TSTP Solution File: SYO096^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO096^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:50:39 EDT 2022
% Result : Theorem 2.45s 2.62s
% Output : Proof 2.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO096^5 : TPTP v7.5.0. Released v4.0.0.
% 0.00/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n018.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 : Fri Mar 11 15:01:23 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'
% 0.20/0.34 Python 2.7.5
% 1.38/1.57 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 1.38/1.57 FOF formula (<kernel.Constant object at 0x2b8fc6853dd0>, <kernel.Constant object at 0x2b8fc6853a70>) of role type named cA
% 1.38/1.57 Using role type
% 1.38/1.57 Declaring cA:fofType
% 1.38/1.57 FOF formula (<kernel.Constant object at 0x2b8fc68538c0>, <kernel.DependentProduct object at 0x1406cb0>) of role type named cQ
% 1.38/1.57 Using role type
% 1.38/1.57 Declaring cQ:(fofType->(fofType->Prop))
% 1.38/1.57 FOF formula (<kernel.Constant object at 0x142c3b0>, <kernel.Single object at 0x2b8fc68532d8>) of role type named cB
% 1.38/1.57 Using role type
% 1.38/1.57 Declaring cB:fofType
% 1.38/1.57 FOF formula (<kernel.Constant object at 0x2b8fc6853a70>, <kernel.DependentProduct object at 0x1406998>) of role type named cR
% 1.38/1.57 Using role type
% 1.38/1.57 Declaring cR:(fofType->(fofType->Prop))
% 1.38/1.57 FOF formula (((and ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))->((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) of role conjecture named cLX1
% 1.38/1.57 Conjecture to prove = (((and ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))->((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))):Prop
% 1.38/1.57 We need to prove ['(((and ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))->((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))))']
% 1.38/1.57 Parameter fofType:Type.
% 1.38/1.57 Parameter cA:fofType.
% 1.38/1.57 Parameter cQ:(fofType->(fofType->Prop)).
% 1.38/1.57 Parameter cB:fofType.
% 1.38/1.57 Parameter cR:(fofType->(fofType->Prop)).
% 1.38/1.57 Trying to prove (((and ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))->((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))))
% 1.38/1.57 Found ex_intro0100:=(ex_intro010 x2):((ex fofType) (fun (Y:fofType)=> ((cR x4) Y)))
% 1.38/1.57 Found (ex_intro010 x2) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x4) Y)))
% 1.38/1.57 Found ((ex_intro01 cB) x2) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x4) Y)))
% 1.38/1.57 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x4) Y)))
% 1.38/1.57 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x4) Y)))
% 1.38/1.57 Found (x30 (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)) as proof of ((cQ x4) cA)
% 1.38/1.57 Found ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)) as proof of ((cQ x4) cA)
% 1.38/1.57 Found ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)) as proof of ((cQ x4) cA)
% 1.38/1.57 Found ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)) as proof of ((cQ x4) cA)
% 1.38/1.57 Found ex_intro0100:=(ex_intro010 x3):((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.38/1.57 Found (ex_intro010 x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.38/1.57 Found ((ex_intro01 cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.38/1.57 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.38/1.57 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.38/1.57 Found (x40 (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)) as proof of ((cQ x2) cA)
% 1.38/1.57 Found ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)) as proof of ((cQ x2) cA)
% 1.38/1.57 Found ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)) as proof of ((cQ x2) cA)
% 1.38/1.57 Found ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)) as proof of ((cQ x2) cA)
% 1.38/1.57 Found ex_intro0100:=(ex_intro010 x3):((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.38/1.57 Found (ex_intro010 x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.38/1.57 Found ((ex_intro01 cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.38/1.57 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.66/1.86 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.66/1.86 Found (x40 (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 1.66/1.86 Found ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 1.66/1.86 Found ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 1.66/1.86 Found ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 1.66/1.86 Found ex_intro0100:=(ex_intro010 x3):((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.66/1.86 Found (ex_intro010 x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.66/1.86 Found ((ex_intro01 cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.66/1.86 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.66/1.86 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 1.66/1.86 Found (x40 (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 1.66/1.86 Found ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 1.66/1.86 Found ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 1.66/1.86 Found (fun (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3))) as proof of ((cQ x0) cA)
% 1.66/1.86 Found (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3))) as proof of ((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->((cQ x0) cA))
% 1.66/1.86 Found (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3))) as proof of (((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->((cQ x0) cA)))
% 1.66/1.86 Found (and_rect10 (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))) as proof of ((cQ x0) cA)
% 1.66/1.86 Found ((and_rect1 ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))) as proof of ((cQ x0) cA)
% 1.66/1.86 Found (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))) as proof of ((cQ x0) cA)
% 1.66/1.86 Found (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))) as proof of ((cQ x0) cA)
% 1.66/1.86 Found ex_intro0100:=(ex_intro010 x3):((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.66/1.86 Found (ex_intro010 x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.66/1.86 Found ((ex_intro01 cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.66/1.86 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.66/1.86 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x2) Y)))
% 1.66/1.86 Found (x40 (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)) as proof of ((cQ x2) cA)
% 2.15/2.31 Found ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)) as proof of ((cQ x2) cA)
% 2.15/2.31 Found ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)) as proof of ((cQ x2) cA)
% 2.15/2.31 Found (fun (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3))) as proof of ((cQ x2) cA)
% 2.15/2.31 Found (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3))) as proof of ((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->((cQ x2) cA))
% 2.15/2.31 Found (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3))) as proof of (((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->((cQ x2) cA)))
% 2.15/2.31 Found (and_rect10 (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)))) as proof of ((cQ x2) cA)
% 2.15/2.31 Found ((and_rect1 ((cQ x2) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)))) as proof of ((cQ x2) cA)
% 2.15/2.31 Found (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x0)) ((cQ x2) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)))) as proof of ((cQ x2) cA)
% 2.15/2.31 Found (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x0)) ((cQ x2) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x2) (((ex_intro0 (fun (Y:fofType)=> ((cR x2) Y))) cB) x3)))) as proof of ((cQ x2) cA)
% 2.15/2.31 Found ex_intro0100:=(ex_intro010 x3):((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 2.15/2.31 Found (ex_intro010 x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 2.15/2.31 Found ((ex_intro01 cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 2.15/2.31 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 2.15/2.31 Found (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR x0) Y)))
% 2.15/2.31 Found (x40 (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 2.15/2.31 Found ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 2.15/2.31 Found ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)) as proof of ((cQ x0) cA)
% 2.15/2.31 Found (fun (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3))) as proof of ((cQ x0) cA)
% 2.15/2.31 Found (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3))) as proof of ((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->((cQ x0) cA))
% 2.15/2.31 Found (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3))) as proof of (((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->((cQ x0) cA)))
% 2.15/2.31 Found (and_rect10 (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))) as proof of ((cQ x0) cA)
% 2.15/2.31 Found ((and_rect1 ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))) as proof of ((cQ x0) cA)
% 2.15/2.31 Found (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))) as proof of ((cQ x0) cA)
% 2.15/2.31 Found (fun (x2:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3))))) as proof of ((cQ x0) cA)
% 2.15/2.31 Found (fun (x1:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x2:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3))))) as proof of ((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->((cQ x0) cA))
% 2.15/2.31 Found (fun (x1:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x2:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3))))) as proof of (((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))->((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->((cQ x0) cA)))
% 2.15/2.31 Found (and_rect00 (fun (x1:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x2:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))))) as proof of ((cQ x0) cA)
% 2.15/2.31 Found ((and_rect0 ((cQ x0) cA)) (fun (x1:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x2:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))))) as proof of ((cQ x0) cA)
% 2.45/2.61 Found (((fun (P:Type) (x1:(((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))->((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->P)))=> (((((and_rect ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))) P) x1) x)) ((cQ x0) cA)) (fun (x1:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x2:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))))) as proof of ((cQ x0) cA)
% 2.45/2.61 Found (((fun (P:Type) (x1:(((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))->((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->P)))=> (((((and_rect ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))) P) x1) x)) ((cQ x0) cA)) (fun (x1:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x2:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x3:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x3) x1)) ((cQ x0) cA)) (fun (x3:((cR cA) cB)) (x4:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((x4 x0) (((ex_intro0 (fun (Y:fofType)=> ((cR x0) Y))) cB) x3)))))) as proof of ((cQ x0) cA)
% 2.45/2.61 Found ex_intro0100:=(ex_intro010 x2):((ex fofType) (fun (Y:fofType)=> ((cR U) Y)))
% 2.45/2.61 Found (ex_intro010 x2) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR U) Y)))
% 2.45/2.61 Found ((ex_intro01 cB) x2) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR U) Y)))
% 2.45/2.61 Found (((ex_intro0 (fun (Y:fofType)=> ((cR U) Y))) cB) x2) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR U) Y)))
% 2.45/2.61 Found (((ex_intro0 (fun (Y:fofType)=> ((cR U) Y))) cB) x2) as proof of ((ex fofType) (fun (Y:fofType)=> ((cR U) Y)))
% 2.45/2.61 Found (x30 (((ex_intro0 (fun (Y:fofType)=> ((cR U) Y))) cB) x2)) as proof of ((cQ U) x4)
% 2.45/2.61 Found ((x3 U) (((ex_intro0 (fun (Y:fofType)=> ((cR U) Y))) cB) x2)) as proof of ((cQ U) x4)
% 2.45/2.61 Found ((x3 U) (((ex_intro0 (fun (Y:fofType)=> ((cR U) Y))) cB) x2)) as proof of ((cQ U) x4)
% 2.45/2.61 Found ((x3 U) (((ex_intro0 (fun (Y:fofType)=> ((cR U) Y))) cB) x2)) as proof of ((cQ U) x4)
% 2.45/2.61 Found (x1000 ((x3 U) (((ex_intro0 (fun (Y:fofType)=> ((cR U) Y))) cB) x2))) as proof of ((cR cB) x4)
% 2.45/2.61 Found ((x100 x4) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2))) as proof of ((cR cB) x4)
% 2.45/2.61 Found (((fun (U:fofType) (x5:((cQ U) x4))=> (((x10 U) x5) cB)) x4) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2))) as proof of ((cR cB) x4)
% 2.45/2.61 Found (((fun (U:fofType) (x5:((cQ U) x4))=> ((((fun (U:fofType)=> ((x1 U) x4)) U) x5) cB)) x4) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2))) as proof of ((cR cB) x4)
% 2.45/2.61 Found (((fun (U:fofType) (x5:((cQ U) x4))=> ((((fun (U:fofType)=> ((x1 U) x4)) U) x5) cB)) x4) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2))) as proof of ((cR cB) x4)
% 2.45/2.61 Found ((conj00 (((fun (U:fofType) (x5:((cQ U) x4))=> ((((fun (U:fofType)=> ((x1 U) x4)) U) x5) cB)) x4) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)))) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2))) as proof of ((and ((cR cB) x4)) ((cQ x4) cA))
% 2.45/2.61 Found (((conj0 ((cQ x4) cA)) (((fun (U:fofType) (x5:((cQ U) x4))=> ((((fun (U:fofType)=> ((x1 U) x4)) U) x5) cB)) x4) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)))) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2))) as proof of ((and ((cR cB) x4)) ((cQ x4) cA))
% 2.45/2.61 Found ((((conj ((cR cB) x4)) ((cQ x4) cA)) (((fun (U:fofType) (x5:((cQ U) x4))=> ((((fun (U:fofType)=> ((x1 U) x4)) U) x5) cB)) x4) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)))) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2))) as proof of ((and ((cR cB) x4)) ((cQ x4) cA))
% 2.45/2.61 Found ((((conj ((cR cB) x4)) ((cQ x4) cA)) (((fun (U:fofType) (x5:((cQ U) x4))=> ((((fun (U:fofType)=> ((x1 U) x4)) U) x5) cB)) x4) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)))) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2))) as proof of ((and ((cR cB) x4)) ((cQ x4) cA))
% 2.45/2.61 Found (ex_intro000 ((((conj ((cR cB) x4)) ((cQ x4) cA)) (((fun (U:fofType) (x5:((cQ U) x4))=> ((((fun (U:fofType)=> ((x1 U) x4)) U) x5) cB)) x4) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)))) ((x3 x4) (((ex_intro0 (fun (Y:fofType)=> ((cR x4) Y))) cB) x2)))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.61 Found ((ex_intro00 cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) (((ex_intro0 (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) (((ex_intro0 (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.61 Found (((ex_intro0 (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) (((ex_intro0 (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) (((ex_intro0 (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.61 Found ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.61 Found (fun (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2))))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.61 Found (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2))))) as proof of ((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))))
% 2.45/2.61 Found (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2))))) as proof of (((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))))
% 2.45/2.61 Found (and_rect10 (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.61 Found ((and_rect1 ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.61 Found (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.61 Found (fun (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2))))))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.61 Found (fun (x0:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2))))))) as proof of ((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))))
% 2.45/2.62 Found (fun (x0:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2))))))) as proof of (((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))->((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))))
% 2.45/2.62 Found (and_rect00 (fun (x0:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))))))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.62 Found ((and_rect0 ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x0:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))))))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.62 Found (((fun (P:Type) (x0:(((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))->((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->P)))=> (((((and_rect ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))) P) x0) x)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x0:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))))))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.62 Found (fun (x:((and ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))))=> (((fun (P:Type) (x0:(((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))->((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->P)))=> (((((and_rect ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))) P) x0) x)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x0:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2))))))))) as proof of ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))
% 2.45/2.62 Found (fun (x:((and ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))))=> (((fun (P:Type) (x0:(((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))->((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->P)))=> (((((and_rect ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))) P) x0) x)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x0:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2))))))))) as proof of (((and ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))->((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))))
% 2.45/2.62 Got proof (fun (x:((and ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))))=> (((fun (P:Type) (x0:(((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))->((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->P)))=> (((((and_rect ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))) P) x0) x)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x0:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))))))))
% 2.45/2.62 Time elapsed = 1.991121s
% 2.45/2.62 node=443 cost=2065.000000 depth=34
% 2.45/2.62 ::::::::::::::::::::::
% 2.45/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.45/2.62 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.45/2.62 (fun (x:((and ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))))=> (((fun (P:Type) (x0:(((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))->((forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))->P)))=> (((((and_rect ((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V))))) P) x0) x)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x0:((and ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))) (x1:(forall (U:fofType) (V:fofType), (((cQ U) V)->(forall (Z:fofType), ((cR Z) V)))))=> (((fun (P:Type) (x2:(((cR cA) cB)->((forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))->P)))=> (((((and_rect ((cR cA) cB)) (forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X)))) P) x2) x0)) ((ex fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA))))) (fun (x2:((cR cA) cB)) (x3:(forall (X:fofType), (((ex fofType) (fun (Y:fofType)=> ((cR X) Y)))->((cQ X) X))))=> ((((ex_intro fofType) (fun (W:fofType)=> ((and ((cR cB) W)) ((cQ W) cA)))) cA) ((((conj ((cR cB) cA)) ((cQ cA) cA)) (((fun (U:fofType) (x5:((cQ U) cA))=> ((((fun (U:fofType)=> ((x1 U) cA)) U) x5) cB)) cA) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))) ((x3 cA) ((((ex_intro fofType) (fun (Y:fofType)=> ((cR cA) Y))) cB) x2)))))))))
% 2.45/2.64 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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