TSTP Solution File: SYO146^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO146^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/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 00:50:44 EDT 2022
% Result : Theorem 0.89s 1.15s
% Output : Proof 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : SYO146^5 : TPTP v7.5.0. Released v4.0.0.
% 0.12/0.12 % Command : python CASC.py /export/starexec/sandbox2/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 16:15:45 EST 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.35 Python 2.7.5
% 0.89/1.15 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.89/1.15 FOF formula (<kernel.Constant object at 0xf5f830>, <kernel.Constant object at 0xf5f368>) of role type named a
% 0.89/1.15 Using role type
% 0.89/1.15 Declaring a:fofType
% 0.89/1.15 FOF formula (<kernel.Constant object at 0xf5f248>, <kernel.DependentProduct object at 0x2ad631f8a9e0>) of role type named cQ
% 0.89/1.15 Using role type
% 0.89/1.15 Declaring cQ:(fofType->Prop)
% 0.89/1.15 FOF formula (<kernel.Constant object at 0xf5f368>, <kernel.Single object at 0xf5f830>) of role type named c
% 0.89/1.15 Using role type
% 0.89/1.15 Declaring c:fofType
% 0.89/1.15 FOF formula (<kernel.Constant object at 0xf5fbd8>, <kernel.DependentProduct object at 0x2ad631f8a2d8>) of role type named cP
% 0.89/1.15 Using role type
% 0.89/1.15 Declaring cP:(fofType->(fofType->Prop))
% 0.89/1.15 FOF formula (<kernel.Constant object at 0xf63200>, <kernel.Single object at 0xf5f830>) of role type named b
% 0.89/1.15 Using role type
% 0.89/1.15 Declaring b:fofType
% 0.89/1.15 FOF formula ((forall (Xx:fofType), ((or (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx)))->((or ((and ((cP a) b)) ((cP a) c))) (cQ a))) of role conjecture named cDUP_EXPL_1
% 0.89/1.15 Conjecture to prove = ((forall (Xx:fofType), ((or (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx)))->((or ((and ((cP a) b)) ((cP a) c))) (cQ a))):Prop
% 0.89/1.15 We need to prove ['((forall (Xx:fofType), ((or (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx)))->((or ((and ((cP a) b)) ((cP a) c))) (cQ a)))']
% 0.89/1.15 Parameter fofType:Type.
% 0.89/1.15 Parameter a:fofType.
% 0.89/1.15 Parameter cQ:(fofType->Prop).
% 0.89/1.15 Parameter c:fofType.
% 0.89/1.15 Parameter cP:(fofType->(fofType->Prop)).
% 0.89/1.15 Parameter b:fofType.
% 0.89/1.15 Trying to prove ((forall (Xx:fofType), ((or (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx)))->((or ((and ((cP a) b)) ((cP a) c))) (cQ a)))
% 0.89/1.15 Found or_intror00:=(or_intror0 (cQ Xx)):((cQ Xx)->((or ((and ((cP a) b)) ((cP a) c))) (cQ Xx)))
% 0.89/1.15 Found (or_intror0 (cQ Xx)) as proof of ((cQ Xx)->((or ((and ((cP a) b)) ((cP a) c))) (cQ a)))
% 0.89/1.15 Found ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ Xx)) as proof of ((cQ Xx)->((or ((and ((cP a) b)) ((cP a) c))) (cQ a)))
% 0.89/1.15 Found ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ Xx)) as proof of ((cQ Xx)->((or ((and ((cP a) b)) ((cP a) c))) (cQ a)))
% 0.89/1.15 Found ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ Xx)) as proof of ((cQ Xx)->((or ((and ((cP a) b)) ((cP a) c))) (cQ a)))
% 0.89/1.15 Found x1:(cQ Xx)
% 0.89/1.15 Instantiate: Xx:=a:fofType
% 0.89/1.15 Found (fun (x1:(cQ Xx))=> x1) as proof of (cQ a)
% 0.89/1.15 Found (fun (x1:(cQ Xx))=> x1) as proof of ((cQ Xx)->(cQ a))
% 0.89/1.15 Found or_introl00:=(or_introl0 ((and ((cP a) b)) ((cP a) c))):((cQ Xx)->((or (cQ Xx)) ((and ((cP a) b)) ((cP a) c))))
% 0.89/1.15 Found (or_introl0 ((and ((cP a) b)) ((cP a) c))) as proof of ((cQ Xx)->((or (cQ a)) ((and ((cP a) b)) ((cP a) c))))
% 0.89/1.15 Found ((or_introl (cQ Xx)) ((and ((cP a) b)) ((cP a) c))) as proof of ((cQ Xx)->((or (cQ a)) ((and ((cP a) b)) ((cP a) c))))
% 0.89/1.15 Found ((or_introl (cQ Xx)) ((and ((cP a) b)) ((cP a) c))) as proof of ((cQ Xx)->((or (cQ a)) ((and ((cP a) b)) ((cP a) c))))
% 0.89/1.15 Found ((or_introl (cQ Xx)) ((and ((cP a) b)) ((cP a) c))) as proof of ((cQ Xx)->((or (cQ a)) ((and ((cP a) b)) ((cP a) c))))
% 0.89/1.15 Found x10:=(x1 b):((cP Xx) b)
% 0.89/1.15 Found (x1 b) as proof of ((cP a) b)
% 0.89/1.15 Found (x1 b) as proof of ((cP a) b)
% 0.89/1.15 Found x10:=(x1 c):((cP Xx) c)
% 0.89/1.15 Found (x1 c) as proof of ((cP a) c)
% 0.89/1.15 Found (x1 c) as proof of ((cP a) c)
% 0.89/1.15 Found ((conj00 (x1 b)) (x1 c)) as proof of ((and ((cP a) b)) ((cP a) c))
% 0.89/1.15 Found (((conj0 ((cP a) c)) (x1 b)) (x1 c)) as proof of ((and ((cP a) b)) ((cP a) c))
% 0.89/1.15 Found ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c)) as proof of ((and ((cP a) b)) ((cP a) c))
% 0.89/1.15 Found ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c)) as proof of ((and ((cP a) b)) ((cP a) c))
% 0.89/1.15 Found (or_introl00 ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))) as proof of ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))
% 0.89/1.15 Found ((or_introl0 (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))) as proof of ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))
% 0.89/1.15 Found (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))) as proof of ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))
% 0.89/1.15 Found (fun (x1:(forall (Xy:fofType), ((cP Xx) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c)))) as proof of ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))
% 0.89/1.15 Found (fun (x1:(forall (Xy:fofType), ((cP Xx) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c)))) as proof of ((forall (Xy:fofType), ((cP Xx) Xy))->((or ((and ((cP a) b)) ((cP a) c))) (cQ a)))
% 0.89/1.15 Found ((or_ind00 (fun (x1:(forall (Xy:fofType), ((cP Xx) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))))) ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ Xx))) as proof of ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))
% 0.89/1.15 Found (((or_ind0 ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))) (fun (x1:(forall (Xy:fofType), ((cP Xx) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))))) ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ Xx))) as proof of ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))
% 0.89/1.15 Found ((((fun (P:Prop) (x1:((forall (Xy:fofType), ((cP Xx) Xy))->P)) (x2:((cQ Xx)->P))=> ((((((or_ind (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx)) P) x1) x2) x0)) ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))) (fun (x1:(forall (Xy:fofType), ((cP Xx) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))))) ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ Xx))) as proof of ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))
% 0.89/1.15 Found ((((fun (P:Prop) (x1:((forall (Xy:fofType), ((cP a) Xy))->P)) (x2:((cQ a)->P))=> ((((((or_ind (forall (Xy:fofType), ((cP a) Xy))) (cQ a)) P) x1) x2) (x a))) ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))) (fun (x1:(forall (Xy:fofType), ((cP a) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))))) ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ a))) as proof of ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))
% 0.89/1.15 Found (fun (x:(forall (Xx:fofType), ((or (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx))))=> ((((fun (P:Prop) (x1:((forall (Xy:fofType), ((cP a) Xy))->P)) (x2:((cQ a)->P))=> ((((((or_ind (forall (Xy:fofType), ((cP a) Xy))) (cQ a)) P) x1) x2) (x a))) ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))) (fun (x1:(forall (Xy:fofType), ((cP a) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))))) ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ a)))) as proof of ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))
% 0.89/1.15 Found (fun (x:(forall (Xx:fofType), ((or (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx))))=> ((((fun (P:Prop) (x1:((forall (Xy:fofType), ((cP a) Xy))->P)) (x2:((cQ a)->P))=> ((((((or_ind (forall (Xy:fofType), ((cP a) Xy))) (cQ a)) P) x1) x2) (x a))) ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))) (fun (x1:(forall (Xy:fofType), ((cP a) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))))) ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ a)))) as proof of ((forall (Xx:fofType), ((or (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx)))->((or ((and ((cP a) b)) ((cP a) c))) (cQ a)))
% 0.89/1.15 Got proof (fun (x:(forall (Xx:fofType), ((or (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx))))=> ((((fun (P:Prop) (x1:((forall (Xy:fofType), ((cP a) Xy))->P)) (x2:((cQ a)->P))=> ((((((or_ind (forall (Xy:fofType), ((cP a) Xy))) (cQ a)) P) x1) x2) (x a))) ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))) (fun (x1:(forall (Xy:fofType), ((cP a) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))))) ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ a))))
% 0.89/1.15 Time elapsed = 0.523208s
% 0.89/1.15 node=210 cost=387.000000 depth=16
% 0.89/1.15 ::::::::::::::::::::::
% 0.89/1.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.89/1.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.89/1.15 (fun (x:(forall (Xx:fofType), ((or (forall (Xy:fofType), ((cP Xx) Xy))) (cQ Xx))))=> ((((fun (P:Prop) (x1:((forall (Xy:fofType), ((cP a) Xy))->P)) (x2:((cQ a)->P))=> ((((((or_ind (forall (Xy:fofType), ((cP a) Xy))) (cQ a)) P) x1) x2) (x a))) ((or ((and ((cP a) b)) ((cP a) c))) (cQ a))) (fun (x1:(forall (Xy:fofType), ((cP a) Xy)))=> (((or_introl ((and ((cP a) b)) ((cP a) c))) (cQ a)) ((((conj ((cP a) b)) ((cP a) c)) (x1 b)) (x1 c))))) ((or_intror ((and ((cP a) b)) ((cP a) c))) (cQ a))))
% 0.89/1.16 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------