%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT006-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:07:33 PM UTC 2026
% Result : Unsatisfiable 14.73s 7.77s
% Output : CNFRefutation 14.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 39
% Syntax : Number of clauses : 199 ( 102 unt; 30 nHn; 80 RR)
% Number of literals : 319 ( 128 equ; 132 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 4 con; 0-5 aty)
% Number of variables : 500 ( 162 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Collect__mem__eq_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_insert__def_0,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
cnf(cls_funcset__image_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4)))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__image_0) ).
cnf(cls_Pi__I_H_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X4,X5,X3,X1,X2)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).
cnf(cls_CollectD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_vimage__Collect__eq_0,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(c_COMBB(X2,X1,X3,tc_bool,X4),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
cnf(cls_image__constant__conv_1,axiom,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_subset__Compl__self__eq_0,axiom,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
cnf(cls_vimage__Compl_0,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
cnf(cls_Collect__neg__eq_0,axiom,
c_Collect(c_COMBB(c_Not,X1,tc_bool,tc_bool,X2),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Collect(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(cls_Pow__top_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pow__top_0) ).
cnf(cls_Int__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
cnf(cls_vimage__const_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_le__funD_0,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_double__compl_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_ord_OlessThan__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).
cnf(cls_Pow__bottom_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Set_OPow(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pow__bottom_0) ).
cnf(cls_Diff__eq_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
cnf(c_0_39,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_40,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_41,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_42,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_43,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_disjoint__iff__not__equal_0]) ).
cnf(c_0_45,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
cls_insert__def_0 ).
cnf(c_0_46,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4)))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_funcset__image_0]) ).
cnf(c_0_47,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)),
c_0_41 ).
cnf(c_0_48,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X4,X5,X3,X1,X2)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2))) ),
cls_Pi__I_H_0 ).
cnf(c_0_50,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_44 ).
cnf(c_0_51,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_CollectD_0]) ).
cnf(c_0_52,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
cls_singleton__conv2_0 ).
cnf(c_0_53,plain,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X2,tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[c_0_45,c_0_40]) ).
cnf(c_0_54,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4)))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
c_0_46 ).
cnf(c_0_55,negated_conjecture,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1)),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,plain,
( hBOOL(hAPP(c_FuncSet_OPi(X1,X2,X4,X5),X3))
| hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X1,X2,X3,X4,X5))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_48]),c_0_48]) ).
cnf(c_0_57,plain,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_48]),c_0_48]) ).
cnf(c_0_58,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_59,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(c_COMBB(X2,X1,X3,tc_bool,X4),X4),
cls_vimage__Collect__eq_0 ).
cnf(c_0_60,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
c_0_51 ).
cnf(c_0_61,axiom,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
cls_image__constant__conv_1 ).
cnf(c_0_62,plain,
hAPP(c_fequal(X1),X2) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_40]),c_0_53]) ).
cnf(c_0_63,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
cls_Un__empty__right_0 ).
cnf(c_0_64,plain,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_subset__Compl__self__eq_0]) ).
cnf(c_0_65,plain,
( ~ hBOOL(hAPP(c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4),X1))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool)) ),
inference(rw,[status(thm)],[c_0_54,c_0_48]) ).
cnf(c_0_66,negated_conjecture,
hBOOL(hAPP(c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OLin,X1,X2,X3),X4)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,plain,
( ~ hBOOL(hAPP(X3,X2))
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_fequal(X1),X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
cls_vimage__Compl_0 ).
cnf(c_0_69,plain,
c_Set_Ovimage(X1,X2,X4,X3) = c_COMBB(X2,X1,X3,tc_bool,X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_40]),c_0_40]) ).
cnf(c_0_70,axiom,
c_Collect(c_COMBB(c_Not,X1,tc_bool,tc_bool,X2),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Collect(X1,X2)),
cls_Collect__neg__eq_0 ).
cnf(c_0_71,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_72,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X2,X1))),
cls_Pow__top_0 ).
cnf(c_0_73,plain,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_61,c_0_53]) ).
cnf(c_0_74,plain,
hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2) = hAPP(c_fequal(X1),X2),
inference(rw,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_75,plain,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_64 ).
cnf(c_0_76,negated_conjecture,
c_lessequals(c_Set_Oimage(X1,c_Arrow__Order__Mirabelle_OLin,X2,X3),X4,tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_77,plain,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_fequal(X1),X2),hAPP(c_fequal(X3),X2),tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_67,c_0_58]) ).
cnf(c_0_78,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
cls_Int__absorb_0 ).
cnf(c_0_79,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_vimage__const_1 ).
cnf(c_0_80,plain,
c_COMBB(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X1,X2,tc_bool,X4) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_COMBB(X3,X1,X2,tc_bool,X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_69]) ).
cnf(c_0_81,plain,
c_COMBB(c_Not,X1,tc_bool,tc_bool,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_40]),c_0_40]) ).
cnf(c_0_82,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0 ).
cnf(c_0_83,plain,
( ~ hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(X5,X2))
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_in(X1),X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(spm,[status(thm)],[c_0_57,c_0_48]) ).
cnf(c_0_84,plain,
hBOOL(hAPP(c_Set_OPow(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_85,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = hAPP(c_fequal(X2),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_63]) ).
cnf(c_0_86,negated_conjecture,
c_Set_Oimage(X1,c_Arrow__Order__Mirabelle_OLin,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,plain,
hAPP(c_fequal(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_88,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_COMBB(X4,c_COMBK(X1,X2,X3),X2,tc_bool,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_79,c_0_69]) ).
cnf(c_0_89,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0 ).
cnf(c_0_90,plain,
c_COMBB(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),X1,tc_bool,tc_bool,X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_91,plain,
( ~ hBOOL(hAPP(X3,c_Set_OPow(X2,X5)))
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_in(X1),X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_92,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_bot__least_0]) ).
cnf(c_0_93,plain,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
inference(fof_simplification,[status(thm)],[cls_le__funD_0]) ).
cnf(c_0_94,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
cls_empty__subsetI_0 ).
cnf(c_0_95,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Arrow__Order__Mirabelle_OLin,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
cnf(c_0_96,plain,
( hBOOL(hAPP(X1,X2))
| c_COMBB(X1,c_COMBK(X2,X3,X4),X3,tc_bool,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(rw,[status(thm)],[c_0_88,c_0_48]) ).
cnf(c_0_97,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),hAPP(X1,X2)) = hAPP(X1,X2),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_98,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_99,plain,
( ~ hBOOL(hAPP(c_Set_OPow(X2,X6),X4))
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_in(X1),X2),hAPP(c_in(X3),X4),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(spm,[status(thm)],[c_0_91,c_0_48]) ).
cnf(c_0_100,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_ComplD_0]) ).
cnf(c_0_101,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[cls_order__antisym__conv_0]) ).
cnf(c_0_102,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
c_0_92 ).
cnf(c_0_103,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_104,plain,
( ~ c_lessequals(X2,X4,tc_fun(X5,X1))
| ~ class_HOL_Oord(X1)
| c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1) ),
c_0_93 ).
cnf(c_0_105,plain,
c_lessequals(c_Arrow__Order__Mirabelle_OLin,X1,tc_fun(X2,tc_bool)),
inference(rw,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_106,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_107,plain,
( hBOOL(hAPP(X1,X2))
| c_COMBB(X1,c_COMBK(X2,X3,X4),X3,tc_bool,X4) = c_Arrow__Order__Mirabelle_OLin ),
inference(rw,[status(thm)],[c_0_96,c_0_95]) ).
cnf(c_0_108,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),X1) = X1,
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_109,plain,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_in(X1),X2),hAPP(c_in(X3),X2),tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_99,c_0_84]) ).
cnf(c_0_110,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_100 ).
cnf(c_0_111,plain,
( ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
c_0_101 ).
cnf(c_0_112,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_113,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_114,plain,
c_lessequals(hAPP(c_Arrow__Order__Mirabelle_OLin,X1),hAPP(X2,X1),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106])]) ).
cnf(c_0_115,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_116,plain,
( hBOOL(X1)
| c_COMBK(X1,tc_bool,X2) = c_Arrow__Order__Mirabelle_OLin ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_107]),c_0_108]) ).
cnf(c_0_117,plain,
hAPP(c_in(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_109,c_0_78]) ).
cnf(c_0_118,plain,
( ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_48]),c_0_48]) ).
cnf(c_0_119,plain,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113])]) ).
cnf(c_0_120,plain,
c_lessequals(hAPP(c_Arrow__Order__Mirabelle_OLin,X1),X2,tc_bool),
inference(spm,[status(thm)],[c_0_114,c_0_98]) ).
cnf(c_0_121,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_115 ).
cnf(c_0_122,plain,
( hBOOL(X2)
| hAPP(c_Arrow__Order__Mirabelle_OLin,X1) = X2 ),
inference(spm,[status(thm)],[c_0_98,c_0_116]) ).
cnf(c_0_123,plain,
hAPP(c_in(X1),X2) != c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_117,c_0_95]) ).
cnf(c_0_124,plain,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not)),X2)) ),
inference(spm,[status(thm)],[c_0_118,c_0_108]) ).
cnf(c_0_125,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_126,plain,
( ~ hBOOL(hAPP(hAPP(c_Arrow__Order__Mirabelle_OLin,X1),X2))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_95]) ).
cnf(c_0_127,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,X3) != c_Arrow__Order__Mirabelle_OLin
| hBOOL(hAPP(c_in(X1),X2)) ),
inference(spm,[status(thm)],[c_0_123,c_0_122]) ).
cnf(c_0_128,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_double__compl_0]) ).
cnf(c_0_129,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_124,c_0_82]) ).
cnf(c_0_130,plain,
( hBOOL(X1)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_125,c_0_122]) ).
cnf(c_0_131,plain,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(X1)
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_126,c_0_122]) ).
cnf(c_0_132,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(hAPP(c_in(X1),X2)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_122])]) ).
cnf(c_0_133,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
c_0_128 ).
cnf(c_0_134,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_135,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3) = hAPP(c_Not,hAPP(X2,X3)),
inference(spm,[status(thm)],[c_0_89,c_0_81]) ).
cnf(c_0_136,plain,
( ~ hBOOL(X1)
| hAPP(c_Not,X1) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_137,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(c_in(X1)) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_138,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
cls_ComplI_0 ).
cnf(c_0_139,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = X1,
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_140,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(rw,[status(thm)],[c_0_108,c_0_135]) ).
cnf(c_0_141,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hAPP(c_Not,c_in(X1)) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_142,plain,
( hBOOL(hAPP(X2,X3))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_48]),c_0_48]) ).
cnf(c_0_143,plain,
( ~ hBOOL(X3)
| ~ hBOOL(hAPP(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X3)))
| c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(tc_bool),X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(spm,[status(thm)],[c_0_57,c_0_139]) ).
cnf(c_0_144,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = c_in(X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_145,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_142,c_0_108]) ).
cnf(c_0_146,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OLin,X2),X3) != c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_in(X1)) ),
inference(spm,[status(thm)],[c_0_123,c_0_122]) ).
cnf(c_0_147,plain,
( ~ hBOOL(X2)
| c_HOL_Ouminus__class_Ouminus(tc_bool) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_78]),c_0_139])]) ).
cnf(c_0_148,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,X1) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_136,c_0_130]) ).
cnf(c_0_149,plain,
( hAPP(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X1) != c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_123,c_0_144]) ).
cnf(c_0_150,plain,
( hBOOL(X1)
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(c_Not) ),
inference(spm,[status(thm)],[c_0_131,c_0_145]) ).
cnf(c_0_151,plain,
( ~ hBOOL(hAPP(hAPP(X3,X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1))) ),
inference(fof_simplification,[status(thm)],[cls_ord_OlessThan__iff_1]) ).
cnf(c_0_152,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_bool),X2) != c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_in(X1)) ),
inference(spm,[status(thm)],[c_0_146,c_0_125]) ).
cnf(c_0_153,plain,
( ~ hBOOL(X1)
| c_HOL_Ouminus__class_Ouminus(tc_bool) != c_Arrow__Order__Mirabelle_OLin ),
inference(rw,[status(thm)],[c_0_147,c_0_95]) ).
cnf(c_0_154,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1 ),
inference(spm,[status(thm)],[c_0_140,c_0_148]) ).
cnf(c_0_155,plain,
( ~ hBOOL(X1)
| hAPP(X1,X2) != c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_136]),c_0_140]) ).
cnf(c_0_156,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(c_Not) ),
inference(ef,[status(thm)],[c_0_150]) ).
cnf(c_0_157,plain,
( ~ hBOOL(hAPP(hAPP(X3,X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1))) ),
c_0_151 ).
cnf(c_0_158,plain,
( ~ hBOOL(X2)
| hAPP(hAPP(c_Not,X2),X3) != c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_in(X1)) ),
inference(spm,[status(thm)],[c_0_152,c_0_136]) ).
cnf(c_0_159,plain,
( ~ hBOOL(X1)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Arrow__Order__Mirabelle_OLin
| c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_160,plain,
hBOOL(c_Arrow__Order__Mirabelle_OLin),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_140])]),c_0_156]) ).
cnf(c_0_161,plain,
( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
| hBOOL(hAPP(c_SetInterval_Oord_OlessThan(X1,X2,X3),X4)) ),
inference(rw,[status(thm)],[c_0_157,c_0_48]) ).
cnf(c_0_162,plain,
( ~ hBOOL(hAPP(c_Not,X2))
| hAPP(X2,X3) != c_Arrow__Order__Mirabelle_OLin
| hBOOL(c_in(X1)) ),
inference(spm,[status(thm)],[c_0_158,c_0_140]) ).
cnf(c_0_163,plain,
( ~ hBOOL(X1)
| c_HOL_Ouminus__class_Ouminus(tc_bool) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_136]),c_0_140])]),c_0_160])]) ).
cnf(c_0_164,plain,
hBOOL(hAPP(c_SetInterval_Oord_OlessThan(c_fequal(X1),X2,X3),X2)),
inference(spm,[status(thm)],[c_0_161,c_0_58]) ).
cnf(c_0_165,plain,
( ~ hBOOL(hAPP(c_Not,c_HOL_Ouminus__class_Ouminus(X2)))
| ~ class_Lattices_Oboolean__algebra(X2)
| hBOOL(c_in(X1)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_133])]) ).
cnf(c_0_166,plain,
c_HOL_Ouminus__class_Ouminus(tc_bool) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_167,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Set_OPow(X2,X1))),
cls_Pow__bottom_0 ).
cnf(c_0_168,plain,
hBOOL(c_in(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_134]),c_0_140]),c_0_160])]) ).
cnf(c_0_169,plain,
hBOOL(hAPP(c_Set_OPow(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
inference(rw,[status(thm)],[c_0_167,c_0_48]) ).
cnf(c_0_170,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X1)),X2))
| hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_118,c_0_142]) ).
cnf(c_0_171,plain,
( ~ hBOOL(hAPP(X3,X1))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(spm,[status(thm)],[c_0_57,c_0_84]) ).
cnf(c_0_172,plain,
hAPP(c_Not,c_in(X1)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_136,c_0_168]) ).
cnf(c_0_173,plain,
( ~ hBOOL(hAPP(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(spm,[status(thm)],[c_0_57,c_0_169]) ).
cnf(c_0_174,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(spm,[status(thm)],[c_0_170,c_0_82]) ).
cnf(c_0_175,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),c_Set_OPow(X1,X3),tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_171,c_0_84]) ).
cnf(c_0_176,plain,
hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = c_in(X1),
inference(spm,[status(thm)],[c_0_140,c_0_172]) ).
cnf(c_0_177,plain,
( ~ hBOOL(hAPP(X3,c_Arrow__Order__Mirabelle_OLin))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),X3,tc_fun(X4,tc_bool)) != c_Arrow__Order__Mirabelle_OLin ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_95]),c_0_95]) ).
cnf(c_0_178,plain,
( ~ hBOOL(X2)
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Not),X2)) ),
inference(spm,[status(thm)],[c_0_174,c_0_108]) ).
cnf(c_0_179,plain,
c_Set_OPow(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_175,c_0_78]) ).
cnf(c_0_180,plain,
hAPP(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X1) != c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_123,c_0_176]) ).
cnf(c_0_181,plain,
( ~ hBOOL(c_Arrow__Order__Mirabelle_OLin)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Not),tc_fun(X4,tc_bool)) != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_182,plain,
c_Set_OPow(X1,X2) != c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_179,c_0_95]) ).
cnf(c_0_183,plain,
( ~ hBOOL(X1)
| hAPP(X1,X2) != c_Arrow__Order__Mirabelle_OLin ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_136]),c_0_140]) ).
cnf(c_0_184,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Not),tc_fun(X4,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_160])]) ).
cnf(c_0_185,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)),
cls_Diff__eq_0 ).
cnf(c_0_186,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Arrow__Order__Mirabelle_OLin
| c_Set_OPow(X1,X2) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_182,c_0_154]) ).
cnf(c_0_187,plain,
( ~ hBOOL(c_HOL_Ouminus__class_Ouminus(X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_133])]) ).
cnf(c_0_188,plain,
~ hBOOL(c_Not),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_140])]) ).
cnf(c_0_189,plain,
( hBOOL(X2)
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_122,c_0_122]) ).
cnf(c_0_190,plain,
c_HOL_Ominus__class_Ominus(c_Set_OPow(X1,X2),c_Not,tc_fun(X3,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_191,plain,
c_Set_OPow(X1,X2) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_136]),c_0_140])]),c_0_160])]) ).
cnf(c_0_192,plain,
~ hBOOL(hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_166]),c_0_134])]) ).
cnf(c_0_193,plain,
( hBOOL(X1)
| X1 = c_Not ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_194,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__cancel_0 ).
cnf(c_0_195,plain,
c_HOL_Ominus__class_Ominus(hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),c_Not,tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_196,plain,
hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin) = c_Not,
inference(spm,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_197,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_194,c_0_95]) ).
cnf(c_0_198,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_196]),c_0_197])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT006-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/5.38 % Computer : n012.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Mon Sep 21 04:25:12 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.43 Running first-order theorem proving
% 0.14/5.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.73/7.77 % Version: 3.5.1
% 14.73/7.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 14.73/7.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.73/7.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 14.73/7.77 % Starting new_bool_3 with 300s (1) cores
% 14.73/7.77 % Starting new_bool_1 with 300s (1) cores
% 14.73/7.77 % Starting sh5l with 300s (1) cores
% 14.73/7.77 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1552465 completed with status 0
% 14.73/7.77 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 14.73/7.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 14.73/7.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.73/7.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 14.73/7.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.73/7.77 % No SInE strategy applied
% 14.73/7.77 % Search class: FGHSM-FSLM33-DFFFFFNN
% 14.73/7.77 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 14.73/7.77 % Starting SubtermCWHack with 136s (1) cores
% 14.73/7.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 14.73/7.77 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 14.73/7.77 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 14.73/7.77 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 14.73/7.77 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1552473 completed with status 0
% 14.73/7.77 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 14.73/7.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 14.73/7.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.73/7.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 14.73/7.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.73/7.77 % No SInE strategy applied
% 14.73/7.77 % Search class: FGHSM-FSLM33-DFFFFFNN
% 14.73/7.77 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 14.73/7.77 % Starting SubtermCWHack with 136s (1) cores
% 14.73/7.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 14.73/7.77 % Preprocessing time : 0.010 s
% 14.73/7.77 % Presaturation interreduction done
% 14.73/7.77
% 14.73/7.77 % Proof found!
% 14.73/7.77 % SZS status Unsatisfiable
% 14.73/7.77 % SZS output start CNFRefutation
% See solution above
% 14.73/7.77 % Parsed axioms : 654
% 14.73/7.77 % Removed by relevancy pruning/SinE : 0
% 14.73/7.77 % Initial clauses : 654
% 14.73/7.77 % Removed in clause preprocessing : 3
% 14.73/7.77 % Initial clauses in saturation : 651
% 14.73/7.77 % Processed clauses : 11432
% 14.73/7.77 % ...of these trivial : 489
% 14.73/7.77 % ...subsumed : 7915
% 14.73/7.77 % ...remaining for further processing : 3028
% 14.73/7.77 % Other redundant clauses eliminated : 2095
% 14.73/7.77 % Clauses deleted for lack of memory : 0
% 14.73/7.77 % Backward-subsumed : 302
% 14.73/7.77 % Backward-rewritten : 979
% 14.73/7.77 % Generated clauses : 117791
% 14.73/7.77 % ...of the previous two non-redundant : 102296
% 14.73/7.77 % ...aggressively subsumed : 0
% 14.73/7.77 % Contextual simplify-reflections : 33
% 14.73/7.77 % Paramodulations : 115656
% 14.73/7.77 % Factorizations : 19
% 14.73/7.77 % NegExts : 0
% 14.73/7.77 % Equation resolutions : 2116
% 14.73/7.77 % Disequality decompositions : 0
% 14.73/7.77 % Total rewrite steps : 43185
% 14.73/7.77 % ...of those cached : 39353
% 14.73/7.77 % Propositional unsat checks : 0
% 14.73/7.77 % Propositional check models : 0
% 14.73/7.77 % Propositional check unsatisfiable : 0
% 14.73/7.77 % Propositional clauses : 0
% 14.73/7.77 % Propositional clauses after purity: 0
% 14.73/7.77 % Propositional unsat core size : 0
% 14.73/7.77 % Propositional preprocessing time : 0.000
% 14.73/7.77 % Propositional encoding time : 0.000
% 14.73/7.77 % Propositional solver time : 0.000
% 14.73/7.77 % Success case prop preproc time : 0.000
% 14.73/7.77 % Success case prop encoding time : 0.000
% 14.73/7.77 % Success case prop solver time : 0.000
% 14.73/7.77 % Current number of processed clauses : 1236
% 14.73/7.77 % Positive orientable unit clauses : 203
% 14.73/7.77 % Positive unorientable unit clauses: 15
% 14.73/7.77 % Negative unit clauses : 70
% 14.73/7.77 % Non-unit-clauses : 948
% 14.73/7.77 % Current number of unprocessed clauses: 87197
% 14.73/7.77 % ...number of literals in the above : 258115
% 14.73/7.77 % Current number of archived formulas : 0
% 14.73/7.77 % Current number of archived clauses : 1793
% 14.73/7.77 % Clause-clause subsumption calls (NU) : 387925
% 14.73/7.77 % Rec. Clause-clause subsumption calls : 247203
% 14.73/7.77 % Non-unit clause-clause subsumptions : 5924
% 14.73/7.77 % Unit Clause-clause subsumption calls : 41475
% 14.73/7.77 % Rewrite failures with RHS unbound : 79
% 14.73/7.77 % BW rewrite match attempts : 3422
% 14.73/7.77 % BW rewrite match successes : 506
% 14.73/7.77 % Condensation attempts : 0
% 14.73/7.77 % Condensation successes : 0
% 14.73/7.77 % Termbank termtop insertions : 1647912
% 14.73/7.77 % Search garbage collected termcells : 1238
% 14.73/7.77
% 14.73/7.77 % -------------------------------------------------
% 14.73/7.77 % User time : 2.148 s
% 14.73/7.77 % System time : 0.081 s
% 14.73/7.77 % Total time : 2.229 s
% 14.73/7.77 % Maximum resident set size: 4940 pages
% 14.73/7.77
% 14.73/7.77 % -------------------------------------------------
% 14.73/7.77 % User time : 9.330 s
% 14.73/7.77 % System time : 0.352 s
% 14.73/7.77 % Total time : 9.681 s
% 14.73/7.77 % Maximum resident set size: 5376 pages
% 14.73/7.77 % E exiting
%------------------------------------------------------------------------------