%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT021-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 178.34s 26.51s
% Output : CNFRefutation 178.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 44
% Syntax : Number of clauses : 174 ( 78 unt; 12 nHn; 86 RR)
% Number of literals : 296 ( 82 equ; 131 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-4 aty)
% Number of variables : 314 ( 123 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_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/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(clsarity_bool__HOL_Ominus,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_mem__def_0,axiom,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_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/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_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/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__funD_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_irrefl__def_1,axiom,
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2)))
| c_Relation_Oirrefl(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
cnf(c_0_44,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_45,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_46,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X4,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X2)) ),
c_0_44 ).
cnf(c_0_47,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_45 ).
cnf(c_0_48,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_49,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_50,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_46,c_0_47]),c_0_48])]) ).
cnf(c_0_51,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_52,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_53,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_49 ).
cnf(c_0_54,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_55,plain,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),tc_bool),X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,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_57,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_1]) ).
cnf(c_0_58,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_52 ).
cnf(c_0_59,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_60,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_61,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_53,c_0_54]) ).
cnf(c_0_62,plain,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_51]) ).
cnf(c_0_63,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_56 ).
cnf(c_0_64,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_65,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
c_0_57 ).
cnf(c_0_66,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_58,c_0_59]) ).
cnf(c_0_67,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,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_69,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_62,c_0_63]),c_0_48])]) ).
cnf(c_0_70,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_71,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_64 ).
cnf(c_0_72,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_65,c_0_66]),c_0_67])]) ).
cnf(c_0_73,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_68 ).
cnf(c_0_74,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_75,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_76,plain,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)),
inference(spm,[status(thm)],[c_0_65,c_0_60]) ).
cnf(c_0_77,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_78,plain,
( ~ hBOOL(X2)
| hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X3)) ),
inference(spm,[status(thm)],[c_0_65,c_0_69]) ).
cnf(c_0_79,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_70 ).
cnf(c_0_80,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_71,c_0_72]) ).
cnf(c_0_81,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_73,c_0_59]) ).
cnf(c_0_82,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_74 ).
cnf(c_0_83,axiom,
class_HOL_Ominus(tc_bool),
clsarity_bool__HOL_Ominus ).
cnf(c_0_84,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_75 ).
cnf(c_0_85,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_86,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_71,c_0_76]) ).
cnf(c_0_87,plain,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2 ),
c_0_77 ).
cnf(c_0_88,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_71,c_0_78]) ).
cnf(c_0_89,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_79,c_0_80]),c_0_81]),c_0_48])]) ).
cnf(c_0_90,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_91,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_82,c_0_83]) ).
cnf(c_0_92,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_93,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_84,c_0_85]) ).
cnf(c_0_94,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_61,c_0_86]) ).
cnf(c_0_95,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_96,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_87,c_0_88]),c_0_89]),c_0_90])]) ).
cnf(c_0_97,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
cls_insert__code_1 ).
cnf(c_0_98,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_91,c_0_92]),c_0_93]),c_0_94]) ).
cnf(c_0_99,plain,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_0]) ).
cnf(c_0_100,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_82,c_0_95]),c_0_83])]) ).
cnf(c_0_101,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,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_98,c_0_51]) ).
cnf(c_0_103,plain,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
c_0_99 ).
cnf(c_0_104,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_100,c_0_101]),c_0_102]) ).
cnf(c_0_105,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_106,plain,
( hBOOL(hAPP(X1,v_x))
| c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,v_x) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_107,plain,
( ~ c_Relation_Oirrefl(X3,X2)
| ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))) ),
c_0_105 ).
cnf(c_0_108,plain,
( hBOOL(X1)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_106,c_0_51]) ).
cnf(c_0_109,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_110,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_111,plain,
~ c_Relation_Oirrefl(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1),
inference(spm,[status(thm)],[c_0_107,c_0_72]) ).
cnf(c_0_112,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_96,c_0_108]) ).
cnf(c_0_113,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_114,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_109 ).
cnf(c_0_115,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_103,c_0_110]) ).
cnf(c_0_116,plain,
( ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_bool),X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,plain,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_96,c_0_96]) ).
cnf(c_0_118,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_113 ).
cnf(c_0_119,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_1 ).
cnf(c_0_120,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_121,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_0 ).
cnf(c_0_122,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_123,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_124,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_114,c_0_76]) ).
cnf(c_0_125,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_65,c_0_115]) ).
cnf(c_0_126,plain,
( ~ hBOOL(X1)
| ~ c_Relation_Oirrefl(X1,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_67])]) ).
cnf(c_0_127,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_118,c_0_119])]),c_0_120]),c_0_121])]) ).
cnf(c_0_128,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_129,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
c_0_122 ).
cnf(c_0_130,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_131,plain,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
c_0_123 ).
cnf(c_0_132,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_133,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_134,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_124,c_0_125]) ).
cnf(c_0_135,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_136,negated_conjecture,
( ~ hBOOL(v_F(v_P))
| c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_137,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
c_0_128 ).
cnf(c_0_138,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_129,c_0_85]) ).
cnf(c_0_139,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_140,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_130 ).
cnf(c_0_141,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_131,c_0_132]),c_0_133])]) ).
cnf(c_0_142,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_143,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_144,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_145,negated_conjecture,
v_F(v_P) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_146,plain,
( ~ hBOOL(X1)
| ~ c_Relation_Oirrefl(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) ),
inference(spm,[status(thm)],[c_0_107,c_0_78]) ).
cnf(c_0_147,negated_conjecture,
( v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_136,c_0_108]) ).
cnf(c_0_148,axiom,
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2)))
| c_Relation_Oirrefl(X1,X2) ),
cls_irrefl__def_1 ).
cnf(c_0_149,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_137,c_0_138]),c_0_139])]) ).
cnf(c_0_150,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_140,c_0_141]),c_0_142])]) ).
cnf(c_0_151,plain,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2))) ),
c_0_143 ).
cnf(c_0_152,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_144 ).
cnf(c_0_153,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_154,negated_conjecture,
( ~ hBOOL(X1)
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| v_F(v_P) != X1 ),
inference(spm,[status(thm)],[c_0_145,c_0_117]) ).
cnf(c_0_155,negated_conjecture,
( ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1)
| v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_108]) ).
cnf(c_0_156,plain,
( hBOOL(hAPP(X1,c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2)))
| c_Relation_Oirrefl(X1,X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_148]) ).
cnf(c_0_157,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_149,c_0_150]) ).
cnf(c_0_158,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_93]),c_0_152]) ).
cnf(c_0_159,plain,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(spm,[status(thm)],[c_0_152,c_0_117]) ).
cnf(c_0_160,plain,
hBOOL(hAPP(c_Relation_OId(X1),c_Pair(X2,X2,X1,X1))),
inference(spm,[status(thm)],[c_0_103,c_0_153]) ).
cnf(c_0_161,negated_conjecture,
( ~ hBOOL(v_F(v_P))
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(er,[status(thm)],[c_0_154]) ).
cnf(c_0_162,negated_conjecture,
( ~ c_Relation_Oirrefl(X1,X2)
| hBOOL(X1)
| v_F(v_P) = X1 ),
inference(spm,[status(thm)],[c_0_155,c_0_108]) ).
cnf(c_0_163,plain,
c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158]) ).
cnf(c_0_164,plain,
( ~ hBOOL(c_Relation_OId(X2))
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_165,negated_conjecture,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_161,c_0_108]) ).
cnf(c_0_166,negated_conjecture,
hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_145]) ).
cnf(c_0_167,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| c_Relation_OId(X1) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_164,c_0_108]) ).
cnf(c_0_168,negated_conjecture,
v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_166])]) ).
cnf(c_0_169,plain,
~ c_Relation_Oirrefl(c_Relation_OId(X1),X1),
inference(spm,[status(thm)],[c_0_107,c_0_153]) ).
cnf(c_0_170,plain,
c_Relation_OId(X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_166])]) ).
cnf(c_0_171,negated_conjecture,
c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),tc_Arrow__Order__Mirabelle_Oalt),
inference(rw,[status(thm)],[c_0_127,c_0_168]) ).
cnf(c_0_172,plain,
~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1),
inference(rw,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_173,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_171,c_0_172]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT021-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:26:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 178.34/26.51 % Version: 3.5.1
% 178.34/26.51 % Preprocessing class: FSLMSMSMSSSNFFN.
% 178.34/26.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 178.34/26.51 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 178.34/26.51 % Starting new_bool_3 with 600s (2) cores
% 178.34/26.51 % Starting new_bool_1 with 300s (1) cores
% 178.34/26.51 % Starting sh5l with 300s (1) cores
% 178.34/26.51 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 3132945 completed with status 0
% 178.34/26.51 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 178.34/26.51 % Preprocessing class: FSLMSMSMSSSNFFN.
% 178.34/26.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 178.34/26.51 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 178.34/26.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 178.34/26.51 % No SInE strategy applied
% 178.34/26.51 % Search class: FGHSM-FSLM32-DFFFFFNN
% 178.34/26.51 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 178.34/26.51 % Starting SubtermCWHack with 109s (1) cores
% 178.34/26.51 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 178.34/26.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 178.34/26.51 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 178.34/26.51 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 3132950 completed with status 0
% 178.34/26.51 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 178.34/26.51 % Preprocessing class: FSLMSMSMSSSNFFN.
% 178.34/26.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 178.34/26.51 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 178.34/26.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 178.34/26.51 % No SInE strategy applied
% 178.34/26.51 % Search class: FGHSM-FSLM32-DFFFFFNN
% 178.34/26.51 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 178.34/26.51 % Starting SubtermCWHack with 109s (1) cores
% 178.34/26.51 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 178.34/26.51 % Preprocessing time : 0.010 s
% 178.34/26.51 % Presaturation interreduction done
% 178.34/26.51
% 178.34/26.51 % Proof found!
% 178.34/26.51 % SZS status Unsatisfiable
% 178.34/26.51 % SZS output start CNFRefutation
% See solution above
% 178.34/26.51 % Parsed axioms : 713
% 178.34/26.51 % Removed by relevancy pruning/SinE : 0
% 178.34/26.51 % Initial clauses : 713
% 178.34/26.51 % Removed in clause preprocessing : 4
% 178.34/26.51 % Initial clauses in saturation : 709
% 178.34/26.51 % Processed clauses : 56582
% 178.34/26.51 % ...of these trivial : 1042
% 178.34/26.51 % ...subsumed : 41986
% 178.34/26.51 % ...remaining for further processing : 13554
% 178.34/26.51 % Other redundant clauses eliminated : 2355
% 178.34/26.51 % Clauses deleted for lack of memory : 0
% 178.34/26.51 % Backward-subsumed : 3377
% 178.34/26.51 % Backward-rewritten : 2238
% 178.34/26.51 % Generated clauses : 1367768
% 178.34/26.51 % ...of the previous two non-redundant : 1284734
% 178.34/26.51 % ...aggressively subsumed : 0
% 178.34/26.51 % Contextual simplify-reflections : 154
% 178.34/26.51 % Paramodulations : 1365139
% 178.34/26.51 % Factorizations : 54
% 178.34/26.51 % NegExts : 0
% 178.34/26.51 % Equation resolutions : 2572
% 178.34/26.51 % Disequality decompositions : 0
% 178.34/26.51 % Total rewrite steps : 347266
% 178.34/26.51 % ...of those cached : 315337
% 178.34/26.51 % Propositional unsat checks : 0
% 178.34/26.51 % Propositional check models : 0
% 178.34/26.51 % Propositional check unsatisfiable : 0
% 178.34/26.51 % Propositional clauses : 0
% 178.34/26.51 % Propositional clauses after purity: 0
% 178.34/26.51 % Propositional unsat core size : 0
% 178.34/26.51 % Propositional preprocessing time : 0.000
% 178.34/26.51 % Propositional encoding time : 0.000
% 178.34/26.51 % Propositional solver time : 0.000
% 178.34/26.51 % Success case prop preproc time : 0.000
% 178.34/26.51 % Success case prop encoding time : 0.000
% 178.34/26.51 % Success case prop solver time : 0.000
% 178.34/26.51 % Current number of processed clauses : 7340
% 178.34/26.51 % Positive orientable unit clauses : 666
% 178.34/26.51 % Positive unorientable unit clauses: 31
% 178.34/26.51 % Negative unit clauses : 143
% 178.34/26.51 % Non-unit-clauses : 6500
% 178.34/26.51 % Current number of unprocessed clauses: 1223046
% 178.34/26.51 % ...number of literals in the above : 4398309
% 178.34/26.51 % Current number of archived formulas : 0
% 178.34/26.51 % Current number of archived clauses : 6216
% 178.34/26.51 % Clause-clause subsumption calls (NU) : 13083227
% 178.34/26.51 % Rec. Clause-clause subsumption calls : 3266131
% 178.34/26.51 % Non-unit clause-clause subsumptions : 37532
% 178.34/26.51 % Unit Clause-clause subsumption calls : 171568
% 178.34/26.51 % Rewrite failures with RHS unbound : 65
% 178.34/26.51 % BW rewrite match attempts : 3770
% 178.34/26.51 % BW rewrite match successes : 807
% 178.34/26.51 % Condensation attempts : 0
% 178.34/26.51 % Condensation successes : 0
% 178.34/26.51 % Termbank termtop insertions : 29468510
% 178.34/26.51 % Search garbage collected termcells : 1251
% 178.34/26.51
% 178.34/26.51 % -------------------------------------------------
% 178.34/26.51 % User time : 24.611 s
% 178.34/26.51 % System time : 0.692 s
% 178.34/26.51 % Total time : 25.303 s
% 178.34/26.51 % Maximum resident set size: 5012 pages
% 178.34/26.51
% 178.34/26.51 % -------------------------------------------------
% 178.34/26.51 % User time : 97.754 s
% 178.34/26.51 % System time : 2.978 s
% 178.34/26.51 % Total time : 100.732 s
% 178.34/26.51 % Maximum resident set size: 5376 pages
% 178.34/26.51 % E exiting
%------------------------------------------------------------------------------