TSTP Solution File: SEV185^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV185^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n094.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 13:33:51 EDT 2014
% Result : Theorem 1.54s
% Output : Proof 1.54s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV185^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n094.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 08:24:06 CDT 2014
% % CPUTime : 1.54
% 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 0xc5b9e0>, <kernel.Type object at 0xc5b1b8>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (forall (P:((b->Prop)->(b->Prop))) (S:((b->Prop)->Prop)), ((forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy))))))) of role conjecture named cTHM564_pme
% Conjecture to prove = (forall (P:((b->Prop)->(b->Prop))) (S:((b->Prop)->Prop)), ((forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy))))))):Prop
% Parameter b_DUMMY:b.
% We need to prove ['(forall (P:((b->Prop)->(b->Prop))) (S:((b->Prop)->Prop)), ((forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy)))))))']
% Parameter b:Type.
% Trying to prove (forall (P:((b->Prop)->(b->Prop))) (S:((b->Prop)->Prop)), ((forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy)))))))
% Found x1:(S S0)
% Found x1 as proof of (S S00)
% Found x3:(X0 Xx0)
% Found x3 as proof of (S0 Xx0)
% Found (fun (x3:(X0 Xx0))=> x3) as proof of (S0 Xx0)
% Found (fun (Xx0:b) (x3:(X0 Xx0))=> x3) as proof of ((X0 Xx0)->(S0 Xx0))
% Found (fun (Xx0:b) (x3:(X0 Xx0))=> x3) as proof of (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))
% Found x3:(X0 Xx0)
% Found x3 as proof of (S0 Xx0)
% Found (fun (x3:(X0 Xx0))=> x3) as proof of (S0 Xx0)
% Found (fun (Xx0:b) (x3:(X0 Xx0))=> x3) as proof of ((X0 Xx0)->(S0 Xx0))
% Found (fun (Xx0:b) (x3:(X0 Xx0))=> x3) as proof of (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))
% Found x3:((P X) Xy)
% Instantiate: X0:=X:(b->Prop)
% Found x3 as proof of ((P X0) Xy)
% Found x3:((P X) Xy)
% Instantiate: X0:=X:(b->Prop)
% Found x3 as proof of ((P X0) Xy)
% Found x5:(X0 Xx0)
% Found x5 as proof of (S0 Xx0)
% Found (fun (x5:(X0 Xx0))=> x5) as proof of (S0 Xx0)
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> x5) as proof of ((X0 Xx0)->(S0 Xx0))
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> x5) as proof of (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))
% Found x5:(X0 Xx0)
% Found x5 as proof of (S0 Xx0)
% Found (fun (x5:(X0 Xx0))=> x5) as proof of (S0 Xx0)
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> x5) as proof of ((X0 Xx0)->(S0 Xx0))
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> x5) as proof of (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))
% Found x4:((P X) Xy)
% Instantiate: X0:=X:(b->Prop)
% Found (fun (x4:((P X) Xy))=> x4) as proof of ((P X0) Xy)
% Found (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4) as proof of (((P X) Xy)->((P X0) Xy))
% Found (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4) as proof of ((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->((P X0) Xy)))
% Found (and_rect00 (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4)) as proof of ((P X0) Xy)
% Found ((and_rect0 ((P X0) Xy)) (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4)) as proof of ((P X0) Xy)
% Found (((fun (P0:Type) (x3:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x3) x0)) ((P X0) Xy)) (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4)) as proof of ((P X0) Xy)
% Found (((fun (P0:Type) (x3:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x3) x0)) ((P X0) Xy)) (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4)) as proof of ((P X0) Xy)
% Found x4:((P X) Xy)
% Instantiate: X0:=X:(b->Prop)
% Found (fun (x4:((P X) Xy))=> x4) as proof of ((P X0) Xy)
% Found (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4) as proof of (((P X) Xy)->((P X0) Xy))
% Found (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4) as proof of ((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->((P X0) Xy)))
% Found (and_rect00 (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4)) as proof of ((P X0) Xy)
% Found ((and_rect0 ((P X0) Xy)) (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4)) as proof of ((P X0) Xy)
% Found (((fun (P0:Type) (x3:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x3) x0)) ((P X0) Xy)) (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4)) as proof of ((P X0) Xy)
% Found (((fun (P0:Type) (x3:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x3) x0)) ((P X0) Xy)) (fun (x3:(forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) (x4:((P X) Xy))=> x4)) as proof of ((P X0) Xy)
% Found x4:((P X) Xy)
% Instantiate: X0:=X:(b->Prop)
% Found x4 as proof of ((P X0) Xy)
% Found x4:((P X) Xy)
% Instantiate: X0:=X:(b->Prop)
% Found x4 as proof of ((P X0) Xy)
% Found x5:(X0 Xx0)
% Instantiate: X0:=S0:(b->Prop)
% Found x5 as proof of (S0 Xx0)
% Found (fun (x5:(X0 Xx0))=> x5) as proof of (S0 Xx0)
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> x5) as proof of ((X0 Xx0)->(S0 Xx0))
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> x5) as proof of (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))
% Found x5:(X0 Xx0)
% Instantiate: X0:=S0:(b->Prop)
% Found x5 as proof of (S0 Xx0)
% Found (fun (x5:(X0 Xx0))=> x5) as proof of (S0 Xx0)
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> x5) as proof of ((X0 Xx0)->(S0 Xx0))
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> x5) as proof of (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))
% Found x20000:=(x2000 x1):(S0 Xx0)
% Found (x2000 x1) as proof of (S0 Xx0)
% Found ((x200 S0) x1) as proof of (S0 Xx0)
% Found (((x20 x5) S0) x1) as proof of (S0 Xx0)
% Found ((((x2 Xx0) x5) S0) x1) as proof of (S0 Xx0)
% Found (fun (x5:(X0 Xx0))=> ((((x2 Xx0) x5) S0) x1)) as proof of (S0 Xx0)
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> ((((x2 Xx0) x5) S0) x1)) as proof of ((X0 Xx0)->(S0 Xx0))
% Found (fun (Xx0:b) (x5:(X0 Xx0))=> ((((x2 Xx0) x5) S0) x1)) as proof of (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))
% Found ((conj00 (fun (Xx0:b) (x5:(X0 Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3) as proof of ((and (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))) ((P X0) Xy))
% Found (((conj0 ((P X0) Xy)) (fun (Xx0:b) (x5:(X0 Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3) as proof of ((and (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))) ((P X0) Xy))
% Found ((((conj (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))) ((P X0) Xy)) (fun (Xx0:b) (x5:(X0 Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3) as proof of ((and (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))) ((P X0) Xy))
% Found ((((conj (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))) ((P X0) Xy)) (fun (Xx0:b) (x5:(X0 Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3) as proof of ((and (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))) ((P X0) Xy))
% Found (x4000 ((((conj (forall (Xx0:b), ((X0 Xx0)->(S0 Xx0)))) ((P X0) Xy)) (fun (Xx0:b) (x5:(X0 Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)) as proof of (S0 Xy)
% Found ((x400 X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)) as proof of (S0 Xy)
% Found (((fun (X0:(b->Prop))=> ((x40 X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)) as proof of (S0 Xy)
% Found (((fun (X0:(b->Prop))=> (((x4 x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)) as proof of (S0 Xy)
% Found (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)) as proof of (S0 Xy)
% Found (fun (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))) as proof of (S0 Xy)
% Found (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))) as proof of (((P X) Xy)->(S0 Xy))
% Found (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))) as proof of ((forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))->(((P X) Xy)->(S0 Xy)))
% Found (and_rect00 (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)))) as proof of (S0 Xy)
% Found ((and_rect0 (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)))) as proof of (S0 Xy)
% Found (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)))) as proof of (S0 Xy)
% Found (fun (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))))) as proof of (S0 Xy)
% Found (fun (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))))) as proof of ((S S0)->(S0 Xy))
% Found (fun (x0:((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))) (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))))) as proof of (forall (S0:(b->Prop)), ((S S0)->(S0 Xy)))
% Found (fun (Xy:b) (x0:((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))) (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))))) as proof of (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy))))
% Found (fun (X:(b->Prop)) (Xy:b) (x0:((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))) (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))))) as proof of (forall (Xy:b), (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy)))))
% Found (fun (x:(forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))) (X:(b->Prop)) (Xy:b) (x0:((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))) (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))))) as proof of (forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy)))))
% Found (fun (S:((b->Prop)->Prop)) (x:(forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))) (X:(b->Prop)) (Xy:b) (x0:((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))) (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))))) as proof of ((forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy))))))
% Found (fun (P:((b->Prop)->(b->Prop))) (S:((b->Prop)->Prop)) (x:(forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))) (X:(b->Prop)) (Xy:b) (x0:((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))) (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))))) as proof of (forall (S:((b->Prop)->Prop)), ((forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy)))))))
% Found (fun (P:((b->Prop)->(b->Prop))) (S:((b->Prop)->Prop)) (x:(forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))) (X:(b->Prop)) (Xy:b) (x0:((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))) (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3))))) as proof of (forall (P:((b->Prop)->(b->Prop))) (S:((b->Prop)->Prop)), ((forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))->(forall (S0:(b->Prop)), ((S S0)->(S0 Xy)))))))
% Got proof (fun (P:((b->Prop)->(b->Prop))) (S:((b->Prop)->Prop)) (x:(forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))) (X:(b->Prop)) (Xy:b) (x0:((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))) (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)))))
% Time elapsed = 1.220782s
% node=279 cost=925.000000 depth=30
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (P:((b->Prop)->(b->Prop))) (S:((b->Prop)->Prop)) (x:(forall (Xx:(b->Prop)), ((S Xx)->(forall (X:(b->Prop)) (Xy:b), (((and (forall (Xx0:b), ((X Xx0)->(Xx Xx0)))) ((P X) Xy))->(Xx Xy)))))) (X:(b->Prop)) (Xy:b) (x0:((and (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy))) (S0:(b->Prop)) (x1:(S S0))=> (((fun (P0:Type) (x2:((forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))->(((P X) Xy)->P0)))=> (((((and_rect (forall (Xx:b), ((X Xx)->(forall (S0:(b->Prop)), ((S S0)->(S0 Xx)))))) ((P X) Xy)) P0) x2) x0)) (S0 Xy)) (fun (x2:(forall (Xx:b), ((X Xx)->(forall (S00:(b->Prop)), ((S S00)->(S00 Xx)))))) (x3:((P X) Xy))=> (((fun (X0:(b->Prop))=> ((((x S0) x1) X0) Xy)) X) ((((conj (forall (Xx0:b), ((X Xx0)->(S0 Xx0)))) ((P X) Xy)) (fun (Xx0:b) (x5:(X Xx0))=> ((((x2 Xx0) x5) S0) x1))) x3)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------