%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG349-1 : 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 : n019.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 11:55:57 AM UTC 2026
% Result : Unsatisfiable 10.99s 2.08s
% Output : CNFRefutation 10.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 36
% Syntax : Number of clauses : 188 ( 89 unt; 35 nHn; 101 RR)
% Number of literals : 322 ( 132 equ; 122 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 302 ( 134 sgn)
% Comments :
%------------------------------------------------------------------------------
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_Collect__cong_0,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| c_Collect(X1,X2) = c_Collect(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__cong_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_bot__fun__eq_0,axiom,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
cnf(cls_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_mem__def_1,axiom,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_inf__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
cnf(cls_top__fun__eq_0,axiom,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
cnf(cls_UNIV__def_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Collect(c_COMBK(c_True,tc_bool,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__def_0) ).
cnf(cls_inf__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(cls_top__greatest_0,axiom,
( ~ class_Orderings_Otop(X1)
| c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
cnf(cls_inf__eq__top__eq2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| X3 = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_thx_0,axiom,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_thx_0) ).
cnf(cls_Collect__cong_1,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| c_Collect(X1,X2) = c_Collect(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__cong_1) ).
cnf(cls_sup__absorb1_0,axiom,
( ~ c_lessequals(X3,X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_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_UNIV__I_0,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
cnf(cls_Int__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
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_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__iff__sup_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
cnf(cls_Int__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
cnf(cls_sup__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
cnf(cls_assms_I1_J_0,axiom,
hBOOL(hAPP(v_P,v_sko__local__Xassms__1__1(v_P))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I1_J_0) ).
cnf(cls_sup__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(c_0_36,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_37,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| c_Collect(X1,X2) = c_Collect(X3,X2) ),
cls_Collect__cong_0 ).
cnf(c_0_38,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_39,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_36 ).
cnf(c_0_40,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| X1 = X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_38]) ).
cnf(c_0_41,plain,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1) ),
inference(fof_simplification,[status(thm)],[cls_bot__fun__eq_0]) ).
cnf(c_0_42,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[cls_emptyE_0]) ).
cnf(c_0_43,plain,
( hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3)))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,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_45,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_1]) ).
cnf(c_0_46,plain,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1) ),
c_0_41 ).
cnf(c_0_47,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_48,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
c_0_42 ).
cnf(c_0_49,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_39,c_0_43]) ).
cnf(c_0_50,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_44 ).
cnf(c_0_51,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_52,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
c_0_45 ).
cnf(c_0_53,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_46,c_0_47]) ).
cnf(c_0_54,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__bot__right_0]) ).
cnf(c_0_56,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_top__fun__eq_0]) ).
cnf(c_0_57,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Collect(c_COMBK(c_True,tc_bool,X1),X1),
cls_UNIV__def_0 ).
cnf(c_0_58,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
inference(fof_simplification,[status(thm)],[cls_inf__commute_0]) ).
cnf(c_0_59,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_50,c_0_51]) ).
cnf(c_0_60,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_61,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1) ),
c_0_55 ).
cnf(c_0_62,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
c_0_56 ).
cnf(c_0_63,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_64,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_65,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_COMBK(c_True,tc_bool,X1),
inference(rw,[status(thm)],[c_0_57,c_0_38]) ).
cnf(c_0_66,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
c_0_58 ).
cnf(c_0_67,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_59]),c_0_60]) ).
cnf(c_0_68,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_61,c_0_51]) ).
cnf(c_0_69,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_70,plain,
( ~ class_Orderings_Otop(X1)
| c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_top__greatest_0]) ).
cnf(c_0_71,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| X3 = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__eq__top__eq2_0]) ).
cnf(c_0_72,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_62,c_0_63]) ).
cnf(c_0_73,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = c_True,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,plain,
( hBOOL(X2)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_COMBK(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_64]) ).
cnf(c_0_75,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = 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_66,c_0_67]),c_0_68]),c_0_69])]) ).
cnf(c_0_76,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[cls_disjoint__iff__not__equal_0]) ).
cnf(c_0_77,axiom,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal)),
cls_thx_0 ).
cnf(c_0_78,plain,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| c_Collect(X1,X2) = c_Collect(X3,X2) ),
inference(fof_simplification,[status(thm)],[cls_Collect__cong_1]) ).
cnf(c_0_79,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2 ),
inference(fof_simplification,[status(thm)],[cls_sup__absorb1_0]) ).
cnf(c_0_80,plain,
( ~ class_Orderings_Otop(X1)
| c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1) ),
c_0_70 ).
cnf(c_0_81,negated_conjecture,
~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal),X1)),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_82,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| X3 = c_Orderings_Otop__class_Otop(X1) ),
c_0_71 ).
cnf(c_0_83,plain,
c_Orderings_Otop__class_Otop(tc_bool) = c_True,
inference(rw,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_84,plain,
( hBOOL(X1)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_74]),c_0_75]) ).
cnf(c_0_85,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_76 ).
cnf(c_0_86,plain,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),v_P,tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_77,c_0_38]) ).
cnf(c_0_87,plain,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| c_Collect(X1,X2) = c_Collect(X3,X2) ),
c_0_78 ).
cnf(c_0_88,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2 ),
c_0_79 ).
cnf(c_0_89,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_80,c_0_63]) ).
cnf(c_0_90,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_91,negated_conjecture,
~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal),X1)),
c_0_81 ).
cnf(c_0_92,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),X1) != c_True
| X1 = c_True ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_51])]) ).
cnf(c_0_93,plain,
( hBOOL(X2)
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_84,c_0_84]) ).
cnf(c_0_94,plain,
( ~ hBOOL(c_in(v_sko__local__Xthx__1(v_P),X1,tc_RealDef_Oreal))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_RealDef_Oreal,tc_bool)),v_P),X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_RealDef_Oreal,tc_bool)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_95,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
cls_UNIV__I_0 ).
cnf(c_0_96,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = X2,
cls_Int__UNIV__right_0 ).
cnf(c_0_97,axiom,
hAPP(c_COMBI(X1),X2) = X2,
cls_COMBI__def_0 ).
cnf(c_0_98,plain,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| X1 = X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_38]),c_0_38]) ).
cnf(c_0_99,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).
cnf(c_0_100,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_101,negated_conjecture,
~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),v_P,tc_RealDef_Oreal),X1)),
inference(rw,[status(thm)],[c_0_91,c_0_38]) ).
cnf(c_0_102,plain,
( hAPP(hAPP(X2,X3),X1) != c_True
| hBOOL(X2)
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool))
| X1 = c_True ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_103,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_RealDef_Oreal,tc_bool)) != v_P,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
cnf(c_0_104,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
inference(fof_simplification,[status(thm)],[cls_le__iff__sup_0]) ).
cnf(c_0_105,plain,
( ~ hBOOL(X1)
| hBOOL(c_in(X1,c_COMBI(X2),X3)) ),
inference(spm,[status(thm)],[c_0_52,c_0_97]) ).
cnf(c_0_106,plain,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,c_COMBK(X2,X3,X4),X5)))
| X1 = c_COMBK(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_98,c_0_64]) ).
cnf(c_0_107,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_True),X1) = c_True,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_83]),c_0_83]) ).
cnf(c_0_108,plain,
hBOOL(c_True),
inference(rw,[status(thm)],[c_0_100,c_0_73]) ).
cnf(c_0_109,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),v_P,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_101,c_0_43]) ).
cnf(c_0_110,plain,
( hAPP(X3,X1) != c_True
| hBOOL(c_COMBI(X2))
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool))
| X1 = c_True ),
inference(spm,[status(thm)],[c_0_102,c_0_97]) ).
cnf(c_0_111,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != v_P,
inference(spm,[status(thm)],[c_0_103,c_0_49]) ).
cnf(c_0_112,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
c_0_104 ).
cnf(c_0_113,plain,
( ~ hBOOL(X4)
| ~ hBOOL(c_in(X4,X3,X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_COMBI(X2)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_85,c_0_105]) ).
cnf(c_0_114,plain,
( ~ hBOOL(X1)
| c_COMBK(X1,X2,X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_True) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108])]) ).
cnf(c_0_115,negated_conjecture,
~ hBOOL(c_in(X1,c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),v_P,tc_RealDef_Oreal),X2)),
inference(spm,[status(thm)],[c_0_54,c_0_109]) ).
cnf(c_0_116,plain,
( hBOOL(c_COMBI(X2))
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool))
| X1 = c_True ),
inference(spm,[status(thm)],[c_0_110,c_0_73]) ).
cnf(c_0_117,plain,
hBOOL(c_in(X1,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_52,c_0_73]),c_0_108])]) ).
cnf(c_0_118,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| hBOOL(c_in(c_Orderings_Obot__class_Obot(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_67]) ).
cnf(c_0_119,plain,
( hBOOL(v_P)
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_93])]) ).
cnf(c_0_120,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_89]),c_0_90])]) ).
cnf(c_0_121,plain,
( ~ hBOOL(X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_COMBI(X2)),c_COMBI(X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_113,c_0_105]) ).
cnf(c_0_122,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
cls_Int__absorb_0 ).
cnf(c_0_123,plain,
( ~ hBOOL(X1)
| c_True = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_114]),c_0_107]) ).
cnf(c_0_124,negated_conjecture,
( hBOOL(c_COMBI(X1))
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_108])]) ).
cnf(c_0_125,plain,
( ~ hBOOL(c_in(X4,X3,X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_85,c_0_117]) ).
cnf(c_0_126,plain,
( hBOOL(v_P)
| hBOOL(c_in(c_Orderings_Obot__class_Obot(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_127,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
cls_Int__commute_0 ).
cnf(c_0_128,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),c_True) = c_True,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_83]),c_0_83]) ).
cnf(c_0_129,plain,
( ~ hBOOL(X3)
| c_COMBI(X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool))
| c_COMBI(X1) = c_True ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_131,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(v_P) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).
cnf(c_0_132,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) != v_P,
inference(spm,[status(thm)],[c_0_111,c_0_67]) ).
cnf(c_0_133,plain,
( c_True = X1
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_123,c_0_84]) ).
cnf(c_0_134,plain,
hBOOL(c_in(c_True,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_128]),c_0_108])]) ).
cnf(c_0_135,negated_conjecture,
( ~ hBOOL(X2)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_True
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool)) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_136,plain,
( hBOOL(v_P)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_True ),
inference(spm,[status(thm)],[c_0_123,c_0_119]) ).
cnf(c_0_137,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(tc_bool)
| hBOOL(v_P) ),
inference(spm,[status(thm)],[c_0_131,c_0_96]) ).
cnf(c_0_138,plain,
( hBOOL(X2)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_84]) ).
cnf(c_0_139,plain,
( c_Orderings_Obot__class_Obot(tc_bool) != v_P
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_True ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_140,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_125,c_0_134]) ).
cnf(c_0_141,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2) = X2,
cls_Int__UNIV__left_0 ).
cnf(c_0_142,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2 ),
inference(fof_simplification,[status(thm)],[cls_sup__bot__left_0]) ).
cnf(c_0_143,negated_conjecture,
( ~ hBOOL(X1)
| hBOOL(v_P)
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool)) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_144,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1) != c_Lattices_Olower__semilattice__class_Oinf(tc_bool)
| hBOOL(X1)
| hBOOL(v_P) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_145,plain,
( hBOOL(v_P)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),v_P) = c_True ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_93]),c_0_60])]) ).
cnf(c_0_146,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_147,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2 ),
c_0_142 ).
cnf(c_0_148,negated_conjecture,
( hBOOL(v_P)
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool)) ),
inference(spm,[status(thm)],[c_0_143,c_0_124]) ).
cnf(c_0_149,plain,
( c_Lattices_Olower__semilattice__class_Oinf(tc_bool) != c_True
| hBOOL(v_P) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_150,negated_conjecture,
c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),v_P,tc_RealDef_Oreal) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_109,c_0_67]) ).
cnf(c_0_151,plain,
( hAPP(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(X1)
| hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) ),
inference(spm,[status(thm)],[c_0_146,c_0_93]) ).
cnf(c_0_152,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1) = X1,
inference(spm,[status(thm)],[c_0_147,c_0_51]) ).
cnf(c_0_153,negated_conjecture,
hBOOL(v_P),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_148]),c_0_149]) ).
cnf(c_0_154,negated_conjecture,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(X1)
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_93]),c_0_150]) ).
cnf(c_0_155,plain,
( hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152])]) ).
cnf(c_0_156,plain,
~ hBOOL(c_in(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X2)),
inference(spm,[status(thm)],[c_0_54,c_0_67]) ).
cnf(c_0_157,negated_conjecture,
c_True = v_P,
inference(spm,[status(thm)],[c_0_123,c_0_153]) ).
cnf(c_0_158,negated_conjecture,
( hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_159,plain,
( ~ hBOOL(c_in(X2,hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool)),X3))
| hBOOL(X1)
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool)) ),
inference(spm,[status(thm)],[c_0_156,c_0_93]) ).
cnf(c_0_160,plain,
( ~ hBOOL(X1)
| ~ class_Lattices_Obounded__lattice(X2)
| hBOOL(c_in(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),c_Orderings_Obot__class_Obot(X2)),X3)) ),
inference(spm,[status(thm)],[c_0_52,c_0_147]) ).
cnf(c_0_161,axiom,
hBOOL(hAPP(v_P,v_sko__local__Xassms__1__1(v_P))),
cls_assms_I1_J_0 ).
cnf(c_0_162,plain,
( ~ hBOOL(X1)
| v_P = X1 ),
inference(rw,[status(thm)],[c_0_123,c_0_157]) ).
cnf(c_0_163,negated_conjecture,
( hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool))
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_138]),c_0_60]) ).
cnf(c_0_164,plain,
( ~ hBOOL(X1)
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool))
| hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_51])]) ).
cnf(c_0_165,plain,
hBOOL(c_in(v_sko__local__Xassms__1__1(v_P),v_P,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_161]) ).
cnf(c_0_166,negated_conjecture,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_True))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_107]),c_0_108])]) ).
cnf(c_0_167,negated_conjecture,
hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_111]) ).
cnf(c_0_168,plain,
( hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool))
| hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool)) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_169,negated_conjecture,
( hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_True)) ),
inference(spm,[status(thm)],[c_0_166,c_0_67]) ).
cnf(c_0_170,negated_conjecture,
c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = v_P,
inference(spm,[status(thm)],[c_0_162,c_0_167]) ).
cnf(c_0_171,plain,
( hBOOL(c_Lattices_Olower__semilattice__class_Oinf(tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = c_True ),
inference(spm,[status(thm)],[c_0_123,c_0_168]) ).
cnf(c_0_172,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_sup__top__left_0]) ).
cnf(c_0_173,negated_conjecture,
hBOOL(hAPP(v_P,v_P)),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_169]),c_0_157]),c_0_111]),c_0_170]) ).
cnf(c_0_174,plain,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2 ),
inference(fof_simplification,[status(thm)],[cls_sup__idem_0]) ).
cnf(c_0_175,plain,
( c_Lattices_Olower__semilattice__class_Oinf(tc_bool) = c_True
| c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = c_True ),
inference(spm,[status(thm)],[c_0_123,c_0_171]) ).
cnf(c_0_176,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1) ),
c_0_172 ).
cnf(c_0_177,negated_conjecture,
hAPP(v_P,v_P) = v_P,
inference(spm,[status(thm)],[c_0_162,c_0_173]) ).
cnf(c_0_178,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_True),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_114]),c_0_108])]) ).
cnf(c_0_179,plain,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2 ),
c_0_174 ).
cnf(c_0_180,plain,
( c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = v_P
| c_Lattices_Olower__semilattice__class_Oinf(tc_bool) = v_P ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_157]),c_0_157]) ).
cnf(c_0_181,negated_conjecture,
hAPP(v_P,X1) = v_P,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_170]),c_0_83]),c_0_157]),c_0_83]),c_0_157]),c_0_51])]),c_0_177]) ).
cnf(c_0_182,negated_conjecture,
~ hBOOL(hAPP(c_Lubs_OisUb(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_True),v_P,tc_RealDef_Oreal),X1)),
inference(spm,[status(thm)],[c_0_101,c_0_178]) ).
cnf(c_0_183,plain,
( v_P = X1
| c_Lattices_Olower__semilattice__class_Oinf(tc_bool) = v_P ),
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_181]),c_0_90])]) ).
cnf(c_0_184,plain,
c_Orderings_Obot__class_Obot(tc_bool) != v_P,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_157]),c_0_132]) ).
cnf(c_0_185,negated_conjecture,
~ hBOOL(hAPP(c_Lubs_OisUb(hAPP(v_P,v_P),v_P,tc_RealDef_Oreal),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_170]),c_0_157]) ).
cnf(c_0_186,plain,
v_P = X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_183]),c_0_181]),c_0_181]),c_0_51])]),c_0_184]) ).
cnf(c_0_187,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_186]),c_0_153])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG349-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n019.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 13:17:04 UTC 2026
% 0.06/0.41 % CPUTime :
% 0.06/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.50 Running first-order theorem proving
% 0.06/0.50 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
% 10.99/2.08 % Version: 3.5.1
% 10.99/2.08 % Preprocessing class: FSLSSMSMSSSNFFN.
% 10.99/2.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.99/2.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 10.99/2.08 % Starting new_bool_3 with 300s (1) cores
% 10.99/2.08 % Starting new_bool_1 with 300s (1) cores
% 10.99/2.08 % Starting sh5l with 300s (1) cores
% 10.99/2.08 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2661808 completed with status 0
% 10.99/2.08 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 10.99/2.08 % Preprocessing class: FSLSSMSMSSSNFFN.
% 10.99/2.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.99/2.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 10.99/2.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.99/2.08 % No SInE strategy applied
% 10.99/2.08 % Search class: FGHSM-FSLM32-DFFFFFNN
% 10.99/2.08 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 10.99/2.08 % Starting SubtermCWHack with 136s (1) cores
% 10.99/2.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 10.99/2.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 113s (1) cores
% 10.99/2.08 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 113s (1) cores
% 10.99/2.08 % Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 10.99/2.08 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2661814 completed with status 0
% 10.99/2.08 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 10.99/2.08 % Preprocessing class: FSLSSMSMSSSNFFN.
% 10.99/2.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.99/2.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 10.99/2.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.99/2.08 % No SInE strategy applied
% 10.99/2.08 % Search class: FGHSM-FSLM32-DFFFFFNN
% 10.99/2.08 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 10.99/2.08 % Starting SubtermCWHack with 136s (1) cores
% 10.99/2.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 10.99/2.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 113s (1) cores
% 10.99/2.08 % Preprocessing time : 0.010 s
% 10.99/2.08 % Presaturation interreduction done
% 10.99/2.08
% 10.99/2.08 % Proof found!
% 10.99/2.08 % SZS status Unsatisfiable
% 10.99/2.08 % SZS output start CNFRefutation
% See solution above
% 10.99/2.08 % Parsed axioms : 394
% 10.99/2.08 % Removed by relevancy pruning/SinE : 0
% 10.99/2.08 % Initial clauses : 394
% 10.99/2.08 % Removed in clause preprocessing : 2
% 10.99/2.08 % Initial clauses in saturation : 392
% 10.99/2.08 % Processed clauses : 3995
% 10.99/2.08 % ...of these trivial : 157
% 10.99/2.08 % ...subsumed : 2118
% 10.99/2.08 % ...remaining for further processing : 1720
% 10.99/2.08 % Other redundant clauses eliminated : 1100
% 10.99/2.08 % Clauses deleted for lack of memory : 0
% 10.99/2.08 % Backward-subsumed : 192
% 10.99/2.08 % Backward-rewritten : 1139
% 10.99/2.08 % Generated clauses : 39931
% 10.99/2.08 % ...of the previous two non-redundant : 33952
% 10.99/2.08 % ...aggressively subsumed : 0
% 10.99/2.08 % Contextual simplify-reflections : 11
% 10.99/2.08 % Paramodulations : 38811
% 10.99/2.08 % Factorizations : 14
% 10.99/2.08 % NegExts : 0
% 10.99/2.08 % Equation resolutions : 1106
% 10.99/2.08 % Disequality decompositions : 0
% 10.99/2.08 % Total rewrite steps : 16137
% 10.99/2.08 % ...of those cached : 14284
% 10.99/2.08 % Propositional unsat checks : 0
% 10.99/2.08 % Propositional check models : 0
% 10.99/2.08 % Propositional check unsatisfiable : 0
% 10.99/2.08 % Propositional clauses : 0
% 10.99/2.08 % Propositional clauses after purity: 0
% 10.99/2.08 % Propositional unsat core size : 0
% 10.99/2.08 % Propositional preprocessing time : 0.000
% 10.99/2.08 % Propositional encoding time : 0.000
% 10.99/2.08 % Propositional solver time : 0.000
% 10.99/2.08 % Success case prop preproc time : 0.000
% 10.99/2.08 % Success case prop encoding time : 0.000
% 10.99/2.08 % Success case prop solver time : 0.000
% 10.99/2.08 % Current number of processed clauses : 55
% 10.99/2.08 % Positive orientable unit clauses : 32
% 10.99/2.08 % Positive unorientable unit clauses: 1
% 10.99/2.08 % Negative unit clauses : 0
% 10.99/2.08 % Non-unit-clauses : 22
% 10.99/2.08 % Current number of unprocessed clauses: 29882
% 10.99/2.08 % ...number of literals in the above : 97199
% 10.99/2.08 % Current number of archived formulas : 0
% 10.99/2.08 % Current number of archived clauses : 1665
% 10.99/2.08 % Clause-clause subsumption calls (NU) : 115735
% 10.99/2.08 % Rec. Clause-clause subsumption calls : 82652
% 10.99/2.08 % Non-unit clause-clause subsumptions : 1864
% 10.99/2.08 % Unit Clause-clause subsumption calls : 4010
% 10.99/2.08 % Rewrite failures with RHS unbound : 54
% 10.99/2.08 % BW rewrite match attempts : 2720
% 10.99/2.08 % BW rewrite match successes : 904
% 10.99/2.08 % Condensation attempts : 0
% 10.99/2.08 % Condensation successes : 0
% 10.99/2.08 % Termbank termtop insertions : 639813
% 10.99/2.08 % Search garbage collected termcells : 751
% 10.99/2.08
% 10.99/2.08 % -------------------------------------------------
% 10.99/2.08 % User time : 1.403 s
% 10.99/2.08 % System time : 0.052 s
% 10.99/2.08 % Total time : 1.455 s
% 10.99/2.08 % Maximum resident set size: 4200 pages
% 10.99/2.08
% 10.99/2.08 % -------------------------------------------------
% 10.99/2.08 % User time : 6.699 s
% 10.99/2.08 % System time : 0.259 s
% 10.99/2.08 % Total time : 6.958 s
% 10.99/2.08 % Maximum resident set size: 5120 pages
% 10.99/2.08 % E exiting
%------------------------------------------------------------------------------