TSTP Solution File: SEV440^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV440^1 : TPTP v6.4.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 16091.75MB
% OS : Linux 3.10.0-327.10.1.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Mar 28 10:09:07 EDT 2016
% Result : Unknown 0.46s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV440^1 : TPTP v6.4.0. Released v6.4.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.22 % Computer : n001.star.cs.uiowa.edu
% 0.02/0.22 % Model : x86_64 x86_64
% 0.02/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.22 % Memory : 16091.75MB
% 0.02/0.22 % OS : Linux 3.10.0-327.10.1.el7.x86_64
% 0.02/0.22 % CPULimit : 300
% 0.02/0.22 % DateTime : Fri Mar 25 14:19:42 CDT 2016
% 0.02/0.22 % CPUTime :
% 0.02/0.24 Python 2.7.8
% 0.08/0.50 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.08/0.50 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/SET008^0.ax, trying next directory
% 0.08/0.50 FOF formula (<kernel.Constant object at 0x2b5aa11c86c8>, <kernel.DependentProduct object at 0x2b5aa11c8bd8>) of role type named in_decl
% 0.08/0.50 Using role type
% 0.08/0.50 Declaring in:(fofType->((fofType->Prop)->Prop))
% 0.08/0.50 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) in) (fun (X:fofType) (M:(fofType->Prop))=> (M X))) of role definition named in
% 0.08/0.50 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) in) (fun (X:fofType) (M:(fofType->Prop))=> (M X)))
% 0.08/0.50 Defined: in:=(fun (X:fofType) (M:(fofType->Prop))=> (M X))
% 0.08/0.50 FOF formula (<kernel.Constant object at 0x2b5aa11c86c8>, <kernel.DependentProduct object at 0x2b5aa11c8b90>) of role type named is_a_decl
% 0.08/0.50 Using role type
% 0.08/0.50 Declaring is_a:(fofType->((fofType->Prop)->Prop))
% 0.08/0.50 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) is_a) (fun (X:fofType) (M:(fofType->Prop))=> (M X))) of role definition named is_a
% 0.08/0.50 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) is_a) (fun (X:fofType) (M:(fofType->Prop))=> (M X)))
% 0.08/0.50 Defined: is_a:=(fun (X:fofType) (M:(fofType->Prop))=> (M X))
% 0.08/0.50 FOF formula (<kernel.Constant object at 0x2b5aa11c8b90>, <kernel.DependentProduct object at 0x2b5aa11c8638>) of role type named emptyset_decl
% 0.08/0.50 Using role type
% 0.08/0.50 Declaring emptyset:(fofType->Prop)
% 0.08/0.50 FOF formula (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False)) of role definition named emptyset
% 0.08/0.50 A new definition: (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False))
% 0.08/0.50 Defined: emptyset:=(fun (X:fofType)=> False)
% 0.08/0.50 FOF formula (<kernel.Constant object at 0x2b5aa11c8638>, <kernel.DependentProduct object at 0x2b5aa11c8908>) of role type named unord_pair_decl
% 0.08/0.50 Using role type
% 0.08/0.50 Declaring unord_pair:(fofType->(fofType->(fofType->Prop)))
% 0.08/0.50 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) unord_pair) (fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y)))) of role definition named unord_pair
% 0.08/0.50 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) unord_pair) (fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y))))
% 0.08/0.50 Defined: unord_pair:=(fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y)))
% 0.08/0.50 FOF formula (<kernel.Constant object at 0x2b5aa11c8830>, <kernel.DependentProduct object at 0x2b5aa11c8b90>) of role type named singleton_decl
% 0.08/0.50 Using role type
% 0.08/0.50 Declaring singleton:(fofType->(fofType->Prop))
% 0.08/0.50 FOF formula (((eq (fofType->(fofType->Prop))) singleton) (fun (X:fofType) (U:fofType)=> (((eq fofType) U) X))) of role definition named singleton
% 0.08/0.50 A new definition: (((eq (fofType->(fofType->Prop))) singleton) (fun (X:fofType) (U:fofType)=> (((eq fofType) U) X)))
% 0.08/0.50 Defined: singleton:=(fun (X:fofType) (U:fofType)=> (((eq fofType) U) X))
% 0.08/0.50 FOF formula (<kernel.Constant object at 0x2b5aa11c85a8>, <kernel.DependentProduct object at 0x2b5aa11c8998>) of role type named union_decl
% 0.08/0.50 Using role type
% 0.08/0.50 Declaring union:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.08/0.50 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))) of role definition named union
% 0.08/0.50 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))))
% 0.08/0.50 Defined: union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))
% 0.08/0.50 FOF formula (<kernel.Constant object at 0x2b5aa11c8f38>, <kernel.DependentProduct object at 0x2b5aa11c8908>) of role type named excl_union_decl
% 0.08/0.50 Using role type
% 0.08/0.50 Declaring excl_union:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.08/0.50 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) excl_union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))) of role definition named excl_union
% 0.08/0.50 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) excl_union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))))
% 0.08/0.52 Defined: excl_union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2b5aa11c8998>, <kernel.DependentProduct object at 0x2b5a9eedebd8>) of role type named intersection_decl
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring intersection:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.08/0.52 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) intersection) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))) of role definition named intersection
% 0.08/0.52 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) intersection) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))))
% 0.08/0.52 Defined: intersection:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2b5aa11c8998>, <kernel.DependentProduct object at 0x2b5a9eede998>) of role type named setminus_decl
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring setminus:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.08/0.52 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) setminus) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False)))) of role definition named setminus
% 0.08/0.52 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) setminus) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False))))
% 0.08/0.52 Defined: setminus:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False)))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2b5aa11c8998>, <kernel.DependentProduct object at 0x2b5a9eede518>) of role type named complement_decl
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring complement:((fofType->Prop)->(fofType->Prop))
% 0.08/0.52 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) complement) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))) of role definition named complement
% 0.08/0.52 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) complement) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)))
% 0.08/0.52 Defined: complement:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2b5a9eede5a8>, <kernel.DependentProduct object at 0x2b5a9eedebd8>) of role type named disjoint_decl
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring disjoint:((fofType->Prop)->((fofType->Prop)->Prop))
% 0.08/0.52 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) disjoint) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset))) of role definition named disjoint
% 0.08/0.52 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) disjoint) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset)))
% 0.08/0.52 Defined: disjoint:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2b5a9eede878>, <kernel.DependentProduct object at 0x2b5a96faecf8>) of role type named subset_decl
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring subset:((fofType->Prop)->((fofType->Prop)->Prop))
% 0.08/0.52 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))) of role definition named subset
% 0.08/0.52 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))))
% 0.08/0.52 Defined: subset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2b5a9eedebd8>, <kernel.DependentProduct object at 0x2b5a96faeb48>) of role type named meets_decl
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring meets:((fofType->Prop)->((fofType->Prop)->Prop))
% 0.08/0.52 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) meets) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U)))))) of role definition named meets
% 0.08/0.53 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) meets) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))))
% 0.08/0.53 Defined: meets:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U)))))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2b5a9eedebd8>, <kernel.DependentProduct object at 0x2b5a9ea8dea8>) of role type named misses_decl
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring misses:((fofType->Prop)->((fofType->Prop)->Prop))
% 0.08/0.53 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) misses) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False))) of role definition named misses
% 0.08/0.53 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) misses) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False)))
% 0.08/0.53 Defined: misses:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False))
% 0.08/0.53 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/SET008^1.ax, trying next directory
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2b5aa11c87e8>, <kernel.DependentProduct object at 0x2b5aa11c8b90>) of role type named fun_image_decl
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring fun_image:((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))
% 0.08/0.53 FOF formula (((eq ((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))) fun_image) (fun (F:(fofType->fofType)) (A:(fofType->Prop)) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((and (A X)) (((eq fofType) Y) (F X))))))) of role definition named fun_image
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))) fun_image) (fun (F:(fofType->fofType)) (A:(fofType->Prop)) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((and (A X)) (((eq fofType) Y) (F X)))))))
% 0.08/0.53 Defined: fun_image:=(fun (F:(fofType->fofType)) (A:(fofType->Prop)) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((and (A X)) (((eq fofType) Y) (F X))))))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2b5aa11c8b90>, <kernel.DependentProduct object at 0x2b5aa11c8908>) of role type named fun_composition_decl
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring fun_composition:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))
% 0.08/0.53 FOF formula (((eq ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) fun_composition) (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (X:fofType)=> (G (F X)))) of role definition named fun_composition
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) fun_composition) (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (X:fofType)=> (G (F X))))
% 0.08/0.53 Defined: fun_composition:=(fun (F:(fofType->fofType)) (G:(fofType->fofType)) (X:fofType)=> (G (F X)))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2b5aa11c85a8>, <kernel.DependentProduct object at 0x2b5aa11c8f38>) of role type named fun_inv_image_decl
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring fun_inv_image:((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))
% 0.08/0.53 FOF formula (((eq ((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))) fun_inv_image) (fun (F:(fofType->fofType)) (B:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and (B Y)) (((eq fofType) Y) (F X))))))) of role definition named fun_inv_image
% 0.08/0.53 A new definition: (((eq ((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))) fun_inv_image) (fun (F:(fofType->fofType)) (B:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and (B Y)) (((eq fofType) Y) (F X)))))))
% 0.08/0.53 Defined: fun_inv_image:=(fun (F:(fofType->fofType)) (B:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and (B Y)) (((eq fofType) Y) (F X))))))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2b5aa11c8f38>, <kernel.DependentProduct object at 0x2b5aa11c8368>) of role type named fun_injective_decl
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring fun_injective:((fofType->fofType)->Prop)
% 0.08/0.53 FOF formula (((eq ((fofType->fofType)->Prop)) fun_injective) (fun (F:(fofType->fofType))=> (forall (X:fofType) (Y:fofType), ((((eq fofType) (F X)) (F Y))->(((eq fofType) X) Y))))) of role definition named fun_injective
% 0.08/0.55 A new definition: (((eq ((fofType->fofType)->Prop)) fun_injective) (fun (F:(fofType->fofType))=> (forall (X:fofType) (Y:fofType), ((((eq fofType) (F X)) (F Y))->(((eq fofType) X) Y)))))
% 0.08/0.55 Defined: fun_injective:=(fun (F:(fofType->fofType))=> (forall (X:fofType) (Y:fofType), ((((eq fofType) (F X)) (F Y))->(((eq fofType) X) Y))))
% 0.08/0.55 FOF formula (<kernel.Constant object at 0x2b5aa11c8b90>, <kernel.DependentProduct object at 0x2b5aa11c8638>) of role type named fun_surjective_decl
% 0.08/0.55 Using role type
% 0.08/0.55 Declaring fun_surjective:((fofType->fofType)->Prop)
% 0.08/0.55 FOF formula (((eq ((fofType->fofType)->Prop)) fun_surjective) (fun (F:(fofType->fofType))=> (forall (Y:fofType), ((ex fofType) (fun (X:fofType)=> (((eq fofType) Y) (F X))))))) of role definition named fun_surjective
% 0.08/0.55 A new definition: (((eq ((fofType->fofType)->Prop)) fun_surjective) (fun (F:(fofType->fofType))=> (forall (Y:fofType), ((ex fofType) (fun (X:fofType)=> (((eq fofType) Y) (F X)))))))
% 0.08/0.55 Defined: fun_surjective:=(fun (F:(fofType->fofType))=> (forall (Y:fofType), ((ex fofType) (fun (X:fofType)=> (((eq fofType) Y) (F X))))))
% 0.08/0.55 FOF formula (<kernel.Constant object at 0x2b5aa11c85a8>, <kernel.DependentProduct object at 0x2b5a9eede878>) of role type named fun_bijective_decl
% 0.08/0.55 Using role type
% 0.08/0.55 Declaring fun_bijective:((fofType->fofType)->Prop)
% 0.08/0.55 FOF formula (((eq ((fofType->fofType)->Prop)) fun_bijective) (fun (F:(fofType->fofType))=> ((and (fun_injective F)) (fun_surjective F)))) of role definition named fun_bijective
% 0.08/0.55 A new definition: (((eq ((fofType->fofType)->Prop)) fun_bijective) (fun (F:(fofType->fofType))=> ((and (fun_injective F)) (fun_surjective F))))
% 0.08/0.55 Defined: fun_bijective:=(fun (F:(fofType->fofType))=> ((and (fun_injective F)) (fun_surjective F)))
% 0.08/0.55 FOF formula (<kernel.Constant object at 0x2b5aa11c8998>, <kernel.DependentProduct object at 0x2b5a9eede518>) of role type named fun_decreasing_decl
% 0.08/0.55 Using role type
% 0.08/0.55 Declaring fun_decreasing:((fofType->fofType)->((fofType->(fofType->Prop))->Prop))
% 0.08/0.55 FOF formula (((eq ((fofType->fofType)->((fofType->(fofType->Prop))->Prop))) fun_decreasing) (fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F Y)) (F X)))))) of role definition named fun_decreasing
% 0.08/0.55 A new definition: (((eq ((fofType->fofType)->((fofType->(fofType->Prop))->Prop))) fun_decreasing) (fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F Y)) (F X))))))
% 0.08/0.55 Defined: fun_decreasing:=(fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F Y)) (F X)))))
% 0.08/0.55 FOF formula (<kernel.Constant object at 0x2b5aa11c8998>, <kernel.DependentProduct object at 0x2b5a9ea8db48>) of role type named fun_increasing_decl
% 0.08/0.55 Using role type
% 0.08/0.55 Declaring fun_increasing:((fofType->fofType)->((fofType->(fofType->Prop))->Prop))
% 0.08/0.55 FOF formula (((eq ((fofType->fofType)->((fofType->(fofType->Prop))->Prop))) fun_increasing) (fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F X)) (F Y)))))) of role definition named fun_increasing
% 0.08/0.55 A new definition: (((eq ((fofType->fofType)->((fofType->(fofType->Prop))->Prop))) fun_increasing) (fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F X)) (F Y))))))
% 0.08/0.55 Defined: fun_increasing:=(fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F X)) (F Y)))))
% 0.08/0.55 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/SET008^2.ax, trying next directory
% 0.08/0.55 FOF formula (<kernel.Constant object at 0x2b5aa11c88c0>, <kernel.DependentProduct object at 0x2b5aa11c8b90>) of role type named cartesian_product_decl
% 0.08/0.55 Using role type
% 0.08/0.55 Declaring cartesian_product:((fofType->Prop)->((fofType->Prop)->(fofType->(fofType->Prop))))
% 0.08/0.55 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->(fofType->Prop))))) cartesian_product) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType) (V:fofType)=> ((and (X U)) (Y V)))) of role definition named cartesian_product
% 0.08/0.56 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->(fofType->Prop))))) cartesian_product) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType) (V:fofType)=> ((and (X U)) (Y V))))
% 0.08/0.56 Defined: cartesian_product:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType) (V:fofType)=> ((and (X U)) (Y V)))
% 0.08/0.56 FOF formula (<kernel.Constant object at 0x2b5a9eede878>, <kernel.DependentProduct object at 0x2b5aa11c8710>) of role type named pair_rel_decl
% 0.08/0.56 Using role type
% 0.08/0.56 Declaring pair_rel:(fofType->(fofType->(fofType->(fofType->Prop))))
% 0.08/0.56 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) pair_rel) (fun (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) V) Y)))) of role definition named pair_rel
% 0.08/0.56 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) pair_rel) (fun (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) V) Y))))
% 0.08/0.56 Defined: pair_rel:=(fun (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) V) Y)))
% 0.08/0.56 FOF formula (<kernel.Constant object at 0x2b5a9eede518>, <kernel.DependentProduct object at 0x2b5aa11c85a8>) of role type named id_rel_decl
% 0.08/0.56 Using role type
% 0.08/0.56 Declaring id_rel:((fofType->Prop)->(fofType->(fofType->Prop)))
% 0.08/0.56 FOF formula (((eq ((fofType->Prop)->(fofType->(fofType->Prop)))) id_rel) (fun (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) (((eq fofType) X) Y)))) of role definition named id_rel
% 0.08/0.56 A new definition: (((eq ((fofType->Prop)->(fofType->(fofType->Prop)))) id_rel) (fun (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) (((eq fofType) X) Y))))
% 0.08/0.56 Defined: id_rel:=(fun (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) (((eq fofType) X) Y)))
% 0.08/0.56 FOF formula (<kernel.Constant object at 0x2b5a9eede518>, <kernel.DependentProduct object at 0x2b5aa11c8bd8>) of role type named sub_rel_decl
% 0.08/0.56 Using role type
% 0.08/0.56 Declaring sub_rel:((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))
% 0.08/0.56 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))) sub_rel) (fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R1 X) Y)->((R2 X) Y))))) of role definition named sub_rel
% 0.08/0.56 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))) sub_rel) (fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R1 X) Y)->((R2 X) Y)))))
% 0.08/0.56 Defined: sub_rel:=(fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R1 X) Y)->((R2 X) Y))))
% 0.08/0.56 FOF formula (<kernel.Constant object at 0x2b5a9eede518>, <kernel.DependentProduct object at 0x2b5aa11c88c0>) of role type named is_rel_on_decl
% 0.08/0.56 Using role type
% 0.08/0.56 Declaring is_rel_on:((fofType->(fofType->Prop))->((fofType->Prop)->((fofType->Prop)->Prop)))
% 0.08/0.56 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->((fofType->Prop)->Prop)))) is_rel_on) (fun (R:(fofType->(fofType->Prop))) (A:(fofType->Prop)) (B:(fofType->Prop))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((and (A X)) (B Y)))))) of role definition named is_rel_on
% 0.08/0.56 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->((fofType->Prop)->Prop)))) is_rel_on) (fun (R:(fofType->(fofType->Prop))) (A:(fofType->Prop)) (B:(fofType->Prop))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((and (A X)) (B Y))))))
% 0.08/0.56 Defined: is_rel_on:=(fun (R:(fofType->(fofType->Prop))) (A:(fofType->Prop)) (B:(fofType->Prop))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((and (A X)) (B Y)))))
% 0.08/0.56 FOF formula (<kernel.Constant object at 0x2b5aa11c88c0>, <kernel.DependentProduct object at 0x2b5aa11c8830>) of role type named restrict_rel_domain_decl
% 0.08/0.56 Using role type
% 0.08/0.56 Declaring restrict_rel_domain:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))
% 0.08/0.56 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))) restrict_rel_domain) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) ((R X) Y)))) of role definition named restrict_rel_domain
% 0.40/0.57 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))) restrict_rel_domain) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) ((R X) Y))))
% 0.40/0.57 Defined: restrict_rel_domain:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) ((R X) Y)))
% 0.40/0.57 FOF formula (<kernel.Constant object at 0x2b5a9ea8db90>, <kernel.DependentProduct object at 0x2b5aa11c8638>) of role type named rel_diagonal_decl
% 0.40/0.57 Using role type
% 0.40/0.57 Declaring rel_diagonal:(fofType->(fofType->Prop))
% 0.40/0.57 FOF formula (((eq (fofType->(fofType->Prop))) rel_diagonal) (fun (X:fofType) (Y:fofType)=> (((eq fofType) X) Y))) of role definition named rel_diagonal
% 0.40/0.57 A new definition: (((eq (fofType->(fofType->Prop))) rel_diagonal) (fun (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)))
% 0.40/0.57 Defined: rel_diagonal:=(fun (X:fofType) (Y:fofType)=> (((eq fofType) X) Y))
% 0.40/0.57 FOF formula (<kernel.Constant object at 0x2b5a9ea8db90>, <kernel.DependentProduct object at 0x2b5aa11c8830>) of role type named rel_composition_decl
% 0.40/0.57 Using role type
% 0.40/0.57 Declaring rel_composition:((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.40/0.57 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) rel_composition) (fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop))) (X:fofType) (Z:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R1 X) Y)) ((R2 Y) Z)))))) of role definition named rel_composition
% 0.40/0.57 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) rel_composition) (fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop))) (X:fofType) (Z:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R1 X) Y)) ((R2 Y) Z))))))
% 0.40/0.57 Defined: rel_composition:=(fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop))) (X:fofType) (Z:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R1 X) Y)) ((R2 Y) Z)))))
% 0.40/0.57 FOF formula (<kernel.Constant object at 0x2b5a9ea8db00>, <kernel.DependentProduct object at 0x2b5aa11c8f38>) of role type named reflexive_decl
% 0.40/0.57 Using role type
% 0.40/0.57 Declaring reflexive:((fofType->(fofType->Prop))->Prop)
% 0.40/0.57 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) reflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X)))) of role definition named reflexive
% 0.40/0.57 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) reflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X))))
% 0.40/0.57 Defined: reflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X)))
% 0.40/0.57 FOF formula (<kernel.Constant object at 0x2b5aa11c8f38>, <kernel.DependentProduct object at 0x2b5aa11c8b90>) of role type named irreflexive_decl
% 0.40/0.57 Using role type
% 0.40/0.57 Declaring irreflexive:((fofType->(fofType->Prop))->Prop)
% 0.40/0.57 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) irreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False)))) of role definition named irreflexive
% 0.40/0.57 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) irreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False))))
% 0.40/0.57 Defined: irreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False)))
% 0.40/0.57 FOF formula (<kernel.Constant object at 0x2b5aa11c8b90>, <kernel.DependentProduct object at 0x2b5aa11c8ea8>) of role type named symmetric_decl
% 0.40/0.57 Using role type
% 0.40/0.57 Declaring symmetric:((fofType->(fofType->Prop))->Prop)
% 0.40/0.57 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) symmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X))))) of role definition named symmetric
% 0.40/0.57 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) symmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X)))))
% 0.41/0.59 Defined: symmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X))))
% 0.41/0.59 FOF formula (<kernel.Constant object at 0x2b5aa11c8ea8>, <kernel.DependentProduct object at 0x2b5aa11c87e8>) of role type named transitive_decl
% 0.41/0.59 Using role type
% 0.41/0.59 Declaring transitive:((fofType->(fofType->Prop))->Prop)
% 0.41/0.59 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) transitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z))))) of role definition named transitive
% 0.41/0.59 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) transitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))))
% 0.41/0.59 Defined: transitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z))))
% 0.41/0.59 FOF formula (<kernel.Constant object at 0x2b5aa11c8f38>, <kernel.DependentProduct object at 0x2b5a96fae950>) of role type named equiv_rel__decl
% 0.41/0.59 Using role type
% 0.41/0.59 Declaring equiv_rel:((fofType->(fofType->Prop))->Prop)
% 0.41/0.59 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) equiv_rel) (fun (R:(fofType->(fofType->Prop)))=> ((and ((and (reflexive R)) (symmetric R))) (transitive R)))) of role definition named equiv_rel
% 0.41/0.59 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) equiv_rel) (fun (R:(fofType->(fofType->Prop)))=> ((and ((and (reflexive R)) (symmetric R))) (transitive R))))
% 0.41/0.59 Defined: equiv_rel:=(fun (R:(fofType->(fofType->Prop)))=> ((and ((and (reflexive R)) (symmetric R))) (transitive R)))
% 0.41/0.59 FOF formula (<kernel.Constant object at 0x2b5aa11c85f0>, <kernel.DependentProduct object at 0x2b5a96fae3b0>) of role type named rel_codomain_decl
% 0.41/0.59 Using role type
% 0.41/0.59 Declaring rel_codomain:((fofType->(fofType->Prop))->(fofType->Prop))
% 0.41/0.59 FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_codomain) (fun (R:(fofType->(fofType->Prop))) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((R X) Y))))) of role definition named rel_codomain
% 0.41/0.59 A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_codomain) (fun (R:(fofType->(fofType->Prop))) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((R X) Y)))))
% 0.41/0.59 Defined: rel_codomain:=(fun (R:(fofType->(fofType->Prop))) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((R X) Y))))
% 0.41/0.59 FOF formula (<kernel.Constant object at 0x2b5aa11c85f0>, <kernel.DependentProduct object at 0x2b5a96faeb48>) of role type named rel_domain_decl
% 0.41/0.59 Using role type
% 0.41/0.59 Declaring rel_domain:((fofType->(fofType->Prop))->(fofType->Prop))
% 0.41/0.59 FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_domain) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((R X) Y))))) of role definition named rel_domain
% 0.41/0.59 A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_domain) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((R X) Y)))))
% 0.41/0.59 Defined: rel_domain:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((R X) Y))))
% 0.41/0.59 FOF formula (<kernel.Constant object at 0x2b5aa11c85f0>, <kernel.DependentProduct object at 0x2b5a96fae1b8>) of role type named rel_inverse_decl
% 0.41/0.59 Using role type
% 0.41/0.59 Declaring rel_inverse:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% 0.41/0.59 FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) rel_inverse) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X))) of role definition named rel_inverse
% 0.41/0.59 A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) rel_inverse) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X)))
% 0.41/0.59 Defined: rel_inverse:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X))
% 0.41/0.59 FOF formula (<kernel.Constant object at 0x2b5a96fae0e0>, <kernel.DependentProduct object at 0x2b5a96faecf8>) of role type named equiv_classes_decl
% 0.41/0.59 Using role type
% 0.41/0.59 Declaring equiv_classes:((fofType->(fofType->Prop))->((fofType->Prop)->Prop))
% 0.41/0.59 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->Prop))) equiv_classes) (fun (R:(fofType->(fofType->Prop))) (S1:(fofType->Prop))=> ((ex fofType) (fun (X:fofType)=> ((and (S1 X)) (forall (Y:fofType), ((iff (S1 Y)) ((R X) Y)))))))) of role definition named equiv_classes
% 0.41/0.60 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->Prop))) equiv_classes) (fun (R:(fofType->(fofType->Prop))) (S1:(fofType->Prop))=> ((ex fofType) (fun (X:fofType)=> ((and (S1 X)) (forall (Y:fofType), ((iff (S1 Y)) ((R X) Y))))))))
% 0.41/0.60 Defined: equiv_classes:=(fun (R:(fofType->(fofType->Prop))) (S1:(fofType->Prop))=> ((ex fofType) (fun (X:fofType)=> ((and (S1 X)) (forall (Y:fofType), ((iff (S1 Y)) ((R X) Y)))))))
% 0.41/0.60 FOF formula (<kernel.Constant object at 0x2b5a9eee2050>, <kernel.DependentProduct object at 0x2b5a96fae8c0>) of role type named restrict_rel_codomain_decl
% 0.41/0.60 Using role type
% 0.41/0.60 Declaring restrict_rel_codomain:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))
% 0.41/0.60 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))) restrict_rel_codomain) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S Y)) ((R X) Y)))) of role definition named restrict_rel_codomain
% 0.41/0.60 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop))))) restrict_rel_codomain) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S Y)) ((R X) Y))))
% 0.41/0.60 Defined: restrict_rel_codomain:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S Y)) ((R X) Y)))
% 0.41/0.60 FOF formula (<kernel.Constant object at 0x2b5a9eee2170>, <kernel.DependentProduct object at 0x2b5a96faecf8>) of role type named rel_field_decl
% 0.41/0.60 Using role type
% 0.41/0.60 Declaring rel_field:((fofType->(fofType->Prop))->(fofType->Prop))
% 0.41/0.60 FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_field) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((or ((rel_domain R) X)) ((rel_codomain R) X)))) of role definition named rel_field
% 0.41/0.60 A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) rel_field) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((or ((rel_domain R) X)) ((rel_codomain R) X))))
% 0.41/0.60 Defined: rel_field:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((or ((rel_domain R) X)) ((rel_codomain R) X)))
% 0.41/0.60 FOF formula (<kernel.Constant object at 0x2b5a9eee25f0>, <kernel.DependentProduct object at 0x2b5a96faee18>) of role type named well_founded_decl
% 0.41/0.60 Using role type
% 0.41/0.60 Declaring well_founded:((fofType->(fofType->Prop))->Prop)
% 0.41/0.60 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) well_founded) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) W)->((X W)->False)))))))))) of role definition named well_founded
% 0.41/0.60 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) well_founded) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) W)->((X W)->False))))))))))
% 0.41/0.60 Defined: well_founded:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) W)->((X W)->False)))))))))
% 0.41/0.60 FOF formula (<kernel.Constant object at 0x2b5a9eee25f0>, <kernel.DependentProduct object at 0x2b5a96fae3b0>) of role type named upwards_well_founded_decl
% 0.41/0.60 Using role type
% 0.41/0.60 Declaring upwards_well_founded:((fofType->(fofType->Prop))->Prop)
% 0.41/0.60 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) upwards_well_founded) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) Y)->((X W)->False)))))))))) of role definition named upwards_well_founded
% 0.41/0.60 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) upwards_well_founded) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) Y)->((X W)->False))))))))))
% 0.41/0.60 Defined: upwards_well_founded:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) Y)->((X W)->False)))))))))
% 0.41/0.60 Parameter fofType_DUMMY:fofType.
% 0.41/0.60 We need to prove []
% 0.41/0.60 Parameter fofType:Type.
% 0.41/0.60 Definition in:=(fun (X:fofType) (M:(fofType->Prop))=> (M X)):(fofType->((fofType->Prop)->Prop)).
% 0.41/0.60 Definition is_a:=(fun (X:fofType) (M:(fofType->Prop))=> (M X)):(fofType->((fofType->Prop)->Prop)).
% 0.41/0.60 Definition emptyset:=(fun (X:fofType)=> False):(fofType->Prop).
% 0.41/0.60 Definition unord_pair:=(fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y))):(fofType->(fofType->(fofType->Prop))).
% 0.41/0.60 Definition singleton:=(fun (X:fofType) (U:fofType)=> (((eq fofType) U) X)):(fofType->(fofType->Prop)).
% 0.41/0.60 Definition union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.41/0.60 Definition excl_union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.41/0.60 Definition intersection:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.41/0.60 Definition setminus:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.41/0.60 Definition complement:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.41/0.60 Definition disjoint:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset)):((fofType->Prop)->((fofType->Prop)->Prop)).
% 0.41/0.60 Definition subset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))):((fofType->Prop)->((fofType->Prop)->Prop)).
% 0.41/0.60 Definition meets:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))):((fofType->Prop)->((fofType->Prop)->Prop)).
% 0.41/0.60 Definition misses:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False)):((fofType->Prop)->((fofType->Prop)->Prop)).
% 0.41/0.60 Definition fun_image:=(fun (F:(fofType->fofType)) (A:(fofType->Prop)) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((and (A X)) (((eq fofType) Y) (F X)))))):((fofType->fofType)->((fofType->Prop)->(fofType->Prop))).
% 0.41/0.60 Definition fun_composition:=(fun (F:(fofType->fofType)) (G:(fofType->fofType)) (X:fofType)=> (G (F X))):((fofType->fofType)->((fofType->fofType)->(fofType->fofType))).
% 0.41/0.60 Definition fun_inv_image:=(fun (F:(fofType->fofType)) (B:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and (B Y)) (((eq fofType) Y) (F X)))))):((fofType->fofType)->((fofType->Prop)->(fofType->Prop))).
% 0.41/0.60 Definition fun_injective:=(fun (F:(fofType->fofType))=> (forall (X:fofType) (Y:fofType), ((((eq fofType) (F X)) (F Y))->(((eq fofType) X) Y)))):((fofType->fofType)->Prop).
% 0.41/0.60 Definition fun_surjective:=(fun (F:(fofType->fofType))=> (forall (Y:fofType), ((ex fofType) (fun (X:fofType)=> (((eq fofType) Y) (F X)))))):((fofType->fofType)->Prop).
% 0.41/0.60 Definition fun_bijective:=(fun (F:(fofType->fofType))=> ((and (fun_injective F)) (fun_surjective F))):((fofType->fofType)->Prop).
% 0.41/0.60 Definition fun_decreasing:=(fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F Y)) (F X))))):((fofType->fofType)->((fofType->(fofType->Prop))->Prop)).
% 0.41/0.60 Definition fun_increasing:=(fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F X)) (F Y))))):((fofType->fofType)->((fofType->(fofType->Prop))->Prop)).
% 0.41/0.60 Definition cartesian_product:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType) (V:fofType)=> ((and (X U)) (Y V))):((fofType->Prop)->((fofType->Prop)->(fofType->(fofType->Prop)))).
% 0.41/0.60 Definition pair_rel:=(fun (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) V) Y))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 0.45/0.62 Definition id_rel:=(fun (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) (((eq fofType) X) Y))):((fofType->Prop)->(fofType->(fofType->Prop))).
% 0.45/0.62 Definition sub_rel:=(fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R1 X) Y)->((R2 X) Y)))):((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop)).
% 0.45/0.62 Definition is_rel_on:=(fun (R:(fofType->(fofType->Prop))) (A:(fofType->Prop)) (B:(fofType->Prop))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((and (A X)) (B Y))))):((fofType->(fofType->Prop))->((fofType->Prop)->((fofType->Prop)->Prop))).
% 0.45/0.62 Definition restrict_rel_domain:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S X)) ((R X) Y))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop)))).
% 0.45/0.62 Definition rel_diagonal:=(fun (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)):(fofType->(fofType->Prop)).
% 0.45/0.62 Definition rel_composition:=(fun (R1:(fofType->(fofType->Prop))) (R2:(fofType->(fofType->Prop))) (X:fofType) (Z:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and ((R1 X) Y)) ((R2 Y) Z))))):((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% 0.45/0.62 Definition reflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X))):((fofType->(fofType->Prop))->Prop).
% 0.45/0.62 Definition irreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False))):((fofType->(fofType->Prop))->Prop).
% 0.45/0.62 Definition symmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X)))):((fofType->(fofType->Prop))->Prop).
% 0.45/0.62 Definition transitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))):((fofType->(fofType->Prop))->Prop).
% 0.45/0.62 Definition equiv_rel:=(fun (R:(fofType->(fofType->Prop)))=> ((and ((and (reflexive R)) (symmetric R))) (transitive R))):((fofType->(fofType->Prop))->Prop).
% 0.45/0.62 Definition rel_codomain:=(fun (R:(fofType->(fofType->Prop))) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((R X) Y)))):((fofType->(fofType->Prop))->(fofType->Prop)).
% 0.45/0.62 Definition rel_domain:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((R X) Y)))):((fofType->(fofType->Prop))->(fofType->Prop)).
% 0.45/0.62 Definition rel_inverse:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X)):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% 0.45/0.62 Definition equiv_classes:=(fun (R:(fofType->(fofType->Prop))) (S1:(fofType->Prop))=> ((ex fofType) (fun (X:fofType)=> ((and (S1 X)) (forall (Y:fofType), ((iff (S1 Y)) ((R X) Y))))))):((fofType->(fofType->Prop))->((fofType->Prop)->Prop)).
% 0.45/0.62 Definition restrict_rel_codomain:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->Prop)) (X:fofType) (Y:fofType)=> ((and (S Y)) ((R X) Y))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->(fofType->Prop)))).
% 0.45/0.62 Definition rel_field:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> ((or ((rel_domain R) X)) ((rel_codomain R) X))):((fofType->(fofType->Prop))->(fofType->Prop)).
% 0.45/0.62 Definition well_founded:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) W)->((X W)->False))))))))):((fofType->(fofType->Prop))->Prop).
% 0.45/0.62 Definition upwards_well_founded:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:(fofType->Prop)) (Z:fofType), ((X Z)->((ex fofType) (fun (Y:fofType)=> ((and (X Y)) (forall (W:fofType), (((R Y) Y)->((X W)->False))))))))):((fofType->(fofType->Prop))->Prop).
% 0.45/0.62 There are no conjectures!
% 0.45/0.62 Adding conjecture False, to look for Unsatisfiability
% 0.45/0.62 Trying to prove False
% 0.45/0.62 % SZS status GaveUp for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------