TSTP Solution File: SCT020-1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SCT020-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:17:07 EDT 2023
% Result : Unsatisfiable 34.04s 4.91s
% Output : CNFRefutation 34.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 72
% Syntax : Number of clauses : 260 ( 137 unt; 26 nHn; 101 RR)
% Number of literals : 420 ( 132 equ; 159 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 : 35 ( 35 usr; 7 con; 0-5 aty)
% Number of variables : 568 ( 220 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_inf1I_0) ).
cnf(cls_Diff__disjoint_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Diff__disjoint_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_bot1E_0) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( 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
| hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Diff__insert__absorb_0) ).
cnf(cls_bex__UNIV_2,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_bex__UNIV_2) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_insert__code_1) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_top1I_0) ).
cnf(cls_UNIV__eq__I_0,axiom,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_UNIV__eq__I_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_COMBK__def_0) ).
cnf(cls_subset__UNIV_0,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_subset__UNIV_0) ).
cnf(cls_in__mkbot_0,axiom,
~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_in__mkbot_0) ).
cnf(cls_not__acc__down_0,axiom,
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3)))
| hBOOL(c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_not__acc__down_0) ).
cnf(cls_le__funD_0,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_le__funD_0) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_bool__HOL_Oord) ).
cnf(cls_bex__UNIV_0,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_bex__UNIV_0) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_UNIV__I_0) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_mem__def_0) ).
cnf(cls_le__sup__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X1),X2),X3,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_le__sup__iff_1) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_insert__absorb_0,axiom,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_insert__absorb_0) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_mem__def_1) ).
cnf(cls_ball__UNIV_2,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2(X1,X3))) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_ball__UNIV_2) ).
cnf(cls_sup__absorb1_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_sup__absorb1_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_inf__sup__aci_I5_J_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_Image__Id_0,axiom,
hAPP(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2) = X2,
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Image__Id_0) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X1,X2),X3),X2)),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_insert__iff_1) ).
cnf(cls_top__fun__eq_0,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_top__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_order__eq__iff_2) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_inf__absorb2_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_inf__absorb2_0) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(cls_inf__fun__eq_0,axiom,
( 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))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_inf__fun__eq_0) ).
cnf(cls_Sup__upper_0,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X2,X3,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Sup__upper_0) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
cnf(cls_bot__fun__eq_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_bot__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_bool__Orderings_Obot) ).
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/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_conjecture_3) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Set_Oinsert(X2,X1),X3),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_empty__not__insert_0) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_emptyE_0) ).
cnf(cls_irrefl__def_1,axiom,
( c_Relation_Oirrefl(X1,X2)
| 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))) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_irrefl__def_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/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_conjecture_2) ).
cnf(cls_inf__top__left_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X1),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_inf__top__left_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_Relation_Oirrefl(v_F(X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_conjecture_6) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_conjecture_1) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_inf__sup__ord_I1_J_0) ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Int__UNIV__left_0) ).
cnf(cls_Int__insert__right_1,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X3,X2),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X4)
| hBOOL(c_in(X3,X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Int__insert__right_1) ).
cnf(cls_irrefl__def_0,axiom,
( ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Oirrefl(X3,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_irrefl__def_0) ).
cnf(cls_rtrancl_Ortrancl__refl_0,axiom,
hBOOL(c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_rtrancl_Ortrancl__refl_0) ).
cnf(cls_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_le__infE_0) ).
cnf(cls_inf__bot__right_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_inf__bot__right_0) ).
cnf(cls_le__iff__inf_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_le__iff__inf_0) ).
cnf(cls_Domain__iff_1,axiom,
( hBOOL(c_in(X1,c_Relation_ODomain(X2,X3,X4),X3))
| ~ hBOOL(c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Domain__iff_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/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_pair__in__Id__conv_1) ).
cnf(cls_irrefl__diff__Id_0,axiom,
c_Relation_Oirrefl(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)),X2),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_irrefl__diff__Id_0) ).
cnf(cls_Diff__triv_0,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3) = X1
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Diff__triv_0) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_UNIV__not__empty_0) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Int__absorb_0) ).
cnf(cls_trancl__id_0,axiom,
( c_Transitive__Closure_Otrancl(X1,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_trancl__id_0) ).
cnf(cls_trancl__unfold__left_0,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_trancl__unfold__left_0) ).
cnf(cls_rtrancl__reflcl_0,axiom,
c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_rtrancl__reflcl_0) ).
cnf(cls_Un__empty__left_0,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Un__empty__left_0) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_sup__eq__bot__eq2_0) ).
cnf(cls_rtrancl__reflcl__absorb_0,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_rtrancl__reflcl__absorb_0) ).
cnf(cls_trans__Id_0,axiom,
c_Relation_Otrans(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_trans__Id_0) ).
cnf(cls_Id__O__R_0,axiom,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_Id__O__R_0) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',clsarity_fun__Lattices_Obounded__lattice) ).
cnf(cls_pair__in__Id__conv_0,axiom,
( X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3))) ),
file('/export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p',cls_pair__in__Id__conv_0) ).
cnf(c_0_72,axiom,
( hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
cls_inf1I_0 ).
cnf(c_0_73,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__disjoint_0 ).
cnf(c_0_74,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_75,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_76,axiom,
( 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
| hBOOL(c_in(X1,X3,X2)) ),
cls_Diff__insert__absorb_0 ).
cnf(c_0_77,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
cls_bex__UNIV_2 ).
cnf(c_0_78,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
cls_insert__code_1 ).
cnf(c_0_79,plain,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_Set_Oinsert(X1,X2),X3),X4))),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,plain,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_Set_Oinsert(X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X4))) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_82,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_83,axiom,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1)) ),
cls_UNIV__eq__I_0 ).
cnf(c_0_84,plain,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_86,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
cls_subset__UNIV_0 ).
cnf(c_0_87,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_83,c_0_84]) ).
cnf(c_0_88,plain,
( hBOOL(c_in(X1,c_COMBK(X2,X3,X4),X5))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_85]) ).
cnf(c_0_89,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_90,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_COMBK(X2,X3,X4)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_88]) ).
cnf(c_0_91,axiom,
~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
cls_in__mkbot_0 ).
cnf(c_0_92,axiom,
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3)))
| hBOOL(c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)) ),
cls_not__acc__down_0 ).
cnf(c_0_93,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
cls_le__funD_0 ).
cnf(c_0_94,plain,
( c_lessequals(X1,c_COMBK(X2,X3,X4),tc_fun(X5,tc_bool))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_95,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_96,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)) ),
cls_bex__UNIV_0 ).
cnf(c_0_97,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
cls_UNIV__I_0 ).
cnf(c_0_98,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
cls_mem__def_0 ).
cnf(c_0_99,plain,
hBOOL(c_in(X1,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X1),X2),X3,X1) ),
cls_le__sup__iff_1 ).
cnf(c_0_101,plain,
( c_lessequals(hAPP(X1,X2),X3,tc_bool)
| ~ hBOOL(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_85]),c_0_95])]) ).
cnf(c_0_102,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_103,axiom,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_insert__absorb_0 ).
cnf(c_0_104,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
cls_mem__def_1 ).
cnf(c_0_105,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97])]) ).
cnf(c_0_106,plain,
hBOOL(hAPP(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X2)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_107,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2(X1,X3))) ),
cls_ball__UNIV_2 ).
cnf(c_0_108,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_sup__absorb1_0 ).
cnf(c_0_109,plain,
( c_lessequals(X1,X2,tc_bool)
| ~ hBOOL(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102])]) ).
cnf(c_0_110,plain,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(hAPP(X3,X1)) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,plain,
hBOOL(hAPP(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X3))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2(X1,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_97])]) ).
cnf(c_0_113,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) = X1
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_102])]) ).
cnf(c_0_114,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I5_J_0 ).
cnf(c_0_115,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_116,axiom,
hAPP(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2) = X2,
cls_Image__Id_0 ).
cnf(c_0_117,axiom,
hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X1,X2),X3),X2)),
cls_insert__iff_1 ).
cnf(c_0_118,plain,
hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X3),X4),c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt)) = c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_119,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_120,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X1),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_121,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__fun__eq_0 ).
cnf(c_0_122,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_123,plain,
( hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2))
| ~ hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_116]),c_0_116]) ).
cnf(c_0_124,plain,
hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X3),c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X4)),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_125,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__eq__iff_2 ).
cnf(c_0_126,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_127,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_128,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_inf__absorb2_0 ).
cnf(c_0_129,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_130,axiom,
( 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))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__fun__eq_0 ).
cnf(c_0_131,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_121,c_0_122]) ).
cnf(c_0_132,plain,
( hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2))
| ~ hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_116]),c_0_116]) ).
cnf(c_0_133,plain,
hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2)),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_134,plain,
( X1 = X2
| ~ hBOOL(X1)
| ~ c_lessequals(X1,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_109]),c_0_126])]) ).
cnf(c_0_135,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X2,X3,X1)) ),
cls_Sup__upper_0 ).
cnf(c_0_136,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_137,plain,
( hAPP(c_Set_Oinsert(X1,X2),c_Lattices_Oupper__semilattice__class_Osup(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X3,tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_127]) ).
cnf(c_0_138,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2) = X2
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_109]),c_0_129])]) ).
cnf(c_0_139,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(t_a,tc_bool)),X2),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X1,v_x),tc_bool),hAPP(X2,v_x)),
inference(spm,[status(thm)],[c_0_130,c_0_115]) ).
cnf(c_0_140,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__fun__eq_0 ).
cnf(c_0_141,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_142,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_131,c_0_87]) ).
cnf(c_0_143,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2)))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_77,c_0_127]) ).
cnf(c_0_144,plain,
hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2)),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_145,plain,
( X1 = c_Complete__Lattice_OSup__class_OSup(X2,tc_bool)
| ~ hBOOL(c_in(X1,X2,tc_bool))
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136])]) ).
cnf(c_0_146,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X3))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_117,c_0_137]) ).
cnf(c_0_147,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(t_a,tc_bool)),X2),v_x) = hAPP(X2,v_x)
| ~ hBOOL(hAPP(X1,v_x)) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_148,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_140,c_0_141]) ).
cnf(c_0_149,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_90]),c_0_85]) ).
cnf(c_0_150,plain,
hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2))),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_151,plain,
( X1 = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_152,plain,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(t_a,tc_bool)),X2),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(hAPP(X2,v_x)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_73]),c_0_148]) ).
cnf(c_0_153,plain,
hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_149,c_0_78]) ).
cnf(c_0_154,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_155,plain,
hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2))),
inference(spm,[status(thm)],[c_0_105,c_0_150]) ).
cnf(c_0_156,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X3,tc_bool),tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_119]) ).
cnf(c_0_157,plain,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(t_a,tc_bool)),hAPP(c_Set_Oinsert(v_x,X2),X3)),v_x) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_153]),c_0_78])]) ).
cnf(c_0_158,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_98,c_0_154]) ).
cnf(c_0_159,plain,
( hBOOL(c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),tc_bool))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_160,plain,
( hAPP(X1,v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_in(v_x,X1,t_a)) ),
inference(spm,[status(thm)],[c_0_157,c_0_76]) ).
cnf(c_0_161,negated_conjecture,
hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_151,c_0_158]) ).
cnf(c_0_162,plain,
hBOOL(c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),tc_bool)),
inference(spm,[status(thm)],[c_0_159,c_0_144]) ).
cnf(c_0_163,plain,
( hAPP(X1,v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(hAPP(X1,v_x)) ),
inference(spm,[status(thm)],[c_0_98,c_0_160]) ).
cnf(c_0_164,negated_conjecture,
hBOOL(hAPP(v_F(v_P),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(v_F(v_P),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_161]),c_0_162])]) ).
cnf(c_0_165,plain,
( X1 = X2
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_134,c_0_109]) ).
cnf(c_0_166,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_163,c_0_85]) ).
cnf(c_0_167,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Set_Oinsert(X2,X1),X3),
cls_empty__not__insert_0 ).
cnf(c_0_168,negated_conjecture,
hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(v_F(v_P),X1),X2),v_F(v_P)) = v_F(v_P),
inference(spm,[status(thm)],[c_0_110,c_0_164]) ).
cnf(c_0_169,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| X1 = X2
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_170,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
cls_emptyE_0 ).
cnf(c_0_171,axiom,
( c_Relation_Oirrefl(X1,X2)
| 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))) ),
cls_irrefl__def_1 ).
cnf(c_0_172,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != v_F(v_P),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_173,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| X2 = c_Orderings_Obot__class_Obot(tc_bool)
| X2 = X1 ),
inference(spm,[status(thm)],[c_0_169,c_0_166]) ).
cnf(c_0_174,plain,
c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_175,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173])]) ).
cnf(c_0_176,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_177,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X1),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__left_0 ).
cnf(c_0_178,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_179,negated_conjecture,
( c_Relation_Oirrefl(v_F(X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
cls_conjecture_6 ).
cnf(c_0_180,negated_conjecture,
( v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1) ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_181,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),hAPP(v_P,X2),tc_Arrow__Order__Mirabelle_Oalt),
inference(spm,[status(thm)],[c_0_176,c_0_87]) ).
cnf(c_0_182,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_0 ).
cnf(c_0_183,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_1 ).
cnf(c_0_184,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I1_J_0 ).
cnf(c_0_185,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1) = X1,
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_186,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_187,negated_conjecture,
( c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181]),c_0_182]),c_0_183])]) ).
cnf(c_0_188,plain,
c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2),X1,tc_bool),
inference(spm,[status(thm)],[c_0_184,c_0_115]) ).
cnf(c_0_189,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1),tc_bool),X4) = X4,
inference(spm,[status(thm)],[c_0_185,c_0_153]) ).
cnf(c_0_190,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X3,X2),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X4)
| hBOOL(c_in(X3,X1,X2)) ),
cls_Int__insert__right_1 ).
cnf(c_0_191,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X2,tc_bool)),X3) = X3,
inference(spm,[status(thm)],[c_0_186,c_0_87]) ).
cnf(c_0_192,axiom,
( ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Oirrefl(X3,X2) ),
cls_irrefl__def_0 ).
cnf(c_0_193,axiom,
hBOOL(c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))),
cls_rtrancl_Ortrancl__refl_0 ).
cnf(c_0_194,negated_conjecture,
c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),tc_Arrow__Order__Mirabelle_Oalt),
inference(ef,[status(thm)],[c_0_187]) ).
cnf(c_0_195,plain,
( X1 = X2
| hBOOL(X2)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_166,c_0_166]) ).
cnf(c_0_196,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_148]),c_0_74]) ).
cnf(c_0_197,plain,
c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2,X3),X4),X2),tc_bool),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_198,plain,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_191]) ).
cnf(c_0_199,plain,
~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X1,X2),X2),
inference(spm,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_200,negated_conjecture,
( c_Relation_Oirrefl(X1,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_196]) ).
cnf(c_0_201,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
cls_le__infE_0 ).
cnf(c_0_202,plain,
( hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3))
| c_lessequals(X4,hAPP(X5,X1),tc_bool) ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_203,negated_conjecture,
hBOOL(c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt)),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_204,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__right_0 ).
cnf(c_0_205,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__inf_0 ).
cnf(c_0_206,plain,
( hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3))
| c_lessequals(X4,X5,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_129])]) ).
cnf(c_0_207,negated_conjecture,
( X1 = c_Transitive__Closure_Ortrancl(X2,tc_Arrow__Order__Mirabelle_Oalt)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_169,c_0_203]) ).
cnf(c_0_208,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_204,c_0_178]) ).
cnf(c_0_209,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2) = X1
| hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X5)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_129])]) ).
cnf(c_0_210,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(hAPP(X1,c_Pair(X3,X3,X2,X2))) ),
inference(spm,[status(thm)],[c_0_192,c_0_104]) ).
cnf(c_0_211,negated_conjecture,
hAPP(v_P,X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_207]),c_0_199]) ).
cnf(c_0_212,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_in(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X4)) ),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_213,plain,
~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2),
inference(spm,[status(thm)],[c_0_210,c_0_82]) ).
cnf(c_0_214,plain,
~ hBOOL(hAPP(v_P,tc_bool)),
inference(rw,[status(thm)],[c_0_196,c_0_211]) ).
cnf(c_0_215,negated_conjecture,
hAPP(v_P,X1) = hAPP(v_P,X2),
inference(spm,[status(thm)],[c_0_211,c_0_211]) ).
cnf(c_0_216,axiom,
( hBOOL(c_in(X1,c_Relation_ODomain(X2,X3,X4),X3))
| ~ hBOOL(c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4))) ),
cls_Domain__iff_1 ).
cnf(c_0_217,plain,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_212]),c_0_196]) ).
cnf(c_0_218,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_219,axiom,
c_Relation_Oirrefl(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)),X2),
cls_irrefl__diff__Id_0 ).
cnf(c_0_220,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3) = X1
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
cls_Diff__triv_0 ).
cnf(c_0_221,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_UNIV__not__empty_0 ).
cnf(c_0_222,negated_conjecture,
( c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt) = X2
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_165,c_0_203]) ).
cnf(c_0_223,negated_conjecture,
hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),
inference(spm,[status(thm)],[c_0_213,c_0_200]) ).
cnf(c_0_224,negated_conjecture,
~ hBOOL(hAPP(v_P,X1)),
inference(spm,[status(thm)],[c_0_214,c_0_215]) ).
cnf(c_0_225,plain,
hBOOL(c_in(X1,c_Relation_ODomain(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X4),X3)),
inference(spm,[status(thm)],[c_0_216,c_0_217]) ).
cnf(c_0_226,plain,
~ c_Relation_Oirrefl(c_Relation_OId(X1),X1),
inference(spm,[status(thm)],[c_0_192,c_0_218]) ).
cnf(c_0_227,plain,
( c_Relation_Oirrefl(X1,X2)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_228,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X1) = X1,
cls_Int__absorb_0 ).
cnf(c_0_229,axiom,
( c_Transitive__Closure_Otrancl(X1,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
cls_trancl__id_0 ).
cnf(c_0_230,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
cls_trancl__unfold__left_0 ).
cnf(c_0_231,axiom,
c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_rtrancl__reflcl_0 ).
cnf(c_0_232,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
cls_Un__empty__left_0 ).
cnf(c_0_233,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_221,c_0_87]) ).
cnf(c_0_234,negated_conjecture,
c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_222,c_0_223]) ).
cnf(c_0_235,negated_conjecture,
( X1 = hAPP(v_P,X2)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_224,c_0_195]) ).
cnf(c_0_236,plain,
c_Relation_ODomain(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X3) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_83,c_0_225]) ).
cnf(c_0_237,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq2_0 ).
cnf(c_0_238,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_rtrancl__reflcl__absorb_0 ).
cnf(c_0_239,plain,
c_Relation_OId(X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_228]) ).
cnf(c_0_240,plain,
( c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
inference(rw,[status(thm)],[c_0_229,c_0_230]) ).
cnf(c_0_241,axiom,
c_Relation_Otrans(c_Relation_OId(X1),X1),
cls_trans__Id_0 ).
cnf(c_0_242,axiom,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
cls_Id__O__R_0 ).
cnf(c_0_243,plain,
c_Transitive__Closure_Ortrancl(c_Relation_OId(X1),X1) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_244,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Transitive__Closure_Ortrancl(tc_bool,tc_Arrow__Order__Mirabelle_Oalt),
inference(rw,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_245,negated_conjecture,
( X1 = hAPP(v_P,tc_bool)
| X1 = c_Transitive__Closure_Ortrancl(X2,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(rw,[status(thm)],[c_0_207,c_0_211]) ).
cnf(c_0_246,negated_conjecture,
c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt) = c_Transitive__Closure_Ortrancl(X2,tc_Arrow__Order__Mirabelle_Oalt),
inference(spm,[status(thm)],[c_0_222,c_0_203]) ).
cnf(c_0_247,negated_conjecture,
hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(tc_bool,tc_Arrow__Order__Mirabelle_Oalt),X2)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_235]),c_0_236]),c_0_234]),c_0_224]) ).
cnf(c_0_248,plain,
( c_Transitive__Closure_Ortrancl(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool))
| ~ class_Lattices_Obounded__lattice(tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_239]) ).
cnf(c_0_249,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
clsarity_fun__Lattices_Obounded__lattice ).
cnf(c_0_250,axiom,
( X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3))) ),
cls_pair__in__Id__conv_0 ).
cnf(c_0_251,plain,
c_Relation_OId(X1) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_241]),c_0_242]),c_0_243]) ).
cnf(c_0_252,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(v_P,tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_246]) ).
cnf(c_0_253,negated_conjecture,
hBOOL(hAPP(c_Transitive__Closure_Ortrancl(tc_bool,tc_Arrow__Order__Mirabelle_Oalt),X1)),
inference(spm,[status(thm)],[c_0_98,c_0_247]) ).
cnf(c_0_254,plain,
c_Transitive__Closure_Ortrancl(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_249]),c_0_178])]) ).
cnf(c_0_255,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(v_P,tc_bool),X3),c_Pair(X1,X2,X3,X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_104]),c_0_251]),c_0_252]) ).
cnf(c_0_256,negated_conjecture,
hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt),X2)),
inference(spm,[status(thm)],[c_0_253,c_0_246]) ).
cnf(c_0_257,plain,
c_Transitive__Closure_Ortrancl(X1,X2) != hAPP(v_P,tc_bool),
inference(rw,[status(thm)],[c_0_254,c_0_252]) ).
cnf(c_0_258,negated_conjecture,
X1 = X2,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_245]),c_0_256])]),c_0_257]) ).
cnf(c_0_259,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_257,c_0_258]),c_0_258])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SCT020-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 2400
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Oct 2 11:42:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.41/0.59 Running first-order model finding
% 0.41/0.59 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.1CuYxEEryo/E---3.1_31444.p
% 34.04/4.91 # Version: 3.1pre001
% 34.04/4.91 # Preprocessing class: FSLMSMSMSSSNFFN.
% 34.04/4.91 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 34.04/4.91 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 34.04/4.91 # Starting new_bool_3 with 600s (2) cores
% 34.04/4.91 # Starting new_bool_1 with 300s (1) cores
% 34.04/4.91 # Starting sh5l with 300s (1) cores
% 34.04/4.91 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 31549 completed with status 0
% 34.04/4.91 # Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 34.04/4.91 # Preprocessing class: FSLMSMSMSSSNFFN.
% 34.04/4.91 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 34.04/4.91 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 34.04/4.91 # No SInE strategy applied
% 34.04/4.91 # Search class: FGHSM-FSLM32-DFFFFFNN
% 34.04/4.91 # Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 34.04/4.91 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 90s (1) cores
% 34.04/4.91 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 34.04/4.91 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 34.04/4.91 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 34.04/4.91 # U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 31560 completed with status 0
% 34.04/4.91 # Result found by U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 34.04/4.91 # Preprocessing class: FSLMSMSMSSSNFFN.
% 34.04/4.91 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 34.04/4.91 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 34.04/4.91 # No SInE strategy applied
% 34.04/4.91 # Search class: FGHSM-FSLM32-DFFFFFNN
% 34.04/4.91 # Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 34.04/4.91 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 90s (1) cores
% 34.04/4.91 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 34.04/4.91 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 34.04/4.91 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 34.04/4.91 # Preprocessing time : 0.009 s
% 34.04/4.91 # Presaturation interreduction done
% 34.04/4.91
% 34.04/4.91 # Proof found!
% 34.04/4.91 # SZS status Unsatisfiable
% 34.04/4.91 # SZS output start CNFRefutation
% See solution above
% 34.04/4.91 # Parsed axioms : 713
% 34.04/4.91 # Removed by relevancy pruning/SinE : 0
% 34.04/4.91 # Initial clauses : 713
% 34.04/4.91 # Removed in clause preprocessing : 4
% 34.04/4.91 # Initial clauses in saturation : 709
% 34.04/4.91 # Processed clauses : 12832
% 34.04/4.91 # ...of these trivial : 352
% 34.04/4.91 # ...subsumed : 9039
% 34.04/4.91 # ...remaining for further processing : 3441
% 34.04/4.91 # Other redundant clauses eliminated : 1375
% 34.04/4.91 # Clauses deleted for lack of memory : 0
% 34.04/4.91 # Backward-subsumed : 144
% 34.04/4.91 # Backward-rewritten : 2666
% 34.04/4.91 # Generated clauses : 231550
% 34.04/4.91 # ...of the previous two non-redundant : 215973
% 34.04/4.91 # ...aggressively subsumed : 0
% 34.04/4.91 # Contextual simplify-reflections : 0
% 34.04/4.91 # Paramodulations : 230130
% 34.04/4.91 # Factorizations : 36
% 34.04/4.91 # NegExts : 0
% 34.04/4.91 # Equation resolutions : 1384
% 34.04/4.91 # Total rewrite steps : 55471
% 34.04/4.91 # Propositional unsat checks : 0
% 34.04/4.91 # Propositional check models : 0
% 34.04/4.91 # Propositional check unsatisfiable : 0
% 34.04/4.91 # Propositional clauses : 0
% 34.04/4.91 # Propositional clauses after purity: 0
% 34.04/4.91 # Propositional unsat core size : 0
% 34.04/4.91 # Propositional preprocessing time : 0.000
% 34.04/4.91 # Propositional encoding time : 0.000
% 34.04/4.91 # Propositional solver time : 0.000
% 34.04/4.91 # Success case prop preproc time : 0.000
% 34.04/4.91 # Success case prop encoding time : 0.000
% 34.04/4.91 # Success case prop solver time : 0.000
% 34.04/4.91 # Current number of processed clauses : 36
% 34.04/4.91 # Positive orientable unit clauses : 15
% 34.04/4.91 # Positive unorientable unit clauses: 1
% 34.04/4.91 # Negative unit clauses : 0
% 34.04/4.91 # Non-unit-clauses : 20
% 34.04/4.91 # Current number of unprocessed clauses: 201206
% 34.04/4.91 # ...number of literals in the above : 571585
% 34.04/4.91 # Current number of archived formulas : 0
% 34.04/4.91 # Current number of archived clauses : 3406
% 34.04/4.91 # Clause-clause subsumption calls (NU) : 512272
% 34.04/4.91 # Rec. Clause-clause subsumption calls : 329043
% 34.04/4.91 # Non-unit clause-clause subsumptions : 5780
% 34.04/4.91 # Unit Clause-clause subsumption calls : 49286
% 34.04/4.91 # Rewrite failures with RHS unbound : 0
% 34.04/4.91 # BW rewrite match attempts : 9811
% 34.04/4.91 # BW rewrite match successes : 4318
% 34.04/4.91 # Condensation attempts : 0
% 34.04/4.91 # Condensation successes : 0
% 34.04/4.91 # Termbank termtop insertions : 3539621
% 34.04/4.91
% 34.04/4.91 # -------------------------------------------------
% 34.04/4.91 # User time : 4.025 s
% 34.04/4.91 # System time : 0.143 s
% 34.04/4.91 # Total time : 4.168 s
% 34.04/4.91 # Maximum resident set size: 3232 pages
% 34.04/4.91
% 34.04/4.91 # -------------------------------------------------
% 34.04/4.91 # User time : 16.266 s
% 34.04/4.91 # System time : 0.492 s
% 34.04/4.91 # Total time : 16.758 s
% 34.04/4.91 # Maximum resident set size: 2288 pages
% 34.04/4.91 % E---3.1 exiting
%------------------------------------------------------------------------------