TSTP Solution File: SET200^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET200^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n109.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:30:22 EDT 2014
% Result : Theorem 2.77s
% Output : Proof 2.77s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET200^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n109.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 09:24:41 CDT 2014
% % CPUTime : 2.77
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x2492050>, <kernel.Type object at 0x2492998>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx)))))) of role conjecture named cBOOL_PROP_34_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx)))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx))))))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx))))))
% Found x10:=(x1 Xx):((X Xx)->(Y Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Y Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Y Xx))
% Found x20:=(x2 Xx):((Z Xx)->(V Xx))
% Found (x2 Xx) as proof of ((Z Xx)->(V Xx))
% Found (x2 Xx) as proof of ((Z Xx)->(V Xx))
% Found x10:=(x1 Xx):((X Xx)->(Y Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Y Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Y Xx))
% Found x20:=(x2 Xx):((Z Xx)->(V Xx))
% Found (x2 Xx) as proof of ((Z Xx)->(V Xx))
% Found (x2 Xx) as proof of ((Z Xx)->(V Xx))
% Found x3:(Z Xx)
% Found (fun (x3:(Z Xx))=> x3) as proof of (Z Xx)
% Found (fun (x3:(Z Xx))=> x3) as proof of ((Z Xx)->(Z Xx))
% Found x3:(X Xx)
% Found (fun (x3:(X Xx))=> x3) as proof of (X Xx)
% Found (fun (x3:(X Xx))=> x3) as proof of ((X Xx)->(X Xx))
% Found x3:(X Xx)
% Found (fun (x3:(X Xx))=> x3) as proof of (X Xx)
% Found (fun (x3:(X Xx))=> x3) as proof of ((X Xx)->(X Xx))
% Found x3:(Z Xx)
% Found (fun (x3:(Z Xx))=> x3) as proof of (Z Xx)
% Found (fun (x3:(Z Xx))=> x3) as proof of ((Z Xx)->(Z Xx))
% Found x20:=(x2 Xx):((Z Xx)->(V Xx))
% Found (x2 Xx) as proof of ((Z Xx)->(V Xx))
% Found (x2 Xx) as proof of ((Z Xx)->(V Xx))
% Found x10:=(x1 Xx):((X Xx)->(Y Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Y Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Y Xx))
% Found x20:=(x2 Xx):((Z Xx)->(V Xx))
% Found (x2 Xx) as proof of ((Z Xx)->(V Xx))
% Found (x2 Xx) as proof of ((Z Xx)->(V Xx))
% Found x10:=(x1 Xx):((X Xx)->(Y Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Y Xx))
% Found (x1 Xx) as proof of ((X Xx)->(Y Xx))
% Found x200:=(x20 x3):(V Xx)
% Found (x20 x3) as proof of (V Xx)
% Found ((x2 Xx) x3) as proof of (V Xx)
% Found ((x2 Xx) x3) as proof of (V Xx)
% Found (or_intror00 ((x2 Xx) x3)) as proof of ((or (Y Xx)) (V Xx))
% Found ((or_intror0 (V Xx)) ((x2 Xx) x3)) as proof of ((or (Y Xx)) (V Xx))
% Found (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3)) as proof of ((or (Y Xx)) (V Xx))
% Found (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))) as proof of ((or (Y Xx)) (V Xx))
% Found (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))) as proof of ((Z Xx)->((or (Y Xx)) (V Xx)))
% Found x100:=(x10 x3):(Y Xx)
% Found (x10 x3) as proof of (Y Xx)
% Found ((x1 Xx) x3) as proof of (Y Xx)
% Found ((x1 Xx) x3) as proof of (Y Xx)
% Found (or_introl00 ((x1 Xx) x3)) as proof of ((or (Y Xx)) (V Xx))
% Found ((or_introl0 (V Xx)) ((x1 Xx) x3)) as proof of ((or (Y Xx)) (V Xx))
% Found (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)) as proof of ((or (Y Xx)) (V Xx))
% Found (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3))) as proof of ((or (Y Xx)) (V Xx))
% Found (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3))) as proof of ((X Xx)->((or (Y Xx)) (V Xx)))
% Found ((or_ind00 (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3)))) as proof of ((or (Y Xx)) (V Xx))
% Found (((or_ind0 ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3)))) as proof of ((or (Y Xx)) (V Xx))
% Found ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3)))) as proof of ((or (Y Xx)) (V Xx))
% Found (fun (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))) as proof of ((or (Y Xx)) (V Xx))
% Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))) as proof of ((forall (Xx0:a), ((Z Xx0)->(V Xx0)))->((or (Y Xx)) (V Xx)))
% Found (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))) as proof of ((forall (Xx0:a), ((X Xx0)->(Y Xx0)))->((forall (Xx0:a), ((Z Xx0)->(V Xx0)))->((or (Y Xx)) (V Xx))))
% Found (and_rect00 (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3)))))) as proof of ((or (Y Xx)) (V Xx))
% Found ((and_rect0 ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3)))))) as proof of ((or (Y Xx)) (V Xx))
% Found (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3)))))) as proof of ((or (Y Xx)) (V Xx))
% Found (fun (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))))) as proof of ((or (Y Xx)) (V Xx))
% Found (fun (Xx:a) (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))))) as proof of (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx)))
% Found (fun (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))))) as proof of (forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx))))
% Found (fun (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))))) as proof of (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx)))))
% Found (fun (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))))) as proof of (forall (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx))))))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))))) as proof of (forall (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))))) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3))))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)), (((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))->(forall (Xx:a), (((or (X Xx)) (Z Xx))->((or (Y Xx)) (V Xx))))))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3)))))))
% Time elapsed = 2.422852s
% node=509 cost=574.000000 depth=24
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (V:(a->Prop)) (x:((and (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx))))) (Xx:a) (x0:((or (X Xx)) (Z Xx)))=> (((fun (P:Type) (x1:((forall (Xx:a), ((X Xx)->(Y Xx)))->((forall (Xx:a), ((Z Xx)->(V Xx)))->P)))=> (((((and_rect (forall (Xx:a), ((X Xx)->(Y Xx)))) (forall (Xx:a), ((Z Xx)->(V Xx)))) P) x1) x)) ((or (Y Xx)) (V Xx))) (fun (x1:(forall (Xx0:a), ((X Xx0)->(Y Xx0)))) (x2:(forall (Xx0:a), ((Z Xx0)->(V Xx0))))=> ((((fun (P:Prop) (x3:((X Xx)->P)) (x4:((Z Xx)->P))=> ((((((or_ind (X Xx)) (Z Xx)) P) x3) x4) x0)) ((or (Y Xx)) (V Xx))) (fun (x3:(X Xx))=> (((or_introl (Y Xx)) (V Xx)) ((x1 Xx) x3)))) (fun (x3:(Z Xx))=> (((or_intror (Y Xx)) (V Xx)) ((x2 Xx) x3)))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------