TSTP Solution File: SYO261^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO261^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n028.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 00:51:01 EDT 2022
% Result : Theorem 0.61s 0.79s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO261^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % RAMPerCPU : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % DateTime : Fri Mar 11 22:49:48 EST 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.14/0.34 Python 2.7.5
% 0.61/0.78 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.61/0.78 FOF formula (<kernel.Constant object at 0x2ab4b4f4b8c0>, <kernel.Constant object at 0x2ab4b4f4bab8>) of role type named n
% 0.61/0.78 Using role type
% 0.61/0.78 Declaring n:fofType
% 0.61/0.78 FOF formula (<kernel.Constant object at 0x12ee3f8>, <kernel.DependentProduct object at 0x2ab4b4f4bea8>) of role type named cP
% 0.61/0.78 Using role type
% 0.61/0.78 Declaring cP:(fofType->Prop)
% 0.61/0.78 FOF formula (<kernel.Constant object at 0x2ab4b4f4b8c0>, <kernel.DependentProduct object at 0x2ab4b4f69518>) of role type named c1_plus
% 0.61/0.78 Using role type
% 0.61/0.78 Declaring c1_plus:(fofType->fofType)
% 0.61/0.78 FOF formula (<kernel.Constant object at 0x2ab4b4f4bea8>, <kernel.Single object at 0x2ab4b4f4b5a8>) of role type named cO
% 0.61/0.78 Using role type
% 0.61/0.78 Declaring cO:fofType
% 0.61/0.78 FOF formula (((and ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))->(cP n)) of role conjecture named cBLEDSOE_FENG_SV_I1
% 0.61/0.78 Conjecture to prove = (((and ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))->(cP n)):Prop
% 0.61/0.78 We need to prove ['(((and ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))->(cP n))']
% 0.61/0.78 Parameter fofType:Type.
% 0.61/0.78 Parameter n:fofType.
% 0.61/0.78 Parameter cP:(fofType->Prop).
% 0.61/0.78 Parameter c1_plus:(fofType->fofType).
% 0.61/0.78 Parameter cO:fofType.
% 0.61/0.78 Trying to prove (((and ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))->(cP n))
% 0.61/0.78 Found conj0000:=(conj000 x1):((and (cP cO)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))
% 0.61/0.78 Found (conj000 x1) as proof of ((and (cP cO)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))
% 0.61/0.78 Found ((conj00 (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1) as proof of ((and (cP cO)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))
% 0.61/0.78 Found (((fun (B:Prop)=> ((conj0 B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1) as proof of ((and (cP cO)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))
% 0.61/0.78 Found (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1) as proof of ((and (cP cO)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))
% 0.61/0.78 Found (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1) as proof of ((and (cP cO)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))
% 0.61/0.78 Found (x20 (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)) as proof of (cP n)
% 0.61/0.78 Found ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)) as proof of (cP n)
% 0.61/0.78 Found (fun (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1))) as proof of (cP n)
% 0.61/0.78 Found (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1))) as proof of ((cP cO)->(cP n))
% 0.61/0.78 Found (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1))) as proof of ((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->(cP n)))
% 0.61/0.78 Found (and_rect10 (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)))) as proof of (cP n)
% 0.61/0.78 Found ((and_rect1 (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)))) as proof of (cP n)
% 0.61/0.78 Found (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)))) as proof of (cP n)
% 0.61/0.78 Found (fun (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1))))) as proof of (cP n)
% 0.61/0.78 Found (fun (x0:((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1))))) as proof of ((forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))->(cP n))
% 0.61/0.78 Found (fun (x0:((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1))))) as proof of (((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))->((forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))->(cP n)))
% 0.61/0.78 Found (and_rect00 (fun (x0:((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)))))) as proof of (cP n)
% 0.61/0.78 Found ((and_rect0 (cP n)) (fun (x0:((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)))))) as proof of (cP n)
% 0.61/0.78 Found (((fun (P:Type) (x0:(((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))->((forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))->P)))=> (((((and_rect ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) P) x0) x)) (cP n)) (fun (x0:((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)))))) as proof of (cP n)
% 0.61/0.78 Found (fun (x:((and ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))))=> (((fun (P:Type) (x0:(((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))->((forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))->P)))=> (((((and_rect ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) P) x0) x)) (cP n)) (fun (x0:((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1))))))) as proof of (cP n)
% 0.61/0.78 Found (fun (x:((and ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))))=> (((fun (P:Type) (x0:(((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))->((forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))->P)))=> (((((and_rect ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) P) x0) x)) (cP n)) (fun (x0:((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1))))))) as proof of (((and ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))->(cP n))
% 0.61/0.79 Got proof (fun (x:((and ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))))=> (((fun (P:Type) (x0:(((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))->((forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))->P)))=> (((((and_rect ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) P) x0) x)) (cP n)) (fun (x0:((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)))))))
% 0.61/0.79 Time elapsed = 0.175388s
% 0.61/0.79 node=31 cost=417.000000 depth=20
% 0.61/0.79 ::::::::::::::::::::::
% 0.61/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.79 (fun (x:((and ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))))=> (((fun (P:Type) (x0:(((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))->((forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))->P)))=> (((((and_rect ((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) P) x0) x)) (cP n)) (fun (x0:((and (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO))) (x1:(forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx)))))=> (((fun (P:Type) (x2:((forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))->((cP cO)->P)))=> (((((and_rect (forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (cP cO)) P) x2) x0)) (cP n)) (fun (x2:(forall (A:(fofType->Prop)), (((and (A cO)) (forall (Xx:fofType), ((A Xx)->(A (c1_plus Xx)))))->(A n)))) (x3:(cP cO))=> ((x2 cP) (((fun (B:Prop)=> (((conj (cP cO)) B) x3)) (forall (Xx:fofType), ((cP Xx)->(cP (c1_plus Xx))))) x1)))))))
% 0.61/0.79 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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