%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT022-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:07:35 PM UTC 2026
% Result : Unsatisfiable 270.16s 35.81s
% Output : CNFRefutation 270.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 61
% Syntax : Number of clauses : 248 ( 106 unt; 21 nHn; 118 RR)
% Number of literals : 437 ( 126 equ; 204 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 7 con; 0-4 aty)
% Number of variables : 526 ( 180 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_inf1E_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X4,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
cnf(cls_inf__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_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_top__fun__eq_0,axiom,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_sup__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_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_inf__sup__absorb_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
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_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_UNIV__eq__I_0,axiom,
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__eq__I_0) ).
cnf(cls_sup__top__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(cls_not__acc__down_0,axiom,
( hBOOL(c_in(X2,c_Wellfounded_Oacc(X1,X3),X3))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
cnf(cls_insert__absorb_0,axiom,
( ~ hBOOL(c_in(X1,X3,X2))
| hAPP(c_Set_Oinsert(X1,X2),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_fun__diff__def_0,axiom,
( ~ class_HOL_Ominus(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
cnf(cls_bot__fun__eq_0,axiom,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_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_INF__leI_0,axiom,
( ~ hBOOL(c_in(X5,X2,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,X1),hAPP(X3,X5),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Set_Oinsert(X2,X1),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_pair__in__Id__conv_1,axiom,
hBOOL(c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
cnf(clsarity_bool__HOL_Ominus,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X3,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_INF__const_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X3,X1,X4),X4,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__const_0) ).
cnf(cls_irrefl__def_0,axiom,
( ~ c_Relation_Oirrefl(X3,X2)
| ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
cnf(cls_Diff__UNIV_0,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
cnf(cls_predicate1D_0,axiom,
( ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
cnf(clsarity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( hBOOL(c_in(X1,X3,X2))
| hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X2),X3),tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
cnf(cls_Diff__disjoint_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
cnf(cls_Int__insert__left_1,axiom,
( hBOOL(c_in(X1,X4,X2))
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X1,X2),X3),tc_fun(X2,tc_bool)),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
cnf(cls_mem__def_0,axiom,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_sup__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
cnf(cls_conjecture_3,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Un__Diff__cancel_0,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_conjecture_6,negated_conjecture,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_le__funD_0,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( ~ class_Lattices_Olattice(X2)
| class_Lattices_Oupper__semilattice(tc_fun(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_le__infE_0,axiom,
( ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_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/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(cls_wf__asym_0,axiom,
( ~ c_Wellfounded_Owf(X4,X3)
| ~ hBOOL(c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)))
| ~ hBOOL(c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
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_bex__UNIV_2,axiom,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_2) ).
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_disjoint__iff__not__equal_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_acc__wfI_0,axiom,
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2))
| c_Wellfounded_Owf(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
cnf(c_0_61,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X4,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_inf1E_1]) ).
cnf(c_0_62,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
inference(fof_simplification,[status(thm)],[cls_inf__fun__eq_0]) ).
cnf(c_0_63,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X4,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X2)) ),
c_0_61 ).
cnf(c_0_64,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
c_0_62 ).
cnf(c_0_65,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_66,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_top__fun__eq_0]) ).
cnf(c_0_67,plain,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),tc_bool),hAPP(X1,v_x)))
| hBOOL(hAPP(X1,v_x)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]) ).
cnf(c_0_68,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_69,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_sup__top__left_0]) ).
cnf(c_0_70,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
c_0_66 ).
cnf(c_0_71,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_72,plain,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),tc_bool),X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_inf__sup__absorb_0]) ).
cnf(c_0_74,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_1]) ).
cnf(c_0_75,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1) ),
c_0_69 ).
cnf(c_0_76,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_77,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_78,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_79,plain,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_68]) ).
cnf(c_0_80,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3)) = X2 ),
c_0_73 ).
cnf(c_0_81,plain,
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_UNIV__eq__I_0]) ).
cnf(c_0_82,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
c_0_74 ).
cnf(c_0_83,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_sup__top__right_0]) ).
cnf(c_0_86,plain,
( ~ hBOOL(X1)
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_65])]) ).
cnf(c_0_87,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2) ),
inference(fof_simplification,[status(thm)],[cls_inf__sup__aci_I5_J_0]) ).
cnf(c_0_88,plain,
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
c_0_81 ).
cnf(c_0_89,plain,
hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
cnf(c_0_90,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1) ),
c_0_85 ).
cnf(c_0_91,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[cls_emptyE_0]) ).
cnf(c_0_92,plain,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2 ),
inference(fof_simplification,[status(thm)],[cls_sup__idem_0]) ).
cnf(c_0_93,plain,
( ~ hBOOL(X2)
| hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X3)) ),
inference(spm,[status(thm)],[c_0_82,c_0_86]) ).
cnf(c_0_94,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2) ),
c_0_87 ).
cnf(c_0_95,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,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(spm,[status(thm)],[c_0_90,c_0_76]) ).
cnf(c_0_97,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
c_0_91 ).
cnf(c_0_98,axiom,
( hBOOL(c_in(X2,c_Wellfounded_Oacc(X1,X3),X3))
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3))) ),
cls_not__acc__down_0 ).
cnf(c_0_99,plain,
( ~ hBOOL(c_in(X1,X3,X2))
| hAPP(c_Set_Oinsert(X1,X2),X3) = X3 ),
inference(fof_simplification,[status(thm)],[cls_insert__absorb_0]) ).
cnf(c_0_100,plain,
( ~ class_HOL_Ominus(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
inference(fof_simplification,[status(thm)],[cls_fun__diff__def_0]) ).
cnf(c_0_101,plain,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1) ),
inference(fof_simplification,[status(thm)],[cls_bot__fun__eq_0]) ).
cnf(c_0_102,plain,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)),
inference(spm,[status(thm)],[c_0_82,c_0_77]) ).
cnf(c_0_103,plain,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2 ),
c_0_92 ).
cnf(c_0_104,plain,
( ~ hBOOL(X2)
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_88,c_0_93]) ).
cnf(c_0_105,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_65])]) ).
cnf(c_0_106,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_107,plain,
hBOOL(c_in(X1,c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2)),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_108,plain,
( ~ hBOOL(c_in(X5,X2,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,X1),hAPP(X3,X5),X1) ),
inference(fof_simplification,[status(thm)],[cls_INF__leI_0]) ).
cnf(c_0_109,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Set_Oinsert(X2,X1),X3),
inference(fof_simplification,[status(thm)],[cls_empty__not__insert_0]) ).
cnf(c_0_110,plain,
( ~ hBOOL(c_in(X1,X3,X2))
| hAPP(c_Set_Oinsert(X1,X2),X3) = X3 ),
c_0_99 ).
cnf(c_0_111,axiom,
hBOOL(c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2))),
cls_pair__in__Id__conv_1 ).
cnf(c_0_112,plain,
( ~ class_HOL_Ominus(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
c_0_100 ).
cnf(c_0_113,axiom,
class_HOL_Ominus(tc_bool),
clsarity_bool__HOL_Ominus ).
cnf(c_0_114,plain,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1) ),
c_0_101 ).
cnf(c_0_115,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_116,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_88,c_0_102]) ).
cnf(c_0_117,plain,
( ~ hBOOL(c_in(X1,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X3,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[cls_DiffE_1]) ).
cnf(c_0_118,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
cls_insert__code_1 ).
cnf(c_0_119,plain,
( ~ hBOOL(X1)
| c_Orderings_Otop__class_Otop(tc_bool) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]),c_0_106])]) ).
cnf(c_0_120,plain,
c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_88,c_0_107]) ).
cnf(c_0_121,plain,
( ~ hBOOL(c_in(X5,X2,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,X1),hAPP(X3,X5),X1) ),
c_0_108 ).
cnf(c_0_122,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X3,X1,X4),X4,X1) = X3 ),
inference(fof_simplification,[status(thm)],[cls_INF__const_0]) ).
cnf(c_0_123,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Set_Oinsert(X2,X1),X3),
c_0_109 ).
cnf(c_0_124,plain,
hAPP(c_Set_Oinsert(c_Pair(X1,X1,X2,X2),tc_prod(X2,X2)),c_Relation_OId(X2)) = c_Relation_OId(X2),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_125,plain,
( ~ c_Relation_Oirrefl(X3,X2)
| ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))) ),
inference(fof_simplification,[status(thm)],[cls_irrefl__def_0]) ).
cnf(c_0_126,plain,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(t_a,tc_bool)),X2),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),tc_bool),hAPP(X2,v_x)),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_127,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__UNIV_0 ).
cnf(c_0_128,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_129,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_78,c_0_116]) ).
cnf(c_0_130,plain,
( ~ hBOOL(c_in(X1,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X3,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_117 ).
cnf(c_0_131,plain,
hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X1,X2),X3),X4)),
inference(spm,[status(thm)],[c_0_82,c_0_118]) ).
cnf(c_0_132,plain,
c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) = c_Orderings_Otop__class_Otop(tc_bool),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_107]),c_0_120]) ).
cnf(c_0_133,plain,
( ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_predicate1D_0]) ).
cnf(c_0_134,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Relation_OId(X1),X2,tc_prod(X1,X1),X3),hAPP(X2,c_Pair(X4,X4,X1,X1)),X3) ),
inference(spm,[status(thm)],[c_0_121,c_0_111]) ).
cnf(c_0_135,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X3,X1,X4),X4,X1) = X3 ),
c_0_122 ).
cnf(c_0_136,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) != c_Relation_OId(X1),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_137,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clsarity_fun__Complete__Lattice_Ocomplete__lattice]) ).
cnf(c_0_138,plain,
( ~ c_Relation_Oirrefl(X3,X2)
| ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))) ),
c_0_125 ).
cnf(c_0_139,axiom,
( hBOOL(c_in(X1,X3,X2))
| hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X2),X3),tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3 ),
cls_Diff__insert__absorb_0 ).
cnf(c_0_140,plain,
hAPP(c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]),c_0_129]) ).
cnf(c_0_141,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
cls_Int__UNIV__left_0 ).
cnf(c_0_142,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__disjoint_0 ).
cnf(c_0_143,axiom,
( hBOOL(c_in(X1,X4,X2))
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X1,X2),X3),tc_fun(X2,tc_bool)),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X4) ),
cls_Int__insert__left_1 ).
cnf(c_0_144,plain,
~ hBOOL(c_in(X1,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X3,tc_bool)),hAPP(c_Set_Oinsert(X1,X4),X5)),X3)),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_145,plain,
c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_132,c_0_116]) ).
cnf(c_0_146,plain,
( ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(X1,X2)) ),
c_0_133 ).
cnf(c_0_147,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_lessequals(X1,X1,X2) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_68]),c_0_136]) ).
cnf(c_0_148,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2)) ),
c_0_137 ).
cnf(c_0_149,plain,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_0]) ).
cnf(c_0_150,plain,
( ~ hBOOL(X1)
| ~ c_Relation_Oirrefl(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) ),
inference(spm,[status(thm)],[c_0_138,c_0_93]) ).
cnf(c_0_151,plain,
( hBOOL(c_in(X1,X2,t_a))
| hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1,t_a),X2),v_x),tc_bool),hAPP(hAPP(c_Set_Oinsert(X1,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x)) = hAPP(X2,v_x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_139]),c_0_113])]) ).
cnf(c_0_152,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_119,c_0_118]) ).
cnf(c_0_153,plain,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_140,c_0_68]) ).
cnf(c_0_154,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X2,tc_bool)),X3) = X3,
inference(spm,[status(thm)],[c_0_141,c_0_116]) ).
cnf(c_0_155,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X4,X2),X1))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]) ).
cnf(c_0_156,plain,
hAPP(c_Set_Oinsert(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_145]),c_0_84])]) ).
cnf(c_0_157,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
inference(fof_simplification,[status(thm)],[cls_sup__fun__eq_0]) ).
cnf(c_0_158,plain,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3),X1,tc_fun(X4,tc_bool))
| ~ hBOOL(X2)
| ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_146,c_0_103]) ).
cnf(c_0_159,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(X1,X1,tc_fun(X2,X3)) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_160,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_161,plain,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
c_0_149 ).
cnf(c_0_162,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
cls_conjecture_3 ).
cnf(c_0_163,plain,
( ~ hBOOL(X2)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool))
| ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_bool),X1) ),
inference(spm,[status(thm)],[c_0_150,c_0_119]) ).
cnf(c_0_164,plain,
( hBOOL(c_in(v_x,X1,t_a))
| c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,v_x) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).
cnf(c_0_165,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),X3),
cls_Un__Diff__cancel_0 ).
cnf(c_0_166,plain,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_156]) ).
cnf(c_0_167,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X1,
cls_Un__empty__right_0 ).
cnf(c_0_168,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
c_0_157 ).
cnf(c_0_169,plain,
( ~ hBOOL(X1)
| ~ class_Lattices_Oupper__semilattice(X2)
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_160])]) ).
cnf(c_0_170,negated_conjecture,
hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_171,plain,
( ~ hBOOL(X1)
| ~ hBOOL(X3)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(X3,tc_bool))
| ~ c_Relation_Oirrefl(X1,X2) ),
inference(spm,[status(thm)],[c_0_163,c_0_119]) ).
cnf(c_0_172,plain,
( hBOOL(hAPP(X1,v_x))
| c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,v_x) ),
inference(spm,[status(thm)],[c_0_161,c_0_164]) ).
cnf(c_0_173,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X2,tc_bool)),X3) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_167]) ).
cnf(c_0_174,negated_conjecture,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_6]) ).
cnf(c_0_175,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_bot__least_0]) ).
cnf(c_0_176,plain,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
inference(fof_simplification,[status(thm)],[cls_le__funD_0]) ).
cnf(c_0_177,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(t_a,tc_bool)),X2),v_x) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),tc_bool),hAPP(X2,v_x)),
inference(spm,[status(thm)],[c_0_168,c_0_65]) ).
cnf(c_0_178,plain,
( ~ hBOOL(X1)
| ~ class_Lattices_Oupper__semilattice(X2)
| c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_169]) ).
cnf(c_0_179,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X1) = X1,
inference(spm,[status(thm)],[c_0_103,c_0_106]) ).
cnf(c_0_180,plain,
( ~ class_Lattices_Olattice(X2)
| class_Lattices_Oupper__semilattice(tc_fun(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clsarity_fun__Lattices_Oupper__semilattice]) ).
cnf(c_0_181,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),X1)),
inference(spm,[status(thm)],[c_0_82,c_0_170]) ).
cnf(c_0_182,plain,
( ~ hBOOL(X1)
| ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))
| ~ c_Relation_Oirrefl(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_95]),c_0_84])]) ).
cnf(c_0_183,plain,
( hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_184,negated_conjecture,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
c_0_174 ).
cnf(c_0_185,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_1 ).
cnf(c_0_186,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_2 ).
cnf(c_0_187,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_0 ).
cnf(c_0_188,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[cls_order__eq__iff_2]) ).
cnf(c_0_189,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
c_0_175 ).
cnf(c_0_190,plain,
( ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_le__infE_0]) ).
cnf(c_0_191,plain,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
c_0_176 ).
cnf(c_0_192,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_193,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_194,plain,
( ~ hBOOL(X1)
| ~ class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = hAPP(X1,v_x) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179]) ).
cnf(c_0_195,plain,
( ~ class_Lattices_Olattice(X2)
| class_Lattices_Oupper__semilattice(tc_fun(X1,X2)) ),
c_0_180 ).
cnf(c_0_196,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2),X3))
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),X1) = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_152,c_0_119]) ).
cnf(c_0_197,negated_conjecture,
hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),v_F(v_P)) = v_F(v_P),
inference(spm,[status(thm)],[c_0_110,c_0_181]) ).
cnf(c_0_198,plain,
( ~ c_Wellfounded_Owf(X4,X3)
| ~ hBOOL(c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)))
| ~ hBOOL(c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))) ),
inference(fof_simplification,[status(thm)],[cls_wf__asym_0]) ).
cnf(c_0_199,plain,
( ~ hBOOL(X2)
| ~ c_Relation_Oirrefl(X2,X3)
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_200,negated_conjecture,
c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185])]),c_0_186]),c_0_187])]) ).
cnf(c_0_201,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
c_0_188 ).
cnf(c_0_202,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_189,c_0_115]) ).
cnf(c_0_203,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_204,plain,
( ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X2,X3,X1) ),
c_0_190 ).
cnf(c_0_205,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_191,c_0_192]),c_0_193])]) ).
cnf(c_0_206,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_207,plain,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2))) ),
inference(fof_simplification,[status(thm)],[cls_bex__UNIV_2]) ).
cnf(c_0_208,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[cls_bot1E_0]) ).
cnf(c_0_209,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[cls_disjoint__iff__not__equal_0]) ).
cnf(c_0_210,plain,
( ~ hBOOL(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = hAPP(X1,v_x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_65])]) ).
cnf(c_0_211,negated_conjecture,
( ~ hBOOL(v_F(v_P))
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_212,plain,
( hBOOL(X1)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_172,c_0_68]) ).
cnf(c_0_213,plain,
( ~ c_Wellfounded_Owf(X4,X3)
| ~ hBOOL(c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)))
| ~ hBOOL(c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))) ),
c_0_198 ).
cnf(c_0_214,negated_conjecture,
( ~ hBOOL(v_F(v_P))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_215,plain,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_203])]) ).
cnf(c_0_216,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_204,c_0_205]),c_0_206])]) ).
cnf(c_0_217,plain,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2))) ),
c_0_207 ).
cnf(c_0_218,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_208 ).
cnf(c_0_219,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_209 ).
cnf(c_0_220,plain,
~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2),
inference(spm,[status(thm)],[c_0_138,c_0_102]) ).
cnf(c_0_221,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_183]),c_0_105]) ).
cnf(c_0_222,negated_conjecture,
( v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_223,plain,
~ c_Wellfounded_Owf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_102]),c_0_102])]) ).
cnf(c_0_224,negated_conjecture,
( v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_214,c_0_212]) ).
cnf(c_0_225,plain,
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2))
| c_Wellfounded_Owf(X1,X2) ),
inference(fof_simplification,[status(thm)],[cls_acc__wfI_0]) ).
cnf(c_0_226,plain,
( hBOOL(c_in(X2,c_Wellfounded_Oacc(X1,X3),X3))
| hBOOL(hAPP(X1,c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3))) ),
inference(spm,[status(thm)],[c_0_161,c_0_98]) ).
cnf(c_0_227,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_215,c_0_216]) ).
cnf(c_0_228,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_128]),c_0_218]) ).
cnf(c_0_229,plain,
( ~ hBOOL(c_in(X4,X3,X2))
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X2,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(spm,[status(thm)],[c_0_219,c_0_102]) ).
cnf(c_0_230,plain,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_119,c_0_119]) ).
cnf(c_0_231,plain,
( ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_220,c_0_221]) ).
cnf(c_0_232,negated_conjecture,
( c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),tc_Arrow__Order__Mirabelle_Oalt)
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_200,c_0_222]) ).
cnf(c_0_233,negated_conjecture,
( ~ c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_bool),X1)
| v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_223,c_0_224]) ).
cnf(c_0_234,plain,
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2))
| c_Wellfounded_Owf(X1,X2) ),
c_0_225 ).
cnf(c_0_235,plain,
hBOOL(c_in(X1,c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),X3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_228]) ).
cnf(c_0_236,negated_conjecture,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X2,tc_bool)),v_F(v_P)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_229,c_0_181]) ).
cnf(c_0_237,plain,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(spm,[status(thm)],[c_0_218,c_0_230]) ).
cnf(c_0_238,negated_conjecture,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool)
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_239,negated_conjecture,
( ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(X1)
| v_F(v_P) = X1 ),
inference(spm,[status(thm)],[c_0_233,c_0_212]) ).
cnf(c_0_240,plain,
c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),
inference(spm,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_241,negated_conjecture,
v_F(v_P) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_236,c_0_141]) ).
cnf(c_0_242,negated_conjecture,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_84])]) ).
cnf(c_0_243,negated_conjecture,
hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_241]) ).
cnf(c_0_244,plain,
( ~ hBOOL(X2)
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x)) ),
inference(spm,[status(thm)],[c_0_237,c_0_210]) ).
cnf(c_0_245,negated_conjecture,
hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_242,c_0_243])]) ).
cnf(c_0_246,plain,
~ hBOOL(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_244,c_0_243])]),c_0_245]),c_0_84])]) ).
cnf(c_0_247,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_98,c_0_246]),c_0_246]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT022-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.45 % Computer : n015.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 04:29:50 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.54 Running first-order theorem proving
% 0.26/0.54 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 270.16/35.81 % Version: 3.5.1
% 270.16/35.81 % Preprocessing class: FSLMSMSMSSSNFFN.
% 270.16/35.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 270.16/35.81 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 270.16/35.81 % Starting new_bool_3 with 600s (2) cores
% 270.16/35.81 % Starting new_bool_1 with 300s (1) cores
% 270.16/35.81 % Starting sh5l with 300s (1) cores
% 270.16/35.81 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 555285 completed with status 0
% 270.16/35.81 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 270.16/35.81 % Preprocessing class: FSLMSMSMSSSNFFN.
% 270.16/35.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 270.16/35.81 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 270.16/35.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 270.16/35.81 % No SInE strategy applied
% 270.16/35.81 % Search class: FGHSM-FSLM32-DFFFFFNN
% 270.16/35.81 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 270.16/35.81 % Starting SubtermCWHack with 109s (1) cores
% 270.16/35.81 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 270.16/35.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 270.16/35.81 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 270.16/35.81 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 555294 completed with status 0
% 270.16/35.81 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 270.16/35.81 % Preprocessing class: FSLMSMSMSSSNFFN.
% 270.16/35.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 270.16/35.81 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 270.16/35.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 270.16/35.81 % No SInE strategy applied
% 270.16/35.81 % Search class: FGHSM-FSLM32-DFFFFFNN
% 270.16/35.81 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 270.16/35.81 % Starting SubtermCWHack with 109s (1) cores
% 270.16/35.81 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 270.16/35.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 270.16/35.81 % Preprocessing time : 0.018 s
% 270.16/35.81 % Presaturation interreduction done
% 270.16/35.81
% 270.16/35.81 % Proof found!
% 270.16/35.81 % SZS status Unsatisfiable
% 270.16/35.81 % SZS output start CNFRefutation
% See solution above
% 270.16/35.81 % Parsed axioms : 713
% 270.16/35.81 % Removed by relevancy pruning/SinE : 0
% 270.16/35.81 % Initial clauses : 713
% 270.16/35.81 % Removed in clause preprocessing : 4
% 270.16/35.81 % Initial clauses in saturation : 709
% 270.16/35.81 % Processed clauses : 53573
% 270.16/35.81 % ...of these trivial : 1008
% 270.16/35.81 % ...subsumed : 39445
% 270.16/35.81 % ...remaining for further processing : 13120
% 270.16/35.81 % Other redundant clauses eliminated : 9956
% 270.16/35.81 % Clauses deleted for lack of memory : 0
% 270.16/35.81 % Backward-subsumed : 8005
% 270.16/35.81 % Backward-rewritten : 1685
% 270.16/35.81 % Generated clauses : 1154515
% 270.16/35.81 % ...of the previous two non-redundant : 1074681
% 270.16/35.81 % ...aggressively subsumed : 0
% 270.16/35.81 % Contextual simplify-reflections : 83
% 270.16/35.81 % Paramodulations : 1143907
% 270.16/35.81 % Factorizations : 43
% 270.16/35.81 % NegExts : 0
% 270.16/35.81 % Equation resolutions : 9983
% 270.16/35.81 % Disequality decompositions : 0
% 270.16/35.81 % Total rewrite steps : 310855
% 270.16/35.81 % ...of those cached : 280425
% 270.16/35.81 % Propositional unsat checks : 2
% 270.16/35.81 % Propositional check models : 0
% 270.16/35.81 % Propositional check unsatisfiable : 0
% 270.16/35.81 % Propositional clauses : 0
% 270.16/35.81 % Propositional clauses after purity: 0
% 270.16/35.81 % Propositional unsat core size : 0
% 270.16/35.81 % Propositional preprocessing time : 0.000
% 270.16/35.81 % Propositional encoding time : 1.389
% 270.16/35.81 % Propositional solver time : 0.590
% 270.16/35.81 % Success case prop preproc time : 0.000
% 270.16/35.81 % Success case prop encoding time : 0.000
% 270.16/35.81 % Success case prop solver time : 0.000
% 270.16/35.81 % Current number of processed clauses : 2248
% 270.16/35.81 % Positive orientable unit clauses : 622
% 270.16/35.81 % Positive unorientable unit clauses: 30
% 270.16/35.81 % Negative unit clauses : 121
% 270.16/35.81 % Non-unit-clauses : 1475
% 270.16/35.81 % Current number of unprocessed clauses: 1018798
% 270.16/35.81 % ...number of literals in the above : 3438033
% 270.16/35.81 % Current number of archived formulas : 0
% 270.16/35.81 % Current number of archived clauses : 10870
% 270.16/35.81 % Clause-clause subsumption calls (NU) : 12010305
% 270.16/35.81 % Rec. Clause-clause subsumption calls : 3115377
% 270.16/35.81 % Non-unit clause-clause subsumptions : 34145
% 270.16/35.81 % Unit Clause-clause subsumption calls : 136573
% 270.16/35.81 % Rewrite failures with RHS unbound : 65
% 270.16/35.81 % BW rewrite match attempts : 3738
% 270.16/35.81 % BW rewrite match successes : 790
% 270.16/35.81 % Condensation attempts : 0
% 270.16/35.81 % Condensation successes : 0
% 270.16/35.81 % Termbank termtop insertions : 33632592
% 270.16/35.81 % Search garbage collected termcells : 1251
% 270.16/35.81
% 270.16/35.81 % -------------------------------------------------
% 270.16/35.81 % User time : 33.227 s
% 270.16/35.81 % System time : 0.879 s
% 270.16/35.81 % Total time : 34.106 s
% 270.16/35.81 % Maximum resident set size: 4756 pages
% 270.16/35.81
% 270.16/35.81 % -------------------------------------------------
% 270.16/35.81 % User time : 132.883 s
% 270.16/35.81 % System time : 4.113 s
% 270.16/35.81 % Total time : 136.996 s
% 270.16/35.81 % Maximum resident set size: 5376 pages
% 270.16/35.81 % E exiting
%------------------------------------------------------------------------------