%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT025-1 : 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 : n006.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 103.99s 15.99s
% Output : CNFRefutation 103.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 54
% Syntax : Number of clauses : 246 ( 107 unt; 17 nHn; 119 RR)
% Number of literals : 450 ( 117 equ; 207 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 4 con; 0-5 aty)
% Number of variables : 680 ( 228 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Collect__mem__eq_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_CollectD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).
cnf(cls_UnionI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionI_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_conjecture_0,negated_conjecture,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_L),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_inf__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
cnf(cls_inf__absorb2_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(cls_le__funD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,X1)),X2),X4))
| ~ class_HOL_Oord(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(X2,X3)),hAPP(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(cls_Sup__upper_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
cnf(cls_insert__def_0,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
cnf(cls_PowI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PowI_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(cls_le__infE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(cls_empty__subsetI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)),
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_Sup__UNIV_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
cnf(cls_image__constant_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X4))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
cnf(cls_Union__Pow__eq_0,axiom,
hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),c_Set_OPow(X2,X1)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__Pow__eq_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_le__supE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
cnf(cls_subset__UNIV_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_subset__Un__eq_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
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_vimage__def_0,axiom,
c_Set_Ovimage(X1,X2,X3,X4) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X4),X1,X4,tc_fun(tc_fun(X4,tc_bool),tc_bool),X3),X3,tc_fun(X4,tc_bool),tc_bool),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__def_0) ).
cnf(cls_vimage__const_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_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_bexCI_3,axiom,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X2,X1,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexCI_3) ).
cnf(cls_insert__image_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
cnf(cls_rev__bexI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X3,X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(clsarity_bool__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(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_vimage__const_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
cnf(cls_bexI_1,axiom,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X1,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexI_1) ).
cnf(cls_image__is__empty_0,axiom,
( c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_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_bexE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexE__1__1(X2,X1,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexE_1) ).
cnf(cls_COMBI__def_0,axiom,
hAPP(c_COMBI(X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
cnf(cls_Un__empty_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
cnf(cls_Pow__bottom_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Set_OPow(X2,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pow__bottom_0) ).
cnf(cls_rev__bexI_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
cnf(cls_image__ident_0,axiom,
c_Set_Oimage(c_COMBI(X1),X2,X1,X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_0) ).
cnf(cls_in__mktop_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
cnf(cls_restrict__extensional_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),c_FuncSet_Orestrict(X3,X4,X1,X2)),c_FuncSet_Oextensional(X4,X1,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__extensional_0) ).
cnf(cls_Pow__top_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X2,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pow__top_0) ).
cnf(cls_Lin__irrefl_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_UnionE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionE_1) ).
cnf(c_0_54,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_55,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_56,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_CollectD_0]) ).
cnf(c_0_57,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X3))) ),
inference(fof_simplification,[status(thm)],[cls_UnionI_0]) ).
cnf(c_0_58,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_59,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
c_0_56 ).
cnf(c_0_61,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X3))) ),
c_0_57 ).
cnf(c_0_62,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[c_0_60,c_0_55]) ).
cnf(c_0_64,negated_conjecture,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_L),c_Arrow__Order__Mirabelle_OLin)),
cls_conjecture_0 ).
cnf(c_0_65,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__bot__left_0]) ).
cnf(c_0_66,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3 ),
inference(fof_simplification,[status(thm)],[cls_inf__absorb2_0]) ).
cnf(c_0_67,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,X1)),X2),X4))
| ~ class_HOL_Oord(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(X2,X3)),hAPP(X4,X3))) ),
inference(fof_simplification,[status(thm)],[cls_le__funD_0]) ).
cnf(c_0_68,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3))) ),
inference(fof_simplification,[status(thm)],[cls_Sup__upper_0]) ).
cnf(c_0_69,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3)),X2),
cls_insert__def_0 ).
cnf(c_0_70,plain,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_62]),c_0_62]) ).
cnf(c_0_71,negated_conjecture,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_L)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X3,X1))) ),
inference(fof_simplification,[status(thm)],[cls_PowI_0]) ).
cnf(c_0_73,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
c_0_65 ).
cnf(c_0_74,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_75,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3 ),
c_0_66 ).
cnf(c_0_76,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_77,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_le__infE_0]) ).
cnf(c_0_78,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,X1)),X2),X4))
| ~ class_HOL_Oord(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(X2,X3)),hAPP(X4,X3))) ),
c_0_67 ).
cnf(c_0_79,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)),
cls_empty__subsetI_0 ).
cnf(c_0_80,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_81,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3))) ),
c_0_68 ).
cnf(c_0_82,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_Sup__UNIV_0]) ).
cnf(c_0_83,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X4))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(fof_simplification,[status(thm)],[cls_image__constant_0]) ).
cnf(c_0_84,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
cls_singleton__conv2_0 ).
cnf(c_0_85,plain,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1)),X2),
inference(rw,[status(thm)],[c_0_69,c_0_55]) ).
cnf(c_0_86,negated_conjecture,
( ~ hBOOL(hAPP(X2,c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X2),v_L)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_87,axiom,
hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),c_Set_OPow(X2,X1)) = X2,
cls_Union__Pow__eq_0 ).
cnf(c_0_88,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X3,X1))) ),
c_0_72 ).
cnf(c_0_89,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_90,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X2),X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) = X2 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_91,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
c_0_77 ).
cnf(c_0_92,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),hAPP(X3,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
cnf(c_0_93,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[cls_order__antisym__conv_0]) ).
cnf(c_0_94,plain,
( ~ hBOOL(hAPP(X3,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3))) ),
inference(rw,[status(thm)],[c_0_81,c_0_62]) ).
cnf(c_0_95,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(X1) ),
c_0_82 ).
cnf(c_0_96,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_97,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_le__supE_0]) ).
cnf(c_0_98,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
cls_subset__UNIV_0 ).
cnf(c_0_99,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X4))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
c_0_83 ).
cnf(c_0_100,plain,
hAPP(c_fequal(X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_55]),c_0_85]) ).
cnf(c_0_101,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
cls_Un__empty__right_0 ).
cnf(c_0_102,negated_conjecture,
( ~ hBOOL(hAPP(c_Set_OPow(X1,X2),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(X1,v_L)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_103,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| hBOOL(hAPP(c_Set_OPow(X1,X2),X3)) ),
inference(rw,[status(thm)],[c_0_88,c_0_62]) ).
cnf(c_0_104,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_subset__Un__eq_1]) ).
cnf(c_0_105,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_106,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X1),c_Orderings_Obot__class_Obot(tc_bool)))
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_107,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_76])]) ).
cnf(c_0_108,axiom,
c_Set_Ovimage(X1,X2,X3,X4) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(X4),X1,X4,tc_fun(tc_fun(X4,tc_bool),tc_bool),X3),X3,tc_fun(X4,tc_bool),tc_bool),X2),X3),
cls_vimage__def_0 ).
cnf(c_0_109,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_vimage__const_0]) ).
cnf(c_0_110,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
c_0_93 ).
cnf(c_0_111,plain,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Orderings_Otop__class_Otop(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96])]) ).
cnf(c_0_112,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
c_0_97 ).
cnf(c_0_113,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_98]),c_0_80])]) ).
cnf(c_0_114,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_115,plain,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[cls_bexCI_3]) ).
cnf(c_0_116,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5) ),
inference(fof_simplification,[status(thm)],[cls_insert__image_0]) ).
cnf(c_0_117,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X4))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
inference(rw,[status(thm)],[c_0_99,c_0_85]) ).
cnf(c_0_118,plain,
hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2) = hAPP(c_fequal(X1),X2),
inference(rw,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_119,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Arrow__Order__Mirabelle_OLin),X1))
| hBOOL(hAPP(X1,v_L)) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_120,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_104 ).
cnf(c_0_121,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_105 ).
cnf(c_0_122,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_106,c_0_107]) ).
cnf(c_0_123,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X3,X1)),X2)) ),
inference(fof_simplification,[status(thm)],[cls_rev__bexI_0]) ).
cnf(c_0_124,plain,
c_Set_Ovimage(X1,X2,X3,X4) = hAPP(c_COMBC(c_COMBB(c_in(X4),X1,X4,tc_fun(tc_fun(X4,tc_bool),tc_bool),X3),X3,tc_fun(X4,tc_bool),tc_bool),X2),
inference(rw,[status(thm)],[c_0_108,c_0_55]) ).
cnf(c_0_125,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0 ).
cnf(c_0_126,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) ),
c_0_109 ).
cnf(c_0_127,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Otop__class_Otop(X1)),X2))
| ~ class_Orderings_Oorder(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Orderings_Otop__class_Otop(X1) = X2 ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_128,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X1),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114])]) ).
cnf(c_0_129,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_130,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_131,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_vimage__const_1 ).
cnf(c_0_132,plain,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[cls_bexI_1]) ).
cnf(c_0_133,plain,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X2,X1,X3))) ),
c_0_115 ).
cnf(c_0_134,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5) ),
c_0_116 ).
cnf(c_0_135,plain,
( c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_image__is__empty_0]) ).
cnf(c_0_136,plain,
( ~ hBOOL(hAPP(X4,X5))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = hAPP(c_fequal(X2),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118]),c_0_101]),c_0_62]) ).
cnf(c_0_137,negated_conjecture,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Arrow__Order__Mirabelle_OLin),X1) != X1
| hBOOL(hAPP(X1,v_L)) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_138,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_139,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X3,X1)),X2)) ),
c_0_123 ).
cnf(c_0_140,plain,
hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5) = hAPP(X2,hAPP(X1,X5)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_124]),c_0_125]),c_0_62]) ).
cnf(c_0_141,plain,
( ~ hBOOL(hAPP(X4,X1))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_126,c_0_62]) ).
cnf(c_0_142,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_127,c_0_128]),c_0_129]),c_0_130])]) ).
cnf(c_0_143,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_144,plain,
( hBOOL(hAPP(X4,X1))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_131,c_0_62]) ).
cnf(c_0_145,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexE__1__1(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[cls_bexE_1]) ).
cnf(c_0_146,plain,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X1,X3))) ),
c_0_132 ).
cnf(c_0_147,plain,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexCI__1__1(X2,X1,X3))) ),
inference(rw,[status(thm)],[c_0_133,c_0_62]) ).
cnf(c_0_148,axiom,
hAPP(c_COMBI(X1),X2) = X2,
cls_COMBI__def_0 ).
cnf(c_0_149,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_Un__empty_0]) ).
cnf(c_0_150,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),hAPP(c_COMBC(c_fequal(X5),X5,X5,tc_bool),hAPP(X1,X2))),c_Set_Oimage(X1,X3,X4,X5)) = c_Set_Oimage(X1,X3,X4,X5) ),
inference(rw,[status(thm)],[c_0_134,c_0_85]) ).
cnf(c_0_151,plain,
( c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_135 ).
cnf(c_0_152,negated_conjecture,
c_Set_Oimage(c_COMBK(X1,X2,X3),c_Arrow__Order__Mirabelle_OLin,X3,X2) = hAPP(c_fequal(X2),X1),
inference(spm,[status(thm)],[c_0_136,c_0_71]) ).
cnf(c_0_153,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_101]),c_0_122]),c_0_138]) ).
cnf(c_0_154,plain,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,X2,X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_62]),c_0_62]) ).
cnf(c_0_155,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Set_OPow(X2,X1))),
cls_Pow__bottom_0 ).
cnf(c_0_156,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Otop__class_Otop(tc_bool) = hAPP(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]),c_0_143]) ).
cnf(c_0_157,plain,
( hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_144]),c_0_122]),c_0_143]) ).
cnf(c_0_158,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[cls_rev__bexI_1]) ).
cnf(c_0_159,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexE__1__1(X2,X1,X3))) ),
c_0_145 ).
cnf(c_0_160,plain,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexI__1__1(X2,X1,X3))) ),
inference(rw,[status(thm)],[c_0_146,c_0_62]) ).
cnf(c_0_161,plain,
( ~ hBOOL(X4)
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(c_ATP__Linkup_Osko__Set__XbexCI__1__1(X1,c_COMBI(X2),X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_148]) ).
cnf(c_0_162,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
c_0_149 ).
cnf(c_0_163,plain,
( ~ hBOOL(hAPP(X4,X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),hAPP(X2,X3))),c_Set_Oimage(X2,X4,X5,X1)) = c_Set_Oimage(X2,X4,X5,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_118]),c_0_62]) ).
cnf(c_0_164,negated_conjecture,
hAPP(c_fequal(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).
cnf(c_0_165,plain,
( ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3))) ),
inference(spm,[status(thm)],[c_0_154,c_0_96]) ).
cnf(c_0_166,plain,
hBOOL(hAPP(c_Set_OPow(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
inference(spm,[status(thm)],[c_0_63,c_0_155]) ).
cnf(c_0_167,plain,
( ~ hBOOL(X1)
| c_Orderings_Otop__class_Otop(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_156,c_0_143]) ).
cnf(c_0_168,plain,
( hBOOL(X1)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_157,c_0_143]) ).
cnf(c_0_169,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
c_0_158 ).
cnf(c_0_170,plain,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XbexE__1__1(X2,X1,X3))) ),
inference(rw,[status(thm)],[c_0_159,c_0_62]) ).
cnf(c_0_171,plain,
( ~ hBOOL(X4)
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(c_ATP__Linkup_Osko__Set__XbexI__1__1(X1,c_COMBI(X2),X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_148]),c_0_148]) ).
cnf(c_0_172,plain,
( ~ hBOOL(X4)
| hBOOL(c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_COMBI(X1),c_COMBI(X2),X3)) ),
inference(spm,[status(thm)],[c_0_161,c_0_148]) ).
cnf(c_0_173,plain,
( ~ hBOOL(hAPP(X2,X5))
| c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_164]) ).
cnf(c_0_174,plain,
hBOOL(hAPP(c_Set_OPow(X1,X2),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Set_OPow(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X4))),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_175,negated_conjecture,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_L),
inference(spm,[status(thm)],[c_0_167,c_0_71]) ).
cnf(c_0_176,plain,
( hBOOL(X2)
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_168,c_0_168]) ).
cnf(c_0_177,plain,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
inference(rw,[status(thm)],[c_0_169,c_0_62]) ).
cnf(c_0_178,plain,
( ~ hBOOL(X4)
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(c_ATP__Linkup_Osko__Set__XbexE__1__1(X1,c_COMBI(X2),X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_148]),c_0_148]) ).
cnf(c_0_179,plain,
( ~ hBOOL(X4)
| hBOOL(c_ATP__Linkup_Osko__Set__XbexI__1__1(c_COMBI(X1),c_COMBI(X2),X3)) ),
inference(spm,[status(thm)],[c_0_171,c_0_148]) ).
cnf(c_0_180,negated_conjecture,
hBOOL(c_ATP__Linkup_Osko__Set__XbexCI__1__1(c_COMBI(X1),c_COMBI(X2),X3)),
inference(spm,[status(thm)],[c_0_172,c_0_71]) ).
cnf(c_0_181,plain,
c_Set_Oimage(X1,c_Set_OPow(X2,X3),X4,X5) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_182,axiom,
c_Set_Oimage(c_COMBI(X1),X2,X1,X1) = X2,
cls_image__ident_0 ).
cnf(c_0_183,plain,
( ~ hBOOL(X1)
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_L) = X1 ),
inference(rw,[status(thm)],[c_0_167,c_0_175]) ).
cnf(c_0_184,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_176])]) ).
cnf(c_0_185,plain,
( ~ hBOOL(X5)
| c_Set_Oimage(X1,c_COMBI(X2),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(spm,[status(thm)],[c_0_173,c_0_148]) ).
cnf(c_0_186,plain,
( ~ hBOOL(X4)
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,c_COMBI(X2),X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_148]),c_0_148]) ).
cnf(c_0_187,plain,
( ~ hBOOL(X4)
| hBOOL(c_ATP__Linkup_Osko__Set__XbexE__1__1(c_COMBI(X1),c_COMBI(X2),X3)) ),
inference(spm,[status(thm)],[c_0_178,c_0_148]) ).
cnf(c_0_188,negated_conjecture,
hBOOL(c_ATP__Linkup_Osko__Set__XbexI__1__1(c_COMBI(X1),c_COMBI(X2),X3)),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_189,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X1))),
inference(fof_simplification,[status(thm)],[cls_in__mktop_0]) ).
cnf(c_0_190,plain,
c_Set_OPow(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_191,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_L) ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_192,plain,
( ~ hBOOL(X3)
| c_COMBI(X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(spm,[status(thm)],[c_0_185,c_0_182]) ).
cnf(c_0_193,plain,
( ~ hBOOL(X4)
| hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_COMBI(X1),c_COMBI(X2),X3)) ),
inference(spm,[status(thm)],[c_0_186,c_0_148]) ).
cnf(c_0_194,negated_conjecture,
hBOOL(c_ATP__Linkup_Osko__Set__XbexE__1__1(c_COMBI(X1),c_COMBI(X2),X3)),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_195,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),c_FuncSet_Orestrict(X3,X4,X1,X2)),c_FuncSet_Oextensional(X4,X1,X2))),
cls_restrict__extensional_0 ).
cnf(c_0_196,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X1))),
c_0_189 ).
cnf(c_0_197,negated_conjecture,
( c_Set_OPow(X1,X2) != hAPP(c_Arrow__Order__Mirabelle_OLin,v_L)
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_198,plain,
( hBOOL(X2)
| X1 = X2
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_L) = X1 ),
inference(spm,[status(thm)],[c_0_183,c_0_176]) ).
cnf(c_0_199,negated_conjecture,
( ~ hBOOL(X2)
| c_COMBI(X1) != hAPP(c_Arrow__Order__Mirabelle_OLin,v_L)
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_192,c_0_191]) ).
cnf(c_0_200,plain,
( ~ hBOOL(X4)
| hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_COMBI(X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_148]),c_0_148]) ).
cnf(c_0_201,negated_conjecture,
hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_COMBI(X1),c_COMBI(X2),X3)),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_202,plain,
hBOOL(hAPP(c_FuncSet_Oextensional(X1,X2,X3),c_FuncSet_Orestrict(X4,X1,X2,X3))),
inference(rw,[status(thm)],[c_0_195,c_0_62]) ).
cnf(c_0_203,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X2,X1))),
cls_Pow__top_0 ).
cnf(c_0_204,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omktop(X1,X2),c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(rw,[status(thm)],[c_0_196,c_0_62]) ).
cnf(c_0_205,negated_conjecture,
( hBOOL(X3)
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| c_Set_OPow(X1,X2) = X3 ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_206,negated_conjecture,
( ~ hBOOL(X3)
| hBOOL(X2)
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| c_COMBI(X1) = X2 ),
inference(spm,[status(thm)],[c_0_199,c_0_198]) ).
cnf(c_0_207,negated_conjecture,
hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_COMBI(X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)),
inference(spm,[status(thm)],[c_0_200,c_0_201]) ).
cnf(c_0_208,plain,
c_Set_Oimage(X1,c_FuncSet_Oextensional(X2,X3,X4),X5,X6) != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),
inference(spm,[status(thm)],[c_0_173,c_0_202]) ).
cnf(c_0_209,plain,
hBOOL(hAPP(c_Set_OPow(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_63,c_0_203]) ).
cnf(c_0_210,negated_conjecture,
( ~ hBOOL(c_Set_OPow(X1,X2))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_204]) ).
cnf(c_0_211,negated_conjecture,
( hBOOL(X2)
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| c_COMBI(X1) = X2 ),
inference(spm,[status(thm)],[c_0_206,c_0_207]) ).
cnf(c_0_212,plain,
c_FuncSet_Oextensional(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_208,c_0_182]) ).
cnf(c_0_213,plain,
hAPP(c_Set_OPow(X1,X2),X1) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_L),
inference(spm,[status(thm)],[c_0_183,c_0_209]) ).
cnf(c_0_214,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| c_COMBI(X1) = c_Set_OPow(X2,X3) ),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_215,negated_conjecture,
( c_FuncSet_Oextensional(X1,X2,X3) != hAPP(c_Arrow__Order__Mirabelle_OLin,v_L)
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_212,c_0_191]) ).
cnf(c_0_216,negated_conjecture,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| X1 = hAPP(c_Arrow__Order__Mirabelle_OLin,v_L) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_148]) ).
cnf(c_0_217,negated_conjecture,
hBOOL(c_Arrow__Order__Mirabelle_OLin),
inference(spm,[status(thm)],[c_0_215,c_0_216]) ).
cnf(c_0_218,plain,
( ~ hBOOL(X4)
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,c_COMBI(X2),X3))) ),
inference(spm,[status(thm)],[c_0_154,c_0_148]) ).
cnf(c_0_219,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
inference(fof_simplification,[status(thm)],[cls_Lin__irrefl_0]) ).
cnf(c_0_220,plain,
( ~ class_Orderings_Obot(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2)) ),
inference(fof_simplification,[status(thm)],[cls_bot__least_0]) ).
cnf(c_0_221,negated_conjecture,
hAPP(c_Arrow__Order__Mirabelle_OLin,v_L) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_183,c_0_217]) ).
cnf(c_0_222,plain,
( ~ hBOOL(X3)
| hBOOL(c_COMBI(X2))
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_176])]) ).
cnf(c_0_223,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(hAPP(c_lessequals(tc_bool),X1),c_COMBI(X2),X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_128]),c_0_96])]) ).
cnf(c_0_224,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
c_0_219 ).
cnf(c_0_225,plain,
( ~ class_Orderings_Obot(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2)) ),
c_0_220 ).
cnf(c_0_226,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_227,plain,
( ~ hBOOL(X1)
| c_Arrow__Order__Mirabelle_OLin = X1 ),
inference(rw,[status(thm)],[c_0_183,c_0_221]) ).
cnf(c_0_228,negated_conjecture,
( hBOOL(c_COMBI(X2))
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(spm,[status(thm)],[c_0_222,c_0_201]) ).
cnf(c_0_229,plain,
c_Set_Oimage(X1,hAPP(c_lessequals(tc_bool),X2),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_173,c_0_223]) ).
cnf(c_0_230,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)),X3)) ),
inference(fof_simplification,[status(thm)],[cls_UnionE_1]) ).
cnf(c_0_231,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1))
| ~ hBOOL(hAPP(X1,c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(hAPP(X1,c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_224,c_0_62]),c_0_62]),c_0_62]) ).
cnf(c_0_232,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1)),
inference(spm,[status(thm)],[c_0_225,c_0_226]) ).
cnf(c_0_233,negated_conjecture,
hBOOL(c_COMBI(X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_153]) ).
cnf(c_0_234,plain,
hAPP(c_lessequals(tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_229,c_0_182]) ).
cnf(c_0_235,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X3,X1)),X3)) ),
c_0_230 ).
cnf(c_0_236,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_232])]) ).
cnf(c_0_237,negated_conjecture,
c_COMBI(X1) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_227,c_0_233]) ).
cnf(c_0_238,plain,
( hBOOL(hAPP(c_lessequals(tc_bool),X2))
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_176])]) ).
cnf(c_0_239,plain,
( ~ hBOOL(hAPP(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X2,X1,X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_235,c_0_62]),c_0_62]) ).
cnf(c_0_240,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(c_lessequals(tc_bool),X1)))
| hBOOL(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_176]),c_0_138]) ).
cnf(c_0_241,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,X1) = X1,
inference(rw,[status(thm)],[c_0_148,c_0_237]) ).
cnf(c_0_242,plain,
hBOOL(hAPP(c_lessequals(tc_bool),X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_238]),c_0_153]) ).
cnf(c_0_243,plain,
~ hBOOL(hAPP(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X3)),
inference(spm,[status(thm)],[c_0_121,c_0_239]) ).
cnf(c_0_244,plain,
hBOOL(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_240,c_0_241]),c_0_242])]) ).
cnf(c_0_245,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_243,c_0_244])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT025-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.47 % Computer : n006.cluster.edu
% 0.19/0.47 % Model : x86_64 x86_64
% 0.19/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47 % Memory : 8046.5625MB
% 0.19/0.47 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Mon Sep 21 04:26:42 UTC 2026
% 0.19/0.48 % CPUTime :
% 0.19/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 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
% 103.99/15.99 % Version: 3.5.1
% 103.99/15.99 % Preprocessing class: FSLMSMSMSSSNFFN.
% 103.99/15.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 103.99/15.99 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 103.99/15.99 % Starting new_bool_3 with 600s (2) cores
% 103.99/15.99 % Starting new_bool_1 with 300s (1) cores
% 103.99/15.99 % Starting sh5l with 300s (1) cores
% 103.99/15.99 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 2003003 completed with status 0
% 103.99/15.99 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 103.99/15.99 % Preprocessing class: FSLMSMSMSSSNFFN.
% 103.99/15.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 103.99/15.99 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 103.99/15.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 103.99/15.99 % No SInE strategy applied
% 103.99/15.99 % Search class: FGHSM-FSLM33-DFFFFFNN
% 103.99/15.99 % Scheduled 11 strats onto 4 cores with 1200 seconds (1200 total)
% 103.99/15.99 % Starting SubtermCWHack with 109s (1) cores
% 103.99/15.99 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 103.99/15.99 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 109s (1) cores
% 103.99/15.99 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 109s (1) cores
% 103.99/15.99 % SubtermCWHack with pid 2003011 completed with status 0
% 103.99/15.99 % Result found by SubtermCWHack
% 103.99/15.99 % Preprocessing class: FSLMSMSMSSSNFFN.
% 103.99/15.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 103.99/15.99 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 103.99/15.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 103.99/15.99 % No SInE strategy applied
% 103.99/15.99 % Search class: FGHSM-FSLM33-DFFFFFNN
% 103.99/15.99 % Scheduled 11 strats onto 4 cores with 1200 seconds (1200 total)
% 103.99/15.99 % Starting SubtermCWHack with 109s (1) cores
% 103.99/15.99 % Preprocessing time : 0.017 s
% 103.99/15.99
% 103.99/15.99 % Proof found!
% 103.99/15.99 % SZS status Unsatisfiable
% 103.99/15.99 % SZS output start CNFRefutation
% See solution above
% 103.99/15.99 % Parsed axioms : 738
% 103.99/15.99 % Removed by relevancy pruning/SinE : 0
% 103.99/15.99 % Initial clauses : 738
% 103.99/15.99 % Removed in clause preprocessing : 3
% 103.99/15.99 % Initial clauses in saturation : 735
% 103.99/15.99 % Processed clauses : 8308
% 103.99/15.99 % ...of these trivial : 330
% 103.99/15.99 % ...subsumed : 4900
% 103.99/15.99 % ...remaining for further processing : 3078
% 103.99/15.99 % Other redundant clauses eliminated : 8841
% 103.99/15.99 % Clauses deleted for lack of memory : 0
% 103.99/15.99 % Backward-subsumed : 186
% 103.99/15.99 % Backward-rewritten : 2272
% 103.99/15.99 % Generated clauses : 674711
% 103.99/15.99 % ...of the previous two non-redundant : 630094
% 103.99/15.99 % ...aggressively subsumed : 0
% 103.99/15.99 % Contextual simplify-reflections : 5
% 103.99/15.99 % Paramodulations : 665818
% 103.99/15.99 % Factorizations : 42
% 103.99/15.99 % NegExts : 0
% 103.99/15.99 % Equation resolutions : 8850
% 103.99/15.99 % Disequality decompositions : 0
% 103.99/15.99 % Total rewrite steps : 80604
% 103.99/15.99 % ...of those cached : 75393
% 103.99/15.99 % Propositional unsat checks : 0
% 103.99/15.99 % Propositional check models : 0
% 103.99/15.99 % Propositional check unsatisfiable : 0
% 103.99/15.99 % Propositional clauses : 0
% 103.99/15.99 % Propositional clauses after purity: 0
% 103.99/15.99 % Propositional unsat core size : 0
% 103.99/15.99 % Propositional preprocessing time : 0.000
% 103.99/15.99 % Propositional encoding time : 0.000
% 103.99/15.99 % Propositional solver time : 0.000
% 103.99/15.99 % Success case prop preproc time : 0.000
% 103.99/15.99 % Success case prop encoding time : 0.000
% 103.99/15.99 % Success case prop solver time : 0.000
% 103.99/15.99 % Current number of processed clauses : 617
% 103.99/15.99 % Positive orientable unit clauses : 188
% 103.99/15.99 % Positive unorientable unit clauses: 14
% 103.99/15.99 % Negative unit clauses : 16
% 103.99/15.99 % Non-unit-clauses : 399
% 103.99/15.99 % Current number of unprocessed clauses: 578512
% 103.99/15.99 % ...number of literals in the above : 2495185
% 103.99/15.99 % Current number of archived formulas : 0
% 103.99/15.99 % Current number of archived clauses : 2462
% 103.99/15.99 % Clause-clause subsumption calls (NU) : 473207
% 103.99/15.99 % Rec. Clause-clause subsumption calls : 336821
% 103.99/15.99 % Non-unit clause-clause subsumptions : 4578
% 103.99/15.99 % Unit Clause-clause subsumption calls : 32216
% 103.99/15.99 % Rewrite failures with RHS unbound : 0
% 103.99/15.99 % BW rewrite match attempts : 6033
% 103.99/15.99 % BW rewrite match successes : 1450
% 103.99/15.99 % Condensation attempts : 0
% 103.99/15.99 % Condensation successes : 0
% 103.99/15.99 % Termbank termtop insertions : 9246161
% 103.99/15.99 % Search garbage collected termcells : 1508
% 103.99/15.99
% 103.99/15.99 % -------------------------------------------------
% 103.99/15.99 % User time : 14.283 s
% 103.99/15.99 % System time : 0.545 s
% 103.99/15.99 % Total time : 14.828 s
% 103.99/15.99 % Maximum resident set size: 5040 pages
% 103.99/15.99
% 103.99/15.99 % -------------------------------------------------
% 103.99/15.99 % User time : 56.253 s
% 103.99/15.99 % System time : 1.964 s
% 103.99/15.99 % Total time : 58.217 s
% 103.99/15.99 % Maximum resident set size: 5632 pages
% 103.99/15.99 % E exiting
%------------------------------------------------------------------------------