TSTP Solution File: SYO303^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO303^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n027.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 00:51:07 EDT 2022
% Result : Theorem 13.37s 13.54s
% Output : Proof 13.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO303^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n027.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 : Sat Mar 12 02:24:57 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
% 1.42/1.60 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 1.42/1.60 FOF formula (<kernel.Constant object at 0x2b9a10f031b8>, <kernel.Constant object at 0x2b9a10f03f38>) of role type named b
% 1.42/1.60 Using role type
% 1.42/1.60 Declaring b:fofType
% 1.42/1.60 FOF formula (<kernel.Constant object at 0x199e440>, <kernel.DependentProduct object at 0x2b9a10f03560>) of role type named cS
% 1.42/1.60 Using role type
% 1.42/1.60 Declaring cS:(fofType->Prop)
% 1.42/1.60 FOF formula (<kernel.Constant object at 0x2b9a10f031b8>, <kernel.Single object at 0x2b9a10f034d0>) of role type named a
% 1.42/1.60 Using role type
% 1.42/1.60 Declaring a:fofType
% 1.42/1.60 FOF formula (<kernel.Constant object at 0x2b9a10f03368>, <kernel.DependentProduct object at 0x2b9a10f035a8>) of role type named cT
% 1.42/1.60 Using role type
% 1.42/1.60 Declaring cT:(fofType->Prop)
% 1.42/1.60 FOF formula (<kernel.Constant object at 0x2b9a10f034d0>, <kernel.Single object at 0x2b9a10f031b8>) of role type named c0
% 1.42/1.60 Using role type
% 1.42/1.60 Declaring c0:fofType
% 1.42/1.60 FOF formula ((forall (P:(fofType->Prop)), ((or ((P c0)->False)) (forall (Xx:fofType), (P Xx))))->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))) of role conjecture named cMIN_QUAN_BUG
% 1.42/1.60 Conjecture to prove = ((forall (P:(fofType->Prop)), ((or ((P c0)->False)) (forall (Xx:fofType), (P Xx))))->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))):Prop
% 1.42/1.60 We need to prove ['((forall (P:(fofType->Prop)), ((or ((P c0)->False)) (forall (Xx:fofType), (P Xx))))->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))']
% 1.42/1.60 Parameter fofType:Type.
% 1.42/1.60 Parameter b:fofType.
% 1.42/1.60 Parameter cS:(fofType->Prop).
% 1.42/1.60 Parameter a:fofType.
% 1.42/1.60 Parameter cT:(fofType->Prop).
% 1.42/1.60 Parameter c0:fofType.
% 1.42/1.60 Trying to prove ((forall (P:(fofType->Prop)), ((or ((P c0)->False)) (forall (Xx:fofType), (P Xx))))->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 1.42/1.60 Found or_introl00:=(or_introl0 ((and (cT a)) (cS b))):(((P c0)->False)->((or ((P c0)->False)) ((and (cT a)) (cS b))))
% 1.42/1.60 Found (or_introl0 ((and (cT a)) (cS b))) as proof of (((P c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 1.42/1.60 Found ((or_introl ((P c0)->False)) ((and (cT a)) (cS b))) as proof of (((P c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 1.42/1.60 Found ((or_introl ((P c0)->False)) ((and (cT a)) (cS b))) as proof of (((P c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 1.42/1.60 Found ((or_introl ((P c0)->False)) ((and (cT a)) (cS b))) as proof of (((P c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 1.42/1.60 Found or_introl00:=(or_introl0 ((and (cT a)) (cS b))):((not (P c0))->((or (not (P c0))) ((and (cT a)) (cS b))))
% 1.42/1.60 Found (or_introl0 ((and (cT a)) (cS b))) as proof of ((not (P c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 1.42/1.60 Found ((or_introl (not (P c0))) ((and (cT a)) (cS b))) as proof of ((not (P c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 1.42/1.60 Found ((or_introl (not (P c0))) ((and (cT a)) (cS b))) as proof of ((not (P c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 1.42/1.60 Found ((or_introl (not (P c0))) ((and (cT a)) (cS b))) as proof of ((not (P c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 1.42/1.60 Found or_intror00:=(or_intror0 ((P c0)->False)):(((P c0)->False)->((or ((and (cT a)) (cS b))) ((P c0)->False)))
% 1.42/1.60 Found (or_intror0 ((P c0)->False)) as proof of (((P c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 1.42/1.60 Found ((or_intror ((and (cT a)) (cS b))) ((P c0)->False)) as proof of (((P c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 1.42/1.60 Found ((or_intror ((and (cT a)) (cS b))) ((P c0)->False)) as proof of (((P c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 1.42/1.60 Found ((or_intror ((and (cT a)) (cS b))) ((P c0)->False)) as proof of (((P c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 1.42/1.60 Found or_intror00:=(or_intror0 (not (P c0))):((not (P c0))->((or ((and (cT a)) (cS b))) (not (P c0))))
% 1.42/1.60 Found (or_intror0 (not (P c0))) as proof of ((not (P c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 1.42/1.60 Found ((or_intror ((and (cT a)) (cS b))) (not (P c0))) as proof of ((not (P c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 2.56/2.75 Found ((or_intror ((and (cT a)) (cS b))) (not (P c0))) as proof of ((not (P c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 2.56/2.75 Found ((or_intror ((and (cT a)) (cS b))) (not (P c0))) as proof of ((not (P c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 2.56/2.75 Found x10:=(x1 a):(P a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found x10:=(x1 b):(P b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found x10:=(x1 a):(P a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found x10:=(x1 b):(P b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found x10:=(x1 b):(P b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found x10:=(x1 a):(P a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found x1:(cS c0)
% 2.56/2.75 Instantiate: P:=cS:(fofType->Prop)
% 2.56/2.75 Found x1 as proof of (P c0)
% 2.56/2.75 Found (x4 x1) as proof of False
% 2.56/2.75 Found (fun (x4:((P c0)->False))=> (x4 x1)) as proof of False
% 2.56/2.75 Found (fun (x4:((P c0)->False))=> (x4 x1)) as proof of (((P c0)->False)->False)
% 2.56/2.75 Found x10:=(x1 b):(P b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found x10:=(x1 a):(P a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found x2:((P c0)->False)
% 2.56/2.75 Instantiate: P:=cT:(fofType->Prop)
% 2.56/2.75 Found (fun (x3:(cS c0))=> x2) as proof of ((cT c0)->False)
% 2.56/2.75 Found (fun (x3:(cS c0))=> x2) as proof of ((cS c0)->((cT c0)->False))
% 2.56/2.75 Found (and_rect00 (fun (x3:(cS c0))=> x2)) as proof of False
% 2.56/2.75 Found ((and_rect0 False) (fun (x3:(cS c0))=> x2)) as proof of False
% 2.56/2.75 Found (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2)) as proof of False
% 2.56/2.75 Found (fun (x2:((P c0)->False))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2))) as proof of False
% 2.56/2.75 Found (fun (x2:((P c0)->False))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2))) as proof of (((P c0)->False)->False)
% 2.56/2.75 Found x10:=(x1 a):(P a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found (x1 a) as proof of (cT a)
% 2.56/2.75 Found x10:=(x1 b):(P b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found (x1 b) as proof of (cS b)
% 2.56/2.75 Found x1:(not (P c0))
% 2.56/2.75 Instantiate: P:=cT:(fofType->Prop)
% 2.56/2.75 Found (fun (x3:(cS c0))=> x1) as proof of ((cT c0)->False)
% 2.56/2.75 Found (fun (x3:(cS c0))=> x1) as proof of ((cS c0)->((cT c0)->False))
% 2.56/2.75 Found (and_rect00 (fun (x3:(cS c0))=> x1)) as proof of False
% 2.56/2.75 Found ((and_rect0 False) (fun (x3:(cS c0))=> x1)) as proof of False
% 2.56/2.75 Found (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x2)) False) (fun (x3:(cS c0))=> x1)) as proof of False
% 2.56/2.75 Found (fun (x2:((and (cS c0)) (cT c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x2)) False) (fun (x3:(cS c0))=> x1))) as proof of False
% 2.56/2.75 Found (fun (x1:(not (P c0))) (x2:((and (cS c0)) (cT c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x2)) False) (fun (x3:(cS c0))=> x1))) as proof of (not ((and (cS c0)) (cT c0)))
% 2.56/2.75 Found (fun (x1:(not (P c0))) (x2:((and (cS c0)) (cT c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x2)) False) (fun (x3:(cS c0))=> x1))) as proof of ((not (P c0))->(not ((and (cS c0)) (cT c0))))
% 2.56/2.75 Found x1:(cS c0)
% 2.56/2.75 Instantiate: P:=cS:(fofType->Prop)
% 2.56/2.75 Found x1 as proof of (P c0)
% 2.56/2.75 Found (x4 x1) as proof of False
% 2.56/2.75 Found (fun (x4:(not (P c0)))=> (x4 x1)) as proof of False
% 2.56/2.75 Found (fun (x4:(not (P c0)))=> (x4 x1)) as proof of ((not (P c0))->False)
% 2.56/2.75 Found x10:=(x1 b):(P b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found x10:=(x1 a):(P a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found x10:=(x1 b):(P b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found x10:=(x1 a):(P a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found x2:(not (P c0))
% 3.09/3.29 Instantiate: P:=cT:(fofType->Prop)
% 3.09/3.29 Found (fun (x3:(cS c0))=> x2) as proof of ((cT c0)->False)
% 3.09/3.29 Found (fun (x3:(cS c0))=> x2) as proof of ((cS c0)->((cT c0)->False))
% 3.09/3.29 Found (and_rect00 (fun (x3:(cS c0))=> x2)) as proof of False
% 3.09/3.29 Found ((and_rect0 False) (fun (x3:(cS c0))=> x2)) as proof of False
% 3.09/3.29 Found (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2)) as proof of False
% 3.09/3.29 Found (fun (x2:(not (P c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2))) as proof of False
% 3.09/3.29 Found (fun (x2:(not (P c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2))) as proof of ((not (P c0))->False)
% 3.09/3.29 Found x10:=(x1 b):(P b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found x10:=(x1 a):(P a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found x10:=(x1 b):(P b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 b)) as proof of (cS b)
% 3.09/3.29 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 b)) as proof of ((forall (Xx:fofType), (P Xx))->(cS b))
% 3.09/3.29 Found x10:=(x1 a):(P a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 a)) as proof of (cT a)
% 3.09/3.29 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 a)) as proof of ((forall (Xx:fofType), (P Xx))->(cT a))
% 3.09/3.29 Found x2:((P c0)->False)
% 3.09/3.29 Instantiate: P:=cT:(fofType->Prop)
% 3.09/3.29 Found (fun (x3:(cS c0))=> x2) as proof of ((cT c0)->False)
% 3.09/3.29 Found (fun (x3:(cS c0))=> x2) as proof of ((cS c0)->((cT c0)->False))
% 3.09/3.29 Found (and_rect00 (fun (x3:(cS c0))=> x2)) as proof of False
% 3.09/3.29 Found ((and_rect0 False) (fun (x3:(cS c0))=> x2)) as proof of False
% 3.09/3.29 Found (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2)) as proof of False
% 3.09/3.29 Found (fun (x2:((P c0)->False))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2))) as proof of False
% 3.09/3.29 Found (fun (x2:((P c0)->False))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2))) as proof of (((P c0)->False)->False)
% 3.09/3.29 Found x10:=(x1 b):(P b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (x1 b) as proof of (cS b)
% 3.09/3.29 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 b)) as proof of (cS b)
% 3.09/3.29 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 b)) as proof of ((forall (Xx:fofType), (P Xx))->(cS b))
% 3.09/3.29 Found x10:=(x1 a):(P a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (x1 a) as proof of (cT a)
% 3.09/3.29 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 a)) as proof of (cT a)
% 3.09/3.29 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 a)) as proof of ((forall (Xx:fofType), (P Xx))->(cT a))
% 3.09/3.29 Found x1:(not (P c0))
% 3.09/3.29 Instantiate: P:=cT:(fofType->Prop)
% 3.09/3.29 Found (fun (x3:(cS c0))=> x1) as proof of ((cT c0)->False)
% 3.09/3.29 Found (fun (x3:(cS c0))=> x1) as proof of ((cS c0)->((cT c0)->False))
% 3.09/3.29 Found (and_rect00 (fun (x3:(cS c0))=> x1)) as proof of False
% 3.09/3.29 Found ((and_rect0 False) (fun (x3:(cS c0))=> x1)) as proof of False
% 3.09/3.29 Found (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x2)) False) (fun (x3:(cS c0))=> x1)) as proof of False
% 3.09/3.29 Found (fun (x2:((and (cS c0)) (cT c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x2)) False) (fun (x3:(cS c0))=> x1))) as proof of False
% 3.77/3.96 Found (fun (x1:(not (P c0))) (x2:((and (cS c0)) (cT c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x2)) False) (fun (x3:(cS c0))=> x1))) as proof of (not ((and (cS c0)) (cT c0)))
% 3.77/3.96 Found (fun (x1:(not (P c0))) (x2:((and (cS c0)) (cT c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x2)) False) (fun (x3:(cS c0))=> x1))) as proof of ((not (P c0))->(not ((and (cS c0)) (cT c0))))
% 3.77/3.96 Found or_introl00:=(or_introl0 ((and (cT a)) (cS b))):(((P0 c0)->False)->((or ((P0 c0)->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found (or_introl0 ((and (cT a)) (cS b))) as proof of (((P0 c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found ((or_introl ((P0 c0)->False)) ((and (cT a)) (cS b))) as proof of (((P0 c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found ((or_introl ((P0 c0)->False)) ((and (cT a)) (cS b))) as proof of (((P0 c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found ((or_introl ((P0 c0)->False)) ((and (cT a)) (cS b))) as proof of (((P0 c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found x10:=(x1 a):(P a)
% 3.77/3.96 Found (x1 a) as proof of (cT a)
% 3.77/3.96 Found (x1 a) as proof of (cT a)
% 3.77/3.96 Found (x1 a) as proof of (cT a)
% 3.77/3.96 Found x10:=(x1 b):(P b)
% 3.77/3.96 Found (x1 b) as proof of (cS b)
% 3.77/3.96 Found (x1 b) as proof of (cS b)
% 3.77/3.96 Found (x1 b) as proof of (cS b)
% 3.77/3.96 Found or_introl00:=(or_introl0 ((and (cT a)) (cS b))):(((P0 c0)->False)->((or ((P0 c0)->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found (or_introl0 ((and (cT a)) (cS b))) as proof of (((P0 c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found ((or_introl ((P0 c0)->False)) ((and (cT a)) (cS b))) as proof of (((P0 c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found ((or_introl ((P0 c0)->False)) ((and (cT a)) (cS b))) as proof of (((P0 c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found ((or_introl ((P0 c0)->False)) ((and (cT a)) (cS b))) as proof of (((P0 c0)->False)->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 3.77/3.96 Found x2:(not (P c0))
% 3.77/3.96 Instantiate: P:=cT:(fofType->Prop)
% 3.77/3.96 Found (fun (x3:(cS c0))=> x2) as proof of ((cT c0)->False)
% 3.77/3.96 Found (fun (x3:(cS c0))=> x2) as proof of ((cS c0)->((cT c0)->False))
% 3.77/3.96 Found (and_rect00 (fun (x3:(cS c0))=> x2)) as proof of False
% 3.77/3.96 Found ((and_rect0 False) (fun (x3:(cS c0))=> x2)) as proof of False
% 3.77/3.96 Found (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2)) as proof of False
% 3.77/3.96 Found (fun (x2:(not (P c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2))) as proof of False
% 3.77/3.96 Found (fun (x2:(not (P c0)))=> (((fun (P0:Type) (x3:((cS c0)->((cT c0)->P0)))=> (((((and_rect (cS c0)) (cT c0)) P0) x3) x0)) False) (fun (x3:(cS c0))=> x2))) as proof of ((not (P c0))->False)
% 3.77/3.96 Found or_introl00:=(or_introl0 ((and (cT a)) (cS b))):((not (P0 c0))->((or (not (P0 c0))) ((and (cT a)) (cS b))))
% 3.77/3.96 Found (or_introl0 ((and (cT a)) (cS b))) as proof of ((not (P0 c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 3.77/3.96 Found ((or_introl (not (P0 c0))) ((and (cT a)) (cS b))) as proof of ((not (P0 c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 3.77/3.96 Found ((or_introl (not (P0 c0))) ((and (cT a)) (cS b))) as proof of ((not (P0 c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 3.77/3.96 Found ((or_introl (not (P0 c0))) ((and (cT a)) (cS b))) as proof of ((not (P0 c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 3.77/3.96 Found x10:=(x1 b):(P b)
% 3.77/3.96 Found (x1 b) as proof of (cS b)
% 3.77/3.96 Found (x1 b) as proof of (cS b)
% 3.77/3.96 Found (x1 b) as proof of (cS b)
% 3.77/3.96 Found x10:=(x1 a):(P a)
% 3.77/3.96 Found (x1 a) as proof of (cT a)
% 3.77/3.96 Found (x1 a) as proof of (cT a)
% 3.77/3.96 Found (x1 a) as proof of (cT a)
% 3.77/3.96 Found or_introl00:=(or_introl0 ((and (cT a)) (cS b))):((not (P0 c0))->((or (not (P0 c0))) ((and (cT a)) (cS b))))
% 3.77/3.96 Found (or_introl0 ((and (cT a)) (cS b))) as proof of ((not (P0 c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 5.44/5.62 Found ((or_introl (not (P0 c0))) ((and (cT a)) (cS b))) as proof of ((not (P0 c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 5.44/5.62 Found ((or_introl (not (P0 c0))) ((and (cT a)) (cS b))) as proof of ((not (P0 c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 5.44/5.62 Found ((or_introl (not (P0 c0))) ((and (cT a)) (cS b))) as proof of ((not (P0 c0))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 5.44/5.62 Found x10:=(x1 a):(P a)
% 5.44/5.62 Found (x1 a) as proof of (cT a)
% 5.44/5.62 Found (x1 a) as proof of (cT a)
% 5.44/5.62 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 a)) as proof of (cT a)
% 5.44/5.62 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 a)) as proof of ((forall (Xx:fofType), (P Xx))->(cT a))
% 5.44/5.62 Found x10:=(x1 b):(P b)
% 5.44/5.62 Found (x1 b) as proof of (cS b)
% 5.44/5.62 Found (x1 b) as proof of (cS b)
% 5.44/5.62 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 b)) as proof of (cS b)
% 5.44/5.62 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 b)) as proof of ((forall (Xx:fofType), (P Xx))->(cS b))
% 5.44/5.62 Found x10:=(x1 a):(P a)
% 5.44/5.62 Found (x1 a) as proof of (cT a)
% 5.44/5.62 Found (x1 a) as proof of (cT a)
% 5.44/5.62 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 a)) as proof of (cT a)
% 5.44/5.62 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 a)) as proof of ((forall (Xx:fofType), (P Xx))->(cT a))
% 5.44/5.62 Found x10:=(x1 b):(P b)
% 5.44/5.62 Found (x1 b) as proof of (cS b)
% 5.44/5.62 Found (x1 b) as proof of (cS b)
% 5.44/5.62 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 b)) as proof of (cS b)
% 5.44/5.62 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (x1 b)) as proof of ((forall (Xx:fofType), (P Xx))->(cS b))
% 5.44/5.62 Found or_intror00:=(or_intror0 ((P0 c0)->False)):(((P0 c0)->False)->((or ((and (cT a)) (cS b))) ((P0 c0)->False)))
% 5.44/5.62 Found (or_intror0 ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found or_intror00:=(or_intror0 ((P0 c0)->False)):(((P0 c0)->False)->((or ((and (cT a)) (cS b))) ((P0 c0)->False)))
% 5.44/5.62 Found (or_intror0 ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found or_intror00:=(or_intror0 ((P0 c0)->False)):(((P0 c0)->False)->((or ((and (cT a)) (cS b))) ((P0 c0)->False)))
% 5.44/5.62 Found (or_intror0 ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found or_intror00:=(or_intror0 ((P0 c0)->False)):(((P0 c0)->False)->((or ((and (cT a)) (cS b))) ((P0 c0)->False)))
% 5.44/5.62 Found (or_intror0 ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 5.44/5.62 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) ((P0 c0)->False)) as proof of (((P0 c0)->False)->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 7.14/7.29 Found or_intror00:=(or_intror0 (not (P0 c0))):((not (P0 c0))->((or ((and (cT a)) (cS b))) (not (P0 c0))))
% 7.14/7.29 Found (or_intror0 (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found or_intror00:=(or_intror0 (not (P0 c0))):((not (P0 c0))->((or ((and (cT a)) (cS b))) (not (P0 c0))))
% 7.14/7.29 Found (or_intror0 (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found or_intror00:=(or_intror0 (not (P0 c0))):((not (P0 c0))->((or ((and (cT a)) (cS b))) (not (P0 c0))))
% 7.14/7.29 Found (or_intror0 (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found or_intror00:=(or_intror0 (not (P0 c0))):((not (P0 c0))->((or ((and (cT a)) (cS b))) (not (P0 c0))))
% 7.14/7.29 Found (or_intror0 (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found ((or_intror ((and (cT a)) (cS b))) (not (P0 c0))) as proof of ((not (P0 c0))->((or ((and (cT a)) (cS b))) (not ((and (cS c0)) (cT c0)))))
% 7.14/7.29 Found x2:(cS Xx)
% 7.14/7.29 Instantiate: Xx:=b:fofType
% 7.14/7.29 Found x2 as proof of (cS b)
% 7.14/7.29 Found x3:(cT Xx)
% 7.14/7.29 Instantiate: Xx:=a:fofType
% 7.14/7.29 Found x3 as proof of (cT a)
% 7.14/7.29 Found x10:=(x1 b):(P b)
% 7.14/7.29 Found (x1 b) as proof of (cS b)
% 7.14/7.29 Found (x1 b) as proof of (cS b)
% 7.14/7.29 Found (x1 b) as proof of (cS b)
% 7.14/7.29 Found x30:=(x3 a):(P0 a)
% 7.14/7.29 Found (x3 a) as proof of (cT a)
% 7.14/7.29 Found (x3 a) as proof of (cT a)
% 7.14/7.29 Found (x3 a) as proof of (cT a)
% 7.14/7.29 Found ((conj00 (x3 a)) (x1 b)) as proof of ((and (cT a)) (cS b))
% 7.14/7.29 Found (((conj0 (cS b)) (x3 a)) (x1 b)) as proof of ((and (cT a)) (cS b))
% 7.14/7.29 Found ((((conj (cT a)) (cS b)) (x3 a)) (x1 b)) as proof of ((and (cT a)) (cS b))
% 7.14/7.29 Found ((((conj (cT a)) (cS b)) (x3 a)) (x1 b)) as proof of ((and (cT a)) (cS b))
% 7.14/7.29 Found (or_intror00 ((((conj (cT a)) (cS b)) (x3 a)) (x1 b))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 7.14/7.29 Found ((or_intror0 ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (x3 a)) (x1 b))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 7.14/7.29 Found (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (x3 a)) (x1 b))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 9.53/9.72 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (x3 a)) (x1 b)))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 9.53/9.72 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (x3 a)) (x1 b)))) as proof of ((forall (Xx:fofType), (P0 Xx))->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 9.53/9.72 Found x10:=(x1 b):(P b)
% 9.53/9.72 Found (x1 b) as proof of (cS b)
% 9.53/9.72 Found (x1 b) as proof of (cS b)
% 9.53/9.72 Found (x1 b) as proof of (cS b)
% 9.53/9.72 Found x10:=(x1 a):(P a)
% 9.53/9.72 Found (x1 a) as proof of (cT a)
% 9.53/9.72 Found (x1 a) as proof of (cT a)
% 9.53/9.72 Found (x1 a) as proof of (cT a)
% 9.53/9.72 Found x30:=(x3 b):(P0 b)
% 9.53/9.72 Found (x3 b) as proof of (cS b)
% 9.53/9.72 Found (x3 b) as proof of (cS b)
% 9.53/9.72 Found (x3 b) as proof of (cS b)
% 9.53/9.72 Found x30:=(x3 a):(P0 a)
% 9.53/9.72 Found (x3 a) as proof of (cT a)
% 9.53/9.72 Found (x3 a) as proof of (cT a)
% 9.53/9.72 Found (x3 a) as proof of (cT a)
% 9.53/9.72 Found x3:(cT Xx)
% 9.53/9.72 Instantiate: Xx:=a:fofType
% 9.53/9.72 Found x3 as proof of (cT a)
% 9.53/9.72 Found x2:(cS Xx)
% 9.53/9.72 Instantiate: Xx:=b:fofType
% 9.53/9.72 Found x2 as proof of (cS b)
% 9.53/9.72 Found x3:(cT Xx)
% 9.53/9.72 Instantiate: Xx:=a:fofType
% 9.53/9.72 Found x3 as proof of (cT a)
% 9.53/9.72 Found x2:(cS Xx)
% 9.53/9.72 Instantiate: Xx:=b:fofType
% 9.53/9.72 Found x2 as proof of (cS b)
% 9.53/9.72 Found x10:=(x1 b):(P b)
% 9.53/9.72 Found (x1 b) as proof of (cS b)
% 9.53/9.72 Found (x1 b) as proof of (cS b)
% 9.53/9.72 Found (x1 b) as proof of (cS b)
% 9.53/9.72 Found x10:=(x1 a):(P a)
% 9.53/9.72 Found (x1 a) as proof of (cT a)
% 9.53/9.72 Found (x1 a) as proof of (cT a)
% 9.53/9.72 Found (x1 a) as proof of (cT a)
% 9.53/9.72 Found x30:=(x3 a):(P0 a)
% 9.53/9.72 Found (x3 a) as proof of (cT a)
% 9.53/9.72 Found (x3 a) as proof of (cT a)
% 9.53/9.72 Found (x3 a) as proof of (cT a)
% 9.53/9.72 Found ((conj00 (x3 a)) (x1 b)) as proof of ((and (cT a)) (cS b))
% 9.53/9.72 Found (((conj0 (cS b)) (x3 a)) (x1 b)) as proof of ((and (cT a)) (cS b))
% 9.53/9.72 Found ((((conj (cT a)) (cS b)) (x3 a)) (x1 b)) as proof of ((and (cT a)) (cS b))
% 9.53/9.72 Found ((((conj (cT a)) (cS b)) (x3 a)) (x1 b)) as proof of ((and (cT a)) (cS b))
% 9.53/9.72 Found (or_intror00 ((((conj (cT a)) (cS b)) (x3 a)) (x1 b))) as proof of ((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b)))
% 9.53/9.72 Found ((or_intror0 ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (x3 a)) (x1 b))) as proof of ((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b)))
% 9.53/9.72 Found (((or_intror (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (x3 a)) (x1 b))) as proof of ((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b)))
% 9.53/9.72 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (((or_intror (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (x3 a)) (x1 b)))) as proof of ((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b)))
% 9.53/9.72 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (((or_intror (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (x3 a)) (x1 b)))) as proof of ((forall (Xx:fofType), (P0 Xx))->((or (not ((and (cS c0)) (cT c0)))) ((and (cT a)) (cS b))))
% 9.53/9.72 Found x20:=(x2 c0):(P c0)
% 9.53/9.72 Found (x2 c0) as proof of (P0 c0)
% 9.53/9.72 Found (x2 c0) as proof of (P0 c0)
% 9.53/9.72 Found (x2 c0) as proof of (P0 c0)
% 9.53/9.72 Found (x4 (x2 c0)) as proof of False
% 9.53/9.72 Found (fun (x4:((P0 c0)->False))=> (x4 (x2 c0))) as proof of False
% 9.53/9.72 Found (fun (x4:((P0 c0)->False))=> (x4 (x2 c0))) as proof of (((P0 c0)->False)->False)
% 9.53/9.72 Found x10:=(x1 a):(P a)
% 9.53/9.72 Found (x1 a) as proof of (cT a)
% 9.53/9.72 Found (x1 a) as proof of (cT a)
% 9.53/9.72 Found (x1 a) as proof of (cT a)
% 9.53/9.72 Found x10:=(x1 b):(P b)
% 9.53/9.72 Found (x1 b) as proof of (cS b)
% 9.53/9.72 Found (x1 b) as proof of (cS b)
% 9.53/9.72 Found (x1 b) as proof of (cS b)
% 9.53/9.72 Found x30:=(x3 b):(P0 b)
% 9.53/9.72 Found (x3 b) as proof of (cS b)
% 9.53/9.72 Found (x3 b) as proof of (cS b)
% 9.53/9.72 Found (x3 b) as proof of (cS b)
% 9.53/9.72 Found x30:=(x3 a):(P0 a)
% 9.53/9.72 Found (x3 a) as proof of (cT a)
% 9.53/9.72 Found (x3 a) as proof of (cT a)
% 9.53/9.72 Found (x3 a) as proof of (cT a)
% 9.53/9.72 Found x3:(cT Xx)
% 9.53/9.72 Instantiate: Xx:=a:fofType
% 9.53/9.72 Found x3 as proof of (cT a)
% 9.53/9.72 Found x2:(cS Xx)
% 9.53/9.72 Instantiate: Xx:=b:fofType
% 9.53/9.72 Found x2 as proof of (cS b)
% 9.53/9.72 Found x30:=(x3 b):(P0 b)
% 9.53/9.72 Found (x3 b) as proof of (cS b)
% 9.53/9.72 Found (x3 b) as proof of (cS b)
% 9.53/9.72 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (x3 b)) as proof of (cS b)
% 9.53/9.72 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (x3 b)) as proof of ((forall (Xx:fofType), (P0 Xx))->(cS b))
% 11.92/12.11 Found x10:=(x1 c0):(P c0)
% 11.92/12.11 Found (x1 c0) as proof of (P0 c0)
% 11.92/12.11 Found (x1 c0) as proof of (P0 c0)
% 11.92/12.11 Found (x1 c0) as proof of (P0 c0)
% 11.92/12.11 Found (x4 (x1 c0)) as proof of False
% 11.92/12.11 Found (fun (x4:(not (P0 c0)))=> (x4 (x1 c0))) as proof of False
% 11.92/12.11 Found (fun (x4:(not (P0 c0)))=> (x4 (x1 c0))) as proof of ((not (P0 c0))->False)
% 11.92/12.11 Found x2:(cS Xx)
% 11.92/12.11 Instantiate: Xx:=b:fofType
% 11.92/12.11 Found x2 as proof of (cS b)
% 11.92/12.11 Found x3:(cT Xx)
% 11.92/12.11 Instantiate: Xx:=a:fofType
% 11.92/12.11 Found x3 as proof of (cT a)
% 11.92/12.11 Found x20:=(x2 c0):(P c0)
% 11.92/12.11 Found (x2 c0) as proof of (P0 c0)
% 11.92/12.11 Found (x2 c0) as proof of (P0 c0)
% 11.92/12.11 Found (x2 c0) as proof of (P0 c0)
% 11.92/12.11 Found (x4 (x2 c0)) as proof of False
% 11.92/12.11 Found (fun (x4:(not (P0 c0)))=> (x4 (x2 c0))) as proof of False
% 11.92/12.11 Found (fun (x4:(not (P0 c0)))=> (x4 (x2 c0))) as proof of ((not (P0 c0))->False)
% 11.92/12.11 Found x10:=(x1 c0):(P c0)
% 11.92/12.11 Found (x1 c0) as proof of (P0 c0)
% 11.92/12.11 Found (x1 c0) as proof of (P0 c0)
% 11.92/12.11 Found (x1 c0) as proof of (P0 c0)
% 11.92/12.11 Found (x3 (x1 c0)) as proof of False
% 11.92/12.11 Found (fun (x4:((and (cS c0)) (cT c0)))=> (x3 (x1 c0))) as proof of False
% 11.92/12.11 Found (fun (x3:(not (P0 c0))) (x4:((and (cS c0)) (cT c0)))=> (x3 (x1 c0))) as proof of (not ((and (cS c0)) (cT c0)))
% 11.92/12.11 Found (fun (x3:(not (P0 c0))) (x4:((and (cS c0)) (cT c0)))=> (x3 (x1 c0))) as proof of ((not (P0 c0))->(not ((and (cS c0)) (cT c0))))
% 11.92/12.11 Found x30:=(x3 b):(P0 b)
% 11.92/12.11 Found (x3 b) as proof of (cS b)
% 11.92/12.11 Found (x3 b) as proof of (cS b)
% 11.92/12.11 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (x3 b)) as proof of (cS b)
% 11.92/12.11 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (x3 b)) as proof of ((forall (Xx:fofType), (P0 Xx))->(cS b))
% 11.92/12.11 Found x10:=(x1 a):(P a)
% 11.92/12.11 Found (x1 a) as proof of (cT a)
% 11.92/12.11 Found (x1 a) as proof of (cT a)
% 11.92/12.11 Found (x1 a) as proof of (cT a)
% 11.92/12.11 Found x10:=(x1 b):(P b)
% 11.92/12.11 Found (x1 b) as proof of (cS b)
% 11.92/12.11 Found (x1 b) as proof of (cS b)
% 11.92/12.11 Found (x1 b) as proof of (cS b)
% 11.92/12.11 Found x30:=(x3 b):(P0 b)
% 11.92/12.11 Found (x3 b) as proof of (cS b)
% 11.92/12.11 Found (x3 b) as proof of (cS b)
% 11.92/12.11 Found (x3 b) as proof of (cS b)
% 11.92/12.11 Found x30:=(x3 a):(P0 a)
% 11.92/12.11 Found (x3 a) as proof of (cT a)
% 11.92/12.11 Found (x3 a) as proof of (cT a)
% 11.92/12.11 Found (x3 a) as proof of (cT a)
% 11.92/12.11 Found x4:((P0 c0)->False)
% 11.92/12.11 Instantiate: P0:=cT:(fofType->Prop)
% 11.92/12.11 Found (fun (x5:(cS c0))=> x4) as proof of ((cT c0)->False)
% 11.92/12.11 Found (fun (x5:(cS c0))=> x4) as proof of ((cS c0)->((cT c0)->False))
% 11.92/12.11 Found (and_rect00 (fun (x5:(cS c0))=> x4)) as proof of False
% 11.92/12.11 Found ((and_rect0 False) (fun (x5:(cS c0))=> x4)) as proof of False
% 11.92/12.11 Found (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x2)) False) (fun (x5:(cS c0))=> x4)) as proof of False
% 11.92/12.11 Found (fun (x4:((P0 c0)->False))=> (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x2)) False) (fun (x5:(cS c0))=> x4))) as proof of False
% 11.92/12.11 Found (fun (x4:((P0 c0)->False))=> (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x2)) False) (fun (x5:(cS c0))=> x4))) as proof of (((P0 c0)->False)->False)
% 11.92/12.11 Found x2:(cS Xx)
% 11.92/12.11 Instantiate: Xx:=b:fofType
% 11.92/12.11 Found x2 as proof of (cS b)
% 11.92/12.11 Found x3:(cT Xx)
% 11.92/12.11 Instantiate: Xx:=a:fofType
% 11.92/12.11 Found x3 as proof of (cT a)
% 11.92/12.11 Found x10:=(x1 a):(P a)
% 11.92/12.11 Found (x1 a) as proof of (cT a)
% 11.92/12.11 Found (x1 a) as proof of (cT a)
% 11.92/12.11 Found (x1 a) as proof of (cT a)
% 11.92/12.11 Found x10:=(x1 b):(P b)
% 11.92/12.11 Found (x1 b) as proof of (cS b)
% 11.92/12.11 Found (x1 b) as proof of (cS b)
% 11.92/12.11 Found (x1 b) as proof of (cS b)
% 11.92/12.11 Found x30:=(x3 b):(P0 b)
% 11.92/12.11 Found (x3 b) as proof of (cS b)
% 11.92/12.11 Found (x3 b) as proof of (cS b)
% 11.92/12.11 Found (x3 b) as proof of (cS b)
% 11.92/12.11 Found ((conj00 (x1 a)) (x3 b)) as proof of ((and (cT a)) (cS b))
% 11.92/12.11 Found (((conj0 (cS b)) (x1 a)) (x3 b)) as proof of ((and (cT a)) (cS b))
% 11.92/12.11 Found ((((conj (cT a)) (cS b)) (x1 a)) (x3 b)) as proof of ((and (cT a)) (cS b))
% 11.92/12.11 Found ((((conj (cT a)) (cS b)) (x1 a)) (x3 b)) as proof of ((and (cT a)) (cS b))
% 11.92/12.11 Found (or_introl00 ((((conj (cT a)) (cS b)) (x1 a)) (x3 b))) as proof of ((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False))
% 11.92/12.11 Found ((or_introl0 (((and (cS c0)) (cT c0))->False)) ((((conj (cT a)) (cS b)) (x1 a)) (x3 b))) as proof of ((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False))
% 11.92/12.11 Found (((or_introl ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)) ((((conj (cT a)) (cS b)) (x1 a)) (x3 b))) as proof of ((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False))
% 12.92/13.07 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (((or_introl ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)) ((((conj (cT a)) (cS b)) (x1 a)) (x3 b)))) as proof of ((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False))
% 12.92/13.07 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (((or_introl ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)) ((((conj (cT a)) (cS b)) (x1 a)) (x3 b)))) as proof of ((forall (Xx:fofType), (P0 Xx))->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 12.92/13.07 Found x4:((P0 c0)->False)
% 12.92/13.07 Instantiate: P0:=cT:(fofType->Prop)
% 12.92/13.07 Found (fun (x5:(cS c0))=> x4) as proof of ((cT c0)->False)
% 12.92/13.07 Found (fun (x5:(cS c0))=> x4) as proof of ((cS c0)->((cT c0)->False))
% 12.92/13.07 Found (and_rect00 (fun (x5:(cS c0))=> x4)) as proof of False
% 12.92/13.07 Found ((and_rect0 False) (fun (x5:(cS c0))=> x4)) as proof of False
% 12.92/13.07 Found (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x2)) False) (fun (x5:(cS c0))=> x4)) as proof of False
% 12.92/13.07 Found (fun (x4:((P0 c0)->False))=> (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x2)) False) (fun (x5:(cS c0))=> x4))) as proof of False
% 12.92/13.07 Found (fun (x4:((P0 c0)->False))=> (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x2)) False) (fun (x5:(cS c0))=> x4))) as proof of (((P0 c0)->False)->False)
% 12.92/13.07 Found x10:=(x1 a):(P a)
% 12.92/13.07 Found (x1 a) as proof of (cT a)
% 12.92/13.07 Found (x1 a) as proof of (cT a)
% 12.92/13.07 Found (x1 a) as proof of (cT a)
% 12.92/13.07 Found x10:=(x1 b):(P b)
% 12.92/13.07 Found (x1 b) as proof of (cS b)
% 12.92/13.07 Found (x1 b) as proof of (cS b)
% 12.92/13.07 Found (x1 b) as proof of (cS b)
% 12.92/13.07 Found x30:=(x3 b):(P0 b)
% 12.92/13.07 Found (x3 b) as proof of (cS b)
% 12.92/13.07 Found (x3 b) as proof of (cS b)
% 12.92/13.07 Found (x3 b) as proof of (cS b)
% 12.92/13.07 Found x30:=(x3 a):(P0 a)
% 12.92/13.07 Found (x3 a) as proof of (cT a)
% 12.92/13.07 Found (x3 a) as proof of (cT a)
% 12.92/13.07 Found (x3 a) as proof of (cT a)
% 12.92/13.07 Found x3:(cT Xx)
% 12.92/13.07 Instantiate: Xx:=a:fofType
% 12.92/13.07 Found x3 as proof of (cT a)
% 12.92/13.07 Found x2:(cS Xx)
% 12.92/13.07 Instantiate: Xx:=b:fofType
% 12.92/13.07 Found x2 as proof of (cS b)
% 12.92/13.07 Found x2:(cS Xx)
% 12.92/13.07 Instantiate: Xx:=b:fofType
% 12.92/13.07 Found x2 as proof of (cS b)
% 12.92/13.07 Found x3:(cT Xx)
% 12.92/13.07 Instantiate: Xx:=a:fofType
% 12.92/13.07 Found x3 as proof of (cT a)
% 12.92/13.07 Found x30:=(x3 b):(P0 b)
% 12.92/13.07 Found (x3 b) as proof of (cS b)
% 12.92/13.07 Found (x3 b) as proof of (cS b)
% 12.92/13.07 Found (x3 b) as proof of (cS b)
% 12.92/13.07 Found x10:=(x1 a):(P a)
% 12.92/13.07 Found (x1 a) as proof of (cT a)
% 12.92/13.07 Found (x1 a) as proof of (cT a)
% 12.92/13.07 Found (x1 a) as proof of (cT a)
% 12.92/13.07 Found ((conj00 (x1 a)) (x3 b)) as proof of ((and (cT a)) (cS b))
% 12.92/13.07 Found (((conj0 (cS b)) (x1 a)) (x3 b)) as proof of ((and (cT a)) (cS b))
% 12.92/13.07 Found ((((conj (cT a)) (cS b)) (x1 a)) (x3 b)) as proof of ((and (cT a)) (cS b))
% 12.92/13.07 Found ((((conj (cT a)) (cS b)) (x1 a)) (x3 b)) as proof of ((and (cT a)) (cS b))
% 12.92/13.07 Found (or_introl00 ((((conj (cT a)) (cS b)) (x1 a)) (x3 b))) as proof of ((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False))
% 12.92/13.07 Found ((or_introl0 (((and (cS c0)) (cT c0))->False)) ((((conj (cT a)) (cS b)) (x1 a)) (x3 b))) as proof of ((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False))
% 12.92/13.07 Found (((or_introl ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)) ((((conj (cT a)) (cS b)) (x1 a)) (x3 b))) as proof of ((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False))
% 12.92/13.07 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (((or_introl ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)) ((((conj (cT a)) (cS b)) (x1 a)) (x3 b)))) as proof of ((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False))
% 12.92/13.07 Found (fun (x3:(forall (Xx:fofType), (P0 Xx)))=> (((or_introl ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)) ((((conj (cT a)) (cS b)) (x1 a)) (x3 b)))) as proof of ((forall (Xx:fofType), (P0 Xx))->((or ((and (cT a)) (cS b))) (((and (cS c0)) (cT c0))->False)))
% 12.92/13.07 Found x3:(not (P0 c0))
% 12.92/13.07 Instantiate: P0:=cT:(fofType->Prop)
% 12.92/13.07 Found (fun (x5:(cS c0))=> x3) as proof of ((cT c0)->False)
% 12.92/13.07 Found (fun (x5:(cS c0))=> x3) as proof of ((cS c0)->((cT c0)->False))
% 12.92/13.07 Found (and_rect00 (fun (x5:(cS c0))=> x3)) as proof of False
% 12.92/13.07 Found ((and_rect0 False) (fun (x5:(cS c0))=> x3)) as proof of False
% 12.92/13.07 Found (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x4)) False) (fun (x5:(cS c0))=> x3)) as proof of False
% 13.08/13.31 Found (fun (x4:((and (cS c0)) (cT c0)))=> (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x4)) False) (fun (x5:(cS c0))=> x3))) as proof of False
% 13.08/13.31 Found (fun (x3:(not (P0 c0))) (x4:((and (cS c0)) (cT c0)))=> (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x4)) False) (fun (x5:(cS c0))=> x3))) as proof of (not ((and (cS c0)) (cT c0)))
% 13.08/13.31 Found (fun (x3:(not (P0 c0))) (x4:((and (cS c0)) (cT c0)))=> (((fun (P1:Type) (x5:((cS c0)->((cT c0)->P1)))=> (((((and_rect (cS c0)) (cT c0)) P1) x5) x4)) False) (fun (x5:(cS c0))=> x3))) as proof of ((not (P0 c0))->(not ((and (cS c0)) (cT c0))))
% 13.08/13.31 Found x2:(cS Xx)
% 13.08/13.31 Instantiate: Xx:=b:fofType
% 13.08/13.31 Found x2 as proof of (cS b)
% 13.08/13.31 Found x3:(cT Xx)
% 13.08/13.31 Instantiate: Xx:=a:fofType
% 13.08/13.31 Found x3 as proof of (cT a)
% 13.08/13.31 Found x3:(cT Xx)
% 13.08/13.31 Instantiate: Xx:=a:fofType
% 13.08/13.31 Found (fun (x3:(cT Xx))=> x3) as proof of (cT a)
% 13.08/13.31 Found (fun (x2:(cS Xx)) (x3:(cT Xx))=> x3) as proof of ((cT Xx)->(cT a))
% 13.08/13.31 Found (fun (x2:(cS Xx)) (x3:(cT Xx))=> x3) as proof of ((cS Xx)->((cT Xx)->(cT a)))
% 13.08/13.31 Found (and_rect00 (fun (x2:(cS Xx)) (x3:(cT Xx))=> x3)) as proof of (cT a)
% 13.08/13.31 Found ((and_rect0 (cT a)) (fun (x2:(cS Xx)) (x3:(cT Xx))=> x3)) as proof of (cT a)
% 13.08/13.31 Found (((fun (P0:Type) (x2:((cS Xx)->((cT Xx)->P0)))=> (((((and_rect (cS Xx)) (cT Xx)) P0) x2) x10)) (cT a)) (fun (x2:(cS Xx)) (x3:(cT Xx))=> x3)) as proof of (cT a)
% 13.08/13.31 Found (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3)) as proof of (cT a)
% 13.08/13.31 Found (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3)) as proof of (cT a)
% 13.08/13.31 Found x2:(cS Xx)
% 13.08/13.31 Instantiate: Xx:=b:fofType
% 13.08/13.31 Found (fun (x3:(cT Xx))=> x2) as proof of (cS b)
% 13.08/13.31 Found (fun (x2:(cS Xx)) (x3:(cT Xx))=> x2) as proof of ((cT Xx)->(cS b))
% 13.08/13.31 Found (fun (x2:(cS Xx)) (x3:(cT Xx))=> x2) as proof of ((cS Xx)->((cT Xx)->(cS b)))
% 13.08/13.31 Found (and_rect00 (fun (x2:(cS Xx)) (x3:(cT Xx))=> x2)) as proof of (cS b)
% 13.08/13.31 Found ((and_rect0 (cS b)) (fun (x2:(cS Xx)) (x3:(cT Xx))=> x2)) as proof of (cS b)
% 13.08/13.31 Found (((fun (P0:Type) (x2:((cS Xx)->((cT Xx)->P0)))=> (((((and_rect (cS Xx)) (cT Xx)) P0) x2) x10)) (cS b)) (fun (x2:(cS Xx)) (x3:(cT Xx))=> x2)) as proof of (cS b)
% 13.08/13.31 Found (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)) as proof of (cS b)
% 13.08/13.31 Found (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)) as proof of (cS b)
% 13.08/13.31 Found ((conj00 (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2))) as proof of ((and (cT a)) (cS b))
% 13.08/13.31 Found (((conj0 (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2))) as proof of ((and (cT a)) (cS b))
% 13.08/13.31 Found ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2))) as proof of ((and (cT a)) (cS b))
% 13.08/13.31 Found ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2))) as proof of ((and (cT a)) (cS b))
% 13.16/13.35 Found (or_intror00 ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 13.16/13.35 Found ((or_intror0 ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 13.16/13.35 Found (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 13.16/13.35 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2))))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 13.16/13.35 Found (fun (x1:(forall (Xx:fofType), (P Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2))))) as proof of ((forall (Xx:fofType), (P Xx))->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 13.16/13.35 Found ((or_ind00 ((or_introl ((P c0)->False)) ((and (cT a)) (cS b)))) (fun (x1:(forall (Xx:fofType), (P Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)))))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 13.16/13.35 Found (((or_ind0 ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))) ((or_introl ((P c0)->False)) ((and (cT a)) (cS b)))) (fun (x1:(forall (Xx:fofType), (P Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)))))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 13.16/13.35 Found ((((fun (P0:Prop) (x1:(((P c0)->False)->P0)) (x2:((forall (Xx:fofType), (P Xx))->P0))=> ((((((or_ind ((P c0)->False)) (forall (Xx:fofType), (P Xx))) P0) x1) x2) x0)) ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))) ((or_introl ((P c0)->False)) ((and (cT a)) (cS b)))) (fun (x1:(forall (Xx:fofType), (P Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)))))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 13.16/13.35 Found ((((fun (P0:Prop) (x1:((((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)->P0)) (x2:((forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))->P0))=> ((((((or_ind (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) (forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))) P0) x1) x2) (x (fun (x2:fofType)=> ((and (cS x2)) (cT x2)))))) ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))) ((or_introl (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) ((and (cT a)) (cS b)))) (fun (x1:(forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)))))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 13.16/13.35 Found (fun (x:(forall (P:(fofType->Prop)), ((or ((P c0)->False)) (forall (Xx:fofType), (P Xx)))))=> ((((fun (P0:Prop) (x1:((((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)->P0)) (x2:((forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))->P0))=> ((((((or_ind (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) (forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))) P0) x1) x2) (x (fun (x2:fofType)=> ((and (cS x2)) (cT x2)))))) ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))) ((or_introl (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) ((and (cT a)) (cS b)))) (fun (x1:(forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2))))))) as proof of ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))
% 13.16/13.35 Found (fun (x:(forall (P:(fofType->Prop)), ((or ((P c0)->False)) (forall (Xx:fofType), (P Xx)))))=> ((((fun (P0:Prop) (x1:((((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)->P0)) (x2:((forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))->P0))=> ((((((or_ind (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) (forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))) P0) x1) x2) (x (fun (x2:fofType)=> ((and (cS x2)) (cT x2)))))) ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))) ((or_introl (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) ((and (cT a)) (cS b)))) (fun (x1:(forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2))))))) as proof of ((forall (P:(fofType->Prop)), ((or ((P c0)->False)) (forall (Xx:fofType), (P Xx))))->((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))))
% 13.16/13.35 Got proof (fun (x:(forall (P:(fofType->Prop)), ((or ((P c0)->False)) (forall (Xx:fofType), (P Xx)))))=> ((((fun (P0:Prop) (x1:((((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)->P0)) (x2:((forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))->P0))=> ((((((or_ind (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) (forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))) P0) x1) x2) (x (fun (x2:fofType)=> ((and (cS x2)) (cT x2)))))) ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))) ((or_introl (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) ((and (cT a)) (cS b)))) (fun (x1:(forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)))))))
% 13.37/13.54 Time elapsed = 12.742740s
% 13.37/13.54 node=4628 cost=1387.000000 depth=22
% 13.37/13.54 ::::::::::::::::::::::
% 13.37/13.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.37/13.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.37/13.54 (fun (x:(forall (P:(fofType->Prop)), ((or ((P c0)->False)) (forall (Xx:fofType), (P Xx)))))=> ((((fun (P0:Prop) (x1:((((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)->P0)) (x2:((forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))->P0))=> ((((((or_ind (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) (forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx))) P0) x1) x2) (x (fun (x2:fofType)=> ((and (cS x2)) (cT x2)))))) ((or (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b)))) ((or_introl (((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) c0)->False)) ((and (cT a)) (cS b)))) (fun (x1:(forall (Xx:fofType), ((fun (x2:fofType)=> ((and (cS x2)) (cT x2))) Xx)))=> (((or_intror (((and (cS c0)) (cT c0))->False)) ((and (cT a)) (cS b))) ((((conj (cT a)) (cS b)) (((fun (P0:Type) (x2:((cS a)->((cT a)->P0)))=> (((((and_rect (cS a)) (cT a)) P0) x2) (x1 a))) (cT a)) (fun (x2:(cS a)) (x3:(cT a))=> x3))) (((fun (P0:Type) (x2:((cS b)->((cT b)->P0)))=> (((((and_rect (cS b)) (cT b)) P0) x2) (x1 b))) (cS b)) (fun (x2:(cS b)) (x3:(cT b))=> x2)))))))
% 13.37/13.54 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------