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cocATP---0.2.0.THM-Prf.s

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Problem Process solution in
SystemOnTSTP Download .tgz 
%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV168^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n186.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 13:33:49 EDT 2014

% Result   : Theorem 31.35s
% Output   : Proof 31.35s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV168^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n186.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 08:19:01 CDT 2014
% % CPUTime  : 31.35 
% 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 0xab0830>, <kernel.Type object at 0xab0f38>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0xe88050>, <kernel.DependentProduct object at 0xab05f0>) of role type named q
% Using role type
% Declaring q:((a->(a->a))->a)
% FOF formula (<kernel.Constant object at 0xab0dd0>, <kernel.DependentProduct object at 0xab0518>) of role type named p
% Using role type
% Declaring p:((a->(a->a))->a)
% FOF formula (((and (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))->(((eq ((a->(a->a))->a)) p) q)) of role conjecture named cTHM188_PARTIAL_pme
% Conjecture to prove = (((and (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))->(((eq ((a->(a->a))->a)) p) q)):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(((and (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))->(((eq ((a->(a->a))->a)) p) q))']
% Parameter a:Type.
% Parameter q:((a->(a->a))->a).
% Parameter p:((a->(a->a))->a).
% Trying to prove (((and (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))->(((eq ((a->(a->a))->a)) p) q))
% Found eq_ref000:=(eq_ref00 P):((P p)->(P p))
% Found (eq_ref00 P) as proof of (P0 p)
% Found ((eq_ref0 p) P) as proof of (P0 p)
% Found (((eq_ref ((a->(a->a))->a)) p) P) as proof of (P0 p)
% Found (((eq_ref ((a->(a->a))->a)) p) P) as proof of (P0 p)
% Found eq_ref000:=(eq_ref00 P):((P p)->(P p))
% Found (eq_ref00 P) as proof of (P0 p)
% Found ((eq_ref0 p) P) as proof of (P0 p)
% Found (((eq_ref ((a->(a->a))->a)) p) P) as proof of (P0 p)
% Found (((eq_ref ((a->(a->a))->a)) p) P) as proof of (P0 p)
% Found eq_ref000:=(eq_ref00 P):((P p)->(P p))
% Found (eq_ref00 P) as proof of (P0 p)
% Found ((eq_ref0 p) P) as proof of (P0 p)
% Found (((eq_ref ((a->(a->a))->a)) p) P) as proof of (P0 p)
% Found (((eq_ref ((a->(a->a))->a)) p) P) as proof of (P0 p)
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->(a->a))->a)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->(a->a))->a)) b) q)
% Found ((eq_ref ((a->(a->a))->a)) b) as proof of (((eq ((a->(a->a))->a)) b) q)
% Found ((eq_ref ((a->(a->a))->a)) b) as proof of (((eq ((a->(a->a))->a)) b) q)
% Found ((eq_ref ((a->(a->a))->a)) b) as proof of (((eq ((a->(a->a))->a)) b) q)
% Found eq_ref00:=(eq_ref0 p):(((eq ((a->(a->a))->a)) p) p)
% Found (eq_ref0 p) as proof of (((eq ((a->(a->a))->a)) p) b)
% Found ((eq_ref ((a->(a->a))->a)) p) as proof of (((eq ((a->(a->a))->a)) p) b)
% Found ((eq_ref ((a->(a->a))->a)) p) as proof of (((eq ((a->(a->a))->a)) p) b)
% Found ((eq_ref ((a->(a->a))->a)) p) as proof of (((eq ((a->(a->a))->a)) p) b)
% Found x00:=(x0 (fun (x2:((a->(a->a))->a))=> (P p))):((P p)->(P p))
% Found (x0 (fun (x2:((a->(a->a))->a))=> (P p))) as proof of (P0 p)
% Found (x0 (fun (x2:((a->(a->a))->a))=> (P p))) as proof of (P0 p)
% Found x00:=(x0 (fun (x2:((a->(a->a))->a))=> (P p))):((P p)->(P p))
% Found (x0 (fun (x2:((a->(a->a))->a))=> (P p))) as proof of (P0 p)
% Found (x0 (fun (x2:((a->(a->a))->a))=> (P p))) as proof of (P0 p)
% Found x00:=(x0 (fun (x2:((a->(a->a))->a))=> (P p))):((P p)->(P p))
% Found (x0 (fun (x2:((a->(a->a))->a))=> (P p))) as proof of (P0 p)
% Found (x0 (fun (x2:((a->(a->a))->a))=> (P p))) as proof of (P0 p)
% Found eq_ref000:=(eq_ref00 P):((P q)->(P q))
% Found (eq_ref00 P) as proof of (P0 q)
% Found ((eq_ref0 q) P) as proof of (P0 q)
% Found (((eq_ref ((a->(a->a))->a)) q) P) as proof of (P0 q)
% Found (((eq_ref ((a->(a->a))->a)) q) P) as proof of (P0 q)
% Found eq_ref000:=(eq_ref00 P):((P q)->(P q))
% Found (eq_ref00 P) as proof of (P0 q)
% Found ((eq_ref0 q) P) as proof of (P0 q)
% Found (((eq_ref ((a->(a->a))->a)) q) P) as proof of (P0 q)
% Found (((eq_ref ((a->(a->a))->a)) q) P) as proof of (P0 q)
% Found eq_ref000:=(eq_ref00 P):((P (p x0))->(P (p x0)))
% Found (eq_ref00 P) as proof of (P0 (p x0))
% Found ((eq_ref0 (p x0)) P) as proof of (P0 (p x0))
% Found (((eq_ref a) (p x0)) P) as proof of (P0 (p x0))
% Found (((eq_ref a) (p x0)) P) as proof of (P0 (p x0))
% Found eq_ref000:=(eq_ref00 P):((P (p x0))->(P (p x0)))
% Found (eq_ref00 P) as proof of (P0 (p x0))
% Found ((eq_ref0 (p x0)) P) as proof of (P0 (p x0))
% Found (((eq_ref a) (p x0)) P) as proof of (P0 (p x0))
% Found (((eq_ref a) (p x0)) P) as proof of (P0 (p x0))
% Found eq_ref00:=(eq_ref0 b):(((eq ((a->(a->a))->a)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((a->(a->a))->a)) b) p)
% Found ((eq_ref ((a->(a->a))->a)) b) as proof of (((eq ((a->(a->a))->a)) b) p)
% Found ((eq_ref ((a->(a->a))->a)) b) as proof of (((eq ((a->(a->a))->a)) b) p)
% Found ((eq_ref ((a->(a->a))->a)) b) as proof of (((eq ((a->(a->a))->a)) b) p)
% Found eta_expansion000:=(eta_expansion00 q):(((eq ((a->(a->a))->a)) q) (fun (x:(a->(a->a)))=> (q x)))
% Found (eta_expansion00 q) as proof of (((eq ((a->(a->a))->a)) q) b)
% Found ((eta_expansion0 a) q) as proof of (((eq ((a->(a->a))->a)) q) b)
% Found (((eta_expansion (a->(a->a))) a) q) as proof of (((eq ((a->(a->a))->a)) q) b)
% Found (((eta_expansion (a->(a->a))) a) q) as proof of (((eq ((a->(a->a))->a)) q) b)
% Found (((eta_expansion (a->(a->a))) a) q) as proof of (((eq ((a->(a->a))->a)) q) b)
% Found x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))
% Found x1 as proof of (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))
% Found eq_ref00:=(eq_ref0 (p x0)):(((eq a) (p x0)) (p x0))
% Found (eq_ref0 (p x0)) as proof of (((eq a) (p x0)) b)
% Found ((eq_ref a) (p x0)) as proof of (((eq a) (p x0)) b)
% Found ((eq_ref a) (p x0)) as proof of (((eq a) (p x0)) b)
% Found ((eq_ref a) (p x0)) as proof of (((eq a) (p x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) (q x0))
% Found ((eq_ref a) b) as proof of (((eq a) b) (q x0))
% Found ((eq_ref a) b) as proof of (((eq a) b) (q x0))
% Found ((eq_ref a) b) as proof of (((eq a) b) (q x0))
% Found eq_ref00:=(eq_ref0 (p x0)):(((eq a) (p x0)) (p x0))
% Found (eq_ref0 (p x0)) as proof of (((eq a) (p x0)) b)
% Found ((eq_ref a) (p x0)) as proof of (((eq a) (p x0)) b)
% Found ((eq_ref a) (p x0)) as proof of (((eq a) (p x0)) b)
% Found ((eq_ref a) (p x0)) as proof of (((eq a) (p x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) (q x0))
% Found ((eq_ref a) b) as proof of (((eq a) b) (q x0))
% Found ((eq_ref a) b) as proof of (((eq a) b) (q x0))
% Found ((eq_ref a) b) as proof of (((eq a) b) (q x0))
% Found eq_ref00:=(eq_ref0 q):(((eq ((a->(a->a))->a)) q) q)
% Found (eq_ref0 q) as proof of (((eq ((a->(a->a))->a)) q) q)
% Found ((eq_ref ((a->(a->a))->a)) q) as proof of (((eq ((a->(a->a))->a)) q) q)
% Found ((eq_ref ((a->(a->a))->a)) q) as proof of (((eq ((a->(a->a))->a)) q) q)
% Found (x00 ((eq_ref ((a->(a->a))->a)) q)) as proof of (((eq ((a->(a->a))->a)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) q)
% Found ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q)) as proof of (((eq ((a->(a->a))->a)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) q)
% Found ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q)) as proof of (((eq ((a->(a->a))->a)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) q)
% Found ((eq_trans0000 x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found (((eq_trans000 (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found ((((fun (b:((a->(a->a))->a))=> ((eq_trans00 b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found ((((fun (b:((a->(a->a))->a))=> (((eq_trans0 p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found (fun (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q)))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found (fun (x0:(((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q)))) as proof of ((((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->(((eq ((a->(a->a))->a)) p) q))
% Found (fun (x0:(((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q)))) as proof of ((((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->((((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->(((eq ((a->(a->a))->a)) p) q)))
% Found (and_rect00 (fun (x0:(((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found ((and_rect0 (((eq ((a->(a->a))->a)) p) q)) (fun (x0:(((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found (((fun (P:Type) (x0:((((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->((((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->P)))=> (((((and_rect (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) P) x0) x)) (((eq ((a->(a->a))->a)) p) q)) (fun (x0:(((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found (fun (x:((and (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))))=> (((fun (P:Type) (x0:((((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->((((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->P)))=> (((((and_rect (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) P) x0) x)) (((eq ((a->(a->a))->a)) p) q)) (fun (x0:(((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q)))))) as proof of (((eq ((a->(a->a))->a)) p) q)
% Found (fun (x:((and (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))))=> (((fun (P:Type) (x0:((((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->((((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->P)))=> (((((and_rect (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) P) x0) x)) (((eq ((a->(a->a))->a)) p) q)) (fun (x0:(((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q)))))) as proof of (((and (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))->(((eq ((a->(a->a))->a)) p) q))
% Got proof (fun (x:((and (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))))=> (((fun (P:Type) (x0:((((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->((((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->P)))=> (((((and_rect (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) P) x0) x)) (((eq ((a->(a->a))->a)) p) q)) (fun (x0:(((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))))))
% Time elapsed = 30.823890s
% node=3941 cost=489.000000 depth=18
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:((and (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))))=> (((fun (P:Type) (x0:((((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->((((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))->P)))=> (((((and_rect (((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) P) x0) x)) (((eq ((a->(a->a))->a)) p) q)) (fun (x0:(((eq ((a->(a->a))->a)) q) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy)))))) (x1:(((eq ((a->(a->a))->a)) p) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))))=> ((((fun (b:((a->(a->a))->a))=> ((((eq_trans ((a->(a->a))->a)) p) b) q)) (fun (Xg:(a->(a->a)))=> ((Xg (q (fun (Xx:a) (Xy:a)=> Xx))) (q (fun (Xx:a) (Xy:a)=> Xy))))) x1) ((x0 (fun (x3:((a->(a->a))->a))=> (((eq ((a->(a->a))->a)) x3) q))) ((eq_ref ((a->(a->a))->a)) q))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------