TSTP Solution File: SWV447^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SWV447^1 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n112.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 13:36:00 EDT 2014
% Result : Theorem 2.20s
% Output : Proof 2.20s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SWV447^1 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n112.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 09:57:41 CDT 2014
% % CPUTime : 2.20
% 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 0xa15ea8>, <kernel.Constant object at 0xbed710>) of role type named nil_type
% Using role type
% Declaring nil:fofType
% FOF formula (<kernel.Constant object at 0xbee638>, <kernel.DependentProduct object at 0xbed680>) of role type named cons_type
% Using role type
% Declaring cons:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xa15ea8>, <kernel.DependentProduct object at 0xbed710>) of role type named map_type
% Using role type
% Declaring map:((fofType->fofType)->(fofType->fofType))
% FOF formula (forall (F:(fofType->fofType)), (((eq fofType) ((map F) nil)) nil)) of role axiom named ax1
% A new axiom: (forall (F:(fofType->fofType)), (((eq fofType) ((map F) nil)) nil))
% FOF formula (forall (F:(fofType->fofType)) (X:fofType) (Y:fofType), (((eq fofType) ((map F) ((cons X) Y))) ((cons (F X)) ((map F) Y)))) of role axiom named ax2
% A new axiom: (forall (F:(fofType->fofType)) (X:fofType) (Y:fofType), (((eq fofType) ((map F) ((cons X) Y))) ((cons (F X)) ((map F) Y))))
% FOF formula (forall (A:fofType), (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil))) of role conjecture named test
% Conjecture to prove = (forall (A:fofType), (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil))):Prop
% We need to prove ['(forall (A:fofType), (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil)))']
% Parameter fofType:Type.
% Parameter nil:fofType.
% Parameter cons:(fofType->(fofType->fofType)).
% Parameter map:((fofType->fofType)->(fofType->fofType)).
% Axiom ax1:(forall (F:(fofType->fofType)), (((eq fofType) ((map F) nil)) nil)).
% Axiom ax2:(forall (F:(fofType->fofType)) (X:fofType) (Y:fofType), (((eq fofType) ((map F) ((cons X) Y))) ((cons (F X)) ((map F) Y)))).
% Trying to prove (forall (A:fofType), (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil)))
% Found ax1__eq_sym00:=(ax1__eq_sym0 (fun (x:fofType)=> (P ((cons A) x)))):((P ((cons A) nil))->(P ((cons A) ((map (fun (X:fofType)=> X)) nil))))
% Found (ax1__eq_sym0 (fun (x:fofType)=> (P ((cons A) x)))) as proof of ((P ((cons A) nil))->(P ((cons A) ((map (fun (X:fofType)=> X)) nil))))
% Found ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x)))) as proof of ((P ((cons A) nil))->(P ((cons A) ((map (fun (X:fofType)=> X)) nil))))
% Found ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x)))) as proof of ((P ((cons A) nil))->(P ((cons A) ((map (fun (X:fofType)=> X)) nil))))
% Found (ax2__eq_sym0000 ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))) as proof of ((P ((cons A) nil))->(P ((map (fun (X:fofType)=> X)) ((cons A) nil))))
% Found ((ax2__eq_sym000 (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))) as proof of ((P ((cons A) nil))->(P ((map (fun (X:fofType)=> X)) ((cons A) nil))))
% Found (((ax2__eq_sym00 nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))) as proof of ((P ((cons A) nil))->(P ((map (fun (X:fofType)=> X)) ((cons A) nil))))
% Found ((((ax2__eq_sym0 A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))) as proof of ((P ((cons A) nil))->(P ((map (fun (X:fofType)=> X)) ((cons A) nil))))
% Found (((((ax2__eq_sym (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))) as proof of ((P ((cons A) nil))->(P ((map (fun (X:fofType)=> X)) ((cons A) nil))))
% Found (fun (P:(fofType->Prop))=> (((((ax2__eq_sym (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x)))))) as proof of ((P ((cons A) nil))->(P ((map (fun (X:fofType)=> X)) ((cons A) nil))))
% Found (fun (P:(fofType->Prop))=> (((((ax2__eq_sym (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x)))))) as proof of (((eq fofType) ((cons A) nil)) ((map (fun (X:fofType)=> X)) ((cons A) nil)))
% Found (eq_sym000 (fun (P:(fofType->Prop))=> (((((ax2__eq_sym (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))))) as proof of (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil))
% Found ((eq_sym00 ((map (fun (X:fofType)=> X)) ((cons A) nil))) (fun (P:(fofType->Prop))=> (((((ax2__eq_sym (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))))) as proof of (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil))
% Found (((eq_sym0 ((cons A) nil)) ((map (fun (X:fofType)=> X)) ((cons A) nil))) (fun (P:(fofType->Prop))=> (((((ax2__eq_sym (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))))) as proof of (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil))
% Found ((((eq_sym fofType) ((cons A) nil)) ((map (fun (X:fofType)=> X)) ((cons A) nil))) (fun (P:(fofType->Prop))=> (((((ax2__eq_sym (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))))) as proof of (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil))
% Found (fun (A:fofType)=> ((((eq_sym fofType) ((cons A) nil)) ((map (fun (X:fofType)=> X)) ((cons A) nil))) (fun (P:(fofType->Prop))=> (((((ax2__eq_sym (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x)))))))) as proof of (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil))
% Found (fun (A:fofType)=> ((((eq_sym fofType) ((cons A) nil)) ((map (fun (X:fofType)=> X)) ((cons A) nil))) (fun (P:(fofType->Prop))=> (((((ax2__eq_sym (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) ((ax1__eq_sym (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x)))))))) as proof of (forall (A:fofType), (((eq fofType) ((map (fun (X:fofType)=> X)) ((cons A) nil))) ((cons A) nil)))
% Got proof (fun (A:fofType)=> ((((eq_sym fofType) ((cons A) nil)) ((map (fun (X:fofType)=> X)) ((cons A) nil))) (fun (P:(fofType->Prop))=> ((((((fun (F:(fofType->fofType)) (X:fofType) (Y:fofType)=> ((((eq_sym fofType) ((map F) ((cons X) Y))) ((cons (F X)) ((map F) Y))) (((ax2 F) X) Y))) (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) (((fun (F:(fofType->fofType))=> ((((eq_sym fofType) ((map F) nil)) nil) (ax1 F))) (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))))))
% Time elapsed = 1.865263s
% node=335 cost=185.000000 depth=15
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (A:fofType)=> ((((eq_sym fofType) ((cons A) nil)) ((map (fun (X:fofType)=> X)) ((cons A) nil))) (fun (P:(fofType->Prop))=> ((((((fun (F:(fofType->fofType)) (X:fofType) (Y:fofType)=> ((((eq_sym fofType) ((map F) ((cons X) Y))) ((cons (F X)) ((map F) Y))) (((ax2 F) X) Y))) (fun (X:fofType)=> X)) A) nil) (fun (x0:fofType)=> ((P ((cons A) nil))->(P x0)))) (((fun (F:(fofType->fofType))=> ((((eq_sym fofType) ((map F) nil)) nil) (ax1 F))) (fun (X:fofType)=> X)) (fun (x:fofType)=> (P ((cons A) x))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------