TSTP Solution File: SEV236^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV236^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n093.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 13:33:55 EDT 2014
% Result : Theorem 0.79s
% Output : Proof 0.79s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV236^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n093.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 08:35:01 CDT 2014
% % CPUTime : 0.79
% 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 0xf01368>, <kernel.Type object at 0xf01680>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0xd0c7e8>, <kernel.DependentProduct object at 0xf013f8>) of role type named cS
% Using role type
% Declaring cS:(a->Prop)
% FOF formula (<kernel.Constant object at 0xf01bd8>, <kernel.DependentProduct object at 0xf01998>) of role type named cK
% Using role type
% Declaring cK:((a->Prop)->(a->Prop))
% FOF formula ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), (((cK cS) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) Xx)))) of role conjecture named cTHM91_pme
% Conjecture to prove = ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), (((cK cS) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) Xx)))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), (((cK cS) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) Xx))))']
% Parameter a:Type.
% Parameter cS:(a->Prop).
% Parameter cK:((a->Prop)->(a->Prop)).
% Trying to prove ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), (((cK cS) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) Xx))))
% Found x0:((cK cS) Xx)
% Instantiate: X:=cS:(a->Prop)
% Found x0 as proof of ((cK X) Xx)
% Found x2:(X Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0))))
% Found (fun (x2:(X Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx))))))
% Found x01:(x2 Xx1)
% Found x01 as proof of (cS Xx1)
% Found (fun (x01:(x2 Xx1))=> x01) as proof of (cS Xx1)
% Found (fun (Xx1:a) (x01:(x2 Xx1))=> x01) as proof of ((x2 Xx1)->(cS Xx1))
% Found (fun (Xx1:a) (x01:(x2 Xx1))=> x01) as proof of (forall (Xx1:a), ((x2 Xx1)->(cS Xx1)))
% Found x1:(cS Xx)
% Found x1 as proof of (x2 Xx)
% Found ((conj00 (fun (Xx1:a) (x01:(x2 Xx1))=> x01)) x1) as proof of ((and (forall (Xx1:a), ((x2 Xx1)->(cS Xx1)))) (x2 Xx))
% Found (((conj0 (x2 Xx)) (fun (Xx1:a) (x01:(x2 Xx1))=> x01)) x1) as proof of ((and (forall (Xx1:a), ((x2 Xx1)->(cS Xx1)))) (x2 Xx))
% Found ((((conj (forall (Xx1:a), ((x2 Xx1)->(cS Xx1)))) (x2 Xx)) (fun (Xx1:a) (x01:(x2 Xx1))=> x01)) x1) as proof of ((and (forall (Xx1:a), ((x2 Xx1)->(cS Xx1)))) (x2 Xx))
% Found ((((conj (forall (Xx1:a), ((x2 Xx1)->(cS Xx1)))) (x2 Xx)) (fun (Xx1:a) (x01:(x2 Xx1))=> x01)) x1) as proof of ((and (forall (Xx1:a), ((x2 Xx1)->(cS Xx1)))) (x2 Xx))
% Found (ex_intro000 ((((conj (forall (Xx1:a), ((x2 Xx1)->(cS Xx1)))) (x2 Xx)) (fun (Xx1:a) (x01:(x2 Xx1))=> x01)) x1)) as proof of ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx))))
% Found ((ex_intro00 (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1)) as proof of ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx))))
% Found (((ex_intro0 (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1)) as proof of ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx))))
% Found ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1)) as proof of ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx))))
% Found (fun (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1))) as proof of ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx))))
% Found (fun (Xx:a) (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1))) as proof of ((cS Xx)->((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))))
% Found (fun (Xx:a) (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1))) as proof of (forall (Xx:a), ((cS Xx)->((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx))))))
% Found (x00 (fun (Xx:a) (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1)))) as proof of (forall (Xx:a), (((cK cS) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) Xx)))
% Found ((x0 (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) (fun (Xx:a) (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1)))) as proof of (forall (Xx:a), (((cK cS) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) Xx)))
% Found (((x cS) (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) (fun (Xx:a) (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1)))) as proof of (forall (Xx:a), (((cK cS) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) Xx)))
% Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx))))))=> (((x cS) (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) (fun (Xx:a) (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1))))) as proof of (forall (Xx:a), (((cK cS) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) Xx)))
% Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx))))))=> (((x cS) (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) (fun (Xx:a) (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1))))) as proof of ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), (((cK cS) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) Xx))))
% Got proof (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx))))))=> (((x cS) (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) (fun (Xx:a) (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1)))))
% Time elapsed = 0.467674s
% node=66 cost=472.000000 depth=16
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx))))))=> (((x cS) (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx0)))))) (fun (Xx:a) (x1:(cS Xx))=> ((((ex_intro (a->Prop)) (fun (S_3:(a->Prop))=> ((and (forall (Xx1:a), ((S_3 Xx1)->(cS Xx1)))) (S_3 Xx)))) (fun (a0:a)=> (cS a0))) ((((conj (forall (Xx1:a), (((fun (a0:a)=> (cS a0)) Xx1)->(cS Xx1)))) ((fun (a0:a)=> (cS a0)) Xx)) (fun (Xx1:a) (x01:((fun (a0:a)=> (cS a0)) Xx1))=> x01)) x1)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------