TSTP Solution File: SEV310^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV310^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n107.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 13:34:01 EDT 2014
% Result : Theorem 2.16s
% Output : Proof 2.16s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV310^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n107.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 08:48:16 CDT 2014
% % CPUTime : 2.16
% 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 0xd583f8>, <kernel.Type object at 0xd76c20>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0xfd93b0>, <kernel.DependentProduct object at 0xd76cf8>) of role type named cK
% Using role type
% Declaring cK:((a->Prop)->(a->Prop))
% FOF formula ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)))) of role conjecture named cTHM90A_pme
% Conjecture to prove = ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx))))']
% Parameter a:Type.
% Parameter cK:((a->Prop)->(a->Prop)).
% Trying to prove ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx))))
% Found x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0)
% Instantiate: X:=(cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))):(a->Prop)
% Found x1 as proof of ((cK X) Xx0)
% Found x3:(X Xx1)
% Found x3 as proof of (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1)))
% Found (fun (x3:(X Xx1))=> x3) as proof of (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1)))
% Found (fun (Xx1:a) (x3:(X Xx1))=> x3) as proof of ((X Xx1)->(forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1))))
% Found (fun (Xx1:a) (x3:(X Xx1))=> x3) as proof of (forall (Xx:a), ((X Xx)->(forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx)))))
% Found x2:(X Xx0)
% Found x2 as proof of (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0)))
% Found (fun (x2:(X Xx0))=> x2) as proof of (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0)))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->(forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->(forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx)))))
% Found x2:((cK (cK X)) Xx0)
% Instantiate: X0:=(cK X):(a->Prop)
% Found x2 as proof of ((cK X0) Xx0)
% Found x2:((cK (cK X)) Xx0)
% Instantiate: X0:=(cK X):(a->Prop)
% Found x2 as proof of ((cK X0) Xx0)
% Found x4:(X0 Xx1)
% Found x4 as proof of (X Xx1)
% Found (fun (x4:(X0 Xx1))=> x4) as proof of (X Xx1)
% Found (fun (Xx1:a) (x4:(X0 Xx1))=> x4) as proof of ((X0 Xx1)->(X Xx1))
% Found (fun (Xx1:a) (x4:(X0 Xx1))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x2:(X0 Xx0)
% Found x2 as proof of (X Xx0)
% Found (fun (x2:(X0 Xx0))=> x2) as proof of (X Xx0)
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x3:(X Xx1)
% Instantiate: X0:=(fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))):(a->Prop)
% Found x3 as proof of ((cK X0) Xx1)
% Found x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))
% Instantiate: X0:=(cK S0):(a->Prop)
% Found x30 as proof of (forall (Xx:a), ((X0 Xx)->(S0 Xx)))
% Found x20:(X0 Xx0)
% Instantiate: X:=X0:(a->Prop)
% Found (fun (x20:(X0 Xx0))=> x20) as proof of (X Xx0)
% Found (fun (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20) as proof of (((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)->((X0 Xx0)->(X Xx0)))
% Found (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20) as proof of (forall (Xx00:a), (((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)->((X0 Xx0)->(X Xx0))))
% Found (x00 (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20)) as proof of ((X0 Xx0)->(X Xx0))
% Found ((x0 (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20)) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a)=> ((x0 (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20))) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a)=> ((x0 (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) (fun (Xx00:a) (x2:((cK (fun (x3:a)=> ((X0 Xx0)->(X Xx0)))) Xx00)) (x20:(X0 Xx0))=> x20))) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x500:=(x50 x30):(S0 Xx2)
% Found (x50 x30) as proof of (S0 Xx2)
% Found ((x5 S0) x30) as proof of (S0 Xx2)
% Found (fun (x5:(X0 Xx2))=> ((x5 S0) x30)) as proof of (S0 Xx2)
% Found (fun (Xx2:a) (x5:(X0 Xx2))=> ((x5 S0) x30)) as proof of ((X0 Xx2)->(S0 Xx2))
% Found (fun (Xx2:a) (x5:(X0 Xx2))=> ((x5 S0) x30)) as proof of (forall (Xx:a), ((X0 Xx)->(S0 Xx)))
% Found ((x400 (fun (Xx2:a) (x5:(X0 Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1)
% Found (((x40 S0) (fun (Xx2:a) (x5:(X0 Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1)
% Found ((((x4 (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1)
% Found (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1)
% Found (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3) as proof of ((cK S0) Xx1)
% Found (x300 (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)) as proof of (S0 Xx1)
% Found ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)) as proof of (S0 Xx1)
% Found (fun (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of (S0 Xx1)
% Found (fun (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1))
% Found (fun (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1)))
% Found (fun (Xx1:a) (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of ((X Xx1)->(forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx1))))
% Found (fun (Xx1:a) (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3))) as proof of (forall (Xx:a), ((X Xx)->(forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx)))))
% Found ((x200 (fun (Xx1:a) (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)))) x1) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0)
% Found (((x20 (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (fun (Xx1:a) (x3:(X Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)))) x1) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0)
% Found ((((x2 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (fun (Xx1:a) (x3:((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0))))) S0) (fun (Xx2:a) (x5:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx0)))) Xx2))=> ((x5 S0) x30))) x3)))) x1) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0)
% Found (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0)
% Found (fun (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)) as proof of ((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0)
% Found (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)) as proof of (((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0)->((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0))
% Found (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)) as proof of (forall (Xx0:a), (((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0)->((cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) Xx0)))
% Found (x00 (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1))) as proof of ((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)
% Found ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1))) as proof of ((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)
% Found (fun (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) as proof of ((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)
% Found (fun (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) as proof of ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx))
% Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))) (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) as proof of (forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)))
% Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))) (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1)))) as proof of ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx)))->((cK (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cK S) Xx1)->(S Xx1)))->(S Xx0))))) Xx))))
% Got proof (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))) (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1))))
% Time elapsed = 1.831115s
% node=343 cost=1482.000000 depth=29
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))) (Xx:a) (x0:(forall (S:(a->Prop)), ((forall (Xx0:a), (((cK S) Xx0)->(S Xx0)))->(S Xx))))=> ((x0 (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) (fun (Xx0:a) (x1:((cK (cK (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))))) Xx0))=> (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx0)) (cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00)))))) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) (fun (Xx1:a) (x3:((cK (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cK S0) Xx1)->(S0 Xx1)))->(S0 Xx00))))) Xx1)) (S0:(a->Prop)) (x30:(forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10))))=> ((x30 Xx1) (((((fun (X0:(a->Prop)) (Y:(a->Prop)) (x4:(forall (Xx:a), ((X0 Xx)->(Y Xx))))=> ((((x X0) Y) x4) Xx1)) (fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00))))) S0) (fun (Xx2:a) (x5:((fun (Xx00:a)=> (forall (S0:(a->Prop)), ((forall (Xx10:a), (((cK S0) Xx10)->(S0 Xx10)))->(S0 Xx00)))) Xx2))=> ((x5 S0) x30))) x3)))) x1))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------