%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SCT045-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:08:14 PM UTC 2026
% Result : Unsatisfiable 208.95s 31.32s
% Output : CNFRefutation 208.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 63
% Syntax : Number of clauses : 314 ( 130 unt; 47 nHn; 125 RR)
% Number of literals : 566 ( 153 equ; 245 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 2 con; 0-5 aty)
% Number of variables : 793 ( 236 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_xt1_I11_J_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_inf__le1_0,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_order__trans_0,axiom,
( ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(cls_le__funD_0,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(cls_Collect__mem__eq_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_insert__def_0,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
cnf(cls_funcset__image_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4)))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__image_0) ).
cnf(cls_Pi__I_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X4,X5,X3,X1,X2)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_0) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
cnf(cls_inf__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
cnf(cls_inf__absorb2_0,axiom,
( ~ c_lessequals(X3,X2,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
cnf(cls_diff__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
cnf(cls_order__le__less__trans_0,axiom,
( ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_compl__inf_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(cls_double__compl_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_inf__le2_0,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
cnf(cls_image__constant__conv_1,axiom,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
cnf(cls_subset__empty_0,axiom,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_less__infI2_0,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
cnf(cls_rev__bexI_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
( ~ class_Lattices_Oboolean__algebra(X2)
| class_Lattices_Oboolean__algebra(tc_fun(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
cnf(cls_Collect__neg__eq_0,axiom,
c_Collect(hAPP(c_COMBB(c_Not,tc_bool,tc_bool,X1),X2),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Collect(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(cls_UN__extend__simps_I3_J_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X3,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X1,hAPP(X5,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_inf__compl__bot_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
cnf(cls_Diff__empty_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
cnf(cls_subset__Compl__self__eq_0,axiom,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
cnf(cls_inf__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_le__iff__sup_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_ball__conj__distrib_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X4,X5,X1,X3)),X4))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_1) ).
cnf(cls_inf__sup__absorb_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_less__infI1_0,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_not__Cons__self_0,axiom,
X1 != c_List_Olist_OCons(X2,X1,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
cnf(cls_list_Osimps_I2_J_0,axiom,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
cnf(c_0_63,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_xt1_I11_J_0]) ).
cnf(c_0_64,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__le1_0]) ).
cnf(c_0_65,plain,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1) ),
inference(fof_simplification,[status(thm)],[cls_less__le__not__le_1]) ).
cnf(c_0_66,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
c_0_63 ).
cnf(c_0_67,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_68,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_bot__least_0]) ).
cnf(c_0_69,plain,
( ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_order__trans_0]) ).
cnf(c_0_70,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1) ),
c_0_64 ).
cnf(c_0_71,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_72,plain,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
inference(fof_simplification,[status(thm)],[cls_le__funD_0]) ).
cnf(c_0_73,plain,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1) ),
c_0_65 ).
cnf(c_0_74,plain,
( ~ c_lessequals(X1,X2,tc_bool)
| c_HOL_Oord__class_Oless(X1,X2,tc_bool)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder ).
cnf(c_0_76,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
c_0_68 ).
cnf(c_0_77,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_78,plain,
( ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X2,X3,X1) ),
c_0_69 ).
cnf(c_0_79,plain,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2),X1,tc_bool),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,plain,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
c_0_72 ).
cnf(c_0_81,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
cls_empty__subsetI_0 ).
cnf(c_0_82,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_83,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_84,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_85,plain,
( ~ c_lessequals(X1,X2,tc_bool)
| ~ c_lessequals(X2,X1,tc_bool)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_86,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_87,plain,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),X3),tc_bool)
| c_lessequals(X1,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_75])]) ).
cnf(c_0_88,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),hAPP(X3,X2),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).
cnf(c_0_89,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_90,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[cls_bot1E_0]) ).
cnf(c_0_92,plain,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3,tc_bool),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_94,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3)),X2),
cls_insert__def_0 ).
cnf(c_0_95,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4)))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_funcset__image_0]) ).
cnf(c_0_96,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X4,X5,X3,X1,X2)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2))) ),
cls_Pi__I_0 ).
cnf(c_0_97,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_98,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_91 ).
cnf(c_0_99,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_100,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
inference(fof_simplification,[status(thm)],[cls_empty__not__insert_0]) ).
cnf(c_0_101,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
cls_singleton__conv2_0 ).
cnf(c_0_102,plain,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1)),X2),
inference(rw,[status(thm)],[c_0_94,c_0_84]) ).
cnf(c_0_103,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
inference(fof_simplification,[status(thm)],[cls_inf__commute_0]) ).
cnf(c_0_104,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3 ),
inference(fof_simplification,[status(thm)],[cls_inf__absorb2_0]) ).
cnf(c_0_105,plain,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__sup__ord_I3_J_0]) ).
cnf(c_0_106,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
inference(fof_simplification,[status(thm)],[cls_diff__eq_0]) ).
cnf(c_0_107,plain,
( ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_order__le__less__trans_0]) ).
cnf(c_0_108,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4)))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
c_0_95 ).
cnf(c_0_109,plain,
( hBOOL(hAPP(c_FuncSet_OPi(X1,X2,X4,X5),X3))
| hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X1,X2,X3,X4,X5))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_97]) ).
cnf(c_0_110,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_111,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
c_0_100 ).
cnf(c_0_112,plain,
hAPP(c_fequal(X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_84]),c_0_102]) ).
cnf(c_0_113,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
cls_Un__empty__right_0 ).
cnf(c_0_114,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
c_0_103 ).
cnf(c_0_115,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3 ),
c_0_104 ).
cnf(c_0_116,plain,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X1) ),
c_0_105 ).
cnf(c_0_117,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_118,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
inference(fof_simplification,[status(thm)],[cls_compl__inf_0]) ).
cnf(c_0_119,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
c_0_106 ).
cnf(c_0_120,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_121,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_double__compl_0]) ).
cnf(c_0_122,plain,
( ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
c_0_107 ).
cnf(c_0_123,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__le2_0]) ).
cnf(c_0_124,axiom,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
cls_image__constant__conv_1 ).
cnf(c_0_125,plain,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_subset__empty_0]) ).
cnf(c_0_126,plain,
( ~ hBOOL(hAPP(c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4),X1))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
inference(rw,[status(thm)],[c_0_108,c_0_97]) ).
cnf(c_0_127,plain,
hBOOL(hAPP(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3,X4),X5)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_99]),c_0_110]) ).
cnf(c_0_128,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2)),X3),
inference(rw,[status(thm)],[c_0_111,c_0_102]) ).
cnf(c_0_129,plain,
hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2) = hAPP(c_fequal(X1),X2),
inference(rw,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_130,plain,
( ~ c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(fof_simplification,[status(thm)],[cls_order__less__le_1]) ).
cnf(c_0_131,plain,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_less__infI2_0]) ).
cnf(c_0_132,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),X1),
inference(spm,[status(thm)],[c_0_114,c_0_71]) ).
cnf(c_0_133,plain,
( ~ c_lessequals(X2,X1,tc_bool)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) = X2 ),
inference(spm,[status(thm)],[c_0_115,c_0_71]) ).
cnf(c_0_134,plain,
c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2),tc_bool),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_135,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
c_0_118 ).
cnf(c_0_136,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_bool),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_137,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
c_0_121 ).
cnf(c_0_138,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[cls_rev__bexI_1]) ).
cnf(c_0_139,plain,
( ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_order__less__le__trans_0]) ).
cnf(c_0_140,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_bool)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_86]),c_0_75])]) ).
cnf(c_0_141,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1) ),
c_0_123 ).
cnf(c_0_142,plain,
( ~ class_Lattices_Oboolean__algebra(X2)
| class_Lattices_Oboolean__algebra(tc_fun(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clsarity_fun__Lattices_Oboolean__algebra]) ).
cnf(c_0_143,axiom,
c_Collect(hAPP(c_COMBB(c_Not,tc_bool,tc_bool,X1),X2),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Collect(X2,X1)),
cls_Collect__neg__eq_0 ).
cnf(c_0_144,plain,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_124,c_0_102]) ).
cnf(c_0_145,plain,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_125 ).
cnf(c_0_146,plain,
c_lessequals(c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5,tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_147,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_148,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = X2,
cls_UN__extend__simps_I3_J_0 ).
cnf(c_0_149,plain,
( ~ c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
c_0_130 ).
cnf(c_0_150,plain,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) ),
c_0_131 ).
cnf(c_0_151,plain,
( ~ c_lessequals(X1,X2,tc_bool)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_152,plain,
c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_120])]) ).
cnf(c_0_153,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)),X2) = c_HOL_Ominus__class_Ominus(X2,X1,tc_bool),
inference(spm,[status(thm)],[c_0_132,c_0_136]) ).
cnf(c_0_154,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = X1,
inference(spm,[status(thm)],[c_0_137,c_0_120]) ).
cnf(c_0_155,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
c_0_138 ).
cnf(c_0_156,plain,
( ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
c_0_139 ).
cnf(c_0_157,plain,
( ~ c_lessequals(X1,X2,tc_bool)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X2,tc_bool)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_140,c_0_74]) ).
cnf(c_0_158,plain,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2),X2,tc_bool),
inference(spm,[status(thm)],[c_0_141,c_0_71]) ).
cnf(c_0_159,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X3,tc_fun(X1,tc_bool)),
cls_Int__lower2_0 ).
cnf(c_0_160,plain,
( ~ class_Lattices_Oboolean__algebra(X2)
| class_Lattices_Oboolean__algebra(tc_fun(X1,X2)) ),
c_0_142 ).
cnf(c_0_161,axiom,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X1,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_162,plain,
hAPP(c_COMBB(c_Not,tc_bool,tc_bool,X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_84]),c_0_84]) ).
cnf(c_0_163,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = hAPP(c_fequal(X2),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_129]),c_0_113]) ).
cnf(c_0_164,plain,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_165,plain,
hAPP(c_fequal(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_166,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_167,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2),X1)
| ~ class_Orderings_Oorder(X1) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_168,plain,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2),tc_bool)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_151,c_0_136]) ).
cnf(c_0_169,plain,
c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_HOL_Ominus__class_Ominus(X2,X1,tc_bool)),tc_bool),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).
cnf(c_0_170,plain,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
inference(rw,[status(thm)],[c_0_155,c_0_97]) ).
cnf(c_0_171,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_172,plain,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),X3),tc_bool)
| c_HOL_Oord__class_Oless(X1,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_79]),c_0_75])]) ).
cnf(c_0_173,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_157,c_0_86]) ).
cnf(c_0_174,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__compl__bot_0]) ).
cnf(c_0_175,plain,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X3),X2),tc_bool)
| c_lessequals(X1,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_158]),c_0_75])]) ).
cnf(c_0_176,plain,
c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4),hAPP(X3,X4),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_159]),c_0_82])]) ).
cnf(c_0_177,plain,
( ~ class_Lattices_Oboolean__algebra(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,X2)),X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,X2)),X4)) = c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,X2)) ),
inference(spm,[status(thm)],[c_0_119,c_0_160]) ).
cnf(c_0_178,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3) = hAPP(c_Not,hAPP(X2,X3)),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_179,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
cls_Diff__empty_0 ).
cnf(c_0_180,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_165]) ).
cnf(c_0_181,plain,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_subset__Compl__self__eq_0]) ).
cnf(c_0_182,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_FuncSet_OPi(c_COMBK(X1,X2,X3),X4,X5,X6),X7)) ),
inference(spm,[status(thm)],[c_0_109,c_0_166]) ).
cnf(c_0_183,plain,
~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_bool),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_136]),c_0_67]),c_0_71])]) ).
cnf(c_0_184,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_bool),tc_bool) = X1,
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_185,plain,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(hAPP(c_fequal(X2),X3),X1,X4))) ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_186,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_187,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1) ),
c_0_174 ).
cnf(c_0_188,plain,
( ~ c_lessequals(X3,X2,tc_bool)
| ~ c_lessequals(X1,X3,tc_bool)
| c_lessequals(X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_175,c_0_151]) ).
cnf(c_0_189,plain,
c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4),hAPP(c_Not,hAPP(X2,X4)),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_178]),c_0_120])]) ).
cnf(c_0_190,plain,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X3,tc_bool)) = X1,
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_191,plain,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_181 ).
cnf(c_0_192,plain,
( c_lessequals(c_Set_Oimage(X2,c_COMBK(X1,X3,X4),X5,X6),X7,tc_fun(X6,tc_bool))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_182]) ).
cnf(c_0_193,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__bot__left_0]) ).
cnf(c_0_194,plain,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2),X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__sup__ord_I4_J_0]) ).
cnf(c_0_195,plain,
~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_HOL_Ominus__class_Ominus(X1,X2,tc_bool)),X2,tc_bool),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_196,plain,
( ~ c_lessequals(X1,X2,tc_bool)
| c_HOL_Ominus__class_Ominus(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2),tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_168,c_0_154]) ).
cnf(c_0_197,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2))
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_110]) ).
cnf(c_0_198,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_187,c_0_120]) ).
cnf(c_0_199,plain,
( ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_HOL_Ominus__class_Ominus(X3,X1,tc_bool)),X2,tc_bool)
| c_lessequals(X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_188,c_0_169]) ).
cnf(c_0_200,plain,
c_lessequals(hAPP(X1,X2),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_99]),c_0_190]) ).
cnf(c_0_201,plain,
( hBOOL(X2)
| c_Set_Oimage(X1,c_COMBK(X2,X3,X4),X5,X6) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_202,plain,
hAPP(c_fequal(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_165,c_0_180]) ).
cnf(c_0_203,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
c_0_193 ).
cnf(c_0_204,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_205,plain,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2),X1) ),
c_0_194 ).
cnf(c_0_206,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) ),
inference(fof_simplification,[status(thm)],[cls_inf__sup__aci_I5_J_0]) ).
cnf(c_0_207,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
inference(fof_simplification,[status(thm)],[cls_le__iff__sup_0]) ).
cnf(c_0_208,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
cls_ComplI_0 ).
cnf(c_0_209,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_ComplD_0]) ).
cnf(c_0_210,plain,
( ~ c_lessequals(X1,X2,tc_bool)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2),tc_bool) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_211,plain,
( ~ c_lessequals(X2,X1,tc_bool)
| ~ hBOOL(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
inference(spm,[status(thm)],[c_0_197,c_0_133]) ).
cnf(c_0_212,plain,
( ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),X1,tc_bool)
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_198,c_0_133]) ).
cnf(c_0_213,plain,
c_lessequals(X1,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_214,plain,
( hBOOL(X1)
| c_COMBK(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_201]),c_0_202]) ).
cnf(c_0_215,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0 ).
cnf(c_0_216,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_217,plain,
c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1),tc_bool),
inference(spm,[status(thm)],[c_0_205,c_0_117]) ).
cnf(c_0_218,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) ),
c_0_206 ).
cnf(c_0_219,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
c_0_207 ).
cnf(c_0_220,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_221,plain,
( ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_bool),tc_bool)
| c_lessequals(X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_87,c_0_136]) ).
cnf(c_0_222,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_79,c_0_136]) ).
cnf(c_0_223,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X4,X5,X1,X3)),X4))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_ball__conj__distrib_1]) ).
cnf(c_0_224,plain,
( hBOOL(hAPP(X2,X3))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_208,c_0_97]),c_0_97]) ).
cnf(c_0_225,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_209 ).
cnf(c_0_226,plain,
( ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),X2,tc_bool)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2),tc_bool) ),
inference(spm,[status(thm)],[c_0_210,c_0_154]) ).
cnf(c_0_227,plain,
( ~ hBOOL(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_HOL_Ominus__class_Ominus(X1,X2,tc_bool)),tc_bool) ),
inference(spm,[status(thm)],[c_0_211,c_0_169]) ).
cnf(c_0_228,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_229,plain,
( hBOOL(X1)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_214]),c_0_166]) ).
cnf(c_0_230,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_215]),c_0_178]) ).
cnf(c_0_231,plain,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_216,c_0_136]) ).
cnf(c_0_232,plain,
( ~ c_HOL_Oord__class_Oless(X1,X3,tc_bool)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X3),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_217]),c_0_75])]) ).
cnf(c_0_233,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1),
inference(spm,[status(thm)],[c_0_218,c_0_117]) ).
cnf(c_0_234,plain,
( ~ c_lessequals(X1,X2,tc_bool)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = X2 ),
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_235,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_bool),X3,tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_236,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X4,X5,X1,X3)),X4))
| hBOOL(hAPP(X1,X2)) ),
c_0_223 ).
cnf(c_0_237,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Not,hAPP(X1,X2))) ),
inference(rw,[status(thm)],[c_0_224,c_0_178]) ).
cnf(c_0_238,plain,
( ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_225,c_0_97]),c_0_97]) ).
cnf(c_0_239,plain,
( ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_HOL_Ominus__class_Ominus(X2,X1,tc_bool),tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_240,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_154,c_0_228]) ).
cnf(c_0_241,plain,
( c_lessequals(X2,hAPP(c_Not,X1),tc_bool)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_213,c_0_229]) ).
cnf(c_0_242,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_230,c_0_166]) ).
cnf(c_0_243,plain,
c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(spm,[status(thm)],[c_0_169,c_0_231]) ).
cnf(c_0_244,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2),X2,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_232]),c_0_67])]) ).
cnf(c_0_245,plain,
( ~ c_lessequals(X2,X1,tc_bool)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_246,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_bool),X3,tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_157,c_0_235]) ).
cnf(c_0_247,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_inf__sup__absorb_0]) ).
cnf(c_0_248,plain,
( ~ hBOOL(hAPP(X1,X5))
| hBOOL(hAPP(X3,X5))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(X1,X2,X3,X4))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_236,c_0_97]),c_0_97]) ).
cnf(c_0_249,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_237,c_0_166]) ).
cnf(c_0_250,plain,
( ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Not,hAPP(X1,X2))) ),
inference(rw,[status(thm)],[c_0_238,c_0_178]) ).
cnf(c_0_251,plain,
( ~ c_lessequals(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),c_HOL_Ominus__class_Ominus(X2,X1,tc_bool),tc_bool)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_239,c_0_240]) ).
cnf(c_0_252,plain,
( c_lessequals(X2,X1,tc_bool)
| hBOOL(hAPP(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_253,plain,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X1,
inference(spm,[status(thm)],[c_0_168,c_0_243]) ).
cnf(c_0_254,plain,
c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),X2,tc_bool) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2),X1,tc_bool),
inference(spm,[status(thm)],[c_0_136,c_0_153]) ).
cnf(c_0_255,plain,
( ~ c_lessequals(X2,X1,tc_bool)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_244,c_0_245]) ).
cnf(c_0_256,plain,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
inference(spm,[status(thm)],[c_0_169,c_0_246]) ).
cnf(c_0_257,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2 ),
c_0_247 ).
cnf(c_0_258,plain,
( hBOOL(X4)
| hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(c_Not,X1,X2,X3))) ),
inference(spm,[status(thm)],[c_0_248,c_0_249]) ).
cnf(c_0_259,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_250,c_0_166]) ).
cnf(c_0_260,plain,
( ~ hBOOL(X2)
| hBOOL(hAPP(c_Not,c_HOL_Ominus__class_Ominus(X1,X2,tc_bool))) ),
inference(spm,[status(thm)],[c_0_251,c_0_252]) ).
cnf(c_0_261,plain,
c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1,tc_bool) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_262,plain,
( ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2),tc_bool) ),
inference(spm,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_263,plain,
( ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_less__infI1_0]) ).
cnf(c_0_264,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)) = X1,
inference(spm,[status(thm)],[c_0_257,c_0_117]) ).
cnf(c_0_265,plain,
( hBOOL(X4)
| hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(c_Not,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_99]),c_0_110]) ).
cnf(c_0_266,plain,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_198,c_0_151]) ).
cnf(c_0_267,plain,
( ~ c_lessequals(X2,X3,tc_bool)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2),X3,tc_bool) ),
inference(spm,[status(thm)],[c_0_188,c_0_158]) ).
cnf(c_0_268,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2),tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2),
inference(spm,[status(thm)],[c_0_136,c_0_154]) ).
cnf(c_0_269,plain,
( ~ hBOOL(X2)
| ~ hBOOL(c_HOL_Ominus__class_Ominus(X1,X2,tc_bool)) ),
inference(spm,[status(thm)],[c_0_259,c_0_260]) ).
cnf(c_0_270,plain,
c_HOL_Ominus__class_Ominus(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X1,tc_bool) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),
inference(rw,[status(thm)],[c_0_261,c_0_240]) ).
cnf(c_0_271,plain,
( ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_lessequals(X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_262,c_0_154]) ).
cnf(c_0_272,plain,
( c_lessequals(X1,X2,tc_bool)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_229]) ).
cnf(c_0_273,plain,
( ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) ),
c_0_263 ).
cnf(c_0_274,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X2,tc_bool)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) = X2 ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_275,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_264,c_0_233]) ).
cnf(c_0_276,plain,
hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(c_Not,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3))),
inference(ef,[status(thm)],[c_0_265]) ).
cnf(c_0_277,plain,
( ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)),tc_bool)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_266,c_0_267]) ).
cnf(c_0_278,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_268,c_0_228]),c_0_253]) ).
cnf(c_0_279,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_269,c_0_270]) ).
cnf(c_0_280,plain,
( c_lessequals(X2,X1,tc_bool)
| hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_271,c_0_272]) ).
cnf(c_0_281,plain,
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_bool)
| c_HOL_Oord__class_Oless(X1,X2,tc_bool)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_274]),c_0_71])]) ).
cnf(c_0_282,plain,
( ~ hBOOL(X1)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
inference(spm,[status(thm)],[c_0_197,c_0_275]) ).
cnf(c_0_283,plain,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(X3)
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,X1,X2))) ),
inference(spm,[status(thm)],[c_0_170,c_0_249]) ).
cnf(c_0_284,plain,
~ hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(c_Not,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),
inference(spm,[status(thm)],[c_0_259,c_0_276]) ).
cnf(c_0_285,plain,
( ~ c_lessequals(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_277,c_0_278]) ).
cnf(c_0_286,plain,
( ~ hBOOL(X2)
| c_lessequals(X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_279,c_0_280]) ).
cnf(c_0_287,plain,
( ~ hBOOL(X2)
| c_HOL_Oord__class_Oless(X1,X2,tc_bool)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
inference(spm,[status(thm)],[c_0_281,c_0_282]) ).
cnf(c_0_288,plain,
hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,c_Not,X1))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_276]),c_0_284]) ).
cnf(c_0_289,plain,
( ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_285,c_0_286]) ).
cnf(c_0_290,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[cls_order__antisym__conv_0]) ).
cnf(c_0_291,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool)
| c_HOL_Oord__class_Oless(X1,hAPP(c_Not,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,c_Not,X2)),tc_bool) ),
inference(spm,[status(thm)],[c_0_287,c_0_288]) ).
cnf(c_0_292,plain,
X1 != c_List_Olist_OCons(X2,X1,X3),
inference(fof_simplification,[status(thm)],[cls_not__Cons__self_0]) ).
cnf(c_0_293,plain,
( c_lessequals(X2,X1,tc_bool)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_289,c_0_280]) ).
cnf(c_0_294,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
c_0_290 ).
cnf(c_0_295,plain,
c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Not,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,c_Not,X1)),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_291]),c_0_67])]) ).
cnf(c_0_296,plain,
X1 != c_List_Olist_OCons(X2,X1,X3),
c_0_292 ).
cnf(c_0_297,plain,
( c_lessequals(X3,X2,tc_bool)
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_229,c_0_293]) ).
cnf(c_0_298,plain,
( ~ c_lessequals(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X1,tc_bool)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_213]),c_0_67])]) ).
cnf(c_0_299,plain,
~ c_lessequals(hAPP(c_Not,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,c_Not,X1)),c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_255,c_0_295]) ).
cnf(c_0_300,plain,
( c_lessequals(X4,X2,tc_bool)
| hBOOL(c_List_Olist_OCons(X1,X2,X3)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_297])]) ).
cnf(c_0_301,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
inference(fof_simplification,[status(thm)],[cls_list_Osimps_I2_J_0]) ).
cnf(c_0_302,plain,
( ~ hBOOL(X1)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1 ),
inference(spm,[status(thm)],[c_0_298,c_0_286]) ).
cnf(c_0_303,plain,
hBOOL(c_List_Olist_OCons(X1,c_Orderings_Obot__class_Obot(tc_bool),X2)),
inference(spm,[status(thm)],[c_0_299,c_0_300]) ).
cnf(c_0_304,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
c_0_301 ).
cnf(c_0_305,plain,
c_List_Olist_OCons(X1,c_Orderings_Obot__class_Obot(tc_bool),X2) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_302,c_0_303]) ).
cnf(c_0_306,plain,
( hBOOL(X1)
| hBOOL(X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_229,c_0_229]) ).
cnf(c_0_307,plain,
c_List_Olist_ONil(X1) != hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_304,c_0_305]) ).
cnf(c_0_308,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1 ),
inference(spm,[status(thm)],[c_0_302,c_0_229]) ).
cnf(c_0_309,plain,
( hBOOL(c_List_Olist_ONil(X3))
| hBOOL(c_List_Olist_OCons(X1,X2,X3)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_304,c_0_306])]) ).
cnf(c_0_310,plain,
c_List_Olist_ONil(X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_307,c_0_308]) ).
cnf(c_0_311,plain,
hBOOL(c_List_Olist_OCons(X1,X2,X3)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_309,c_0_310]),c_0_110]) ).
cnf(c_0_312,plain,
c_List_Olist_OCons(X1,X2,X3) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_302,c_0_311]) ).
cnf(c_0_313,plain,
$false,
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_296,c_0_312])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SCT045-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/1.07 % Computer : n012.cluster.edu
% 0.05/1.07 % Model : x86_64 x86_64
% 0.05/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/1.07 % Memory : 8046.5625MB
% 0.05/1.07 % OS : Linux 6.8.0-71-generic
% 0.05/1.07 % CPULimit : 300
% 0.05/1.07 % WCLimit : 300
% 0.05/1.07 % DateTime : Mon Sep 21 04:28:00 UTC 2026
% 0.05/1.07 % CPUTime :
% 0.05/1.07 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/1.09 Running first-order theorem proving
% 0.05/1.09 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 208.95/31.32 % Version: 3.5.1
% 208.95/31.32 % Preprocessing class: FSLMSMSMSSSNFFN.
% 208.95/31.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 208.95/31.32 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 208.95/31.32 % Starting new_bool_3 with 600s (2) cores
% 208.95/31.32 % Starting new_bool_1 with 300s (1) cores
% 208.95/31.32 % Starting sh5l with 300s (1) cores
% 208.95/31.32 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 1555851 completed with status 0
% 208.95/31.32 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 208.95/31.32 % Preprocessing class: FSLMSMSMSSSNFFN.
% 208.95/31.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 208.95/31.32 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 208.95/31.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 208.95/31.32 % No SInE strategy applied
% 208.95/31.32 % Search class: FGHSM-FSLM33-DFFFFFNN
% 208.95/31.32 % Scheduled 11 strats onto 4 cores with 1200 seconds (1200 total)
% 208.95/31.32 % Starting SubtermCWHack with 109s (1) cores
% 208.95/31.32 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 208.95/31.32 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 109s (1) cores
% 208.95/31.32 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 109s (1) cores
% 208.95/31.32 % SubtermCWHack with pid 1555859 completed with status 0
% 208.95/31.32 % Result found by SubtermCWHack
% 208.95/31.32 % Preprocessing class: FSLMSMSMSSSNFFN.
% 208.95/31.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 208.95/31.32 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 208.95/31.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 208.95/31.32 % No SInE strategy applied
% 208.95/31.32 % Search class: FGHSM-FSLM33-DFFFFFNN
% 208.95/31.32 % Scheduled 11 strats onto 4 cores with 1200 seconds (1200 total)
% 208.95/31.32 % Starting SubtermCWHack with 109s (1) cores
% 208.95/31.32 % Preprocessing time : 0.006 s
% 208.95/31.32
% 208.95/31.32 % Proof found!
% 208.95/31.32 % SZS status Unsatisfiable
% 208.95/31.32 % SZS output start CNFRefutation
% See solution above
% 208.95/31.32 % Parsed axioms : 704
% 208.95/31.32 % Removed by relevancy pruning/SinE : 0
% 208.95/31.32 % Initial clauses : 704
% 208.95/31.32 % Removed in clause preprocessing : 3
% 208.95/31.32 % Initial clauses in saturation : 701
% 208.95/31.32 % Processed clauses : 66823
% 208.95/31.32 % ...of these trivial : 1315
% 208.95/31.32 % ...subsumed : 57834
% 208.95/31.32 % ...remaining for further processing : 7674
% 208.95/31.32 % Other redundant clauses eliminated : 30741
% 208.95/31.32 % Clauses deleted for lack of memory : 142367
% 208.95/31.32 % Backward-subsumed : 336
% 208.95/31.32 % Backward-rewritten : 394
% 208.95/31.32 % Generated clauses : 2803046
% 208.95/31.32 % ...of the previous two non-redundant : 2632793
% 208.95/31.32 % ...aggressively subsumed : 0
% 208.95/31.32 % Contextual simplify-reflections : 17
% 208.95/31.32 % Paramodulations : 2771709
% 208.95/31.32 % Factorizations : 583
% 208.95/31.32 % NegExts : 0
% 208.95/31.32 % Equation resolutions : 30754
% 208.95/31.32 % Disequality decompositions : 0
% 208.95/31.32 % Total rewrite steps : 774536
% 208.95/31.32 % ...of those cached : 749851
% 208.95/31.32 % Propositional unsat checks : 0
% 208.95/31.32 % Propositional check models : 0
% 208.95/31.32 % Propositional check unsatisfiable : 0
% 208.95/31.32 % Propositional clauses : 0
% 208.95/31.32 % Propositional clauses after purity: 0
% 208.95/31.32 % Propositional unsat core size : 0
% 208.95/31.32 % Propositional preprocessing time : 0.000
% 208.95/31.32 % Propositional encoding time : 0.000
% 208.95/31.32 % Propositional solver time : 0.000
% 208.95/31.32 % Success case prop preproc time : 0.000
% 208.95/31.32 % Success case prop encoding time : 0.000
% 208.95/31.32 % Success case prop solver time : 0.000
% 208.95/31.32 % Current number of processed clauses : 6942
% 208.95/31.32 % Positive orientable unit clauses : 766
% 208.95/31.32 % Positive unorientable unit clauses: 22
% 208.95/31.32 % Negative unit clauses : 429
% 208.95/31.32 % Non-unit-clauses : 5725
% 208.95/31.32 % Current number of unprocessed clauses: 1283624
% 208.95/31.32 % ...number of literals in the above : 4782512
% 208.95/31.32 % Current number of archived formulas : 0
% 208.95/31.32 % Current number of archived clauses : 733
% 208.95/31.32 % Clause-clause subsumption calls (NU) : 3902291
% 208.95/31.32 % Rec. Clause-clause subsumption calls : 2087787
% 208.95/31.32 % Non-unit clause-clause subsumptions : 40228
% 208.95/31.32 % Unit Clause-clause subsumption calls : 142424
% 208.95/31.32 % Rewrite failures with RHS unbound : 45
% 208.95/31.32 % BW rewrite match attempts : 13142
% 208.95/31.32 % BW rewrite match successes : 383
% 208.95/31.32 % Condensation attempts : 0
% 208.95/31.32 % Condensation successes : 0
% 208.95/31.32 % Termbank termtop insertions : 56973323
% 208.95/31.32 % Search garbage collected termcells : 591949
% 208.95/31.32
% 208.95/31.32 % -------------------------------------------------
% 208.95/31.32 % User time : 28.636 s
% 208.95/31.32 % System time : 1.068 s
% 208.95/31.32 % Total time : 29.704 s
% 208.95/31.32 % Maximum resident set size: 5012 pages
% 208.95/31.32
% 208.95/31.32 % -------------------------------------------------
% 208.95/31.32 % User time : 115.579 s
% 208.95/31.32 % System time : 3.733 s
% 208.95/31.32 % Total time : 119.312 s
% 208.95/31.32 % Maximum resident set size: 5120 pages
% 208.95/31.32 % E exiting
%------------------------------------------------------------------------------