TSTP Solution File: NUM812^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM812^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n153.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:11:49 EST 2018
% Result : Theorem 5.03s
% Output : Proof 5.03s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM812^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.23 % Computer : n153.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.625MB
% 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Fri Jan 5 14:31:50 CST 2018
% 0.03/0.23 % CPUTime :
% 0.06/0.24 Python 2.7.13
% 4.97/5.17 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 4.97/5.17 FOF formula (<kernel.Constant object at 0x2b7f314903f8>, <kernel.Constant object at 0x2b7f31490cf8>) of role type named c0_type
% 4.97/5.17 Using role type
% 4.97/5.17 Declaring c0:fofType
% 4.97/5.17 FOF formula (<kernel.Constant object at 0x2b7f31badb48>, <kernel.DependentProduct object at 0x2b7f31490f38>) of role type named cS_type
% 4.97/5.17 Using role type
% 4.97/5.17 Declaring cS:(fofType->fofType)
% 4.97/5.17 FOF formula (<kernel.Constant object at 0x2b7f314907a0>, <kernel.Sort object at 0x2b7f297f9200>) of role type named cIND_type
% 4.97/5.17 Using role type
% 4.97/5.17 Declaring cIND:Prop
% 4.97/5.17 FOF formula (((eq Prop) cIND) (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx))))) of role definition named cIND_def
% 4.97/5.17 A new definition: (((eq Prop) cIND) (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx)))))
% 4.97/5.17 Defined: cIND:=(forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx))))
% 4.97/5.17 FOF formula (cIND->(forall (Xn:fofType), ((or (((eq fofType) Xn) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xn) (cS Xm))))))) of role conjecture named cTHM578
% 4.97/5.17 Conjecture to prove = (cIND->(forall (Xn:fofType), ((or (((eq fofType) Xn) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xn) (cS Xm))))))):Prop
% 4.97/5.17 We need to prove ['(cIND->(forall (Xn:fofType), ((or (((eq fofType) Xn) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xn) (cS Xm)))))))']
% 4.97/5.17 Parameter fofType:Type.
% 4.97/5.17 Parameter c0:fofType.
% 4.97/5.17 Parameter cS:(fofType->fofType).
% 4.97/5.17 Definition cIND:=(forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx)))):Prop.
% 4.97/5.17 Trying to prove (cIND->(forall (Xn:fofType), ((or (((eq fofType) Xn) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xn) (cS Xm)))))))
% 4.97/5.17 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 4.97/5.17 Found (eq_ref0 c0) as proof of (((eq fofType) c0) c0)
% 4.97/5.17 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 4.97/5.17 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 4.97/5.17 Found (or_introl00 ((eq_ref fofType) c0)) as proof of ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))
% 4.97/5.17 Found ((or_introl0 ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0)) as proof of ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))
% 4.97/5.17 Found (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0)) as proof of ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))
% 4.97/5.17 Found (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0)) as proof of ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))
% 4.97/5.17 Found x00:(P Xn)
% 4.97/5.17 Found (fun (x00:(P Xn))=> x00) as proof of (P Xn)
% 4.97/5.17 Found (fun (x00:(P Xn))=> x00) as proof of (P0 Xn)
% 4.97/5.17 Found eq_ref00:=(eq_ref0 Xn):(((eq fofType) Xn) Xn)
% 4.97/5.17 Found (eq_ref0 Xn) as proof of (((eq fofType) Xn) b)
% 4.97/5.17 Found ((eq_ref fofType) Xn) as proof of (((eq fofType) Xn) b)
% 4.97/5.17 Found ((eq_ref fofType) Xn) as proof of (((eq fofType) Xn) b)
% 4.97/5.17 Found ((eq_ref fofType) Xn) as proof of (((eq fofType) Xn) b)
% 4.97/5.17 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 4.97/5.17 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 4.97/5.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 4.97/5.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 4.97/5.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 4.97/5.17 Found eq_ref00:=(eq_ref0 (cS Xx)):(((eq fofType) (cS Xx)) (cS Xx))
% 4.97/5.17 Found (eq_ref0 (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS x2))
% 4.97/5.17 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS x2))
% 4.97/5.17 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS x2))
% 4.97/5.17 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS x2))
% 4.97/5.18 Found (ex_intro000 ((eq_ref fofType) (cS Xx))) as proof of ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))
% 4.97/5.18 Found ((ex_intro00 Xx) ((eq_ref fofType) (cS Xx))) as proof of ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))
% 4.97/5.18 Found (((ex_intro0 (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))) as proof of ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))
% 4.97/5.18 Found ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))) as proof of ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))
% 4.97/5.18 Found ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))) as proof of ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))
% 4.97/5.18 Found (or_intror00 ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx)))) as proof of ((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))
% 4.97/5.18 Found ((or_intror0 ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx)))) as proof of ((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))
% 4.97/5.18 Found (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx)))) as proof of ((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))
% 4.97/5.18 Found (fun (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))))) as proof of ((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))
% 4.97/5.18 Found (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))))) as proof of (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))))
% 4.97/5.18 Found (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))))) as proof of (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))
% 4.97/5.18 Found ((conj00 (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx)))))) as proof of ((and ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))))))
% 4.97/5.20 Found (((conj0 (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))) (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx)))))) as proof of ((and ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))))))
% 4.97/5.20 Found ((((conj ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))) (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx)))))) as proof of ((and ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))))))
% 4.97/5.20 Found ((((conj ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))) (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx)))))) as proof of ((and ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))))))
% 4.97/5.20 Found (x0 ((((conj ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))) (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))))))) as proof of (forall (Xn:fofType), ((or (((eq fofType) Xn) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xn) (cS Xm))))))
% 4.97/5.20 Found ((x (fun (x2:fofType)=> ((or (((eq fofType) x2) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) x2) (cS Xm))))))) ((((conj ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))) (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))))))) as proof of (forall (Xn:fofType), ((or (((eq fofType) Xn) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xn) (cS Xm))))))
% 4.97/5.20 Found (fun (x:cIND)=> ((x (fun (x2:fofType)=> ((or (((eq fofType) x2) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) x2) (cS Xm))))))) ((((conj ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))) (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx)))))))) as proof of (forall (Xn:fofType), ((or (((eq fofType) Xn) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xn) (cS Xm))))))
% 4.97/5.20 Found (fun (x:cIND)=> ((x (fun (x2:fofType)=> ((or (((eq fofType) x2) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) x2) (cS Xm))))))) ((((conj ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))) (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx)))))))) as proof of (cIND->(forall (Xn:fofType), ((or (((eq fofType) Xn) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xn) (cS Xm)))))))
% 4.97/5.20 Got proof (fun (x:cIND)=> ((x (fun (x2:fofType)=> ((or (((eq fofType) x2) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) x2) (cS Xm))))))) ((((conj ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))) (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))))))))
% 5.03/5.24 Time elapsed = 4.698301s
% 5.03/5.24 node=908 cost=469.000000 depth=22
% 5.03/5.24::::::::::::::::::::::
% 5.03/5.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/5.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/5.24 (fun (x:cIND)=> ((x (fun (x2:fofType)=> ((or (((eq fofType) x2) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) x2) (cS Xm))))))) ((((conj ((or (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm)))))) (forall (Xx:fofType), (((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm)))))->((or (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))))))) (((or_introl (((eq fofType) c0) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) c0) (cS Xm))))) ((eq_ref fofType) c0))) (fun (Xx:fofType) (x1:((or (((eq fofType) Xx) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) Xx) (cS Xm))))))=> (((or_intror (((eq fofType) (cS Xx)) c0)) ((ex fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm))))) ((((ex_intro fofType) (fun (Xm:fofType)=> (((eq fofType) (cS Xx)) (cS Xm)))) Xx) ((eq_ref fofType) (cS Xx))))))))
% 5.03/5.24 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------