TSTP Solution File: SYO149^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO149^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n023.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 00:50:45 EDT 2022
% Result : Theorem 0.52s 0.73s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO149^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n023.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 17:40:27 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
% 0.52/0.72 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.52/0.72 FOF formula (<kernel.Constant object at 0x10b51b8>, <kernel.Constant object at 0x10b5dd0>) of role type named a
% 0.52/0.72 Using role type
% 0.52/0.72 Declaring a:fofType
% 0.52/0.72 FOF formula (<kernel.Constant object at 0x10b1368>, <kernel.DependentProduct object at 0x1393a28>) of role type named f
% 0.52/0.72 Using role type
% 0.52/0.72 Declaring f:(fofType->fofType)
% 0.52/0.72 FOF formula (<kernel.Constant object at 0x10ace18>, <kernel.DependentProduct object at 0x1393ea8>) of role type named cP
% 0.52/0.72 Using role type
% 0.52/0.72 Declaring cP:(fofType->Prop)
% 0.52/0.72 FOF formula (<kernel.Constant object at 0x10b5fc8>, <kernel.DependentProduct object at 0x1393fc8>) of role type named cQ
% 0.52/0.72 Using role type
% 0.52/0.72 Declaring cQ:(fofType->Prop)
% 0.52/0.72 FOF formula (((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a))) of role conjecture named cSIMPLEPQ
% 0.52/0.72 Conjecture to prove = (((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a))):Prop
% 0.52/0.72 We need to prove ['(((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a)))']
% 0.52/0.72 Parameter fofType:Type.
% 0.52/0.72 Parameter a:fofType.
% 0.52/0.72 Parameter f:(fofType->fofType).
% 0.52/0.72 Parameter cP:(fofType->Prop).
% 0.52/0.72 Parameter cQ:(fofType->Prop).
% 0.52/0.72 Trying to prove (((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a)))
% 0.52/0.72 Found x200:=(x20 x1):(cQ (f a))
% 0.52/0.72 Found (x20 x1) as proof of (cQ (f a))
% 0.52/0.72 Found ((x2 a) x1) as proof of (cQ (f a))
% 0.52/0.72 Found ((x2 a) x1) as proof of (cQ (f a))
% 0.52/0.72 Found (x30 ((x2 a) x1)) as proof of (cP (f a))
% 0.52/0.72 Found ((x3 (f a)) ((x2 a) x1)) as proof of (cP (f a))
% 0.52/0.72 Found (fun (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))) as proof of (cP (f a))
% 0.52/0.72 Found (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))) as proof of ((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->(cP (f a)))
% 0.52/0.72 Found (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))) as proof of ((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->(cP (f a))))
% 0.52/0.72 Found (and_rect10 (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))) as proof of (cP (f a))
% 0.52/0.72 Found ((and_rect1 (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))) as proof of (cP (f a))
% 0.52/0.72 Found (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))) as proof of (cP (f a))
% 0.52/0.72 Found (fun (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))) as proof of (cP (f a))
% 0.52/0.72 Found (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))) as proof of ((cP a)->(cP (f a)))
% 0.52/0.72 Found (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))) as proof of (((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->(cP (f a))))
% 0.52/0.72 Found (and_rect00 (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))))) as proof of (cP (f a))
% 0.52/0.72 Found ((and_rect0 (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))))) as proof of (cP (f a))
% 0.52/0.72 Found (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))))) as proof of (cP (f a))
% 0.52/0.72 Found (fun (x:((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)))=> (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))))) as proof of (cP (f a))
% 0.52/0.72 Found (fun (x:((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)))=> (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))))) as proof of (((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a)))
% 0.52/0.73 Got proof (fun (x:((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)))=> (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))))))
% 0.52/0.73 Time elapsed = 0.105628s
% 0.52/0.73 node=18 cost=288.000000 depth=18
% 0.52/0.73 ::::::::::::::::::::::
% 0.52/0.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.73 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.73 (fun (x:((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)))=> (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))))))
% 0.52/0.73 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------