TSTP Solution File: SYN358^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYN358^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n113.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 13:38:16 EDT 2014
% Result : Theorem 3.17s
% Output : Proof 3.17s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SYN358^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n113.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 09:25:56 CDT 2014
% % CPUTime: 3.17
% 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 0x251bbd8>, <kernel.DependentProduct object at 0x26f2d40>) of role type named cQ
% Using role type
% Declaring cQ:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x26f4ab8>, <kernel.Sort object at 0x23e5ea8>) of role type named p
% Using role type
% Declaring p:Prop
% FOF formula ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) of role conjecture named cX2109
% Conjecture to prove = ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))']
% Parameter fofType:Type.
% Parameter cQ:(fofType->Prop).
% Parameter p:Prop.
% Trying to prove ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))
% Found x2:p
% Found x2 as proof of p
% Found x0:p
% Found x0 as proof of p
% Found x1:p
% Found x1 as proof of p
% Found x2:p
% Found x2 as proof of p
% Found x2:p
% Found (fun (x3:(cQ x0))=> x2) as proof of p
% Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of ((cQ x0)->p)
% Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of (p->((cQ x0)->p))
% Found (and_rect00 (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found ((and_rect0 p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found x0:p
% Found x0 as proof of p
% Found conj100:=(conj10 (cQ x3)):((cQ x3)->((and p) (cQ x3)))
% Found (conj10 (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found ((fun (B:Prop)=> ((conj1 B) x1)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found ((fun (B:Prop)=> (((conj p) B) x1)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found ((fun (B:Prop)=> (((conj p) B) x1)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found conj100:=(conj10 (cQ x3)):((cQ x3)->((and p) (cQ x3)))
% Found (conj10 (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found ((fun (B:Prop)=> ((conj1 B) x0)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found ((fun (B:Prop)=> (((conj p) B) x0)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found ((fun (B:Prop)=> (((conj p) B) x0)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found x1:p
% Found x1 as proof of p
% Found x1:p
% Found (fun (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1) as proof of p
% Found (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1) as proof of (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->p)
% Found (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1) as proof of (p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->p))
% Found (and_rect00 (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1)) as proof of p
% Found ((and_rect0 p) (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1)) as proof of p
% Found (((fun (P:Type) (x1:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x1) x)) p) (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1)) as proof of p
% Found (((fun (P:Type) (x1:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x1) x)) p) (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1)) as proof of p
% Found x2:p
% Found (fun (x3:(cQ x0))=> x2) as proof of p
% Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of ((cQ x0)->p)
% Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of (p->((cQ x0)->p))
% Found (and_rect00 (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found ((and_rect0 p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found (fun (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2))) as proof of p
% Found (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2))) as proof of (((and p) (cQ x0))->p)
% Found (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2))) as proof of (forall (x:fofType), (((and p) (cQ x))->p))
% Found (ex_ind00 (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)))) as proof of p
% Found ((ex_ind0 p) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)))) as proof of p
% Found (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) p) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)))) as proof of p
% Found (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) p) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)))) as proof of p
% Found x2:p
% Found (fun (x3:(cQ x0))=> x2) as proof of p
% Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of ((cQ x0)->p)
% Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of (p->((cQ x0)->p))
% Found (and_rect00 (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found ((and_rect0 p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p
% Found conj100:=(conj10 x0):((cQ x3)->((and p) (cQ x3)))
% Found (conj10 x0) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found ((conj1 (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found (((conj p) (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found (((conj p) (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found conj100:=(conj10 x1):((cQ x3)->((and p) (cQ x3)))
% Found (conj10 x1) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found ((conj1 (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found (((conj p) (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found (((conj p) (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found x0:p
% Found x0 as proof of p
% Found (conj10 x0) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found ((conj1 (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found (((conj p) (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found (((conj p) (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2)))
% Found x1:p
% Found x1 as proof of p
% Found (conj10 x1) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found ((conj1 (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found (((conj p) (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found (((conj p) (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0)))
% Found ex_intro0000:=(ex_intro000 x3):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 x0) x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) x0) x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((conj10 x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((conj1 ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (fun (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))) as proof of ((cQ x0)->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))
% Found (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))) as proof of (p->((cQ x0)->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))))
% Found (and_rect00 (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found ((and_rect0 ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (fun (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))) as proof of (((and p) (cQ x0))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))
% Found (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))) as proof of (forall (x:fofType), (((and p) (cQ x))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))))
% Found (ex_ind00 (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found ((ex_ind0 ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))))) as proof of (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))
% Found x3:(cQ x2)
% Instantiate: x4:=x2:fofType
% Found x3 as proof of (cQ x4)
% Found (conj100 x3) as proof of ((and p) (cQ x4))
% Found ((conj10 (cQ x4)) x3) as proof of ((and p) (cQ x4))
% Found (((fun (B:Prop)=> ((conj1 B) x0)) (cQ x4)) x3) as proof of ((and p) (cQ x4))
% Found (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x4)) x3) as proof of ((and p) (cQ x4))
% Found (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x4)) x3) as proof of ((and p) (cQ x4))
% Found (ex_intro000 (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x4)) x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found ((ex_intro00 x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found (((ex_intro0 (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found (fun (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))) as proof of ((cQ x2)->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))
% Found (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))) as proof of (forall (x:fofType), ((cQ x)->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))))
% Found (ex_ind00 (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found ((ex_ind0 ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found (fun (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))) as proof of (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))
% Found (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))) as proof of (p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))))
% Found (and_rect00 (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found ((and_rect0 ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))
% Found (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))))) as proof of (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))
% Found ((conj00 (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))
% Found (((conj0 (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))
% Found ((((conj (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))
% Found ((((conj (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))
% Got proof ((((conj (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))))))
% Time elapsed = 2.831967s
% node=551 cost=830.000000 depth=27
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% ((((conj (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------