TSTP Solution File: SYO378^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO378^5 : TPTP v7.5.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 00:51:17 EDT 2022
% Result : Theorem 5.46s 5.68s
% Output : Proof 5.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO378^5 : TPTP v7.5.0. Bugfixed v5.2.0.
% 0.06/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Mar 12 09:29:00 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.76/0.93 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.76/0.93 FOF formula (<kernel.Constant object at 0x275fd40>, <kernel.Constant object at 0x275f2d8>) of role type named c_type
% 0.76/0.93 Using role type
% 0.76/0.93 Declaring c:fofType
% 0.76/0.93 FOF formula (<kernel.Constant object at 0x2b59c933aa70>, <kernel.DependentProduct object at 0x275f098>) of role type named cQDP0_type
% 0.76/0.93 Using role type
% 0.76/0.93 Declaring cQDP0:(fofType->Prop)
% 0.76/0.93 FOF formula (<kernel.Constant object at 0x275fd40>, <kernel.DependentProduct object at 0x275f440>) of role type named cQDP1_type
% 0.76/0.93 Using role type
% 0.76/0.93 Declaring cQDP1:((fofType->Prop)->Prop)
% 0.76/0.93 FOF formula (<kernel.Constant object at 0x275f098>, <kernel.DependentProduct object at 0x2b59c931cef0>) of role type named cQDP2_type
% 0.76/0.93 Using role type
% 0.76/0.93 Declaring cQDP2:(((fofType->Prop)->Prop)->Prop)
% 0.76/0.93 FOF formula (((eq (fofType->Prop)) cQDP0) (fun (Xz:fofType)=> (((eq fofType) Xz) c))) of role definition named cQDP0_def
% 0.76/0.93 A new definition: (((eq (fofType->Prop)) cQDP0) (fun (Xz:fofType)=> (((eq fofType) Xz) c)))
% 0.76/0.93 Defined: cQDP0:=(fun (Xz:fofType)=> (((eq fofType) Xz) c))
% 0.76/0.93 FOF formula (((eq ((fofType->Prop)->Prop)) cQDP1) (fun (Xz:(fofType->Prop))=> ((and (((eq (fofType->Prop)) Xz) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (Xz Xt)))))) of role definition named cQDP1_def
% 0.76/0.93 A new definition: (((eq ((fofType->Prop)->Prop)) cQDP1) (fun (Xz:(fofType->Prop))=> ((and (((eq (fofType->Prop)) Xz) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (Xz Xt))))))
% 0.76/0.93 Defined: cQDP1:=(fun (Xz:(fofType->Prop))=> ((and (((eq (fofType->Prop)) Xz) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (Xz Xt)))))
% 0.76/0.93 FOF formula (((eq (((fofType->Prop)->Prop)->Prop)) cQDP2) (fun (Xz:((fofType->Prop)->Prop))=> ((and (((eq ((fofType->Prop)->Prop)) Xz) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (Xz Xt)))))) of role definition named cQDP2_def
% 0.76/0.93 A new definition: (((eq (((fofType->Prop)->Prop)->Prop)) cQDP2) (fun (Xz:((fofType->Prop)->Prop))=> ((and (((eq ((fofType->Prop)->Prop)) Xz) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (Xz Xt))))))
% 0.76/0.93 Defined: cQDP2:=(fun (Xz:((fofType->Prop)->Prop))=> ((and (((eq ((fofType->Prop)->Prop)) Xz) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (Xz Xt)))))
% 0.76/0.93 FOF formula ((ex ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs))) of role conjecture named cQDTHM2
% 0.76/0.93 Conjecture to prove = ((ex ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs))):Prop
% 0.76/0.93 We need to prove ['((ex ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs)))']
% 0.76/0.93 Parameter fofType:Type.
% 0.76/0.93 Parameter c:fofType.
% 0.76/0.93 Definition cQDP0:=(fun (Xz:fofType)=> (((eq fofType) Xz) c)):(fofType->Prop).
% 0.76/0.93 Definition cQDP1:=(fun (Xz:(fofType->Prop))=> ((and (((eq (fofType->Prop)) Xz) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (Xz Xt))))):((fofType->Prop)->Prop).
% 0.76/0.93 Definition cQDP2:=(fun (Xz:((fofType->Prop)->Prop))=> ((and (((eq ((fofType->Prop)->Prop)) Xz) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (Xz Xt))))):(((fofType->Prop)->Prop)->Prop).
% 0.76/0.93 Trying to prove ((ex ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs)))
% 0.76/0.93 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 0.76/0.93 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 0.76/0.93 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 0.76/0.93 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 0.76/0.93 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 0.76/0.93 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 0.76/0.93 Found eq_ref00:=(eq_ref0 x):(((eq ((fofType->Prop)->Prop)) x) x)
% 0.76/0.93 Found (eq_ref0 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 0.76/0.93 Found ((eq_ref ((fofType->Prop)->Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 0.76/0.93 Found ((eq_ref ((fofType->Prop)->Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 0.76/0.93 Found ((eq_ref ((fofType->Prop)->Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 1.66/1.87 Found eq_ref00:=(eq_ref0 ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))):(((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 1.66/1.87 Found (eq_ref0 ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) as proof of (((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) b)
% 1.66/1.87 Found ((eq_ref Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) as proof of (((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) b)
% 1.66/1.87 Found ((eq_ref Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) as proof of (((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) b)
% 1.66/1.87 Found ((eq_ref Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) as proof of (((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) b)
% 1.66/1.87 Found eq_ref00:=(eq_ref0 ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))):(((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 1.66/1.87 Found (eq_ref0 ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) as proof of (((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) b)
% 1.66/1.87 Found ((eq_ref Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) as proof of (((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) b)
% 1.66/1.87 Found ((eq_ref Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) as proof of (((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) b)
% 1.66/1.87 Found ((eq_ref Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) as proof of (((eq Prop) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) b)
% 1.66/1.87 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a)
% 1.66/1.87 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x)))
% 1.66/1.87 Found (eta_expansion00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a)
% 1.66/1.87 Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x)))
% 1.66/1.87 Found (eta_expansion00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 1.66/1.87 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) a) as proof of (((eq ((fofType->Prop)->Prop)) a) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 3.52/3.70 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 3.52/3.70 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 3.52/3.70 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 3.52/3.70 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found eta_expansion_dep000:=(eta_expansion_dep00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 3.52/3.70 Found (eta_expansion_dep00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found eq_ref00:=(eq_ref0 x0):(((eq (fofType->Prop)) x0) x0)
% 3.52/3.70 Found (eq_ref0 x0) as proof of (((eq (fofType->Prop)) x0) cQDP0)
% 3.52/3.70 Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) cQDP0)
% 3.52/3.70 Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) cQDP0)
% 3.52/3.70 Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) cQDP0)
% 3.52/3.70 Found eq_ref00:=(eq_ref0 x0):(((eq (fofType->Prop)) x0) x0)
% 3.52/3.70 Found (eq_ref0 x0) as proof of (((eq (fofType->Prop)) x0) cQDP0)
% 3.52/3.70 Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) cQDP0)
% 3.52/3.70 Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) cQDP0)
% 3.52/3.70 Found ((eq_ref (fofType->Prop)) x0) as proof of (((eq (fofType->Prop)) x0) cQDP0)
% 3.52/3.70 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 3.52/3.70 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 3.52/3.70 Found iff_sym as proof of b
% 3.52/3.70 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 3.52/3.70 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 3.52/3.70 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found ((conj00 (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b)
% 4.05/4.23 Found (((conj0 b) (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b)
% 4.05/4.23 Found ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b) (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b)
% 4.05/4.23 Found ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b) (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b)
% 4.05/4.23 Found ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b) (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of (P b)
% 4.05/4.23 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 4.05/4.23 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found eta_expansion_dep000:=(eta_expansion_dep00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 4.05/4.23 Found (eta_expansion_dep00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 4.05/4.23 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 4.05/4.23 Found iff_sym as proof of b
% 4.05/4.23 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 4.05/4.23 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.05/4.23 Found ((conj00 (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b)
% 4.05/4.23 Found (((conj0 b) (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b)
% 4.05/4.23 Found ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b) (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b)
% 4.05/4.23 Found ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b) (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b)
% 4.05/4.23 Found ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) b) (((eta_expansion (fofType->Prop)) Prop) x)) iff_sym) as proof of (P b)
% 4.05/4.23 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 4.86/5.09 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 4.86/5.09 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found eq_ref00:=(eq_ref0 x):(((eq ((fofType->Prop)->Prop)) x) x)
% 4.86/5.09 Found (eq_ref0 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found ((eq_ref ((fofType->Prop)->Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found ((eq_ref ((fofType->Prop)->Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found ((eq_ref ((fofType->Prop)->Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found eta_expansion_dep000:=(eta_expansion_dep00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 4.86/5.09 Found (eta_expansion_dep00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 4.86/5.09 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 4.86/5.09 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found eta_expansion_dep000:=(eta_expansion_dep00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 4.86/5.09 Found (eta_expansion_dep00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 4.86/5.09 Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 5.43/5.60 Found eta_expansion000:=(eta_expansion00 x):(((eq ((fofType->Prop)->Prop)) x) (fun (x0:(fofType->Prop))=> (x x0)))
% 5.43/5.60 Found (eta_expansion00 x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 5.43/5.60 Found ((eta_expansion0 Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 5.43/5.60 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 5.43/5.60 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 5.43/5.60 Found (((eta_expansion (fofType->Prop)) Prop) x) as proof of (((eq ((fofType->Prop)->Prop)) x) cQDP1)
% 5.43/5.60 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 5.43/5.60 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 5.43/5.60 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 5.43/5.60 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 5.43/5.60 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 5.43/5.60 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 5.43/5.60 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 5.43/5.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 5.43/5.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 5.43/5.60 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 5.43/5.60 Found x2:(P x1)
% 5.43/5.60 Instantiate: x1:=c:fofType
% 5.43/5.60 Found (fun (x2:(P x1))=> x2) as proof of (P c)
% 5.43/5.60 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of ((P x1)->(P c))
% 5.43/5.60 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (x0 x1)
% 5.43/5.60 Found (ex_intro200 (fun (P:(fofType->Prop)) (x2:(P x1))=> x2)) as proof of ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))
% 5.43/5.60 Found ((ex_intro20 c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)) as proof of ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))
% 5.43/5.60 Found (((ex_intro2 (fun (Xt:fofType)=> (x0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)) as proof of ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))
% 5.43/5.60 Found ((((ex_intro fofType) (fun (Xt:fofType)=> (x0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)) as proof of ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))
% 5.43/5.60 Found ((((ex_intro fofType) (fun (Xt:fofType)=> (x0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)) as proof of ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))
% 5.43/5.60 Found ((conj10 ((eq_ref (fofType->Prop)) x0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (x0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))) as proof of ((and (((eq (fofType->Prop)) x0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x0 Xt))))
% 5.43/5.60 Found (((conj1 ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))) ((eq_ref (fofType->Prop)) x0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (x0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))) as proof of ((and (((eq (fofType->Prop)) x0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x0 Xt))))
% 5.43/5.60 Found ((((conj (((eq (fofType->Prop)) x0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))) ((eq_ref (fofType->Prop)) x0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (x0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))) as proof of ((and (((eq (fofType->Prop)) x0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x0 Xt))))
% 5.43/5.60 Found ((((conj (((eq (fofType->Prop)) x0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))) ((eq_ref (fofType->Prop)) x0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (x0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))) as proof of ((and (((eq (fofType->Prop)) x0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x0 Xt))))
% 5.43/5.60 Found ((((conj (((eq (fofType->Prop)) x0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))) ((eq_ref (fofType->Prop)) x0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (x0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))) as proof of (x x0)
% 5.43/5.60 Found (ex_intro100 ((((conj (((eq (fofType->Prop)) x0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x0 Xt)))) ((eq_ref (fofType->Prop)) x0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (x0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))) as proof of ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 5.43/5.60 Found ((ex_intro10 cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))) as proof of ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 5.43/5.61 Found (((ex_intro1 (fun (Xt:(fofType->Prop))=> (x Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))) as proof of ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 5.43/5.61 Found ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))) as proof of ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 5.43/5.61 Found ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))) as proof of ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))
% 5.43/5.61 Found ((conj00 (((eta_expansion (fofType->Prop)) Prop) x)) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))))) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 5.43/5.61 Found (((conj0 ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) (((eta_expansion (fofType->Prop)) Prop) x)) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))))) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 5.43/5.61 Found ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) (((eta_expansion (fofType->Prop)) Prop) x)) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))))) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 5.43/5.61 Found ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) (((eta_expansion (fofType->Prop)) Prop) x)) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))))) as proof of ((and (((eq ((fofType->Prop)->Prop)) x) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))))
% 5.43/5.61 Found ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) (((eta_expansion (fofType->Prop)) Prop) x)) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))))) as proof of (cQDP2 x)
% 5.43/5.61 Found (ex_intro000 ((((conj (((eq ((fofType->Prop)->Prop)) x) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt)))) (((eta_expansion (fofType->Prop)) Prop) x)) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> (x Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs)))
% 5.46/5.62 Found ((ex_intro00 (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) ((((conj (((eq ((fofType->Prop)->Prop)) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt)))) (((eta_expansion (fofType->Prop)) Prop) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))))) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs)))
% 5.46/5.62 Found (((ex_intro0 (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs))) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) ((((conj (((eq ((fofType->Prop)->Prop)) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt)))) (((eta_expansion (fofType->Prop)) Prop) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))))) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs)))
% 5.46/5.62 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs))) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) ((((conj (((eq ((fofType->Prop)->Prop)) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt)))) (((eta_expansion (fofType->Prop)) Prop) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))))) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs)))
% 5.46/5.68 Found ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs))) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) ((((conj (((eq ((fofType->Prop)->Prop)) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt)))) (((eta_expansion (fofType->Prop)) Prop) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))))) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2)))))) as proof of ((ex ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs)))
% 5.46/5.68 Got proof ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs))) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) ((((conj (((eq ((fofType->Prop)->Prop)) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt)))) (((eta_expansion (fofType->Prop)) Prop) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))))) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))))))
% 5.46/5.68 Time elapsed = 5.014801s
% 5.46/5.68 node=1314 cost=5476.000000 depth=27
% 5.46/5.68 ::::::::::::::::::::::
% 5.46/5.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.46/5.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.46/5.68 ((((ex_intro ((fofType->Prop)->Prop)) (fun (Xs:((fofType->Prop)->Prop))=> (cQDP2 Xs))) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) ((((conj (((eq ((fofType->Prop)->Prop)) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt)))))) cQDP1)) ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt)))) (((eta_expansion (fofType->Prop)) Prop) (fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))))) ((((ex_intro (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((fun (x3:(fofType->Prop))=> ((and (((eq (fofType->Prop)) x3) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (x3 Xt))))) Xt))) cQDP0) ((((conj (((eq (fofType->Prop)) cQDP0) cQDP0)) ((ex fofType) (fun (Xt:fofType)=> (cQDP0 Xt)))) ((eq_ref (fofType->Prop)) cQDP0)) ((((ex_intro fofType) (fun (Xt:fofType)=> (cQDP0 Xt))) c) (fun (P:(fofType->Prop)) (x2:(P c))=> x2))))))
% 5.46/5.68 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------