%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT006-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 05:05:49 PM UTC 2026
% Result : Unsatisfiable 136.46s 92.83s
% Output : CNFRefutation 136.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 80
% Syntax : Number of clauses : 341 ( 158 unt; 38 nHn; 164 RR)
% Number of literals : 612 ( 187 equ; 285 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 4 con; 0-5 aty)
% Number of variables : 781 ( 238 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_xt1_I11_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_sup__inf__absorb_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(cls_inf__compl__bot_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_vimage__Collect__eq_0,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(c_COMBB(X2,X1,X3,tc_bool,X4),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
cnf(cls_le__funD_0,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(cls_Collect__neg__eq_0,axiom,
c_Collect(c_COMBB(c_Not,X1,tc_bool,tc_bool,X2),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Collect(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_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/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_vimage__const_1,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_ComplD_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/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
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/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_insert__def_0,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_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/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
cnf(cls_Diff__eq_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
cnf(cls_InterI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1)),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterI_0) ).
cnf(cls_insert__Diff_0,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_Un__Diff__cancel_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
cnf(cls_ComplI_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/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_inf1E_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_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/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(cls_le__iff__inf_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
cnf(cls_UN__extend__simps_I3_J_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
cnf(cls_Union__upper_0,axiom,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__upper_0) ).
cnf(cls_Pow__top_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pow__top_0) ).
cnf(cls_inf__left__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
cnf(cls_Un__empty_1,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
cnf(cls_inf__assoc_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_Int__left__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
cnf(cls_IntE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
cnf(cls_Int__absorb2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
cnf(cls_compl__inf__bot_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
cnf(cls_compl__sup_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup_0) ).
cnf(cls_le__supE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_double__compl_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
cnf(cls_sup__bot__right_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_sup__ge1_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
cnf(cls_le__sup__iff_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
cnf(cls_le__iff__sup_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(cls_Sup__upper_0,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
cnf(cls_order__trans_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(cls_le__supI1_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
cnf(cls_order__less__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(cls_sup__absorb1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_sup__left__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
cnf(cls_le__iff__sup_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_sup__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
cnf(cls_Sup__empty_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
cnf(cls_bexCI_3,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_3) ).
cnf(c_0_80,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I11_J_0 ).
cnf(c_0_81,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I4_J_0 ).
cnf(c_0_82,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_xt1_I9_J_0 ).
cnf(c_0_83,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Orderings_Oorder(X3)
| ~ class_Lattices_Olattice(X3) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_84,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_85,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_sup__inf__absorb_0 ).
cnf(c_0_86,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_87,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_inf__compl__bot_0 ).
cnf(c_0_88,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I2_J_0 ).
cnf(c_0_89,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_90,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_91,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(c_COMBB(X2,X1,X3,tc_bool,X4),X4),
cls_vimage__Collect__eq_0 ).
cnf(c_0_92,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_order__antisym__conv_0 ).
cnf(c_0_93,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I1_J_0 ).
cnf(c_0_94,plain,
( c_Orderings_Obot__class_Obot(X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Obot__class_Obot(X1),X1)
| ~ class_Lattices_Olattice(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_95,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X2
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Orderings_Oorder(X3)
| ~ class_Lattices_Olattice(X3) ),
inference(spm,[status(thm)],[c_0_80,c_0_88]) ).
cnf(c_0_96,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
cls_le__funD_0 ).
cnf(c_0_97,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_98,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_99,axiom,
c_Collect(c_COMBB(c_Not,X1,tc_bool,tc_bool,X2),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Collect(X1,X2)),
cls_Collect__neg__eq_0 ).
cnf(c_0_100,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)),
cls_conjecture_0 ).
cnf(c_0_101,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_102,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_103,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_mem__def_1 ).
cnf(c_0_104,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_105,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
cls_vimage__const_1 ).
cnf(c_0_106,plain,
c_Set_Ovimage(X1,X2,X4,X3) = c_COMBB(X2,X1,X3,tc_bool,X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_90]),c_0_90]) ).
cnf(c_0_107,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ class_Orderings_Oorder(X3)
| ~ class_Lattices_Olattice(X3)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_108,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Oboolean__algebra(X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_109,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_96,c_0_97]),c_0_98])]) ).
cnf(c_0_110,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0 ).
cnf(c_0_111,plain,
c_COMBB(c_Not,X1,tc_bool,tc_bool,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_90]),c_0_90]) ).
cnf(c_0_112,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_COMBC(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1,X2,X3),c_Arrow__Order__Mirabelle_OLin),X4)),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_113,plain,
hAPP(X1,X2) = hAPP(hAPP(c_in(X3),X2),X1),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_114,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_ComplD_0 ).
cnf(c_0_115,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_COMBK(X3,X4,X5)))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_116,plain,
( c_COMBB(X4,c_COMBK(X1,X2,X3),X2,tc_bool,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_117,plain,
( c_Orderings_Obot__class_Obot(X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ class_Orderings_Oorder(X1)
| ~ class_Lattices_Olattice(X1)
| ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(X1),X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_118,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3,tc_bool),
inference(spm,[status(thm)],[c_0_109,c_0_104]) ).
cnf(c_0_119,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_120,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_121,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_122,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_110,c_0_111]) ).
cnf(c_0_123,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_124,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
cls_insert__def_0 ).
cnf(c_0_125,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_COMBC(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3,X4,X5),c_Arrow__Order__Mirabelle_OLin))),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_126,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_COMBK(X3,X4,X5))))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_127,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_COMBK(X2,tc_bool,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(c_Not,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_116]),c_0_113]) ).
cnf(c_0_128,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]),c_0_120]),c_0_121])]) ).
cnf(c_0_129,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_122]) ).
cnf(c_0_130,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_131,plain,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X2,tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[c_0_124,c_0_90]) ).
cnf(c_0_132,negated_conjecture,
~ hBOOL(hAPP(hAPP(hAPP(c_in(X1),X2),c_in(X3)),hAPP(c_COMBC(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X4,X5,X6),c_Arrow__Order__Mirabelle_OLin))),
inference(spm,[status(thm)],[c_0_125,c_0_113]) ).
cnf(c_0_133,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_134,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)),
cls_Diff__eq_0 ).
cnf(c_0_135,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1)),X3)) ),
cls_InterI_0 ).
cnf(c_0_136,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_COMBK(X2,X3,X4)),X5))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_126,c_0_113]) ).
cnf(c_0_137,plain,
( hAPP(c_Not,X1) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(hAPP(c_Not,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_127]),c_0_128]),c_0_104]) ).
cnf(c_0_138,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_129,c_0_104]) ).
cnf(c_0_139,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ),
cls_insert__Diff_0 ).
cnf(c_0_140,plain,
hAPP(c_fequal(X1),X2) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_90]),c_0_131]) ).
cnf(c_0_141,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
cls_Un__empty__right_0 ).
cnf(c_0_142,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
cls_Un__Diff__cancel_0 ).
cnf(c_0_143,negated_conjecture,
~ hBOOL(hAPP(hAPP(hAPP(c_in(X1),X2),c_in(X3)),c_Arrow__Order__Mirabelle_OLin)),
inference(spm,[status(thm)],[c_0_132,c_0_102]) ).
cnf(c_0_144,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)) ),
cls_ComplI_0 ).
cnf(c_0_145,plain,
hAPP(hAPP(c_in(X1),X2),hAPP(c_in(X3),X4)) = hAPP(X2,X4),
inference(spm,[status(thm)],[c_0_113,c_0_113]) ).
cnf(c_0_146,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
cls_inf1E_1 ).
cnf(c_0_147,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) = X1,
inference(rw,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_148,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
cls_mem__def_0 ).
cnf(c_0_149,negated_conjecture,
hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(spm,[status(thm)],[c_0_100,c_0_135]) ).
cnf(c_0_150,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
cls_equalityE_0 ).
cnf(c_0_151,plain,
( ~ hBOOL(hAPP(c_Not,X1))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_122]),c_0_104]) ).
cnf(c_0_152,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_153,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),c_HOL_Ominus__class_Ominus(X2,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_131]),c_0_131]) ).
cnf(c_0_154,plain,
hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2) = hAPP(c_fequal(X1),X2),
inference(rw,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_155,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[c_0_142,c_0_134]) ).
cnf(c_0_156,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(X1),c_Arrow__Order__Mirabelle_OLin),hAPP(hAPP(c_in(X2),X3),c_in(X4)))),
inference(spm,[status(thm)],[c_0_143,c_0_113]) ).
cnf(c_0_157,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Not,hAPP(X3,X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_144]),c_0_145]),c_0_122]) ).
cnf(c_0_158,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
cls_empty__not__insert_0 ).
cnf(c_0_159,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_160,negated_conjecture,
hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1)),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_161,plain,
c_lessequals(hAPP(X1,X2),hAPP(X1,X2),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_150]),c_0_98])]) ).
cnf(c_0_162,plain,
( hAPP(c_Not,X1) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_163,plain,
( hAPP(X1,X2) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_116]),c_0_104]),c_0_128]) ).
cnf(c_0_164,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X1),X2),X3,tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_154]),c_0_154]),c_0_141]),c_0_134]),c_0_155]) ).
cnf(c_0_165,negated_conjecture,
hBOOL(hAPP(c_Not,hAPP(hAPP(hAPP(c_in(X1),X2),c_in(X3)),c_Arrow__Order__Mirabelle_OLin))),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_166,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),X3,tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_158,c_0_131]) ).
cnf(c_0_167,negated_conjecture,
hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_168,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
cls_le__infE_0 ).
cnf(c_0_169,plain,
c_lessequals(X1,X1,tc_bool),
inference(spm,[status(thm)],[c_0_161,c_0_104]) ).
cnf(c_0_170,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_171,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__inf_0 ).
cnf(c_0_172,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_138,c_0_162]) ).
cnf(c_0_173,negated_conjecture,
( hBOOL(hAPP(c_in(X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OLin)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_163]),c_0_145]) ).
cnf(c_0_174,plain,
hAPP(hAPP(c_in(X1),X2),c_COMBK(X3,X4,X5)) = X3,
inference(spm,[status(thm)],[c_0_104,c_0_113]) ).
cnf(c_0_175,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X1),X2),X3,tc_fun(X1,tc_bool)) = X3
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_164,c_0_113]) ).
cnf(c_0_176,negated_conjecture,
hBOOL(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_113]),c_0_145]),c_0_113]) ).
cnf(c_0_177,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
cls_Un__commute_0 ).
cnf(c_0_178,plain,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X1),X2),X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_166,c_0_154]) ).
cnf(c_0_179,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
cls_UN__extend__simps_I3_J_0 ).
cnf(c_0_180,axiom,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,tc_bool)),X1),X2)) ),
cls_Union__upper_0 ).
cnf(c_0_181,negated_conjecture,
hBOOL(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
inference(rw,[status(thm)],[c_0_167,c_0_122]) ).
cnf(c_0_182,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X2,X1))),
cls_Pow__top_0 ).
cnf(c_0_183,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),X1,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_170])]) ).
cnf(c_0_184,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__left__commute_0 ).
cnf(c_0_185,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_bool) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_169]),c_0_170])]) ).
cnf(c_0_186,plain,
( X1 = X2
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_172,c_0_172]) ).
cnf(c_0_187,negated_conjecture,
( hBOOL(hAPP(c_in(X1),X2))
| hBOOL(X3)
| ~ hBOOL(hAPP(X3,c_Arrow__Order__Mirabelle_OLin)) ),
inference(spm,[status(thm)],[c_0_173,c_0_152]) ).
cnf(c_0_188,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_104]),c_0_174]) ).
cnf(c_0_189,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_Un__empty_1 ).
cnf(c_0_190,negated_conjecture,
c_Lattices_Oupper__semilattice__class_Osup(c_Not,hAPP(c_fequal(X1),hAPP(c_Arrow__Order__Mirabelle_OLin,X2)),tc_fun(X1,tc_bool)) = c_Not,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_177]) ).
cnf(c_0_191,plain,
hAPP(c_fequal(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_192,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(spm,[status(thm)],[c_0_180,c_0_113]) ).
cnf(c_0_193,negated_conjecture,
hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(rw,[status(thm)],[c_0_181,c_0_128]) ).
cnf(c_0_194,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_114,c_0_113]) ).
cnf(c_0_195,plain,
hBOOL(hAPP(c_Set_OPow(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_148,c_0_182]) ).
cnf(c_0_196,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__assoc_0 ).
cnf(c_0_197,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_183]),c_0_170])]) ).
cnf(c_0_198,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_170])]) ).
cnf(c_0_199,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(X1,c_in(X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(c_in(X3),X4))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_143,c_0_186]) ).
cnf(c_0_200,negated_conjecture,
( hBOOL(hAPP(c_in(X1),X2))
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(c_Not) ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_201,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Not,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_191]) ).
cnf(c_0_202,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_disjoint__iff__not__equal_0 ).
cnf(c_0_203,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
cls_Int__left__absorb_0 ).
cnf(c_0_204,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
cls_IntE_0 ).
cnf(c_0_205,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
cls_Int__absorb2_0 ).
cnf(c_0_206,negated_conjecture,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Not,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_207,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Set_OPow(X2,X3)))),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_208,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf__bot_0 ).
cnf(c_0_209,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_198]),c_0_170])]) ).
cnf(c_0_210,negated_conjecture,
( hBOOL(c_Not)
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(hAPP(hAPP(X1,c_in(X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_211,negated_conjecture,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ hBOOL(c_Not) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_186])]) ).
cnf(c_0_212,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_204]) ).
cnf(c_0_213,negated_conjecture,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Not,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_214,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_in(X3),c_Set_OPow(X2,X4)),c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool))))),
inference(spm,[status(thm)],[c_0_207,c_0_113]) ).
cnf(c_0_215,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup_0 ).
cnf(c_0_216,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_119])]) ).
cnf(c_0_217,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_128]),c_0_211]) ).
cnf(c_0_218,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_113]) ).
cnf(c_0_219,plain,
~ hBOOL(hAPP(hAPP(hAPP(c_in(X1),c_Set_OPow(X2,X3)),c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool))),X2)),
inference(spm,[status(thm)],[c_0_214,c_0_113]) ).
cnf(c_0_220,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
cls_le__supE_1 ).
cnf(c_0_221,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_222,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0 ).
cnf(c_0_223,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_119])]) ).
cnf(c_0_224,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
cls_Int__lower2_0 ).
cnf(c_0_225,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OLin)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_152]),c_0_218]) ).
cnf(c_0_226,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Set_OPow(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_219,c_0_113]) ).
cnf(c_0_227,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_169]),c_0_221])]) ).
cnf(c_0_228,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0 ).
cnf(c_0_229,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_230,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__ge1_0 ).
cnf(c_0_231,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
cls_le__sup__iff_0 ).
cnf(c_0_232,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_119])]) ).
cnf(c_0_233,plain,
c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4),hAPP(X2,X4),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_224]),c_0_98])]) ).
cnf(c_0_234,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_in(X3)))
| ~ hBOOL(hAPP(X4,c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(X4) ),
inference(spm,[status(thm)],[c_0_143,c_0_186]) ).
cnf(c_0_235,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(X1)
| ~ hBOOL(hAPP(X1,c_Arrow__Order__Mirabelle_OLin)) ),
inference(spm,[status(thm)],[c_0_225,c_0_152]) ).
cnf(c_0_236,plain,
~ hBOOL(hAPP(c_Not,hAPP(c_Set_OPow(X1,X2),X1))),
inference(rw,[status(thm)],[c_0_226,c_0_122]) ).
cnf(c_0_237,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__sup_0 ).
cnf(c_0_238,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_229])]) ).
cnf(c_0_239,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X1
| ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(spm,[status(thm)],[c_0_92,c_0_230]) ).
cnf(c_0_240,plain,
( c_lessequals(X1,X2,tc_bool)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_221])]) ).
cnf(c_0_241,plain,
c_lessequals(hAPP(X1,X2),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_147]),c_0_122]),c_0_128]) ).
cnf(c_0_242,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_in(X3)))
| ~ hBOOL(c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,X4)) ),
inference(spm,[status(thm)],[c_0_234,c_0_195]) ).
cnf(c_0_243,negated_conjecture,
( hBOOL(c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,X1))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_235,c_0_195]) ).
cnf(c_0_244,plain,
( ~ hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| ~ hBOOL(c_Set_OPow(X2,X3))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_236,c_0_186]) ).
cnf(c_0_245,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_221])]) ).
cnf(c_0_246,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = X1
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_232]),c_0_120]),c_0_221])]) ).
cnf(c_0_247,plain,
c_lessequals(X1,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(spm,[status(thm)],[c_0_240,c_0_241]) ).
cnf(c_0_248,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_in(X3))) ),
inference(spm,[status(thm)],[c_0_242,c_0_243]) ).
cnf(c_0_249,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(hAPP(c_Not,hAPP(X1,c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_244,c_0_243]) ).
cnf(c_0_250,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_Sup__upper_0 ).
cnf(c_0_251,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_OPow(X2,X3))),
inference(spm,[status(thm)],[c_0_207,c_0_144]) ).
cnf(c_0_252,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_223,c_0_245]) ).
cnf(c_0_253,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_246,c_0_247]) ).
cnf(c_0_254,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(hAPP(c_in(X1),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_113]),c_0_145]) ).
cnf(c_0_255,negated_conjecture,
( hBOOL(hAPP(X1,c_Arrow__Order__Mirabelle_OLin))
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_249,c_0_188]) ).
cnf(c_0_256,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__trans_0 ).
cnf(c_0_257,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X1,X2),X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(spm,[status(thm)],[c_0_250,c_0_251]) ).
cnf(c_0_258,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(rw,[status(thm)],[c_0_252,c_0_253]) ).
cnf(c_0_259,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_260,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(c_in(X1)) ),
inference(spm,[status(thm)],[c_0_254,c_0_255]) ).
cnf(c_0_261,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X2,X3),X4),X4)
| ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| ~ class_Orderings_Opreorder(X4)
| ~ c_lessequals(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_256,c_0_257]) ).
cnf(c_0_262,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_263,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder ).
cnf(c_0_264,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)))
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_222]),c_0_113]) ).
cnf(c_0_265,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_258,c_0_172]) ).
cnf(c_0_266,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_259,c_0_128]) ).
cnf(c_0_267,negated_conjecture,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1)),
inference(spm,[status(thm)],[c_0_112,c_0_102]) ).
cnf(c_0_268,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,tc_fun(X1,tc_bool))))
| hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X2,X3,X1))) ),
inference(rw,[status(thm)],[c_0_135,c_0_113]) ).
cnf(c_0_269,negated_conjecture,
( c_in(X1) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_260,c_0_152]) ).
cnf(c_0_270,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__supI1_0 ).
cnf(c_0_271,plain,
c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X1,X2),tc_bool),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_169]),c_0_262]),c_0_263])]) ).
cnf(c_0_272,plain,
( ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| ~ hBOOL(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_265]),c_0_119])]),c_0_266]) ).
cnf(c_0_273,negated_conjecture,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(X1,tc_bool)))),
inference(spm,[status(thm)],[c_0_267,c_0_268]) ).
cnf(c_0_274,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_254,c_0_269]) ).
cnf(c_0_275,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__le__trans_0 ).
cnf(c_0_276,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| 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_80,c_0_238]),c_0_120])]) ).
cnf(c_0_277,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X1,X2),tc_bool),X3,tc_bool),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_270,c_0_271]),c_0_221])]) ).
cnf(c_0_278,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_sup__absorb1_0 ).
cnf(c_0_279,plain,
( ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_272,c_0_186]) ).
cnf(c_0_280,negated_conjecture,
hBOOL(hAPP(c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(X1,tc_bool)),X2)),
inference(spm,[status(thm)],[c_0_148,c_0_273]) ).
cnf(c_0_281,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_274,c_0_152]) ).
cnf(c_0_282,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_283,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X2,tc_bool)
| ~ c_lessequals(X1,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_263])]) ).
cnf(c_0_284,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_277,c_0_232]) ).
cnf(c_0_285,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__left__commute_0 ).
cnf(c_0_286,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_238]),c_0_221])]) ).
cnf(c_0_287,negated_conjecture,
( ~ hBOOL(c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(X1,tc_bool)))
| ~ hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_279,c_0_280]) ).
cnf(c_0_288,negated_conjecture,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_281,c_0_253]),c_0_193])]) ).
cnf(c_0_289,negated_conjecture,
( hBOOL(c_Complete__Lattice_OInf__class_OInf(c_Arrow__Order__Mirabelle_OLin,tc_fun(X1,tc_bool)))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_235,c_0_280]) ).
cnf(c_0_290,negated_conjecture,
( hBOOL(hAPP(c_fequal(X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_235,c_0_282]) ).
cnf(c_0_291,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool) ),
inference(spm,[status(thm)],[c_0_283,c_0_284]) ).
cnf(c_0_292,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq2_0 ).
cnf(c_0_293,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_286]),c_0_286]),c_0_221])]) ).
cnf(c_0_294,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_288]),c_0_289]) ).
cnf(c_0_295,negated_conjecture,
( hBOOL(c_fequal(X1))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_235,c_0_290]) ).
cnf(c_0_296,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
cls_le__iff__sup_1 ).
cnf(c_0_297,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_less__le__not__le_1 ).
cnf(c_0_298,negated_conjecture,
c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_291]),c_0_291]) ).
cnf(c_0_299,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_293]),c_0_229])]) ).
cnf(c_0_300,negated_conjecture,
hBOOL(c_Arrow__Order__Mirabelle_OLin),
inference(spm,[status(thm)],[c_0_294,c_0_295]) ).
cnf(c_0_301,plain,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool)
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_232]),c_0_221])]) ).
cnf(c_0_302,negated_conjecture,
~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_298]),c_0_263])]) ).
cnf(c_0_303,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_bool),tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_299,c_0_285]),c_0_221])]) ).
cnf(c_0_304,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__commute_0 ).
cnf(c_0_305,plain,
c_Lattices_Oupper__semilattice__class_Osup(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),c_Orderings_Obot__class_Obot(tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_284]),c_0_120]),c_0_221])]) ).
cnf(c_0_306,negated_conjecture,
( c_Arrow__Order__Mirabelle_OLin = X1
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_186,c_0_300]) ).
cnf(c_0_307,plain,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool)
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) != hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(rw,[status(thm)],[c_0_301,c_0_253]) ).
cnf(c_0_308,negated_conjecture,
~ c_lessequals(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(rw,[status(thm)],[c_0_302,c_0_253]) ).
cnf(c_0_309,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),X3,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_304]),c_0_221])]) ).
cnf(c_0_310,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X1,X2),tc_bool),tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(X1,X2),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_271]),c_0_221])]) ).
cnf(c_0_311,plain,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X1,tc_bool) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_305,c_0_253]),c_0_253]) ).
cnf(c_0_312,negated_conjecture,
hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_306,c_0_193]) ).
cnf(c_0_313,plain,
hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_307,c_0_258]),c_0_308]) ).
cnf(c_0_314,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),X3),tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_309,c_0_310]) ).
cnf(c_0_315,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Arrow__Order__Mirabelle_OLin,X1,tc_bool) = c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_311,c_0_312]),c_0_312]) ).
cnf(c_0_316,plain,
c_Orderings_Obot__class_Obot(tc_bool) != c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_313,c_0_312]) ).
cnf(c_0_317,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(X1,tc_bool)) = c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_253]),c_0_193])]),c_0_177]) ).
cnf(c_0_318,plain,
c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,X1),tc_bool) != c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_315]),c_0_316]) ).
cnf(c_0_319,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_317]),c_0_191]) ).
cnf(c_0_320,negated_conjecture,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| c_Arrow__Order__Mirabelle_OLin = X1 ),
inference(spm,[status(thm)],[c_0_306,c_0_152]) ).
cnf(c_0_321,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,X2))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_318,c_0_186]) ).
cnf(c_0_322,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_Sup__empty_0 ).
cnf(c_0_323,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_319,c_0_186])]) ).
cnf(c_0_324,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Arrow__Order__Mirabelle_OLin
| c_Orderings_Obot__class_Obot(tc_bool) != c_Not ),
inference(spm,[status(thm)],[c_0_201,c_0_320]) ).
cnf(c_0_325,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)))
| ~ hBOOL(c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_321,c_0_322]),c_0_262])]) ).
cnf(c_0_326,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(spm,[status(thm)],[c_0_323,c_0_152]) ).
cnf(c_0_327,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Arrow__Order__Mirabelle_OLin
| c_Arrow__Order__Mirabelle_OLin = c_Not ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_320])]) ).
cnf(c_0_328,plain,
( c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,X1) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) ),
inference(spm,[status(thm)],[c_0_325,c_0_152]) ).
cnf(c_0_329,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4)) ),
cls_bexCI_3 ).
cnf(c_0_330,negated_conjecture,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Arrow__Order__Mirabelle_OLin = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_326,c_0_327]),c_0_300])]) ).
cnf(c_0_331,negated_conjecture,
( c_Set_OPow(c_Arrow__Order__Mirabelle_OLin,X1) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Arrow__Order__Mirabelle_OLin = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_328,c_0_327]),c_0_300])]) ).
cnf(c_0_332,negated_conjecture,
( hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X1,c_Not,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),c_Orderings_Obot__class_Obot(tc_bool)),X1)) ),
inference(spm,[status(thm)],[c_0_329,c_0_193]) ).
cnf(c_0_333,negated_conjecture,
( c_Arrow__Order__Mirabelle_OLin = c_Not
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),X1))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_272,c_0_330]) ).
cnf(c_0_334,negated_conjecture,
( c_Arrow__Order__Mirabelle_OLin = c_Not
| hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OLin)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_331]),c_0_113]) ).
cnf(c_0_335,negated_conjecture,
( hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X1,c_Not,X2)))
| ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_332,c_0_113]),c_0_145]) ).
cnf(c_0_336,negated_conjecture,
hAPP(c_Arrow__Order__Mirabelle_OLin,X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_267,c_0_152]) ).
cnf(c_0_337,negated_conjecture,
c_Arrow__Order__Mirabelle_OLin = c_Not,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_334]),c_0_300])]) ).
cnf(c_0_338,negated_conjecture,
hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Set__XbexCI__1__1(hAPP(c_fequal(X1),c_Orderings_Obot__class_Obot(tc_bool)),c_Not,X2))),
inference(spm,[status(thm)],[c_0_335,c_0_282]) ).
cnf(c_0_339,negated_conjecture,
hAPP(c_Not,X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[c_0_336,c_0_337]) ).
cnf(c_0_340,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_338,c_0_339]),c_0_266]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT006-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n002.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 01:55:16 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 136.46/92.83 % Version : CSE_E---1.7
% 136.46/92.83 % Problem : theBenchmark.p
% 136.46/92.83 % SZS status Unsatisfiable for theBenchmark.p
% 136.46/92.83 % SZS output start CNFRefutation
% See solution above
% 136.95/93.30 % Total time : 74.618s
%------------------------------------------------------------------------------