TSTP Solution File: SYO038^1.003.004 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO038^1.003.004 : TPTP v7.5.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 00:50:27 EDT 2022
% Result : Timeout 300.03s 300.64s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO038^1.003.004 : TPTP v7.5.0. Released v5.3.0.
% 0.03/0.11 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Fri Mar 11 05:04:26 EST 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.33 Python 2.7.5
% 2.49/2.70 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 2.49/2.70 FOF formula (<kernel.Constant object at 0x17cb488>, <kernel.Constant object at 0x17c6998>) of role type named one
% 2.49/2.70 Using role type
% 2.49/2.70 Declaring one:fofType
% 2.49/2.70 FOF formula (<kernel.Constant object at 0x17c1d40>, <kernel.DependentProduct object at 0x17c6290>) of role type named s
% 2.49/2.70 Using role type
% 2.49/2.70 Declaring s:(fofType->fofType)
% 2.49/2.70 FOF formula (<kernel.Constant object at 0x17a4d40>, <kernel.DependentProduct object at 0x17c62d8>) of role type named f
% 2.49/2.70 Using role type
% 2.49/2.70 Declaring f:(fofType->(fofType->fofType))
% 2.49/2.70 FOF formula (<kernel.Constant object at 0x17a4d40>, <kernel.DependentProduct object at 0x17c6a28>) of role type named d
% 2.49/2.70 Using role type
% 2.49/2.70 Declaring d:(fofType->Prop)
% 2.49/2.70 FOF formula (forall (N:fofType), (((eq fofType) ((f N) one)) (s one))) of role axiom named ax1
% 2.49/2.70 A new axiom: (forall (N:fofType), (((eq fofType) ((f N) one)) (s one)))
% 2.49/2.70 FOF formula (forall (X:fofType), (((eq fofType) ((f one) (s X))) (s (s ((f one) X))))) of role axiom named ax2
% 2.49/2.70 A new axiom: (forall (X:fofType), (((eq fofType) ((f one) (s X))) (s (s ((f one) X)))))
% 2.49/2.70 FOF formula (forall (N:fofType) (X:fofType), (((eq fofType) ((f (s N)) (s X))) ((f N) ((f (s N)) X)))) of role axiom named ax3
% 2.49/2.70 A new axiom: (forall (N:fofType) (X:fofType), (((eq fofType) ((f (s N)) (s X))) ((f N) ((f (s N)) X))))
% 2.49/2.70 FOF formula (d one) of role axiom named ax4
% 2.49/2.70 A new axiom: (d one)
% 2.49/2.70 FOF formula (forall (X:fofType), ((d X)->(d (s X)))) of role axiom named ax5
% 2.49/2.70 A new axiom: (forall (X:fofType), ((d X)->(d (s X))))
% 2.49/2.70 FOF formula (d ((f (s (s one))) (s (s (s one))))) of role conjecture named conj
% 2.49/2.70 Conjecture to prove = (d ((f (s (s one))) (s (s (s one))))):Prop
% 2.49/2.70 We need to prove ['(d ((f (s (s one))) (s (s (s one)))))']
% 2.49/2.70 Parameter fofType:Type.
% 2.49/2.70 Parameter one:fofType.
% 2.49/2.70 Parameter s:(fofType->fofType).
% 2.49/2.70 Parameter f:(fofType->(fofType->fofType)).
% 2.49/2.70 Parameter d:(fofType->Prop).
% 2.49/2.70 Axiom ax1:(forall (N:fofType), (((eq fofType) ((f N) one)) (s one))).
% 2.49/2.70 Axiom ax2:(forall (X:fofType), (((eq fofType) ((f one) (s X))) (s (s ((f one) X))))).
% 2.49/2.70 Axiom ax3:(forall (N:fofType) (X:fofType), (((eq fofType) ((f (s N)) (s X))) ((f N) ((f (s N)) X)))).
% 2.49/2.70 Axiom ax4:(d one).
% 2.49/2.70 Axiom ax5:(forall (X:fofType), ((d X)->(d (s X)))).
% 2.49/2.70 Trying to prove (d ((f (s (s one))) (s (s (s one)))))
% 2.49/2.70 Found ax3__eq_sym00:=(ax3__eq_sym0 (s (s one))):(((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 2.49/2.70 Instantiate: b:=((f (s (s one))) (s (s (s one)))):fofType
% 2.49/2.70 Found ax3__eq_sym00 as proof of (((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) b)
% 2.49/2.70 Found ax4:(d one)
% 2.49/2.70 Instantiate: b:=one:fofType
% 2.49/2.70 Found ax4 as proof of (P b)
% 2.49/2.70 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 2.49/2.70 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f (s (s one))) (s (s one))))
% 2.49/2.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s (s one))) (s (s one))))
% 2.49/2.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s (s one))) (s (s one))))
% 2.49/2.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s (s one))) (s (s one))))
% 2.49/2.70 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 2.49/2.70 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f (s (s one))) (s (s one))))
% 2.49/2.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s (s one))) (s (s one))))
% 2.49/2.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s (s one))) (s (s one))))
% 2.49/2.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s (s one))) (s (s one))))
% 2.49/2.70 Found ax4:(d one)
% 2.49/2.70 Instantiate: b:=one:fofType
% 2.49/2.70 Found ax4 as proof of (P b)
% 2.49/2.70 Found eq_ref00:=(eq_ref0 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))):(((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 2.49/2.70 Found (eq_ref0 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) b)
% 2.49/2.70 Found ((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) b)
% 2.49/2.70 Found ((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) b)
% 17.32/17.53 Found ((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) b)
% 17.32/17.53 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 17.32/17.53 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f (s one)) ((f (s (s one))) (s one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s (s one))) (s one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s (s one))) (s one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s (s one))) (s one))))
% 17.32/17.53 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 17.32/17.53 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f (s one)) ((f (s (s one))) (s one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s (s one))) (s one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s (s one))) (s one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s (s one))) (s one))))
% 17.32/17.53 Found ax4:(d one)
% 17.32/17.53 Instantiate: b:=one:fofType
% 17.32/17.53 Found ax4 as proof of (P b)
% 17.32/17.53 Found eq_ref00:=(eq_ref0 ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))):(((eq fofType) ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))) ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one)))))
% 17.32/17.53 Found (eq_ref0 ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))) b)
% 17.32/17.53 Found ((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))) b)
% 17.32/17.53 Found ((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))) b)
% 17.32/17.53 Found ((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))) b)
% 17.32/17.53 Found ax4:(d one)
% 17.32/17.53 Instantiate: b:=one:fofType
% 17.32/17.53 Found ax4 as proof of (P b)
% 17.32/17.53 Found ax300:=(ax30 (s ((f N) one))):(((eq fofType) ((f (s ((f N) one))) (s (s ((f N) one))))) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one)))))
% 17.32/17.53 Found (ax30 (s ((f N) one))) as proof of (((eq fofType) ((f (s ((f N) one))) (s (s ((f N) one))))) b)
% 17.32/17.53 Found ((ax3 ((f N) one)) (s ((f N) one))) as proof of (((eq fofType) ((f (s ((f N) one))) (s (s ((f N) one))))) b)
% 17.32/17.53 Found ((ax3 ((f N) one)) (s ((f N) one))) as proof of (((eq fofType) ((f (s ((f N) one))) (s (s ((f N) one))))) b)
% 17.32/17.53 Found ((ax3 ((f N) one)) (s ((f N) one))) as proof of (((eq fofType) ((f (s ((f N) one))) (s (s ((f N) one))))) b)
% 17.32/17.53 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 17.32/17.53 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))
% 17.32/17.53 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 17.32/17.53 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s one)) ((f (s one)) ((f (s (s one))) one))))
% 17.32/17.53 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 17.32/17.53 Found (eq_ref0 a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 17.32/17.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 71.56/71.82 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 71.56/71.82 Found (eq_ref0 a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 71.56/71.82 Found ax3__eq_sym00:=(ax3__eq_sym0 (s (s one))):(((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 71.56/71.82 Found ax3__eq_sym00 as proof of (((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 71.56/71.82 Found ax4:(d one)
% 71.56/71.82 Instantiate: b:=one:fofType
% 71.56/71.82 Found ax4 as proof of (P b)
% 71.56/71.82 Found ax3__eq_sym10:=(ax3__eq_sym1 (s ((f N) one))):(((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) ((f (s ((f N) one))) (s (s ((f N) one)))))
% 71.56/71.82 Found (ax3__eq_sym1 (s ((f N) one))) as proof of (((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) b)
% 71.56/71.82 Found ((ax3__eq_sym ((f N) one)) (s ((f N) one))) as proof of (((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) b)
% 71.56/71.82 Found ((ax3__eq_sym ((f N) one)) (s ((f N) one))) as proof of (((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) b)
% 71.56/71.82 Found ((ax3__eq_sym ((f N) one)) (s ((f N) one))) as proof of (((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) b)
% 71.56/71.82 Found ax3__eq_sym00:=(ax3__eq_sym0 (s (s one))):(((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 71.56/71.82 Instantiate: a:=((f (s one)) ((f (s (s one))) (s (s one)))):fofType;b:=((f (s (s one))) (s (s (s one)))):fofType
% 71.56/71.82 Found ax3__eq_sym00 as proof of (((eq fofType) a) b)
% 71.56/71.82 Found ax4:(d one)
% 71.56/71.82 Instantiate: a:=one:fofType
% 71.56/71.82 Found ax4 as proof of (P a)
% 71.56/71.82 Found ax300:=(ax30 (s (s one))):(((eq fofType) ((f (s (s one))) (s (s (s one))))) ((f (s one)) ((f (s (s one))) (s (s one)))))
% 71.56/71.82 Found (ax30 (s (s one))) as proof of (((eq fofType) b) ((f (s one)) ((f (s (s one))) (s (s one)))))
% 71.56/71.82 Found ((ax3 (s one)) (s (s one))) as proof of (((eq fofType) b) ((f (s one)) ((f (s (s one))) (s (s one)))))
% 71.56/71.82 Found ((ax3 (s one)) (s (s one))) as proof of (((eq fofType) b) ((f (s one)) ((f (s (s one))) (s (s one)))))
% 71.56/71.82 Found ax300:=(ax30 (s ((f N) one))):(((eq fofType) ((f (s ((f N) one))) (s (s ((f N) one))))) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one)))))
% 71.56/71.82 Instantiate: b:=((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one)))):fofType
% 71.56/71.82 Found ax300 as proof of (((eq fofType) ((f (s ((f N) one))) (s (s ((f N) one))))) b)
% 71.56/71.82 Found ax4:(d one)
% 71.56/71.82 Instantiate: b:=one:fofType
% 71.56/71.82 Found ax4 as proof of (P b)
% 71.56/71.82 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 71.56/71.82 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f (s ((f N) one))) (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s ((f N) one))) (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s ((f N) one))) (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s ((f N) one))) (s ((f N) one))))
% 71.56/71.82 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 71.56/71.82 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f (s ((f N) one))) (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s ((f N) one))) (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s ((f N) one))) (s ((f N) one))))
% 71.56/71.82 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f (s ((f N) one))) (s ((f N) one))))
% 71.56/71.82 Found ax4:(d one)
% 71.56/71.82 Instantiate: b:=one:fofType
% 71.56/71.82 Found ax4 as proof of (P b)
% 71.56/71.82 Found eq_ref00:=(eq_ref0 ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))):(((eq fofType) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one)))))
% 71.56/71.82 Found (eq_ref0 ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))) b)
% 71.56/71.82 Found ((eq_ref fofType) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))) b)
% 126.08/126.37 Found ((eq_ref fofType) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))) b)
% 126.08/126.37 Found ((eq_ref fofType) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))) b)
% 126.08/126.37 Found ax3__eq_sym00:=(ax3__eq_sym0 (s (s one))):(((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 126.08/126.37 Found ax3__eq_sym00 as proof of (((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 126.08/126.37 Found ax3__eq_sym00:=(ax3__eq_sym0 (s (s one))):(((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 126.08/126.37 Found ax3__eq_sym00 as proof of (((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 126.08/126.37 Found ax4:(d one)
% 126.08/126.37 Instantiate: a:=one:fofType
% 126.08/126.37 Found ax4 as proof of (P a)
% 126.08/126.37 Found ax3__eq_sym01:=(ax3__eq_sym0 (s one)):(((eq fofType) ((f (s one)) ((f (s (s one))) (s one)))) ((f (s (s one))) (s (s one))))
% 126.08/126.37 Instantiate: a:=((f (s one)) ((f (s (s one))) (s one))):fofType;b:=((f (s (s one))) (s (s one))):fofType
% 126.08/126.37 Found ax3__eq_sym01 as proof of (((eq fofType) a) b)
% 126.08/126.37 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 126.08/126.37 Found (eq_ref0 b) as proof of (((eq fofType) b) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 126.08/126.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 126.08/126.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 126.08/126.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 126.08/126.37 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 126.08/126.37 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 126.08/126.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 126.08/126.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 126.08/126.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 126.08/126.37 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 126.08/126.37 Found (eq_ref0 a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 126.08/126.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 126.08/126.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 126.08/126.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 126.08/126.37 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 126.08/126.37 Found (eq_ref0 a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 126.08/126.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 126.08/126.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 126.08/126.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (s (s ((f N) one))))
% 126.08/126.37 Found ax4:(d one)
% 126.08/126.37 Instantiate: b:=one:fofType
% 126.08/126.37 Found ax4 as proof of (P b)
% 126.08/126.37 Found eq_ref00:=(eq_ref0 ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))):(((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one)))))
% 126.08/126.37 Found (eq_ref0 ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) b)
% 126.08/126.37 Found ((eq_ref fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) b)
% 126.08/126.37 Found ((eq_ref fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) b)
% 126.08/126.37 Found ((eq_ref fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f (s ((f N) one))) (s ((f N) one))))) b)
% 126.08/126.37 Found eq_ref000:=(eq_ref00 P0):((P0 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))->(P0 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))))
% 126.08/126.37 Found (eq_ref00 P0) as proof of (P1 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 216.20/216.59 Found ((eq_ref0 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) P0) as proof of (P1 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 216.20/216.59 Found (((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) P0) as proof of (P1 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 216.20/216.59 Found (((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) P0) as proof of (P1 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 216.20/216.59 Found ax3__eq_sym00:=(ax3__eq_sym0 (s (s one))):(((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 216.20/216.59 Found ax3__eq_sym00 as proof of (((eq fofType) ((f (s one)) ((f (s (s one))) (s (s one))))) ((f (s (s one))) (s (s (s one)))))
% 216.20/216.59 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 216.20/216.59 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))
% 216.20/216.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))
% 216.20/216.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))
% 216.20/216.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))
% 216.20/216.59 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 216.20/216.59 Found (eq_ref0 a) as proof of (((eq fofType) a) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))
% 216.20/216.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))
% 216.20/216.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))
% 216.20/216.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((f ((f N) one)) ((f (s ((f N) one))) ((f N) one))))
% 216.20/216.59 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 216.20/216.59 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% 216.20/216.59 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 216.20/216.59 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 216.20/216.59 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 216.20/216.59 Found eq_ref00:=(eq_ref0 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))):(((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one)))))
% 216.20/216.59 Found (eq_ref0 ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) b0)
% 216.20/216.59 Found ((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) b0)
% 216.20/216.59 Found ((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) b0)
% 216.20/216.59 Found ((eq_ref fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) as proof of (((eq fofType) ((f (s one)) ((f (s one)) ((f (s (s one))) (s one))))) b0)
% 216.20/216.59 Found ax301:=(ax30 (s (s one))):(((eq fofType) ((f (s (s one))) (s (s (s one))))) ((f (s one)) ((f (s (s one))) (s (s one)))))
% 216.20/216.59 Found ax301 as proof of (((eq fofType) ((f (s (s one))) (s (s (s one))))) ((f (s one)) ((f (s (s one))) (s (s one)))))
% 216.20/216.59 Found ax4:(d one)
% 216.20/216.59 Instantiate: b:=one:fofType
% 216.20/216.59 Found ax4 as proof of (P b)
% 216.20/216.59 Found eq_ref00:=(eq_ref0 ((f ((f N) one)) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) one))))):(((eq fofType) ((f ((f N) one)) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) one))))) ((f ((f N) one)) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) one)))))
% 216.20/216.59 Found (eq_ref0 ((f ((f N) one)) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) one))))) b)
% 216.20/216.59 Found ((eq_ref fofType) ((f ((f N) one)) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) one))))) b)
% 216.20/216.59 Found ((eq_ref fofType) ((f ((f N) one)) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) one))))) as proof of (((eq fofType) ((f ((f N) one)) ((f ((f N) one)) ((f ((f N) one)) ((f (s ((f N) one))) one))))) b)
% 216.20/216.59 Fou
%------------------------------------------------------------------------------