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_958]),
[final] ).
cnf(i_0_1695,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_959]),
[final] ).
cnf(i_0_1696,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_960]),
[final] ).
cnf(i_0_1697,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_899]),
[final] ).
cnf(i_0_1698,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_961]),
[final] ).
cnf(i_0_1699,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_962]),
[final] ).
cnf(i_0_1700,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1701,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_964]),
[final] ).
cnf(i_0_1702,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_965]),
[final] ).
cnf(i_0_1703,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_695]),
[final] ).
cnf(i_0_1704,plain,
( c_Wellfounded_Owf(X1,X3)
| ~ c_Wellfounded_Owf(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_966]),
[final] ).
cnf(i_0_1705,plain,
( c_Relation_Oantisym(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,X3)
| ~ c_Relation_Oantisym(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_967]),
[final] ).
cnf(i_0_1706,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_968]),
[final] ).
cnf(i_0_1707,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X2),esk112_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_969]),
[final] ).
cnf(i_0_1708,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk111_2(X2,X1)),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_970]),
[final] ).
cnf(i_0_1709,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_971]),
[final] ).
cnf(i_0_1710,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_972]),
[final] ).
cnf(i_0_1711,plain,
( c_Wellfounded_OwfP(X1,X3)
| ~ c_Wellfounded_OwfP(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_973]),
[final] ).
cnf(i_0_1712,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_974]),
[final] ).
cnf(i_0_1713,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_975]),
[final] ).
cnf(i_0_1714,plain,
( c_Relation_Ototal__on(X3,X2,X1)
| esk68_3(X1,X2,X3) != esk69_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1715,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk56_3(X1,X2,X3) != esk57_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1716,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk51_3(X1,X2,X3) != esk52_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_1717,plain,
( c_Wellfounded_OwfP(X1,X2)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk88_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_976]),
[final] ).
cnf(i_0_1718,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_977]),
[final] ).
cnf(i_0_1719,plain,
hAPP(hAPP(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_978]),
[final] ).
cnf(i_0_1720,plain,
c_Set_Oinsert(X1,X2,c_Set_Oinsert(X1,X2,X3)) = c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_979]),
[final] ).
cnf(i_0_1721,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_980]),
[final] ).
cnf(i_0_1722,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_981]),
[final] ).
cnf(i_0_1723,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1724,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1725,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_984]),
[final] ).
cnf(i_0_1726,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_985]),
[final] ).
cnf(i_0_1727,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_986]),
[final] ).
cnf(i_0_1728,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_970]),
[final] ).
cnf(i_0_1729,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_969]),
[final] ).
cnf(i_0_1730,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_987]),
[final] ).
cnf(i_0_1731,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_988]),
[final] ).
cnf(i_0_1732,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_987]),
[final] ).
cnf(i_0_1733,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_988]),
[final] ).
cnf(i_0_1734,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_989]),
[final] ).
cnf(i_0_1735,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_990]),
[final] ).
cnf(i_0_1736,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_1737,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_992]),
[final] ).
cnf(i_0_1738,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Set_Oinsert(X1,X3,X2)),
inference(split_conjunct,[status(thm)],[i_0_993]),
[final] ).
cnf(i_0_1739,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_994]),
[final] ).
cnf(i_0_1740,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_995]),
[final] ).
cnf(i_0_1741,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_996]),
[final] ).
cnf(i_0_1742,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_997]),
[final] ).
cnf(i_0_1743,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1744,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1745,plain,
c_Wellfounded_Owf(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_1746,plain,
c_Relation_Oantisym(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_1000]),
[final] ).
cnf(i_0_1747,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1001]),
[final] ).
cnf(i_0_1748,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1002]),
[final] ).
cnf(i_0_1749,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_1750,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1004]),
[final] ).
cnf(i_0_1751,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1005]),
[final] ).
cnf(i_0_1752,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1006]),
[final] ).
cnf(i_0_1753,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2))
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1007]),
[final] ).
cnf(i_0_1754,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1008]),
[final] ).
cnf(i_0_1755,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1009]),
[final] ).
cnf(i_0_1756,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1010]),
[final] ).
cnf(i_0_1757,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1758,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_1759,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1011]),
[final] ).
cnf(i_0_1760,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1012]),
[final] ).
cnf(i_0_1761,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2) = X3
| ~ class_Lattices_Osemilattice__sup(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1013]),
[final] ).
cnf(i_0_1762,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1014]),
[final] ).
cnf(i_0_1763,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = X2
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1015]),
[final] ).
cnf(i_0_1764,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1016]),
[final] ).
cnf(i_0_1765,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) != X3
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1012]),
[final] ).
cnf(i_0_1766,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) != X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1014]),
[final] ).
cnf(i_0_1767,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_1017]),
[final] ).
cnf(i_0_1768,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1769,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1019]),
[final] ).
cnf(i_0_1770,plain,
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1020]),
[final] ).
cnf(i_0_1771,plain,
( c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1021]),
[final] ).
cnf(i_0_1772,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk16_2(X2,X1)) != hAPP(esk16_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1773,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_1022]),
[final] ).
cnf(i_0_1774,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_1023]),
[final] ).
cnf(i_0_1775,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_1024]),
[final] ).
cnf(i_0_1776,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_1025]),
[final] ).
cnf(i_0_1777,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1026]),
[final] ).
cnf(i_0_1778,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1027]),
[final] ).
cnf(i_0_1779,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1028]),
[final] ).
cnf(i_0_1780,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1029]),
[final] ).
cnf(i_0_1781,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1782,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_1031]),
[final] ).
cnf(i_0_1783,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_1032]),
[final] ).
cnf(i_0_1784,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_1033]),
[final] ).
cnf(i_0_1785,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1034]),
[final] ).
cnf(i_0_1786,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1035]),
[final] ).
cnf(i_0_1787,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1788,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1789,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1790,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1791,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_1040]),
[final] ).
cnf(i_0_1792,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ c_Wellfounded_OwfP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1793,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ c_Wellfounded_OwfP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_976]),
[final] ).
cnf(i_0_1794,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1795,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1796,plain,
( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1797,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_1044]),
[final] ).
cnf(i_0_1798,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_1045]),
[final] ).
cnf(i_0_1799,plain,
c_Relation_ORange(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1800,plain,
c_Relation_ODomain(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1801,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1802,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1803,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_961]),
[final] ).
cnf(i_0_1804,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_961]),
[final] ).
cnf(i_0_1805,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1806,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1807,plain,
c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1808,plain,
c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1052]),
[final] ).
cnf(i_0_1809,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X3) = c_Orderings_Obot__class_Obot(X2)
| X1 != c_Orderings_Obot__class_Obot(X2)
| X3 != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice__bot(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1810,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1053]),
[final] ).
cnf(i_0_1811,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(split_conjunct,[status(thm)],[i_0_1054]),
[final] ).
cnf(i_0_1812,plain,
( hAPP(hAPP(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_1055]),
[final] ).
cnf(i_0_1813,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1056]),
[final] ).
cnf(i_0_1814,plain,
( hAPP(hAPP(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_1057]),
[final] ).
cnf(i_0_1815,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1058]),
[final] ).
cnf(i_0_1816,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_997]),
[final] ).
cnf(i_0_1817,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_997]),
[final] ).
cnf(i_0_1818,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1059]),
[final] ).
cnf(i_0_1819,plain,
( c_Wellfounded_OwfP(X1,c_Transitive__Closure_Otranclp(X1,X2))
| ~ c_Wellfounded_OwfP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1060]),
[final] ).
cnf(i_0_1820,plain,
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1061]),
[final] ).
cnf(i_0_1821,plain,
( c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1062]),
[final] ).
cnf(i_0_1822,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1063]),
[final] ).
cnf(i_0_1823,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1064]),
[final] ).
cnf(i_0_1824,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1065]),
[final] ).
cnf(i_0_1825,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1066]),
[final] ).
cnf(i_0_1826,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1067]),
[final] ).
cnf(i_0_1827,plain,
( c_Relation_Oantisym(X2,X1)
| esk81_2(X1,X2) != esk82_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_771]),
[final] ).
cnf(i_0_1828,plain,
( c_Relation_Oantisym(X2,X1)
| esk79_2(X1,X2) != esk80_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_700]),
[final] ).
cnf(i_0_1829,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_1068]),
[final] ).
cnf(i_0_1830,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_1069]),
[final] ).
cnf(i_0_1831,plain,
c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1070]),
[final] ).
cnf(i_0_1832,plain,
c_Wellfounded_Owf(X1,c_Wellfounded_Omeasure(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1071]),
[final] ).
cnf(i_0_1833,plain,
c_Relation_Oantisym(X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1072]),
[final] ).
cnf(i_0_1834,plain,
c_HOL_OThe(X1,hAPP(c_fequal,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1073]),
[final] ).
cnf(i_0_1835,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1074]),
[final] ).
cnf(i_0_1836,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1075]),
[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_1076]),
[final] ).
cnf(i_0_1838,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1077]),
[final] ).
cnf(i_0_1839,plain,
( class_Lattices_Osemilattice__sup(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1078]),
[final] ).
cnf(i_0_1840,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1079]),
[final] ).
cnf(i_0_1841,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1080]),
[final] ).
cnf(i_0_1842,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1081]),
[final] ).
cnf(i_0_1843,plain,
( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1082]),
[final] ).
cnf(i_0_1844,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1083]),
[final] ).
cnf(i_0_1845,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1084]),
[final] ).
cnf(i_0_1846,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1085]),
[final] ).
cnf(i_0_1847,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[i_0_1086]),
[final] ).
cnf(i_0_1848,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]),
[final] ).
cnf(i_0_1849,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]),
[final] ).
cnf(i_0_1850,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]),
[final] ).
cnf(i_0_1851,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_1852,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]),
[final] ).
cnf(i_0_1853,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]),
[final] ).
cnf(i_0_1854,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]),
[final] ).
cnf(i_0_1855,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]),
[final] ).
cnf(i_0_1856,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1857,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1858,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1859,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1860,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1861,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1862,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1863,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_1864,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_1865,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]),
[final] ).
cnf(i_0_1866,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
[final] ).
cnf(i_0_1867,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1868,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1869,plain,
v_a____ != v_b_H____,
inference(split_conjunct,[status(thm)],[fact_d2_I1_J]),
[final] ).
cnf(i_0_1870,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact_d1_I1_J]),
[final] ).
cnf(i_0_1871,plain,
v_a_H____ != v_b_H____,
inference(split_conjunct,[status(thm)],[fact_d1_I2_J]),
[final] ).
cnf(i_0_1872,plain,
v_b____ != v_a_H____,
inference(split_conjunct,[status(thm)],[fact_d2_I2_J]),
[final] ).
cnf(i_0_1873,plain,
v_b____ != v_b_H____,
inference(split_conjunct,[status(thm)],[fact__096b_A_126_061_Ab_H_096]),
[final] ).
cnf(i_0_1874,axiom,
X1 = X1 ).
cnf(i_0_1875,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1876,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| esk57_3(X1,X3,X4) = esk57_3(X2,X3,X4) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| esk57_3(X3,X1,X4) = esk57_3(X3,X2,X4) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| esk57_3(X3,X4,X1) = esk57_3(X3,X4,X2) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| esk56_3(X1,X3,X4) = esk56_3(X2,X3,X4) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| esk56_3(X3,X1,X4) = esk56_3(X3,X2,X4) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| esk56_3(X3,X4,X1) = esk56_3(X3,X4,X2) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| esk52_3(X1,X3,X4) = esk52_3(X2,X3,X4) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| esk52_3(X3,X1,X4) = esk52_3(X3,X2,X4) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| esk52_3(X3,X4,X1) = esk52_3(X3,X4,X2) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| esk51_3(X1,X3,X4) = esk51_3(X2,X3,X4) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| esk51_3(X3,X1,X4) = esk51_3(X3,X2,X4) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| esk51_3(X3,X4,X1) = esk51_3(X3,X4,X2) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| esk82_2(X1,X3) = esk82_2(X2,X3) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| esk82_2(X3,X1) = esk82_2(X3,X2) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| esk81_2(X1,X3) = esk81_2(X2,X3) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| esk81_2(X3,X1) = esk81_2(X3,X2) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| esk80_2(X1,X3) = esk80_2(X2,X3) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| esk80_2(X3,X1) = esk80_2(X3,X2) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| esk79_2(X1,X3) = esk79_2(X2,X3) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| esk79_2(X3,X1) = esk79_2(X3,X2) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X1,X3,X4,X5,X6) = c_Product__Type_Ointernal__split(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X3,X1,X4,X5,X6) = c_Product__Type_Ointernal__split(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X3,X4,X1,X5,X6) = c_Product__Type_Ointernal__split(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X3,X4,X5,X1,X6) = c_Product__Type_Ointernal__split(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X3,X4,X5,X6,X1) = c_Product__Type_Ointernal__split(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| esk110_3(X1,X3,X4) = esk110_3(X2,X3,X4) ) ).
cnf(i_0_1913,axiom,
( X1 != X2
| esk110_3(X3,X1,X4) = esk110_3(X3,X2,X4) ) ).
cnf(i_0_1914,axiom,
( X1 != X2
| esk110_3(X3,X4,X1) = esk110_3(X3,X4,X2) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| esk109_3(X1,X3,X4) = esk109_3(X2,X3,X4) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| esk109_3(X3,X1,X4) = esk109_3(X3,X2,X4) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| esk109_3(X3,X4,X1) = esk109_3(X3,X4,X2) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| c_Transitive__Closure_Otrancl(X1,X3) = c_Transitive__Closure_Otrancl(X2,X3) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| c_Transitive__Closure_Otrancl(X3,X1) = c_Transitive__Closure_Otrancl(X3,X2) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X1,X3,X4,X5,X6) = c_Nitpick_Owfrec_H(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X3,X1,X4,X5,X6) = c_Nitpick_Owfrec_H(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1922,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X3,X4,X1,X5,X6) = c_Nitpick_Owfrec_H(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1923,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X3,X4,X5,X1,X6) = c_Nitpick_Owfrec_H(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1924,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X3,X4,X5,X6,X1) = c_Nitpick_Owfrec_H(X3,X4,X5,X6,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
| c_Recdef_Owfrec(X1,X3,X4,X5) = c_Recdef_Owfrec(X2,X3,X4,X5) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| c_Recdef_Owfrec(X3,X1,X4,X5) = c_Recdef_Owfrec(X3,X2,X4,X5) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| c_Recdef_Owfrec(X3,X4,X1,X5) = c_Recdef_Owfrec(X3,X4,X2,X5) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| c_Recdef_Owfrec(X3,X4,X5,X1) = c_Recdef_Owfrec(X3,X4,X5,X2) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| c_Relation_ORange(X1,X3,X4) = c_Relation_ORange(X2,X3,X4) ) ).
cnf(i_0_1935,axiom,
( X1 != X2
| c_Relation_ORange(X3,X1,X4) = c_Relation_ORange(X3,X2,X4) ) ).
cnf(i_0_1936,axiom,
( X1 != X2
| c_Relation_ORange(X3,X4,X1) = c_Relation_ORange(X3,X4,X2) ) ).
cnf(i_0_1937,axiom,
( X1 != X2
| c_Product__Type_OSigma(X1,X3,X4,X5) = c_Product__Type_OSigma(X2,X3,X4,X5) ) ).
cnf(i_0_1938,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X1,X4,X5) = c_Product__Type_OSigma(X3,X2,X4,X5) ) ).
cnf(i_0_1939,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X1,X5) = c_Product__Type_OSigma(X3,X4,X2,X5) ) ).
cnf(i_0_1940,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X5,X1) = c_Product__Type_OSigma(X3,X4,X5,X2) ) ).
cnf(i_0_1941,axiom,
( X1 != X2
| esk108_5(X1,X3,X4,X5,X6) = esk108_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1942,axiom,
( X1 != X2
| esk108_5(X3,X1,X4,X5,X6) = esk108_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1943,axiom,
( X1 != X2
| esk108_5(X3,X4,X1,X5,X6) = esk108_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1944,axiom,
( X1 != X2
| esk108_5(X3,X4,X5,X1,X6) = esk108_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1945,axiom,
( X1 != X2
| esk108_5(X3,X4,X5,X6,X1) = esk108_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1946,axiom,
( X1 != X2
| esk107_5(X1,X3,X4,X5,X6) = esk107_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1947,axiom,
( X1 != X2
| esk107_5(X3,X1,X4,X5,X6) = esk107_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1948,axiom,
( X1 != X2
| esk107_5(X3,X4,X1,X5,X6) = esk107_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1949,axiom,
( X1 != X2
| esk107_5(X3,X4,X5,X1,X6) = esk107_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1950,axiom,
( X1 != X2
| esk107_5(X3,X4,X5,X6,X1) = esk107_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1951,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1952,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1953,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1954,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1955,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X1,X3,X4,X5) = c_FuncSet_Orestrict(X2,X3,X4,X5) ) ).
cnf(i_0_1956,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X1,X4,X5) = c_FuncSet_Orestrict(X3,X2,X4,X5) ) ).
cnf(i_0_1957,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X1,X5) = c_FuncSet_Orestrict(X3,X4,X2,X5) ) ).
cnf(i_0_1958,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X5,X1) = c_FuncSet_Orestrict(X3,X4,X5,X2) ) ).
cnf(i_0_1959,axiom,
( X1 != X2
| c_HOL_OLet(X1,X3,X4,X5) = c_HOL_OLet(X2,X3,X4,X5) ) ).
cnf(i_0_1960,axiom,
( X1 != X2
| c_HOL_OLet(X3,X1,X4,X5) = c_HOL_OLet(X3,X2,X4,X5) ) ).
cnf(i_0_1961,axiom,
( X1 != X2
| c_HOL_OLet(X3,X4,X1,X5) = c_HOL_OLet(X3,X4,X2,X5) ) ).
cnf(i_0_1962,axiom,
( X1 != X2
| c_HOL_OLet(X3,X4,X5,X1) = c_HOL_OLet(X3,X4,X5,X2) ) ).
cnf(i_0_1963,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X1,X3,X4,X5,X6) = c_Fun_Othe__inv__into(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1964,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X3,X1,X4,X5,X6) = c_Fun_Othe__inv__into(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1965,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X3,X4,X1,X5,X6) = c_Fun_Othe__inv__into(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1966,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X3,X4,X5,X1,X6) = c_Fun_Othe__inv__into(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1967,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X3,X4,X5,X6,X1) = c_Fun_Othe__inv__into(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1968,axiom,
( X1 != X2
| esk22_2(X1,X3) = esk22_2(X2,X3) ) ).
cnf(i_0_1969,axiom,
( X1 != X2
| esk22_2(X3,X1) = esk22_2(X3,X2) ) ).
cnf(i_0_1970,axiom,
( X1 != X2
| esk23_2(X1,X3) = esk23_2(X2,X3) ) ).
cnf(i_0_1971,axiom,
( X1 != X2
| esk23_2(X3,X1) = esk23_2(X3,X2) ) ).
cnf(i_0_1972,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1973,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1974,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1975,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1976,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1977,axiom,
( X1 != X2
| c_HOL_Oundefined(X1) = c_HOL_Oundefined(X2) ) ).
cnf(i_0_1978,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X1,X3,X4,X5) = c_FuncSet_Oextensional__funcset(X2,X3,X4,X5) ) ).
cnf(i_0_1979,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X1,X4,X5) = c_FuncSet_Oextensional__funcset(X3,X2,X4,X5) ) ).
cnf(i_0_1980,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X1,X5) = c_FuncSet_Oextensional__funcset(X3,X4,X2,X5) ) ).
cnf(i_0_1981,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X5,X1) = c_FuncSet_Oextensional__funcset(X3,X4,X5,X2) ) ).
cnf(i_0_1982,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1983,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1984,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1985,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X1,X3,X4) = c_FuncSet_Oextensional(X2,X3,X4) ) ).
cnf(i_0_1986,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X3,X1,X4) = c_FuncSet_Oextensional(X3,X2,X4) ) ).
cnf(i_0_1987,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X3,X4,X1) = c_FuncSet_Oextensional(X3,X4,X2) ) ).
cnf(i_0_1988,axiom,
( X1 != X2
| esk86_5(X1,X3,X4,X5,X6) = esk86_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1989,axiom,
( X1 != X2
| esk86_5(X3,X1,X4,X5,X6) = esk86_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1990,axiom,
( X1 != X2
| esk86_5(X3,X4,X1,X5,X6) = esk86_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1991,axiom,
( X1 != X2
| esk86_5(X3,X4,X5,X1,X6) = esk86_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1992,axiom,
( X1 != X2
| esk86_5(X3,X4,X5,X6,X1) = esk86_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1993,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_1994,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_1995,axiom,
( X1 != X2
| esk69_3(X1,X3,X4) = esk69_3(X2,X3,X4) ) ).
cnf(i_0_1996,axiom,
( X1 != X2
| esk69_3(X3,X1,X4) = esk69_3(X3,X2,X4) ) ).
cnf(i_0_1997,axiom,
( X1 != X2
| esk69_3(X3,X4,X1) = esk69_3(X3,X4,X2) ) ).
cnf(i_0_1998,axiom,
( X1 != X2
| esk68_3(X1,X3,X4) = esk68_3(X2,X3,X4) ) ).
cnf(i_0_1999,axiom,
( X1 != X2
| esk68_3(X3,X1,X4) = esk68_3(X3,X2,X4) ) ).
cnf(i_0_2000,axiom,
( X1 != X2
| esk68_3(X3,X4,X1) = esk68_3(X3,X4,X2) ) ).
cnf(i_0_2001,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_2002,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_2003,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_2004,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_2005,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_2006,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_2007,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_2008,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_2009,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_2010,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_2011,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_2012,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_2013,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X1,X3)
| c_Relation_Oantisym(X2,X3) ) ).
cnf(i_0_2014,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X3,X1)
| c_Relation_Oantisym(X3,X2) ) ).
cnf(i_0_2015,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_2016,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_2017,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_2018,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_2019,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_2020,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_2021,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_2022,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X1,X3,X4,X5)
| c_Recdef_Oadm__wf(X2,X3,X4,X5) ) ).
cnf(i_0_2023,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X1,X4,X5)
| c_Recdef_Oadm__wf(X3,X2,X4,X5) ) ).
cnf(i_0_2024,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X1,X5)
| c_Recdef_Oadm__wf(X3,X4,X2,X5) ) ).
cnf(i_0_2025,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X5,X1)
| c_Recdef_Oadm__wf(X3,X4,X5,X2) ) ).
cnf(i_0_2026,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_2027,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__sup(X1)
| class_Lattices_Osemilattice__sup(X2) ) ).
cnf(i_0_2028,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_2029,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2030,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2031,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2032,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__bot(X1)
| class_Lattices_Obounded__lattice__bot(X2) ) ).
cnf(i_0_2033,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_2034,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_2035,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_2036,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_2037,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_2038,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_2039,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_2040,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X1,X3,X4,X5)
| c_Predicate_ODomainP(X2,X3,X4,X5) ) ).
cnf(i_0_2041,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X1,X4,X5)
| c_Predicate_ODomainP(X3,X2,X4,X5) ) ).
cnf(i_0_2042,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X1,X5)
| c_Predicate_ODomainP(X3,X4,X2,X5) ) ).
cnf(i_0_2043,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X5,X1)
| c_Predicate_ODomainP(X3,X4,X5,X2) ) ).
cnf(i_0_2044,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X1,X3,X4,X5)
| c_Predicate_ORangeP(X2,X3,X4,X5) ) ).
cnf(i_0_2045,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X1,X4,X5)
| c_Predicate_ORangeP(X3,X2,X4,X5) ) ).
cnf(i_0_2046,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X1,X5)
| c_Predicate_ORangeP(X3,X4,X2,X5) ) ).
cnf(i_0_2047,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X5,X1)
| c_Predicate_ORangeP(X3,X4,X5,X2) ) ).
cnf(i_0_2048,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X1,X3)
| c_Wellfounded_OwfP(X2,X3) ) ).
cnf(i_0_2049,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X3,X1)
| c_Wellfounded_OwfP(X3,X2) ) ).
cnf(i_0_2050,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_2051,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_2052,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1874_001,axiom,
X1 = X1 ).
cnf(i_0_1875_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1876_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1877_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1878_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1879_006,axiom,
( X1 != X2
| esk57_3(X1,X3,X4) = esk57_3(X2,X3,X4) ) ).
cnf(i_0_1880_007,axiom,
( X1 != X2
| esk57_3(X3,X1,X4) = esk57_3(X3,X2,X4) ) ).
cnf(i_0_1881_008,axiom,
( X1 != X2
| esk57_3(X3,X4,X1) = esk57_3(X3,X4,X2) ) ).
cnf(i_0_1882_009,axiom,
( X1 != X2
| esk56_3(X1,X3,X4) = esk56_3(X2,X3,X4) ) ).
cnf(i_0_1883_010,axiom,
( X1 != X2
| esk56_3(X3,X1,X4) = esk56_3(X3,X2,X4) ) ).
cnf(i_0_1884_011,axiom,
( X1 != X2
| esk56_3(X3,X4,X1) = esk56_3(X3,X4,X2) ) ).
cnf(i_0_1885_012,axiom,
( X1 != X2
| esk52_3(X1,X3,X4) = esk52_3(X2,X3,X4) ) ).
cnf(i_0_1886_013,axiom,
( X1 != X2
| esk52_3(X3,X1,X4) = esk52_3(X3,X2,X4) ) ).
cnf(i_0_1887_014,axiom,
( X1 != X2
| esk52_3(X3,X4,X1) = esk52_3(X3,X4,X2) ) ).
cnf(i_0_1888_015,axiom,
( X1 != X2
| esk51_3(X1,X3,X4) = esk51_3(X2,X3,X4) ) ).
cnf(i_0_1889_016,axiom,
( X1 != X2
| esk51_3(X3,X1,X4) = esk51_3(X3,X2,X4) ) ).
cnf(i_0_1890_017,axiom,
( X1 != X2
| esk51_3(X3,X4,X1) = esk51_3(X3,X4,X2) ) ).
cnf(i_0_1891_018,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1892_019,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_1893_020,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_1894_021,axiom,
( X1 != X2
| esk82_2(X1,X3) = esk82_2(X2,X3) ) ).
cnf(i_0_1895_022,axiom,
( X1 != X2
| esk82_2(X3,X1) = esk82_2(X3,X2) ) ).
cnf(i_0_1896_023,axiom,
( X1 != X2
| esk81_2(X1,X3) = esk81_2(X2,X3) ) ).
cnf(i_0_1897_024,axiom,
( X1 != X2
| esk81_2(X3,X1) = esk81_2(X3,X2) ) ).
cnf(i_0_1898_025,axiom,
( X1 != X2
| esk80_2(X1,X3) = esk80_2(X2,X3) ) ).
cnf(i_0_1899_026,axiom,
( X1 != X2
| esk80_2(X3,X1) = esk80_2(X3,X2) ) ).
cnf(i_0_1900_027,axiom,
( X1 != X2
| esk79_2(X1,X3) = esk79_2(X2,X3) ) ).
cnf(i_0_1901_028,axiom,
( X1 != X2
| esk79_2(X3,X1) = esk79_2(X3,X2) ) ).
cnf(i_0_1902_029,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X1,X3,X4,X5,X6) = c_Product__Type_Ointernal__split(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1903_030,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X3,X1,X4,X5,X6) = c_Product__Type_Ointernal__split(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1904_031,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X3,X4,X1,X5,X6) = c_Product__Type_Ointernal__split(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1905_032,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X3,X4,X5,X1,X6) = c_Product__Type_Ointernal__split(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1906_033,axiom,
( X1 != X2
| c_Product__Type_Ointernal__split(X3,X4,X5,X6,X1) = c_Product__Type_Ointernal__split(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1907_034,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1908_035,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1909_036,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1910_037,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1911_038,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1912_039,axiom,
( X1 != X2
| esk110_3(X1,X3,X4) = esk110_3(X2,X3,X4) ) ).
cnf(i_0_1913_040,axiom,
( X1 != X2
| esk110_3(X3,X1,X4) = esk110_3(X3,X2,X4) ) ).
cnf(i_0_1914_041,axiom,
( X1 != X2
| esk110_3(X3,X4,X1) = esk110_3(X3,X4,X2) ) ).
cnf(i_0_1915_042,axiom,
( X1 != X2
| esk109_3(X1,X3,X4) = esk109_3(X2,X3,X4) ) ).
cnf(i_0_1916_043,axiom,
( X1 != X2
| esk109_3(X3,X1,X4) = esk109_3(X3,X2,X4) ) ).
cnf(i_0_1917_044,axiom,
( X1 != X2
| esk109_3(X3,X4,X1) = esk109_3(X3,X4,X2) ) ).
cnf(i_0_1918_045,axiom,
( X1 != X2
| c_Transitive__Closure_Otrancl(X1,X3) = c_Transitive__Closure_Otrancl(X2,X3) ) ).
cnf(i_0_1919_046,axiom,
( X1 != X2
| c_Transitive__Closure_Otrancl(X3,X1) = c_Transitive__Closure_Otrancl(X3,X2) ) ).
cnf(i_0_1920_047,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X1,X3,X4,X5,X6) = c_Nitpick_Owfrec_H(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1921_048,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X3,X1,X4,X5,X6) = c_Nitpick_Owfrec_H(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1922_049,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X3,X4,X1,X5,X6) = c_Nitpick_Owfrec_H(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1923_050,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X3,X4,X5,X1,X6) = c_Nitpick_Owfrec_H(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1924_051,axiom,
( X1 != X2
| c_Nitpick_Owfrec_H(X3,X4,X5,X6,X1) = c_Nitpick_Owfrec_H(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1925_052,axiom,
( X1 != X2
| c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).
cnf(i_0_1926_053,axiom,
( X1 != X2
| c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).
cnf(i_0_1927_054,axiom,
( X1 != X2
| c_Recdef_Owfrec(X1,X3,X4,X5) = c_Recdef_Owfrec(X2,X3,X4,X5) ) ).
cnf(i_0_1928_055,axiom,
( X1 != X2
| c_Recdef_Owfrec(X3,X1,X4,X5) = c_Recdef_Owfrec(X3,X2,X4,X5) ) ).
cnf(i_0_1929_056,axiom,
( X1 != X2
| c_Recdef_Owfrec(X3,X4,X1,X5) = c_Recdef_Owfrec(X3,X4,X2,X5) ) ).
cnf(i_0_1930_057,axiom,
( X1 != X2
| c_Recdef_Owfrec(X3,X4,X5,X1) = c_Recdef_Owfrec(X3,X4,X5,X2) ) ).
cnf(i_0_1931_058,axiom,
( X1 != X2
| c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).
cnf(i_0_1932_059,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).
cnf(i_0_1933_060,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).
cnf(i_0_1934_061,axiom,
( X1 != X2
| c_Relation_ORange(X1,X3,X4) = c_Relation_ORange(X2,X3,X4) ) ).
cnf(i_0_1935_062,axiom,
( X1 != X2
| c_Relation_ORange(X3,X1,X4) = c_Relation_ORange(X3,X2,X4) ) ).
cnf(i_0_1936_063,axiom,
( X1 != X2
| c_Relation_ORange(X3,X4,X1) = c_Relation_ORange(X3,X4,X2) ) ).
cnf(i_0_1937_064,axiom,
( X1 != X2
| c_Product__Type_OSigma(X1,X3,X4,X5) = c_Product__Type_OSigma(X2,X3,X4,X5) ) ).
cnf(i_0_1938_065,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X1,X4,X5) = c_Product__Type_OSigma(X3,X2,X4,X5) ) ).
cnf(i_0_1939_066,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X1,X5) = c_Product__Type_OSigma(X3,X4,X2,X5) ) ).
cnf(i_0_1940_067,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X5,X1) = c_Product__Type_OSigma(X3,X4,X5,X2) ) ).
cnf(i_0_1941_068,axiom,
( X1 != X2
| esk108_5(X1,X3,X4,X5,X6) = esk108_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1942_069,axiom,
( X1 != X2
| esk108_5(X3,X1,X4,X5,X6) = esk108_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1943_070,axiom,
( X1 != X2
| esk108_5(X3,X4,X1,X5,X6) = esk108_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1944_071,axiom,
( X1 != X2
| esk108_5(X3,X4,X5,X1,X6) = esk108_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1945_072,axiom,
( X1 != X2
| esk108_5(X3,X4,X5,X6,X1) = esk108_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1946_073,axiom,
( X1 != X2
| esk107_5(X1,X3,X4,X5,X6) = esk107_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1947_074,axiom,
( X1 != X2
| esk107_5(X3,X1,X4,X5,X6) = esk107_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1948_075,axiom,
( X1 != X2
| esk107_5(X3,X4,X1,X5,X6) = esk107_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1949_076,axiom,
( X1 != X2
| esk107_5(X3,X4,X5,X1,X6) = esk107_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1950_077,axiom,
( X1 != X2
| esk107_5(X3,X4,X5,X6,X1) = esk107_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1951_078,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1952_079,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1953_080,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1954_081,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1955_082,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X1,X3,X4,X5) = c_FuncSet_Orestrict(X2,X3,X4,X5) ) ).
cnf(i_0_1956_083,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X1,X4,X5) = c_FuncSet_Orestrict(X3,X2,X4,X5) ) ).
cnf(i_0_1957_084,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X1,X5) = c_FuncSet_Orestrict(X3,X4,X2,X5) ) ).
cnf(i_0_1958_085,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X5,X1) = c_FuncSet_Orestrict(X3,X4,X5,X2) ) ).
cnf(i_0_1959_086,axiom,
( X1 != X2
| c_HOL_OLet(X1,X3,X4,X5) = c_HOL_OLet(X2,X3,X4,X5) ) ).
cnf(i_0_1960_087,axiom,
( X1 != X2
| c_HOL_OLet(X3,X1,X4,X5) = c_HOL_OLet(X3,X2,X4,X5) ) ).
cnf(i_0_1961_088,axiom,
( X1 != X2
| c_HOL_OLet(X3,X4,X1,X5) = c_HOL_OLet(X3,X4,X2,X5) ) ).
cnf(i_0_1962_089,axiom,
( X1 != X2
| c_HOL_OLet(X3,X4,X5,X1) = c_HOL_OLet(X3,X4,X5,X2) ) ).
cnf(i_0_1963_090,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X1,X3,X4,X5,X6) = c_Fun_Othe__inv__into(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1964_091,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X3,X1,X4,X5,X6) = c_Fun_Othe__inv__into(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1965_092,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X3,X4,X1,X5,X6) = c_Fun_Othe__inv__into(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1966_093,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X3,X4,X5,X1,X6) = c_Fun_Othe__inv__into(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1967_094,axiom,
( X1 != X2
| c_Fun_Othe__inv__into(X3,X4,X5,X6,X1) = c_Fun_Othe__inv__into(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1968_095,axiom,
( X1 != X2
| esk22_2(X1,X3) = esk22_2(X2,X3) ) ).
cnf(i_0_1969_096,axiom,
( X1 != X2
| esk22_2(X3,X1) = esk22_2(X3,X2) ) ).
cnf(i_0_1970_097,axiom,
( X1 != X2
| esk23_2(X1,X3) = esk23_2(X2,X3) ) ).
cnf(i_0_1971_098,axiom,
( X1 != X2
| esk23_2(X3,X1) = esk23_2(X3,X2) ) ).
cnf(i_0_1972_099,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1973_100,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1974_101,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1975_102,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1976_103,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1977_104,axiom,
( X1 != X2
| c_HOL_Oundefined(X1) = c_HOL_Oundefined(X2) ) ).
cnf(i_0_1978_105,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X1,X3,X4,X5) = c_FuncSet_Oextensional__funcset(X2,X3,X4,X5) ) ).
cnf(i_0_1979_106,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X1,X4,X5) = c_FuncSet_Oextensional__funcset(X3,X2,X4,X5) ) ).
cnf(i_0_1980_107,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X1,X5) = c_FuncSet_Oextensional__funcset(X3,X4,X2,X5) ) ).
cnf(i_0_1981_108,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X5,X1) = c_FuncSet_Oextensional__funcset(X3,X4,X5,X2) ) ).
cnf(i_0_1982_109,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1983_110,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1984_111,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1985_112,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X1,X3,X4) = c_FuncSet_Oextensional(X2,X3,X4) ) ).
cnf(i_0_1986_113,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X3,X1,X4) = c_FuncSet_Oextensional(X3,X2,X4) ) ).
cnf(i_0_1987_114,axiom,
( X1 != X2
| c_FuncSet_Oextensional(X3,X4,X1) = c_FuncSet_Oextensional(X3,X4,X2) ) ).
cnf(i_0_1988_115,axiom,
( X1 != X2
| esk86_5(X1,X3,X4,X5,X6) = esk86_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1989_116,axiom,
( X1 != X2
| esk86_5(X3,X1,X4,X5,X6) = esk86_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1990_117,axiom,
( X1 != X2
| esk86_5(X3,X4,X1,X5,X6) = esk86_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1991_118,axiom,
( X1 != X2
| esk86_5(X3,X4,X5,X1,X6) = esk86_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1992_119,axiom,
( X1 != X2
| esk86_5(X3,X4,X5,X6,X1) = esk86_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1993_120,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_1994_121,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_1995_122,axiom,
( X1 != X2
| esk69_3(X1,X3,X4) = esk69_3(X2,X3,X4) ) ).
cnf(i_0_1996_123,axiom,
( X1 != X2
| esk69_3(X3,X1,X4) = esk69_3(X3,X2,X4) ) ).
cnf(i_0_1997_124,axiom,
( X1 != X2
| esk69_3(X3,X4,X1) = esk69_3(X3,X4,X2) ) ).
cnf(i_0_1998_125,axiom,
( X1 != X2
| esk68_3(X1,X3,X4) = esk68_3(X2,X3,X4) ) ).
cnf(i_0_1999_126,axiom,
( X1 != X2
| esk68_3(X3,X1,X4) = esk68_3(X3,X2,X4) ) ).
cnf(i_0_2000_127,axiom,
( X1 != X2
| esk68_3(X3,X4,X1) = esk68_3(X3,X4,X2) ) ).
cnf(i_0_2001_128,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_2002_129,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_2003_130,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_2004_131,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_2005_132,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_2006_133,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_2007_134,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_2008_135,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_2009_136,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_2010_137,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_2011_138,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_2012_139,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_2013_140,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X1,X3)
| c_Relation_Oantisym(X2,X3) ) ).
cnf(i_0_2014_141,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X3,X1)
| c_Relation_Oantisym(X3,X2) ) ).
cnf(i_0_2015_142,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_2016_143,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_2017_144,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_2018_145,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_2019_146,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_2020_147,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_2021_148,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_2022_149,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X1,X3,X4,X5)
| c_Recdef_Oadm__wf(X2,X3,X4,X5) ) ).
cnf(i_0_2023_150,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X1,X4,X5)
| c_Recdef_Oadm__wf(X3,X2,X4,X5) ) ).
cnf(i_0_2024_151,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X1,X5)
| c_Recdef_Oadm__wf(X3,X4,X2,X5) ) ).
cnf(i_0_2025_152,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X5,X1)
| c_Recdef_Oadm__wf(X3,X4,X5,X2) ) ).
cnf(i_0_2026_153,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_2027_154,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__sup(X1)
| class_Lattices_Osemilattice__sup(X2) ) ).
cnf(i_0_2028_155,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_2029_156,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2030_157,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2031_158,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2032_159,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__bot(X1)
| class_Lattices_Obounded__lattice__bot(X2) ) ).
cnf(i_0_2033_160,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_2034_161,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_2035_162,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_2036_163,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_2037_164,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_2038_165,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_2039_166,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_2040_167,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X1,X3,X4,X5)
| c_Predicate_ODomainP(X2,X3,X4,X5) ) ).
cnf(i_0_2041_168,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X1,X4,X5)
| c_Predicate_ODomainP(X3,X2,X4,X5) ) ).
cnf(i_0_2042_169,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X1,X5)
| c_Predicate_ODomainP(X3,X4,X2,X5) ) ).
cnf(i_0_2043_170,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X5,X1)
| c_Predicate_ODomainP(X3,X4,X5,X2) ) ).
cnf(i_0_2044_171,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X1,X3,X4,X5)
| c_Predicate_ORangeP(X2,X3,X4,X5) ) ).
cnf(i_0_2045_172,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X1,X4,X5)
| c_Predicate_ORangeP(X3,X2,X4,X5) ) ).
cnf(i_0_2046_173,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X1,X5)
| c_Predicate_ORangeP(X3,X4,X2,X5) ) ).
cnf(i_0_2047_174,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X5,X1)
| c_Predicate_ORangeP(X3,X4,X5,X2) ) ).
cnf(i_0_2048_175,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X1,X3)
| c_Wellfounded_OwfP(X2,X3) ) ).
cnf(i_0_2049_176,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X3,X1)
| c_Wellfounded_OwfP(X3,X2) ) ).
cnf(i_0_2050_177,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_2051_178,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_2052_179,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_2053,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,X5),hAPP(hAPP(X4,X6),X5)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk5_7(X6,X5,X4,X3,X2,X1,X6)),X5)),X3)) ),
inference(equality_inference,[],[1099]) ).
cnf(i_0_2054,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,X5),hAPP(hAPP(X4,X6),X5)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk18_7(hAPP(hAPP(X4,X6),X5),X5,X4,X3,X2,X1,X6)),X5)),X3)) ),
inference(equality_inference,[],[1100]) ).
cnf(i_0_2055,plain,
( ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,esk5_7(X5,X6,X4,X3,X2,X1,X5)),hAPP(X5,esk5_7(X5,X6,X4,X3,X2,X1,X5))))
| hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,X6),hAPP(hAPP(X4,X5),X6))) ),
inference(equality_inference,[],[1103]) ).
cnf(i_0_2056,plain,
( hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,X5),hAPP(hAPP(X4,X6),X5)))
| ~ hBOOL(hAPP(c_Recdef_Owfrec__rel(X1,X2,X3,X4,esk18_7(hAPP(hAPP(X4,X6),X5),X5,X4,X3,X2,X1,X6)),hAPP(X6,esk18_7(hAPP(hAPP(X4,X6),X5),X5,X4,X3,X2,X1,X6)))) ),
inference(equality_inference,[],[1104]) ).
cnf(i_0_2057,plain,
( ~ c_Recdef_Oadm__wf(X1,X2,X3,X4)
| hAPP(hAPP(X4,X5),X6) = hAPP(hAPP(X4,X5),X6) ),
inference(equality_inference,[],[1111]) ).
cnf(i_0_2058,plain,
X1 = X1,
inference(equality_inference,[],[1119]) ).
cnf(i_0_2059,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,[],[1142]) ).
cnf(i_0_2060,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk76_4(X2,X2,X3,X1)),esk76_4(X2,X2,X3,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),X2)),X3)) ),
inference(equality_inference,[],[1162]) ).
cnf(i_0_2061,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,[],[1184]) ).
cnf(i_0_2062,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,[],[1197]) ).
cnf(i_0_2063,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,[],[1229]) ).
cnf(i_0_2064,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,[],[1230]) ).
cnf(i_0_2065,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,[],[1233]) ).
cnf(i_0_2066,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,[],[1234]) ).
cnf(i_0_2067,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,[],[1260]) ).
cnf(i_0_2068,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,[],[1262]) ).
cnf(i_0_2069,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,[],[1272]) ).
cnf(i_0_2070,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,[],[1273]) ).
cnf(i_0_2071,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,[],[1275]) ).
cnf(i_0_2072,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,[],[1276]) ).
cnf(i_0_2073,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,[],[1278]) ).
cnf(i_0_2074,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,[],[1281]) ).
cnf(i_0_2075,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,[],[1282]) ).
cnf(i_0_2076,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,[],[1284]) ).
cnf(i_0_2077,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,[],[1312]) ).
cnf(i_0_2078,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,[],[1326]) ).
cnf(i_0_2079,plain,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
inference(equality_inference,[],[1346]) ).
cnf(i_0_2080,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,[],[1365]) ).
cnf(i_0_2081,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,[],[1426]) ).
cnf(i_0_2082,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,[],[1427]) ).
cnf(i_0_2083,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
inference(equality_inference,[],[1432]) ).
cnf(i_0_2084,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,[],[1450]) ).
cnf(i_0_2085,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| hAPP(c_Recdef_Owfrec(X1,X3,X2,X4),X5) = hAPP(hAPP(X4,hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X3),c_Recdef_Owfrec(X1,X3,X2,X4)),X2),X5)),X5) ),
inference(equality_inference,[],[1451]) ).
cnf(i_0_2086,plain,
c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
inference(equality_inference,[],[1457]) ).
cnf(i_0_2087,plain,
X1 = X1,
inference(equality_inference,[],[1473]) ).
cnf(i_0_2088,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,[],[1474]) ).
cnf(i_0_2089,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,[],[1495]) ).
cnf(i_0_2090,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,[],[1496]) ).
cnf(i_0_2091,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1520]) ).
cnf(i_0_2092,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1521]) ).
cnf(i_0_2093,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1522]) ).
cnf(i_0_2094,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1523]) ).
cnf(i_0_2095,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(equality_inference,[],[1622]) ).
cnf(i_0_2096,plain,
X1 = X1,
inference(equality_inference,[],[1643]) ).
cnf(i_0_2097,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(equality_inference,[],[1649]) ).
cnf(i_0_2098,plain,
X1 = X1,
inference(equality_inference,[],[1676]) ).
cnf(i_0_2099,plain,
X1 = X1,
inference(equality_inference,[],[1678]) ).
cnf(i_0_2100,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(equality_inference,[],[1697]) ).
cnf(i_0_2101,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(equality_inference,[],[1729]) ).
cnf(i_0_2102,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(equality_inference,[],[1732]) ).
cnf(i_0_2103,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,[],[1733]) ).
cnf(i_0_2104,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1757]) ).
cnf(i_0_2105,plain,
X1 = X1,
inference(equality_inference,[],[1778]) ).
cnf(i_0_2106,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1805]) ).
cnf(i_0_2107,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1806]) ).
cnf(i_0_2108,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1810]) ).
cnf(i_0_2109,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1816]) ).
cnf(i_0_2110,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1817]) ).
cnf(i_0_2111,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[1818]) ).
cnf(i_0_2112,plain,
$false,
inference(scs_inference,[],[i_0_1436,i_0_1868,i_0_1445,i_0_1499,i_0_1207]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SCT131+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n014.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 01:58:06 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 3.24/5.73 % Version : CSE_E---1.7
% 3.24/5.73 % Problem : theBenchmark.p
% 3.24/5.73 % SZS status Theorem for theBenchmark.p
% 3.24/5.73 % SZS output start CNFRefutation
% See solution above
% 3.43/5.84 % Total time : 5.388s
%------------------------------------------------------------------------------