%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT030-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:05:52 PM UTC 2026
% Result : Unsatisfiable 167.68s 104.10s
% Output : CNFRefutation 168.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 74
% Syntax : Number of clauses : 340 ( 132 unt; 48 nHn; 175 RR)
% Number of literals : 650 ( 176 equ; 299 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 7 con; 0-5 aty)
% Number of variables : 687 ( 184 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_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_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_vimage__Collect__eq_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Collect(X4,X3)) = c_Collect(c_COMBB(X4,X1,X3,tc_bool,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Collect__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_Compl__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = c_Collect(c_COMBB(c_Not,hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),tc_bool,tc_bool,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq_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/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_le__supE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X4),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_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_le__iff__sup_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
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(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/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_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_top__greatest_0,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
cnf(cls_Compl__empty__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_subset__UNIV_0,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_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/sandbox/benchmark/theBenchmark.p',cls_ComplD_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_le__iff__inf_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_vimage__const_0,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(X1,X2,X3),X3,X2),X4) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_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/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_vimage__Compl_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
cnf(cls_vimage__code_1,axiom,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5))
| ~ hBOOL(hAPP(X4,hAPP(X1,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
cnf(cls_diff__eq_0,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
cnf(cls_inf__left__commute_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
cnf(cls_vimage__code_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X2,X4,X5),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
cnf(cls_sup1E_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,tc_fun(X4,tc_bool)),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
cnf(cls_Compl__partition_0,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_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(cls_compl__inf__bot_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_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_inf__absorb2_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_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_compl__bot__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_sup__bot__left_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X1),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
cnf(cls_compl__top__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
cnf(cls_sup__top__left_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(cls_sup__inf__absorb_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_sup__absorb1_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_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_I2_J_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X1),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
cnf(cls_inf__compl__bot_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_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_rev__bexI_1,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
cnf(cls_ballE_1,axiom,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XballE__1__1(X3,X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ballE_1) ).
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_override__on__apply__notin_0,axiom,
( hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| hBOOL(hAPP(hAPP(c_in(X4),X6),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__apply__notin_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_inf__idem_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_sup__left__commute_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X4)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
cnf(cls_le__iff__inf_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_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/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(cls_bexI_1,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexI_1) ).
cnf(cls_le__supE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X1),X2),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
cnf(cls_bexI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexI_0) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
cnf(cls_compl__sup__top_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
cnf(cls_sup__bot__right_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
cnf(c_0_74,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_75,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
cls_equalityE_0 ).
cnf(c_0_76,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_77,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_74,c_0_75]),c_0_76])]) ).
cnf(c_0_78,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_79,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Collect(X4,X3)) = c_Collect(c_COMBB(X4,X1,X3,tc_bool,X2),X2),
cls_vimage__Collect__eq_0 ).
cnf(c_0_80,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_81,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = c_Collect(c_COMBB(c_Not,hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),tc_bool,tc_bool,X1),X1),
cls_Compl__eq_0 ).
cnf(c_0_82,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_83,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X4),X3,X1) ),
cls_le__supE_0 ).
cnf(c_0_84,plain,
c_lessequals(X1,X1,tc_bool),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_86,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__sup_0 ).
cnf(c_0_87,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0 ).
cnf(c_0_88,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0 ).
cnf(c_0_89,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = c_COMBB(X4,X1,X3,tc_bool,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_80]) ).
cnf(c_0_90,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = c_COMBB(c_Not,hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),tc_bool,tc_bool,X1),
inference(rw,[status(thm)],[c_0_81,c_0_80]) ).
cnf(c_0_91,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_82,c_0_80]) ).
cnf(c_0_92,plain,
c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85])]) ).
cnf(c_0_93,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X1),X2) = X2
| ~ class_Orderings_Obot(X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_94,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_95,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_96,plain,
hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5) = hAPP(X4,hAPP(X1,X5)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,plain,
hAPP(c_Set_Ovimage(X1,X2,tc_bool),c_Not) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91]),c_0_89]) ).
cnf(c_0_98,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_99,plain,
c_lessequals(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_92,c_0_93]),c_0_94]),c_0_85])]) ).
cnf(c_0_100,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_101,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
cls_le__infE_0 ).
cnf(c_0_102,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_74,c_0_95]),c_0_76])]) ).
cnf(c_0_103,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_104,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__greatest_0 ).
cnf(c_0_105,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_96,c_0_97]) ).
cnf(c_0_106,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__empty__eq_0 ).
cnf(c_0_107,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100])]) ).
cnf(c_0_108,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103])]) ).
cnf(c_0_109,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2),c_Orderings_Otop__class_Otop(X2)) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Orderings_Otop(X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(spm,[status(thm)],[c_0_86,c_0_104]) ).
cnf(c_0_110,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_111,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
cls_subset__UNIV_0 ).
cnf(c_0_112,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_113,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_107,c_0_108]) ).
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,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_116,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__inf_0 ).
cnf(c_0_117,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_109]),c_0_110]),c_0_85])]) ).
cnf(c_0_118,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(X1,X2,X3),X3,X2),X4) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
cls_vimage__const_0 ).
cnf(c_0_119,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_120,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),
cls_vimage__Compl_0 ).
cnf(c_0_121,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_111]),c_0_76])]),c_0_112]),c_0_113]) ).
cnf(c_0_122,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_COMBC(c_in(X1),X4,X5,X6),X3),X2)) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_123,axiom,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5))
| ~ hBOOL(hAPP(X4,hAPP(X1,X5))) ),
cls_vimage__code_1 ).
cnf(c_0_124,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_diff__eq_0 ).
cnf(c_0_125,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__left__commute_0 ).
cnf(c_0_126,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_103])]) ).
cnf(c_0_127,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X2,X4,X5),X1),X3)) ),
cls_vimage__code_0 ).
cnf(c_0_128,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,tc_fun(X4,tc_bool)),X1),X2)) ),
cls_sup1E_0 ).
cnf(c_0_129,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
cls_Compl__partition_0 ).
cnf(c_0_130,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_131,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Set_Ovimage(c_COMBK(X2,X3,X1),X1,X3),X4)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X2),X4)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
cnf(c_0_132,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_133,plain,
hAPP(X1,X2) = hAPP(hAPP(c_in(X3),X2),X1),
inference(spm,[status(thm)],[c_0_115,c_0_91]) ).
cnf(c_0_134,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_117]),c_0_100])]) ).
cnf(c_0_135,plain,
c_lessequals(X1,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_121]),c_0_85])]) ).
cnf(c_0_136,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_122,c_0_91]) ).
cnf(c_0_137,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_99]),c_0_85])]) ).
cnf(c_0_138,plain,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(X1,X2),X3,X4),X5),X6))
| ~ class_Lattices_Oboolean__algebra(X2)
| ~ hBOOL(hAPP(X5,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X6)))) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_139,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf__bot_0 ).
cnf(c_0_140,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_126]),c_0_103])]) ).
cnf(c_0_141,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_142,plain,
( hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),X2)) ),
inference(spm,[status(thm)],[c_0_127,c_0_97]) ).
cnf(c_0_143,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130])]) ).
cnf(c_0_144,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_inf__absorb2_0 ).
cnf(c_0_145,plain,
( c_COMBK(X1,tc_bool,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Not,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_97]),c_0_132]),c_0_133]) ).
cnf(c_0_146,plain,
hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_147,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_132]),c_0_105]) ).
cnf(c_0_148,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),tc_bool))))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_149,plain,
( hBOOL(hAPP(X1,hAPP(c_HOL_Ominus__class_Ominus(X2,X3),X4)))
| ~ class_Lattices_Oboolean__algebra(X3)
| ~ hBOOL(hAPP(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X3),hAPP(c_HOL_Ouminus__class_Ouminus(X3),X4)))) ),
inference(rw,[status(thm)],[c_0_138,c_0_96]) ).
cnf(c_0_150,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141])]) ).
cnf(c_0_151,plain,
( hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_152,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_117]),c_0_103])]) ).
cnf(c_0_153,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| hBOOL(hAPP(c_Not,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_145]),c_0_112]),c_0_113]),c_0_146]) ).
cnf(c_0_154,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_147,c_0_78]) ).
cnf(c_0_155,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),tc_bool)),X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_148,c_0_133]) ).
cnf(c_0_156,plain,
( hBOOL(hAPP(X1,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_bool),X2)))
| ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_141])]) ).
cnf(c_0_157,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_78]) ).
cnf(c_0_158,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_159,plain,
( hBOOL(hAPP(X1,hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X2)))
| ~ hBOOL(hAPP(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_152]),c_0_141])]) ).
cnf(c_0_160,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
cls_mem__def_0 ).
cnf(c_0_161,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
cls_CHAINED_0 ).
cnf(c_0_162,plain,
( hAPP(c_Not,X1) = c_Orderings_Otop__class_Otop(tc_bool)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_163,plain,
hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_154,c_0_146]) ).
cnf(c_0_164,plain,
( ~ hBOOL(hAPP(c_Not,X1))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_105]),c_0_137]) ).
cnf(c_0_165,plain,
( hBOOL(hAPP(c_Not,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),X1)))
| hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_166,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_167,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1))))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_136,c_0_158]) ).
cnf(c_0_168,plain,
hAPP(hAPP(c_in(X1),X2),hAPP(c_in(X3),X4)) = hAPP(X2,X4),
inference(spm,[status(thm)],[c_0_133,c_0_133]) ).
cnf(c_0_169,plain,
( hBOOL(hAPP(X1,hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2))))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_158]),c_0_141])]) ).
cnf(c_0_170,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_171,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__bot__eq_0 ).
cnf(c_0_172,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_162]),c_0_163]) ).
cnf(c_0_173,plain,
( hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_174,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_166,c_0_113]) ).
cnf(c_0_175,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_133]),c_0_168]) ).
cnf(c_0_176,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____)))),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_177,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = c_Orderings_Otop__class_Otop(tc_bool)
| hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_141])]) ).
cnf(c_0_178,plain,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_172]),c_0_174]) ).
cnf(c_0_179,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
cls_conjecture_0 ).
cnf(c_0_180,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1)),X3))
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
inference(spm,[status(thm)],[c_0_175,c_0_158]) ).
cnf(c_0_181,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)))
| hBOOL(v_P____) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_178]) ).
cnf(c_0_182,negated_conjecture,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)),
inference(rw,[status(thm)],[c_0_179,c_0_133]) ).
cnf(c_0_183,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_mem__def_1 ).
cnf(c_0_184,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X1),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__left_0 ).
cnf(c_0_185,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X3),c_HOL_Ouminus__class_Ouminus(X1))) ),
inference(spm,[status(thm)],[c_0_180,c_0_133]) ).
cnf(c_0_186,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_164,c_0_153]) ).
cnf(c_0_187,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X1))
| hBOOL(v_P____)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_181,c_0_172]) ).
cnf(c_0_188,negated_conjecture,
hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_182,c_0_172]) ).
cnf(c_0_189,plain,
hBOOL(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_106]),c_0_130])]) ).
cnf(c_0_190,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X3)))
| ~ hBOOL(X2)
| ~ class_Lattices_Obounded__lattice(X3) ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_191,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_HOL_Ouminus__class_Ouminus(X1)))
| ~ hBOOL(hAPP(c_Not,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))) ),
inference(rw,[status(thm)],[c_0_185,c_0_105]) ).
cnf(c_0_192,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__top__eq_0 ).
cnf(c_0_193,plain,
( X1 = X2
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_186,c_0_186]) ).
cnf(c_0_194,negated_conjecture,
( hBOOL(v_Q____)
| hBOOL(v_P____) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_174]) ).
cnf(c_0_195,plain,
hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(rw,[status(thm)],[c_0_189,c_0_113]) ).
cnf(c_0_196,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X3))))
| ~ hBOOL(X2)
| ~ class_Lattices_Obounded__lattice(X3) ),
inference(spm,[status(thm)],[c_0_114,c_0_190]) ).
cnf(c_0_197,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)))
| ~ hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_133]) ).
cnf(c_0_198,negated_conjecture,
( X1 = v_Q____
| hBOOL(v_P____)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_199,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
inference(rw,[status(thm)],[c_0_195,c_0_146]) ).
cnf(c_0_200,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__left_0 ).
cnf(c_0_201,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X2)),X3))
| ~ hBOOL(X3)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(spm,[status(thm)],[c_0_196,c_0_133]) ).
cnf(c_0_202,plain,
( hBOOL(c_Orderings_Obot__class_Obot(X1))
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1))) ),
inference(spm,[status(thm)],[c_0_197,c_0_157]) ).
cnf(c_0_203,negated_conjecture,
( c_Orderings_Otop__class_Otop(tc_bool) = v_Q____
| hBOOL(v_P____) ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_204,plain,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2,X3),X4),X5))
| ~ hBOOL(hAPP(X4,c_Orderings_Otop__class_Otop(X1)))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_200]) ).
cnf(c_0_205,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X1),X2))
| ~ hBOOL(X2)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(spm,[status(thm)],[c_0_201,c_0_143]) ).
cnf(c_0_206,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_sup__inf__absorb_0 ).
cnf(c_0_207,negated_conjecture,
( hBOOL(v_P____)
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_Q____)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_141])]),c_0_174]) ).
cnf(c_0_208,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| X1 = v_Q____
| hBOOL(v_P____) ),
inference(spm,[status(thm)],[c_0_198,c_0_172]) ).
cnf(c_0_209,plain,
( hBOOL(hAPP(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X2),X2),X3)))
| ~ hBOOL(hAPP(X1,c_Orderings_Otop__class_Otop(X2)))
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(rw,[status(thm)],[c_0_204,c_0_96]) ).
cnf(c_0_210,plain,
( hBOOL(c_Orderings_Obot__class_Obot(X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X1),X2))
| ~ class_Lattices_Obounded__lattice(X1)
| ~ class_Lattices_Olattice(X1) ),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_211,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I1_J_0 ).
cnf(c_0_212,negated_conjecture,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = v_Q____
| hBOOL(v_P____)
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_Q____)) ),
inference(spm,[status(thm)],[c_0_207,c_0_208]) ).
cnf(c_0_213,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X1),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Otop(X1) ),
inference(spm,[status(thm)],[c_0_144,c_0_104]) ).
cnf(c_0_214,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_sup__absorb1_0 ).
cnf(c_0_215,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2))
| ~ hBOOL(c_Orderings_Otop__class_Otop(X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_91]),c_0_91]) ).
cnf(c_0_216,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_217,plain,
( hBOOL(c_Orderings_Obot__class_Obot(X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),c_Orderings_Obot__class_Obot(X1)))
| ~ class_Lattices_Obounded__lattice(X1)
| ~ class_Lattices_Olattice(X1) ),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_218,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X1),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I2_J_0 ).
cnf(c_0_219,negated_conjecture,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = v_Q____
| X1 = v_Q____
| hBOOL(v_P____)
| ~ hBOOL(hAPP(X1,v_Q____)) ),
inference(spm,[status(thm)],[c_0_212,c_0_208]) ).
cnf(c_0_220,negated_conjecture,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_Q____,tc_bool),X1) = X1
| hBOOL(v_P____) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_203]),c_0_103]),c_0_110])]) ).
cnf(c_0_221,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(spm,[status(thm)],[c_0_214,c_0_104]) ).
cnf(c_0_222,negated_conjecture,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_Q____,tc_bool),X1))
| hBOOL(v_P____) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_203]),c_0_216])]),c_0_194]) ).
cnf(c_0_223,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_inf__compl__bot_0 ).
cnf(c_0_224,plain,
( hBOOL(c_Orderings_Obot__class_Obot(X1))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),c_Orderings_Obot__class_Obot(X1))))
| ~ class_Lattices_Obounded__lattice(X1)
| ~ class_Lattices_Olattice(X1) ),
inference(spm,[status(thm)],[c_0_217,c_0_218]) ).
cnf(c_0_225,negated_conjecture,
( c_Lattices_Olower__semilattice__class_Oinf(v_Q____,tc_bool) = v_Q____
| c_HOL_Ouminus__class_Ouminus(tc_bool) = v_Q____
| hBOOL(v_P____) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_194]) ).
cnf(c_0_226,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_99]),c_0_103])]) ).
cnf(c_0_227,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_228,negated_conjecture,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_Q____,tc_bool),X1) = v_Q____
| hBOOL(v_P____) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_203]),c_0_110]),c_0_85])]) ).
cnf(c_0_229,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(v_Q____,tc_bool) = v_Q____
| c_HOL_Ouminus__class_Ouminus(tc_bool) = v_Q____
| hBOOL(v_P____) ),
inference(spm,[status(thm)],[c_0_219,c_0_222]) ).
cnf(c_0_230,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_152]),c_0_141])]) ).
cnf(c_0_231,negated_conjecture,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = v_Q____
| hBOOL(v_P____)
| ~ hBOOL(hAPP(v_Q____,c_Orderings_Obot__class_Obot(tc_bool))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_226]),c_0_216]),c_0_227])]),c_0_174]) ).
cnf(c_0_232,negated_conjecture,
( hAPP(v_Q____,X1) = v_Q____
| c_HOL_Ouminus__class_Ouminus(tc_bool) = v_Q____
| hBOOL(v_P____) ),
inference(spm,[status(thm)],[c_0_228,c_0_229]) ).
cnf(c_0_233,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
cls_rev__bexI_1 ).
cnf(c_0_234,axiom,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Set__XballE__1__1(X3,X4,X1))) ),
cls_ballE_1 ).
cnf(c_0_235,plain,
( hBOOL(hAPP(X1,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))
| ~ hBOOL(hAPP(X1,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_149,c_0_230]),c_0_141]),c_0_226])]) ).
cnf(c_0_236,negated_conjecture,
( hBOOL(v_P____)
| ~ hBOOL(hAPP(X1,v_Q____))
| ~ hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_207,c_0_193]) ).
cnf(c_0_237,negated_conjecture,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = v_Q____
| hBOOL(v_P____) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_194]) ).
cnf(c_0_238,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,c_Arrow__Order__Mirabelle_OProf,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),v_P____),X1)) ),
inference(spm,[status(thm)],[c_0_233,c_0_170]) ).
cnf(c_0_239,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_240,plain,
( hBOOL(X1)
| ~ hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(X2,c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_152]),c_0_152]) ).
cnf(c_0_241,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),
inference(spm,[status(thm)],[c_0_166,c_0_133]) ).
cnf(c_0_242,axiom,
( hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| hBOOL(hAPP(hAPP(c_in(X4),X6),X3)) ),
cls_override__on__apply__notin_0 ).
cnf(c_0_243,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_244,plain,
( hBOOL(hAPP(c_Not,hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))
| hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(spm,[status(thm)],[c_0_235,c_0_157]) ).
cnf(c_0_245,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__idem_0 ).
cnf(c_0_246,negated_conjecture,
( hBOOL(v_P____)
| ~ hBOOL(hAPP(X1,v_Q____))
| ~ hBOOL(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_237]),c_0_194]) ).
cnf(c_0_247,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,c_Arrow__Order__Mirabelle_OProf,X2)))
| ~ hBOOL(hAPP(X1,v_P____)) ),
inference(spm,[status(thm)],[c_0_238,c_0_133]) ).
cnf(c_0_248,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_fequal(X3),X2))),
inference(spm,[status(thm)],[c_0_183,c_0_239]) ).
cnf(c_0_249,plain,
( hBOOL(X1)
| ~ hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(X2,c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X3))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(spm,[status(thm)],[c_0_240,c_0_133]) ).
cnf(c_0_250,plain,
hAPP(c_Fun_Ooverride__on(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X5),X6) = hAPP(X1,X6),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_251,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I7_J_0 ).
cnf(c_0_252,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_117]),c_0_100])]) ).
cnf(c_0_253,plain,
( hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) ),
inference(spm,[status(thm)],[c_0_164,c_0_244]) ).
cnf(c_0_254,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X2,X3)))
| ~ hBOOL(X2)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(spm,[status(thm)],[c_0_183,c_0_245]) ).
cnf(c_0_255,negated_conjecture,
( hBOOL(v_P____)
| ~ hBOOL(c_Lattices_Olower__semilattice__class_Oinf(v_Q____,tc_bool)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_220]),c_0_194]) ).
cnf(c_0_256,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| c_Orderings_Otop__class_Otop(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_186,c_0_172]) ).
cnf(c_0_257,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,c_Arrow__Order__Mirabelle_OProf,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),v_P____),X1)) ),
inference(spm,[status(thm)],[c_0_247,c_0_133]) ).
cnf(c_0_258,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(c_fequal(X2),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_in(X4),X3)))),
inference(spm,[status(thm)],[c_0_136,c_0_248]) ).
cnf(c_0_259,plain,
( hBOOL(X1)
| ~ hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(c_Fun_Ooverride__on(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5,X6),c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X7))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(spm,[status(thm)],[c_0_249,c_0_250]) ).
cnf(c_0_260,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Oord__class_Oless(X2,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ c_lessequals(X2,X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_252]),c_0_100])]) ).
cnf(c_0_261,plain,
( ~ hBOOL(c_HOL_Ominus__class_Ominus(X1,tc_bool))
| ~ hBOOL(hAPP(X2,X1))
| ~ hBOOL(X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_193]),c_0_174]) ).
cnf(c_0_262,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_230]),c_0_141])]) ).
cnf(c_0_263,negated_conjecture,
( hBOOL(v_P____)
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),v_Q____)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_203]),c_0_174]) ).
cnf(c_0_264,plain,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),X1))
| ~ hBOOL(X1)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(spm,[status(thm)],[c_0_160,c_0_254]) ).
cnf(c_0_265,negated_conjecture,
( c_Lattices_Olower__semilattice__class_Oinf(v_Q____,tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(v_P____) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_256]),c_0_199])]) ).
cnf(c_0_266,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,c_Arrow__Order__Mirabelle_OProf,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),hAPP(c_in(X4),v_P____))) ),
inference(spm,[status(thm)],[c_0_257,c_0_133]) ).
cnf(c_0_267,plain,
hBOOL(hAPP(hAPP(c_in(X1),hAPP(c_fequal(X2),X3)),hAPP(c_in(X4),X3))),
inference(spm,[status(thm)],[c_0_258,c_0_119]) ).
cnf(c_0_268,plain,
~ hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(c_Fun_Ooverride__on(c_Not,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X5)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_189]),c_0_166]) ).
cnf(c_0_269,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
inference(spm,[status(thm)],[c_0_260,c_0_99]) ).
cnf(c_0_270,plain,
( ~ hBOOL(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool))
| ~ hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_262]),c_0_199])]) ).
cnf(c_0_271,negated_conjecture,
( c_HOL_Ominus__class_Ominus(X1,tc_bool) = v_Q____
| hBOOL(v_P____)
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_Q____)) ),
inference(spm,[status(thm)],[c_0_263,c_0_208]) ).
cnf(c_0_272,negated_conjecture,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_Q____))
| hBOOL(v_P____) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_265]),c_0_103])]),c_0_194]) ).
cnf(c_0_273,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(hAPP(c_fequal(X1),v_P____),c_Arrow__Order__Mirabelle_OProf,X2))),
inference(spm,[status(thm)],[c_0_266,c_0_267]) ).
cnf(c_0_274,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ hBOOL(c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(spm,[status(thm)],[c_0_268,c_0_269]) ).
cnf(c_0_275,negated_conjecture,
( hBOOL(v_P____)
| ~ hBOOL(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_270,c_0_237]),c_0_194]) ).
cnf(c_0_276,negated_conjecture,
( c_HOL_Ominus__class_Ominus(X1,tc_bool) = v_Q____
| hBOOL(v_P____) ),
inference(spm,[status(thm)],[c_0_271,c_0_272]) ).
cnf(c_0_277,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X4)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__left__commute_0 ).
cnf(c_0_278,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_99]),c_0_85])]) ).
cnf(c_0_279,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) != X2 ),
cls_le__iff__inf_1 ).
cnf(c_0_280,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_281,plain,
c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_269]),c_0_274]) ).
cnf(c_0_282,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder ).
cnf(c_0_283,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4)) ),
cls_bexI_1 ).
cnf(c_0_284,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X1),X2),X3,X1) ),
cls_le__supE_1 ).
cnf(c_0_285,negated_conjecture,
hBOOL(v_P____),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_194]) ).
cnf(c_0_286,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(X3,X4)) ),
cls_bexI_0 ).
cnf(c_0_287,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq1_0 ).
cnf(c_0_288,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_278]),c_0_278]),c_0_85])]) ).
cnf(c_0_289,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup__top_0 ).
cnf(c_0_290,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(spm,[status(thm)],[c_0_279,c_0_139]) ).
cnf(c_0_291,plain,
~ c_lessequals(c_Orderings_Otop__class_Otop(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_280,c_0_281]),c_0_282])]) ).
cnf(c_0_292,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__XbexI__1__1(X1,c_Arrow__Order__Mirabelle_OProf,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),v_P____),X1)) ),
inference(spm,[status(thm)],[c_0_283,c_0_170]) ).
cnf(c_0_293,plain,
c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X1),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_84]),c_0_85])]) ).
cnf(c_0_294,negated_conjecture,
( X1 = v_P____
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_193,c_0_285]) ).
cnf(c_0_295,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(rw,[status(thm)],[c_0_286,c_0_133]) ).
cnf(c_0_296,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_84]),c_0_103])]) ).
cnf(c_0_297,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_288]),c_0_216])]) ).
cnf(c_0_298,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),c_Orderings_Otop__class_Otop(X1))
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(spm,[status(thm)],[c_0_277,c_0_289]) ).
cnf(c_0_299,plain,
c_Orderings_Otop__class_Otop(tc_bool) != c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_290,c_0_262]),c_0_141]),c_0_103])]),c_0_291]) ).
cnf(c_0_300,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0 ).
cnf(c_0_301,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__XbexI__1__1(X1,c_Arrow__Order__Mirabelle_OProf,X2)))
| ~ hBOOL(hAPP(X1,v_P____)) ),
inference(spm,[status(thm)],[c_0_292,c_0_133]) ).
cnf(c_0_302,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2),tc_bool),X2) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_293]),c_0_103])]) ).
cnf(c_0_303,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_117]),c_0_85])]) ).
cnf(c_0_304,negated_conjecture,
c_Orderings_Otop__class_Otop(tc_bool) = v_P____,
inference(spm,[status(thm)],[c_0_294,c_0_199]) ).
cnf(c_0_305,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X1,c_Arrow__Order__Mirabelle_OProf,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),v_P____),X1)) ),
inference(spm,[status(thm)],[c_0_295,c_0_170]) ).
cnf(c_0_306,plain,
hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool)) = X2,
inference(spm,[status(thm)],[c_0_296,c_0_133]) ).
cnf(c_0_307,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X1)) != c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_298]),c_0_141]),c_0_85])]),c_0_299]) ).
cnf(c_0_308,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2),c_Orderings_Obot__class_Obot(X2))) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2),X1)
| ~ class_Lattices_Obounded__lattice(X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(spm,[status(thm)],[c_0_277,c_0_300]) ).
cnf(c_0_309,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),v_P____),tc_bool),c_Arrow__Order__Mirabelle_OProf,X2)))
| ~ hBOOL(v_P____) ),
inference(spm,[status(thm)],[c_0_301,c_0_302]) ).
cnf(c_0_310,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),v_P____) = v_P____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_303,c_0_304]),c_0_304]) ).
cnf(c_0_311,plain,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_P____,tc_bool),c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Lattices_Olower__semilattice__class_Oinf(v_P____,tc_bool),c_Arrow__Order__Mirabelle_OProf,X1)))
| ~ hBOOL(v_P____) ),
inference(spm,[status(thm)],[c_0_305,c_0_306]) ).
cnf(c_0_312,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_P____,tc_bool),X1) = X1,
inference(rw,[status(thm)],[c_0_152,c_0_304]) ).
cnf(c_0_313,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_307,c_0_308]),c_0_278]),c_0_216]),c_0_85])]) ).
cnf(c_0_314,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____) = c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[c_0_230,c_0_304]) ).
cnf(c_0_315,negated_conjecture,
~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_304]),c_0_141])]),c_0_174]) ).
cnf(c_0_316,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| X1 = v_P____ ),
inference(spm,[status(thm)],[c_0_294,c_0_172]) ).
cnf(c_0_317,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Lattices_Olower__semilattice__class_Oinf(v_P____,tc_bool),c_Arrow__Order__Mirabelle_OProf,X1))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_309,c_0_285])]),c_0_310]) ).
cnf(c_0_318,plain,
hBOOL(c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Lattices_Olower__semilattice__class_Oinf(v_P____,tc_bool),c_Arrow__Order__Mirabelle_OProf,X1)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_311,c_0_285])]),c_0_312]) ).
cnf(c_0_319,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_314]),c_0_137]) ).
cnf(c_0_320,negated_conjecture,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = v_P____
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_P____)) ),
inference(spm,[status(thm)],[c_0_315,c_0_316]) ).
cnf(c_0_321,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X1))
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_317,c_0_193]),c_0_318])]) ).
cnf(c_0_322,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_202,c_0_186]),c_0_141])]),c_0_174]) ).
cnf(c_0_323,plain,
( hAPP(X1,X2) != c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_319,c_0_193]) ).
cnf(c_0_324,negated_conjecture,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = v_P____
| hBOOL(X1)
| ~ hBOOL(hAPP(X1,v_P____)) ),
inference(spm,[status(thm)],[c_0_320,c_0_172]) ).
cnf(c_0_325,negated_conjecture,
( hAPP(c_Arrow__Order__Mirabelle_OProf,X1) = v_P____
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_294,c_0_321]) ).
cnf(c_0_326,plain,
( ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_322,c_0_193]) ).
cnf(c_0_327,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool))
| ~ hBOOL(c_HOL_Ouminus__class_Ouminus(X1)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_323,c_0_158])]) ).
cnf(c_0_328,negated_conjecture,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = v_P____
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_325]),c_0_285])]) ).
cnf(c_0_329,negated_conjecture,
( ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool))
| ~ hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_323,c_0_188]) ).
cnf(c_0_330,plain,
( ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool))
| ~ hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_326,c_0_303]),c_0_199])]) ).
cnf(c_0_331,negated_conjecture,
~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_327,c_0_328]),c_0_141]),c_0_285])]),c_0_329]) ).
cnf(c_0_332,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330,c_0_256]),c_0_199])]) ).
cnf(c_0_333,negated_conjecture,
c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_331,c_0_172]) ).
cnf(c_0_334,plain,
c_Orderings_Obot__class_Obot(tc_bool) != v_P____,
inference(rw,[status(thm)],[c_0_299,c_0_304]) ).
cnf(c_0_335,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| 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_332,c_0_256]),c_0_199])]) ).
cnf(c_0_336,negated_conjecture,
hAPP(c_Orderings_Obot__class_Obot(tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_333]),c_0_216])]),c_0_334]) ).
cnf(c_0_337,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Orderings_Obot__class_Obot(tc_bool),X1) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_335]),c_0_94]),c_0_85])]) ).
cnf(c_0_338,negated_conjecture,
c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_336,c_0_337])]) ).
cnf(c_0_339,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_314,c_0_338]),c_0_336]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT030-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:53:46 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 167.68/104.10 % Version : CSE_E---1.7
% 167.68/104.10 % Problem : theBenchmark.p
% 167.68/104.10 % SZS status Unsatisfiable for theBenchmark.p
% 167.68/104.10 % SZS output start CNFRefutation
% See solution above
% 168.36/104.73 % Total time : 79.207s
%------------------------------------------------------------------------------