TSTP Solution File: SYO268^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO268^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:02 EDT 2022
% Result : Theorem 2.48s 2.66s
% Output : Proof 2.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO268^5 : TPTP v7.5.0. Released v4.0.0.
% 0.06/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 11 23:20:00 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 1.22/1.40 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 1.22/1.40 FOF formula (<kernel.Constant object at 0x1a49b48>, <kernel.Type object at 0x1a496c8>) of role type named a_type
% 1.22/1.40 Using role type
% 1.22/1.40 Declaring a:Type
% 1.22/1.40 FOF formula (<kernel.Constant object at 0x1a4dd88>, <kernel.Type object at 0x1a49ea8>) of role type named b_type
% 1.22/1.40 Using role type
% 1.22/1.40 Declaring b:Type
% 1.22/1.40 FOF formula (<kernel.Constant object at 0x1a49998>, <kernel.DependentProduct object at 0x2ae2c3959680>) of role type named r
% 1.22/1.40 Using role type
% 1.22/1.40 Declaring r:(a->(b->Prop))
% 1.22/1.40 FOF formula (((ex ((b->Prop)->b)) (fun (Xj:((b->Prop)->b))=> (forall (Xp:(b->Prop)), (((ex b) (fun (Xx:b)=> (Xp Xx)))->(Xp (Xj Xp))))))->((iff (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))) ((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) of role conjecture named cX5308
% 1.22/1.40 Conjecture to prove = (((ex ((b->Prop)->b)) (fun (Xj:((b->Prop)->b))=> (forall (Xp:(b->Prop)), (((ex b) (fun (Xx:b)=> (Xp Xx)))->(Xp (Xj Xp))))))->((iff (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))) ((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))):Prop
% 1.22/1.40 Parameter a_DUMMY:a.
% 1.22/1.40 Parameter b_DUMMY:b.
% 1.22/1.40 We need to prove ['(((ex ((b->Prop)->b)) (fun (Xj:((b->Prop)->b))=> (forall (Xp:(b->Prop)), (((ex b) (fun (Xx:b)=> (Xp Xx)))->(Xp (Xj Xp))))))->((iff (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))) ((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))))']
% 1.22/1.40 Parameter a:Type.
% 1.22/1.40 Parameter b:Type.
% 1.22/1.40 Parameter r:(a->(b->Prop)).
% 1.22/1.40 Trying to prove (((ex ((b->Prop)->b)) (fun (Xj:((b->Prop)->b))=> (forall (Xp:(b->Prop)), (((ex b) (fun (Xx:b)=> (Xp Xx)))->(Xp (Xj Xp))))))->((iff (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))) ((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))))
% 1.22/1.40 Found choice000:=(choice00 r):((forall (x:a), ((ex b) (fun (y:b)=> ((r x) y))))->((ex (a->b)) (fun (f:(a->b))=> (forall (x:a), ((r x) (f x))))))
% 1.22/1.40 Found (choice00 r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found ((choice0 b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found choice000:=(choice00 r):((forall (x:a), ((ex b) (fun (y:b)=> ((r x) y))))->((ex (a->b)) (fun (f:(a->b))=> (forall (x:a), ((r x) (f x))))))
% 1.22/1.40 Found (choice00 r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found ((choice0 b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found choice000:=(choice00 r):((forall (x:a), ((ex b) (fun (y:b)=> ((r x) y))))->((ex (a->b)) (fun (f:(a->b))=> (forall (x:a), ((r x) (f x))))))
% 1.22/1.40 Found (choice00 r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found ((choice0 b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 1.22/1.40 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found choice000:=(choice00 r):((forall (x:a), ((ex b) (fun (y:b)=> ((r x) y))))->((ex (a->b)) (fun (f:(a->b))=> (forall (x:a), ((r x) (f x))))))
% 2.48/2.64 Found (choice00 r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found ((choice0 b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found choice000:=(choice00 r):((forall (x:a), ((ex b) (fun (y:b)=> ((r x) y))))->((ex (a->b)) (fun (f:(a->b))=> (forall (x:a), ((r x) (f x))))))
% 2.48/2.64 Found (choice00 r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found ((choice0 b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found choice000:=(choice00 r):((forall (x:a), ((ex b) (fun (y:b)=> ((r x) y))))->((ex (a->b)) (fun (f:(a->b))=> (forall (x:a), ((r x) (f x))))))
% 2.48/2.64 Found (choice00 r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found ((choice0 b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found choice000:=(choice00 r):((forall (x:a), ((ex b) (fun (y:b)=> ((r x) y))))->((ex (a->b)) (fun (f:(a->b))=> (forall (x:a), ((r x) (f x))))))
% 2.48/2.64 Found (choice00 r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found ((choice0 b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found (((choice a) b) r) as proof of ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.64 Found x20:=(x2 Xx):((r Xx) (x1 Xx))
% 2.48/2.64 Found (x2 Xx) as proof of ((r Xx) x3)
% 2.48/2.64 Found (x2 Xx) as proof of ((r Xx) x3)
% 2.48/2.64 Found (x2 Xx) as proof of ((r Xx) x3)
% 2.48/2.64 Found (ex_intro000 (x2 Xx)) as proof of ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))
% 2.48/2.64 Found ((ex_intro00 (x1 Xx)) (x2 Xx)) as proof of ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))
% 2.48/2.64 Found (((ex_intro0 (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)) as proof of ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))
% 2.48/2.64 Found ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)) as proof of ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))
% 2.48/2.64 Found (fun (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx))) as proof of ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))
% 2.48/2.64 Found (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx))) as proof of ((forall (Xx0:a), ((r Xx0) (x1 Xx0)))->((ex b) (fun (Xy:b)=> ((r Xx) Xy))))
% 2.48/2.64 Found (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx))) as proof of (forall (x:(a->b)), ((forall (Xx0:a), ((r Xx0) (x Xx0)))->((ex b) (fun (Xy:b)=> ((r Xx) Xy)))))
% 2.48/2.64 Found (ex_ind00 (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)))) as proof of ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))
% 2.48/2.64 Found ((ex_ind0 ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)))) as proof of ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))
% 2.48/2.64 Found (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)))) as proof of ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))
% 2.48/2.64 Found (fun (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx))))) as proof of ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))
% 2.48/2.64 Found (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx))))) as proof of (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))
% 2.48/2.64 Found (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx))))) as proof of (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))))
% 2.48/2.64 Found ((conj00 (((choice a) b) r)) (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)))))) as proof of ((and ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))))
% 2.48/2.64 Found (((conj0 (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))))) (((choice a) b) r)) (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)))))) as proof of ((and ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))))
% 2.48/2.64 Found ((((conj ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))))) (((choice a) b) r)) (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)))))) as proof of ((and ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))))
% 2.48/2.65 Found ((((conj ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))))) (((choice a) b) r)) (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)))))) as proof of ((and ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))))
% 2.48/2.65 Found (fun (x:((ex ((b->Prop)->b)) (fun (Xj:((b->Prop)->b))=> (forall (Xp:(b->Prop)), (((ex b) (fun (Xx:b)=> (Xp Xx)))->(Xp (Xj Xp)))))))=> ((((conj ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))))) (((choice a) b) r)) (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx))))))) as proof of ((iff (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))) ((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))
% 2.48/2.65 Found (fun (x:((ex ((b->Prop)->b)) (fun (Xj:((b->Prop)->b))=> (forall (Xp:(b->Prop)), (((ex b) (fun (Xx:b)=> (Xp Xx)))->(Xp (Xj Xp)))))))=> ((((conj ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))))) (((choice a) b) r)) (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx))))))) as proof of (((ex ((b->Prop)->b)) (fun (Xj:((b->Prop)->b))=> (forall (Xp:(b->Prop)), (((ex b) (fun (Xx:b)=> (Xp Xx)))->(Xp (Xj Xp))))))->((iff (forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))) ((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))))
% 2.48/2.65 Got proof (fun (x:((ex ((b->Prop)->b)) (fun (Xj:((b->Prop)->b))=> (forall (Xp:(b->Prop)), (((ex b) (fun (Xx:b)=> (Xp Xx)))->(Xp (Xj Xp)))))))=> ((((conj ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))))) (((choice a) b) r)) (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)))))))
% 2.48/2.66 Time elapsed = 2.031132s
% 2.48/2.66 node=484 cost=4535.000000 depth=21
% 2.48/2.66 ::::::::::::::::::::::
% 2.48/2.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.48/2.66 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.48/2.66 (fun (x:((ex ((b->Prop)->b)) (fun (Xj:((b->Prop)->b))=> (forall (Xp:(b->Prop)), (((ex b) (fun (Xx:b)=> (Xp Xx)))->(Xp (Xj Xp)))))))=> ((((conj ((forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy))))->((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))))) (((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))->(forall (Xx:a), ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))))) (((choice a) b) r)) (fun (x0:((ex (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx)))))) (Xx:a)=> (((fun (P:Prop) (x1:(forall (x:(a->b)), ((forall (Xx:a), ((r Xx) (x Xx)))->P)))=> (((((ex_ind (a->b)) (fun (Xf:(a->b))=> (forall (Xx:a), ((r Xx) (Xf Xx))))) P) x1) x0)) ((ex b) (fun (Xy:b)=> ((r Xx) Xy)))) (fun (x1:(a->b)) (x2:(forall (Xx0:a), ((r Xx0) (x1 Xx0))))=> ((((ex_intro b) (fun (Xy:b)=> ((r Xx) Xy))) (x1 Xx)) (x2 Xx)))))))
% 2.48/2.66 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------