TSTP Solution File: SEV017^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV017^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n179.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 13:33:35 EDT 2014
% Result : Theorem 0.64s
% Output : Proof 0.64s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV017^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n179.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 07:30:21 CDT 2014
% % CPUTime : 0.64
% 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 0xdbe830>, <kernel.Type object at 0xdbed40>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))))) of role conjecture named cTHM514_pme
% Conjecture to prove = (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz))))))']
% Parameter a:Type.
% Trying to prove (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz))))))
% Found x0:((Xr Xx) Xy)
% Instantiate: Xy0:=Xy:a
% Found x0 as proof of ((Xr Xx) Xy0)
% Found x1:((Xr Xy) Xz)
% Instantiate: Xy0:=Xy:a
% Found x1 as proof of ((Xr Xy0) Xz)
% Found ((conj00 x0) x1) as proof of ((and ((Xr Xx) Xy0)) ((Xr Xy0) Xz))
% Found (((conj0 ((Xr Xy0) Xz)) x0) x1) as proof of ((and ((Xr Xx) Xy0)) ((Xr Xy0) Xz))
% Found ((((conj ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) x0) x1) as proof of ((and ((Xr Xx) Xy0)) ((Xr Xy0) Xz))
% Found ((((conj ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) x0) x1) as proof of ((and ((Xr Xx) Xy0)) ((Xr Xy0) Xz))
% Found (x3000 ((((conj ((Xr Xx) Xy0)) ((Xr Xy0) Xz)) x0) x1)) as proof of ((Xr Xx) Xz)
% Found ((x300 Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)) as proof of ((Xr Xx) Xz)
% Found (((fun (Xy0:a)=> ((x30 Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)) as proof of ((Xr Xx) Xz)
% Found (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)) as proof of ((Xr Xx) Xz)
% Found (fun (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))) as proof of ((Xr Xx) Xz)
% Found (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))) as proof of ((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0)))->((Xr Xx) Xz))
% Found (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))) as proof of (((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))->((forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0)))->((Xr Xx) Xz)))
% Found (and_rect00 (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)))) as proof of ((Xr Xx) Xz)
% Found ((and_rect0 ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)))) as proof of ((Xr Xx) Xz)
% Found (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)))) as proof of ((Xr Xx) Xz)
% Found (fun (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of ((Xr Xx) Xz)
% Found (fun (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (((Xr Xy) Xz)->((Xr Xx) Xz))
% Found (fun (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))
% Found (fun (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (forall (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (forall (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz))))
% Found (fun (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (forall (Xx:a) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz))))
% Found (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz)))))
% Found (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1))))) as proof of (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a) (Xy:a) (Xz:a), (((Xr Xx) Xy)->(((Xr Xy) Xz)->((Xr Xx) Xz))))))
% Got proof (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)))))
% Time elapsed = 0.320395s
% node=47 cost=642.000000 depth=22
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a) (Xy:a) (Xz:a) (x0:((Xr Xx) Xy)) (x1:((Xr Xy) Xz))=> (((fun (P:Type) (x2:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x2) x)) ((Xr Xx) Xz)) (fun (x2:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x3:(forall (Xx0:a) (Xy:a) (Xz0:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz0))->((Xr Xx0) Xz0))))=> (((fun (Xy0:a)=> (((x3 Xx) Xy0) Xz)) Xy) ((((conj ((Xr Xx) Xy)) ((Xr Xy) Xz)) x0) x1)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------