TSTP Solution File: SEV429^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV429^1 : TPTP v6.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n093.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:34:11 EDT 2014
% Result : Timeout 300.10s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV429^1 : TPTP v6.1.0. Released v5.2.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n093.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 09:12:51 CDT 2014
% % CPUTime : 300.10
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x2bb2f38>, <kernel.DependentProduct object at 0x295c3b0>) of role type named f
% Using role type
% Declaring f:(fofType->fofType)
% FOF formula (forall (X:fofType) (Y:fofType), ((((eq fofType) (f X)) (f Y))->(((eq fofType) X) Y))) of role axiom named finj
% A new axiom: (forall (X:fofType) (Y:fofType), ((((eq fofType) (f X)) (f Y))->(((eq fofType) X) Y)))
% FOF formula ((ex (fofType->fofType)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) of role conjecture named invexists
% Conjecture to prove = ((ex (fofType->fofType)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['((ex (fofType->fofType)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))']
% Parameter fofType:Type.
% Parameter f:(fofType->fofType).
% Axiom finj:(forall (X:fofType) (Y:fofType), ((((eq fofType) (f X)) (f Y))->(((eq fofType) X) Y))).
% Trying to prove ((ex (fofType->fofType)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found eq_ref00:=(eq_ref0 (x (f X))):(((eq fofType) (x (f X))) (x (f X)))
% Found (eq_ref0 (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found eq_ref000:=(eq_ref00 P):((P (x (f X)))->(P (x (f X))))
% Found (eq_ref00 P) as proof of ((P (x (f X)))->(P X))
% Found ((eq_ref0 (x (f X))) P) as proof of ((P (x (f X)))->(P X))
% Found (((eq_ref fofType) (x (f X))) P) as proof of ((P (x (f X)))->(P X))
% Found (((eq_ref fofType) (x (f X))) P) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x (f X))) P)) as proof of ((P (x (f X)))->(P X))
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj00 ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found ((finj0 X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found (((finj (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj__eq_sym00 ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found ((finj__eq_sym0 X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (eq_sym000 (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of (((eq fofType) (x (f X))) X)
% Found ((eq_sym00 (x (f X))) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of (((eq fofType) (x (f X))) X)
% Found (((eq_sym0 X) (x (f X))) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of (((eq fofType) (x (f X))) X)
% Found ((((eq_sym fofType) X) (x (f X))) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of (((eq fofType) (x (f X))) X)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))):(((eq ((fofType->fofType)->Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) (fun (x:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (x (f X))) X))))
% Found (eta_expansion_dep00 (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) b)
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) b)
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) b)
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X)))) b)
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj000 ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found (finj000 ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) (f (x (f X)))) (f X)))=> ((finj00 x0) P)) ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) (f (x (f X)))) (f X)))=> (((finj0 X) x0) P)) ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) (f (x (f X)))) (f X)))=> ((((finj (x (f X))) X) x0) P)) ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> ((fun (x0:(((eq fofType) (f (x (f X)))) (f X)))=> ((((finj (x (f X))) X) x0) P)) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X)))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X)))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X)))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X)))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X))))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X)))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X)))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X)))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X)))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (forall (X:fofType), (((eq fofType) (x (f X))) X))))
% Found eq_ref00:=(eq_ref0 (x (f X))):(((eq fofType) (x (f X))) (x (f X)))
% Found (eq_ref0 (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_trans0000 ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x (f X))) X)
% Found (((eq_trans000 X) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of (((eq fofType) (x (f X))) X)
% Found ((((fun (b:fofType)=> ((eq_trans00 b) X)) X) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of (((eq fofType) (x (f X))) X)
% Found ((((fun (b:fofType)=> (((eq_trans0 (x (f X))) b) X)) X) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of (((eq fofType) (x (f X))) X)
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x (f X))) b) X)) X) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of (((eq fofType) (x (f X))) X)
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj__eq_sym00 ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found ((finj__eq_sym0 X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (eq_sym0000 (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found (eq_sym0000 (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) X) (x (f X))))=> ((eq_sym000 x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) X) (x (f X))))=> (((eq_sym00 (x (f X))) x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) X) (x (f X))))=> ((((eq_sym0 X) (x (f X))) x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) X) (x (f X))))=> (((((eq_sym fofType) X) (x (f X))) x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> ((fun (x0:(((eq fofType) X) (x (f X))))=> (((((eq_sym fofType) X) (x (f X))) x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))))) as proof of ((P (x (f X)))->(P X))
% Found eq_ref00:=(eq_ref0 (x (f X))):(((eq fofType) (x (f X))) (x (f X)))
% Found (eq_ref0 (x (f X))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((eq_ref fofType) (x (f X))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((eq_ref fofType) (x (f X))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((eq_ref fofType) (x (f X))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found eq_ref000:=(eq_ref00 P):((P (x (f X)))->(P (x (f X))))
% Found (eq_ref00 P) as proof of ((P (x (f X)))->(P X))
% Found ((eq_ref0 (x (f X))) P) as proof of ((P (x (f X)))->(P X))
% Found (((eq_ref fofType) (x (f X))) P) as proof of ((P (x (f X)))->(P X))
% Found (((eq_ref fofType) (x (f X))) P) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x (f X))) P)) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x (f X))) P)) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj00 ((eq_ref fofType) (f (x (f X))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((finj0 X) ((eq_ref fofType) (f (x (f X))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found (((finj (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found (((finj (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj__eq_sym00 ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found ((finj__eq_sym0 X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (eq_sym000 (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((eq_sym00 (x (f X))) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found (((eq_sym0 X) (x (f X))) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((((eq_sym fofType) X) (x (f X))) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((((eq_sym fofType) X) (x (f X))) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj000 ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found (finj000 ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) (f (x (f X)))) (f X)))=> ((finj00 x0) P)) ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) (f (x (f X)))) (f X)))=> (((finj0 X) x0) P)) ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) (f (x (f X)))) (f X)))=> ((((finj (x (f X))) X) x0) P)) ((eq_ref fofType) (f (x (f X))))) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> ((fun (x0:(((eq fofType) (f (x (f X)))) (f X)))=> ((((finj (x (f X))) X) x0) P)) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> ((fun (x0:(((eq fofType) (f (x (f X)))) (f X)))=> ((((finj (x (f X))) X) x0) P)) ((eq_ref fofType) (f (x (f X)))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (G:(fofType->fofType))=> (forall (X:fofType), (((eq fofType) (G (f X))) X))))
% Found x0:(P (x (f X)))
% Instantiate: X0:=(x (f X)):fofType
% Found x0 as proof of (P0 X0)
% Found eq_ref00:=(eq_ref0 (f X0)):(((eq fofType) (f X0)) (f X0))
% Found (eq_ref0 (f X0)) as proof of (((eq fofType) (f X0)) (f X))
% Found ((eq_ref fofType) (f X0)) as proof of (((eq fofType) (f X0)) (f X))
% Found ((eq_ref fofType) (f X0)) as proof of (((eq fofType) (f X0)) (f X))
% Found ((eq_ref fofType) (f X0)) as proof of (((eq fofType) (f X0)) (f X))
% Found x0:(P (x (f X)))
% Instantiate: b:=(x (f X)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 (x (f X))):(((eq fofType) (x (f X))) (x (f X)))
% Found (eq_ref0 (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_trans0000 ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) b)) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found (((eq_trans000 X) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((((fun (b:fofType)=> ((eq_trans00 b) X)) X) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((((fun (b:fofType)=> (((eq_trans0 (x (f X))) b) X)) X) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x (f X))) b) X)) X) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x (f X))) b) X)) X) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj__eq_sym00 ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found ((finj__eq_sym0 X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) X) (x (f X)))
% Found (eq_sym0000 (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found (eq_sym0000 (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) X) (x (f X))))=> ((eq_sym000 x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) X) (x (f X))))=> (((eq_sym00 (x (f X))) x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) X) (x (f X))))=> ((((eq_sym0 X) (x (f X))) x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found ((fun (x0:(((eq fofType) X) (x (f X))))=> (((((eq_sym fofType) X) (x (f X))) x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X)))))) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> ((fun (x0:(((eq fofType) X) (x (f X))))=> (((((eq_sym fofType) X) (x (f X))) x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))))) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> ((fun (x0:(((eq fofType) X) (x (f X))))=> (((((eq_sym fofType) X) (x (f X))) x0) P)) (((finj__eq_sym (x (f X))) X) ((eq_ref fofType) (f (x (f X))))))) as proof of (forall (P:(fofType->Prop)), ((P (x (f X)))->(P X)))
% Found eq_ref00:=(eq_ref0 (x (f X))):(((eq fofType) (x (f X))) (x (f X)))
% Found (eq_ref0 (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_trans00000 ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) b)) as proof of ((P (x (f X)))->(P X))
% Found ((eq_trans00000 ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) b)) as proof of ((P (x (f X)))->(P X))
% Found (((fun (x0:(((eq fofType) (x (f X))) b)) (x00:(((eq fofType) b) X))=> (((eq_trans0000 x0) x00) P)) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) b)) as proof of ((P (x (f X)))->(P X))
% Found (((fun (x0:(((eq fofType) (x (f X))) X)) (x00:(((eq fofType) X) X))=> ((((eq_trans000 X) x0) x00) P)) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of ((P (x (f X)))->(P X))
% Found (((fun (x0:(((eq fofType) (x (f X))) X)) (x00:(((eq fofType) X) X))=> (((((fun (b:fofType)=> ((eq_trans00 b) X)) X) x0) x00) P)) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of ((P (x (f X)))->(P X))
% Found (((fun (x0:(((eq fofType) (x (f X))) X)) (x00:(((eq fofType) X) X))=> (((((fun (b:fofType)=> (((eq_trans0 (x (f X))) b) X)) X) x0) x00) P)) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of ((P (x (f X)))->(P X))
% Found (((fun (x0:(((eq fofType) (x (f X))) X)) (x00:(((eq fofType) X) X))=> (((((fun (b:fofType)=> ((((eq_trans fofType) (x (f X))) b) X)) X) x0) x00) P)) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X)) as proof of ((P (x (f X)))->(P X))
% Found (fun (P:(fofType->Prop))=> (((fun (x0:(((eq fofType) (x (f X))) X)) (x00:(((eq fofType) X) X))=> (((((fun (b:fofType)=> ((((eq_trans fofType) (x (f X))) b) X)) X) x0) x00) P)) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) X))) as proof of ((P (x (f X)))->(P X))
% Found x0:(P (x (f X)))
% Instantiate: X0:=(x (f X)):fofType
% Found x0 as proof of (P0 X0)
% Found eq_ref00:=(eq_ref0 (f X0)):(((eq fofType) (f X0)) (f X0))
% Found (eq_ref0 (f X0)) as proof of (((eq fofType) (f X0)) (f X))
% Found ((eq_ref fofType) (f X0)) as proof of (((eq fofType) (f X0)) (f X))
% Found ((eq_ref fofType) (f X0)) as proof of (((eq fofType) (f X0)) (f X))
% Found ((eq_ref fofType) (f X0)) as proof of (((eq fofType) (f X0)) (f X))
% Found eq_ref00:=(eq_ref0 (x (f X))):(((eq fofType) (x (f X))) (x (f X)))
% Found (eq_ref0 (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found x0:(P (x (f X)))
% Instantiate: b:=(x (f X)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 (x (f X)))->(P0 (x (f X))))
% Found (eq_ref00 P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found ((eq_ref0 (x (f X))) P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found (((eq_ref fofType) (x (f X))) P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found (((eq_ref fofType) (x (f X))) P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found (fun (P0:(fofType->Prop))=> (((eq_ref fofType) (x (f X))) P0)) as proof of ((P0 (x (f X)))->(P0 X))
% Found eq_ref00:=(eq_ref0 (x (f X))):(((eq fofType) (x (f X))) (x (f X)))
% Found (eq_ref0 (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found eq_ref00:=(eq_ref0 (x (f X))):(((eq fofType) (x (f X))) (x (f X)))
% Found (eq_ref0 (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) X)
% Found eq_ref000:=(eq_ref00 P0):((P0 (x (f X)))->(P0 (x (f X))))
% Found (eq_ref00 P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found ((eq_ref0 (x (f X))) P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found (((eq_ref fofType) (x (f X))) P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found (((eq_ref fofType) (x (f X))) P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found (fun (P0:(fofType->Prop))=> (((eq_ref fofType) (x (f X))) P0)) as proof of ((P0 (x (f X)))->(P0 X))
% Found eq_ref000:=(eq_ref00 P0):((P0 (x (f X)))->(P0 (x (f X))))
% Found (eq_ref00 P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found ((eq_ref0 (x (f X))) P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found (((eq_ref fofType) (x (f X))) P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found (((eq_ref fofType) (x (f X))) P0) as proof of ((P0 (x (f X)))->(P0 X))
% Found (fun (P0:(fofType->Prop))=> (((eq_ref fofType) (x (f X))) P0)) as proof of ((P0 (x (f X)))->(P0 X))
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj00 ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found ((finj0 X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found (((finj (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj00 ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found ((finj0 X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found (((finj (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found eq_ref00:=(eq_ref0 (f (x (f X)))):(((eq fofType) (f (x (f X)))) (f (x (f X))))
% Found (eq_ref0 (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found ((eq_ref fofType) (f (x (f X)))) as proof of (((eq fofType) (f (x (f X)))) (f X))
% Found (finj00 ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found ((finj0 X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found (((finj (x (f X))) X) ((eq_ref fofType) (f (x (f X))))) as proof of (((eq fofType) (x (f X))) X)
% Found eq_ref00:=(eq_ref0 (x (f X))):(((eq fofType) (x (f X))) (x (f X)))
% Found (eq_ref0 (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found ((eq_ref fofType) (x (f X))) as proof of (((eq fofType) (x (f X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_trans00000 ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) b)) as proof of ((P (x (f X)))->(P X))
% Found ((eq_trans00000 ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) b)) as proof of ((P (x (f X)))->(P X))
% Found (((fun (x0:(((eq fofType) (x (f X))) b)) (x00:(((eq fofType) b) X))=> (((eq_trans0000 x0) x00) P)) ((eq_ref fofType) (x (f X)))) ((eq_ref fofType) b)) as proof of ((P (x (f X)))->(P X))
% EOF
%------------------------------------------------------------------------------