TSTP Solution File: SYO338^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO338^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:11 EDT 2022
% Result : Unknown 10.82s 11.01s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO338^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % RAMPerCPU : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sat Mar 12 04:56:02 EST 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.35 Python 2.7.5
% 8.06/8.27 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 8.06/8.27 FOF formula (<kernel.Constant object at 0x12b4878>, <kernel.Type object at 0x12b4b48>) of role type named a_type
% 8.06/8.27 Using role type
% 8.06/8.27 Declaring a:Type
% 8.06/8.27 FOF formula (forall (R:(a->(a->Prop))) (U:((a->Prop)->a)), ((or ((or ((ex a) (fun (X:a)=> ((ex a) (fun (Y:a)=> ((ex a) (fun (Z:a)=> ((and ((and ((or ((R X) Y)) ((R X) Y))) ((or ((R Y) Z)) ((R Y) Z)))) ((or (((R X) Z)->False)) (((R X) Z)->False)))))))))) ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((or ((ex a) (fun (Xz:a)=> ((and ((or (Xs Xz)) (Xs Xz))) ((or (((R Xz) (U Xs))->False)) (((R Xz) (U Xs))->False)))))) ((ex a) (fun (Xj:a)=> ((and (forall (Xk:a), ((or ((or ((or ((Xs Xk)->False)) ((Xs Xk)->False))) ((R Xk) Xj))) ((R Xk) Xj)))) ((or (((R (U Xs)) Xj)->False)) (((R (U Xs)) Xj)->False)))))))))) (forall (Xf:(a->a)), ((or ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((or ((R Xx) Xy)) ((R Xx) Xy))) ((or (((R (Xf Xx)) (Xf Xy))->False)) (((R (Xf Xx)) (Xf Xy))->False)))))))) ((ex a) (fun (Xw:a)=> ((and ((or ((R Xw) (Xf Xw))) ((R Xw) (Xf Xw)))) ((or ((R (Xf Xw)) Xw)) ((R (Xf Xw)) Xw))))))))) of role conjecture named cT145_DOUBLE
% 8.06/8.27 Conjecture to prove = (forall (R:(a->(a->Prop))) (U:((a->Prop)->a)), ((or ((or ((ex a) (fun (X:a)=> ((ex a) (fun (Y:a)=> ((ex a) (fun (Z:a)=> ((and ((and ((or ((R X) Y)) ((R X) Y))) ((or ((R Y) Z)) ((R Y) Z)))) ((or (((R X) Z)->False)) (((R X) Z)->False)))))))))) ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((or ((ex a) (fun (Xz:a)=> ((and ((or (Xs Xz)) (Xs Xz))) ((or (((R Xz) (U Xs))->False)) (((R Xz) (U Xs))->False)))))) ((ex a) (fun (Xj:a)=> ((and (forall (Xk:a), ((or ((or ((or ((Xs Xk)->False)) ((Xs Xk)->False))) ((R Xk) Xj))) ((R Xk) Xj)))) ((or (((R (U Xs)) Xj)->False)) (((R (U Xs)) Xj)->False)))))))))) (forall (Xf:(a->a)), ((or ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((or ((R Xx) Xy)) ((R Xx) Xy))) ((or (((R (Xf Xx)) (Xf Xy))->False)) (((R (Xf Xx)) (Xf Xy))->False)))))))) ((ex a) (fun (Xw:a)=> ((and ((or ((R Xw) (Xf Xw))) ((R Xw) (Xf Xw)))) ((or ((R (Xf Xw)) Xw)) ((R (Xf Xw)) Xw))))))))):Prop
% 8.06/8.27 Parameter a_DUMMY:a.
% 8.06/8.27 We need to prove ['(forall (R:(a->(a->Prop))) (U:((a->Prop)->a)), ((or ((or ((ex a) (fun (X:a)=> ((ex a) (fun (Y:a)=> ((ex a) (fun (Z:a)=> ((and ((and ((or ((R X) Y)) ((R X) Y))) ((or ((R Y) Z)) ((R Y) Z)))) ((or (((R X) Z)->False)) (((R X) Z)->False)))))))))) ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((or ((ex a) (fun (Xz:a)=> ((and ((or (Xs Xz)) (Xs Xz))) ((or (((R Xz) (U Xs))->False)) (((R Xz) (U Xs))->False)))))) ((ex a) (fun (Xj:a)=> ((and (forall (Xk:a), ((or ((or ((or ((Xs Xk)->False)) ((Xs Xk)->False))) ((R Xk) Xj))) ((R Xk) Xj)))) ((or (((R (U Xs)) Xj)->False)) (((R (U Xs)) Xj)->False)))))))))) (forall (Xf:(a->a)), ((or ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((or ((R Xx) Xy)) ((R Xx) Xy))) ((or (((R (Xf Xx)) (Xf Xy))->False)) (((R (Xf Xx)) (Xf Xy))->False)))))))) ((ex a) (fun (Xw:a)=> ((and ((or ((R Xw) (Xf Xw))) ((R Xw) (Xf Xw)))) ((or ((R (Xf Xw)) Xw)) ((R (Xf Xw)) Xw)))))))))']
% 8.06/8.27 Parameter a:Type.
% 8.06/8.27 Trying to prove (forall (R:(a->(a->Prop))) (U:((a->Prop)->a)), ((or ((or ((ex a) (fun (X:a)=> ((ex a) (fun (Y:a)=> ((ex a) (fun (Z:a)=> ((and ((and ((or ((R X) Y)) ((R X) Y))) ((or ((R Y) Z)) ((R Y) Z)))) ((or (((R X) Z)->False)) (((R X) Z)->False)))))))))) ((ex (a->Prop)) (fun (Xs:(a->Prop))=> ((or ((ex a) (fun (Xz:a)=> ((and ((or (Xs Xz)) (Xs Xz))) ((or (((R Xz) (U Xs))->False)) (((R Xz) (U Xs))->False)))))) ((ex a) (fun (Xj:a)=> ((and (forall (Xk:a), ((or ((or ((or ((Xs Xk)->False)) ((Xs Xk)->False))) ((R Xk) Xj))) ((R Xk) Xj)))) ((or (((R (U Xs)) Xj)->False)) (((R (U Xs)) Xj)->False)))))))))) (forall (Xf:(a->a)), ((or ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((or ((R Xx) Xy)) ((R Xx) Xy))) ((or (((R (Xf Xx)) (Xf Xy))->False)) (((R (Xf Xx)) (Xf Xy))->False)))))))) ((ex a) (fun (Xw:a)=> ((and ((or ((R Xw) (Xf Xw))) ((R Xw) (Xf Xw)))) ((or ((R (Xf Xw)) Xw)) ((R (Xf Xw)) Xw)))))))))
% 8.06/8.27 Found a_DUMMY:a
% 8.06/8.27 Found a_DUMMY as proof of a
% 8.06/8.27 Found (x00 a_DUMMY) as proof of False
% 8.06/8.27 Found (x00 a_DUMMY) as proof of False
% 9.48/9.67 Found (fun (x00:(x Xk))=> (x00 a_DUMMY)) as proof of False
% 9.48/9.67 Found (fun (x00:(x Xk))=> (x00 a_DUMMY)) as proof of ((x Xk)->False)
% 9.48/9.67 Found (or_intror20 (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.67 Found ((or_intror2 ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.67 Found (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.67 Found (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.67 Found (or_introl20 (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.67 Found ((or_introl2 ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.67 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.67 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.67 Found (or_introl10 (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.67 Found ((or_introl1 ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.67 Found (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.67 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.67 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))))) as proof of (forall (Xk:a), ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)))
% 9.48/9.67 Found x0:=??:a
% 9.48/9.67 Found x0 as proof of a
% 9.48/9.67 Found (x00 x0) as proof of False
% 9.48/9.67 Found (x00 x0) as proof of False
% 9.48/9.67 Found (fun (x00:(x Xk))=> (x00 x0)) as proof of False
% 9.48/9.67 Found (fun (x00:(x Xk))=> (x00 x0)) as proof of ((x Xk)->False)
% 9.48/9.67 Found (or_introl40 (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.67 Found ((or_introl4 ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.67 Found (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.67 Found (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.67 Found (or_introl30 (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.67 Found ((or_introl3 ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.67 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.70 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.70 Found (or_introl20 (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.70 Found ((or_introl2 ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.70 Found (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.70 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.70 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))))) as proof of (forall (Xk:a), ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)))
% 9.48/9.70 Found x0:=??:a
% 9.48/9.70 Found x0 as proof of a
% 9.48/9.70 Found (x00 x0) as proof of False
% 9.48/9.70 Found (x00 x0) as proof of False
% 9.48/9.70 Found (fun (x00:(x Xk))=> (x00 x0)) as proof of False
% 9.48/9.70 Found (fun (x00:(x Xk))=> (x00 x0)) as proof of ((x Xk)->False)
% 9.48/9.70 Found (or_introl20 (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.70 Found ((or_introl2 ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.70 Found (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.70 Found (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 9.48/9.70 Found (or_introl10 (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.70 Found ((or_introl1 ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.70 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.70 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 9.48/9.70 Found (or_introl00 (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.70 Found ((or_introl0 ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 9.48/9.70 Found (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.54 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.54 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))))) as proof of (forall (Xk:a), ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)))
% 10.38/10.54 Found x0:=??:a
% 10.38/10.54 Found x0 as proof of a
% 10.38/10.54 Found (x00 x0) as proof of False
% 10.38/10.54 Found (x00 x0) as proof of False
% 10.38/10.54 Found (fun (x00:(x Xk))=> (x00 x0)) as proof of False
% 10.38/10.54 Found (fun (x00:(x Xk))=> (x00 x0)) as proof of ((x Xk)->False)
% 10.38/10.54 Found (or_intror10 (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.54 Found ((or_intror1 ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.54 Found (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.54 Found (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.54 Found (or_introl30 (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.38/10.54 Found ((or_introl3 ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.38/10.54 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.38/10.54 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.38/10.54 Found (or_introl20 (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.54 Found ((or_introl2 ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.54 Found (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.54 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.54 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))))) as proof of (forall (Xk:a), ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)))
% 10.38/10.54 Found a_DUMMY:a
% 10.38/10.54 Found a_DUMMY as proof of a
% 10.38/10.54 Found (x00 a_DUMMY) as proof of False
% 10.38/10.54 Found (x00 a_DUMMY) as proof of False
% 10.38/10.55 Found (fun (x00:(x Xk))=> (x00 a_DUMMY)) as proof of False
% 10.38/10.55 Found (fun (x00:(x Xk))=> (x00 a_DUMMY)) as proof of ((x Xk)->False)
% 10.38/10.55 Found (or_intror00 (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.55 Found ((or_intror0 ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.55 Found (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.55 Found (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.55 Found (or_introl40 (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.38/10.55 Found ((or_introl4 ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.38/10.55 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.38/10.55 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.38/10.55 Found (or_introl30 (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.55 Found ((or_introl3 ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.55 Found (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.55 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.38/10.55 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))))) as proof of (forall (Xk:a), ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)))
% 10.38/10.55 Found a_DUMMY:a
% 10.38/10.55 Found a_DUMMY as proof of a
% 10.38/10.55 Found (x00 a_DUMMY) as proof of False
% 10.38/10.55 Found (x00 a_DUMMY) as proof of False
% 10.38/10.55 Found (fun (x00:(x Xk))=> (x00 a_DUMMY)) as proof of False
% 10.38/10.55 Found (fun (x00:(x Xk))=> (x00 a_DUMMY)) as proof of ((x Xk)->False)
% 10.38/10.55 Found (or_intror20 (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.55 Found ((or_intror2 ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.55 Found (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.55 Found (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.38/10.55 Found (or_introl20 (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.38/10.55 Found ((or_introl2 ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.40/10.56 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.40/10.56 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.40/10.56 Found (or_introl10 (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.40/10.56 Found ((or_introl1 ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.40/10.56 Found (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.40/10.56 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.40/10.56 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_intror ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))))) as proof of (forall (Xk:a), ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)))
% 10.40/10.56 Found a_DUMMY:a
% 10.40/10.56 Found a_DUMMY as proof of a
% 10.40/10.56 Found (x00 a_DUMMY) as proof of False
% 10.40/10.56 Found (x00 a_DUMMY) as proof of False
% 10.40/10.56 Found (fun (x00:(x Xk))=> (x00 a_DUMMY)) as proof of False
% 10.40/10.56 Found (fun (x00:(x Xk))=> (x00 a_DUMMY)) as proof of ((x Xk)->False)
% 10.40/10.56 Found (or_introl30 (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.40/10.56 Found ((or_introl3 ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.40/10.56 Found (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.40/10.56 Found (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.40/10.56 Found (or_introl20 (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.40/10.56 Found ((or_introl2 ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.40/10.56 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.40/10.56 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.40/10.56 Found (or_introl10 (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.40/10.56 Found ((or_introl1 ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.68/10.84 Found (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.68/10.84 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.68/10.84 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 a_DUMMY)))))) as proof of (forall (Xk:a), ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)))
% 10.68/10.84 Found x0:=??:a
% 10.68/10.84 Found x0 as proof of a
% 10.68/10.84 Found (x00 x0) as proof of False
% 10.68/10.84 Found (x00 x0) as proof of False
% 10.68/10.84 Found (fun (x00:(x Xk))=> (x00 x0)) as proof of False
% 10.68/10.84 Found (fun (x00:(x Xk))=> (x00 x0)) as proof of ((x Xk)->False)
% 10.68/10.84 Found (or_introl40 (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.68/10.84 Found ((or_introl4 ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.68/10.84 Found (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.68/10.84 Found (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))) as proof of ((or ((x Xk)->False)) ((x Xk)->False))
% 10.68/10.84 Found (or_introl30 (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.68/10.84 Found ((or_introl3 ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.68/10.84 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.68/10.84 Found (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))) as proof of ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))
% 10.68/10.84 Found (or_introl20 (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.68/10.84 Found ((or_introl2 ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.68/10.84 Found (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.68/10.84 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))))) as proof of ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0))
% 10.68/10.84 Found (fun (Xk:a)=> (((or_introl ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)) (((or_introl ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0)) (((or_introl ((x Xk)->False)) ((x Xk)->False)) (fun (x00:(x Xk))=> (x00 x0)))))) as proof of (forall (Xk:a), ((or ((or ((or ((x Xk)->False)) ((x Xk)->False))) ((R Xk) x0))) ((R Xk) x0)))
% 10.82/10.99 % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------