TSTP Solution File: SYO160^5 by cocATP---0.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SYO160^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n009.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 00:50:48 EDT 2022

% Result   : Theorem 2.39s 2.60s
% Output   : Proof 2.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : SYO160^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12  % Command    : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32  % Computer   : n009.cluster.edu
% 0.12/0.32  % Model      : x86_64 x86_64
% 0.12/0.32  % CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % RAMPerCPU  : 8042.1875MB
% 0.12/0.32  % OS         : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % DateTime   : Fri Mar 11 16:50:22 EST 2022
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34  Python 2.7.5
% 1.69/1.94  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 1.69/1.94  FOF formula (<kernel.Constant object at 0xe513b0>, <kernel.Constant object at 0xe51830>) of role type named c
% 1.69/1.94  Using role type
% 1.69/1.94  Declaring c:fofType
% 1.69/1.94  FOF formula (<kernel.Constant object at 0xe56098>, <kernel.DependentProduct object at 0xe51a70>) of role type named cR
% 1.69/1.94  Using role type
% 1.69/1.94  Declaring cR:(fofType->Prop)
% 1.69/1.94  FOF formula (<kernel.Constant object at 0xe513b0>, <kernel.Single object at 0xe51560>) of role type named b
% 1.69/1.94  Using role type
% 1.69/1.94  Declaring b:fofType
% 1.69/1.94  FOF formula (<kernel.Constant object at 0xe51950>, <kernel.Single object at 0xe51290>) of role type named a
% 1.69/1.94  Using role type
% 1.69/1.94  Declaring a:fofType
% 1.69/1.94  FOF formula (<kernel.Constant object at 0xe515f0>, <kernel.DependentProduct object at 0xe51200>) of role type named cQ
% 1.69/1.94  Using role type
% 1.69/1.94  Declaring cQ:(fofType->Prop)
% 1.69/1.94  FOF formula (<kernel.Constant object at 0xe51290>, <kernel.DependentProduct object at 0xe514d0>) of role type named cP
% 1.69/1.94  Using role type
% 1.69/1.94  Declaring cP:(fofType->Prop)
% 1.69/1.94  FOF formula (((and ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx))))->((and ((and (cR a)) (cR b))) (cR c))) of role conjecture named cDISJ_THIRD
% 1.69/1.94  Conjecture to prove = (((and ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx))))->((and ((and (cR a)) (cR b))) (cR c))):Prop
% 1.69/1.94  We need to prove ['(((and ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx))))->((and ((and (cR a)) (cR b))) (cR c)))']
% 1.69/1.94  Parameter fofType:Type.
% 1.69/1.94  Parameter c:fofType.
% 1.69/1.94  Parameter cR:(fofType->Prop).
% 1.69/1.94  Parameter b:fofType.
% 1.69/1.94  Parameter a:fofType.
% 1.69/1.94  Parameter cQ:(fofType->Prop).
% 1.69/1.94  Parameter cP:(fofType->Prop).
% 1.69/1.94  Trying to prove (((and ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx))))->((and ((and (cR a)) (cR b))) (cR c)))
% 1.69/1.94  Found x40:=(x4 c):(cP c)
% 1.69/1.94  Found (x4 c) as proof of (cP c)
% 1.69/1.94  Found (x4 c) as proof of (cP c)
% 1.69/1.94  Found (x30 (x4 c)) as proof of (cR c)
% 1.69/1.94  Found ((x3 c) (x4 c)) as proof of (cR c)
% 1.69/1.94  Found ((x3 c) (x4 c)) as proof of (cR c)
% 1.69/1.94  Found x40:=(x4 c):(cQ c)
% 1.69/1.94  Found (x4 c) as proof of (cQ c)
% 1.69/1.94  Found (x4 c) as proof of (cQ c)
% 1.69/1.94  Found (x10 (x4 c)) as proof of (cR c)
% 1.69/1.94  Found ((x1 c) (x4 c)) as proof of (cR c)
% 1.69/1.94  Found ((x1 c) (x4 c)) as proof of (cR c)
% 1.69/1.94  Found x40:=(x4 c):(cP c)
% 1.69/1.94  Found (x4 c) as proof of (cP c)
% 1.69/1.94  Found (fun (x4:(forall (Xx:fofType), (cP Xx)))=> (x4 c)) as proof of (cP c)
% 1.69/1.94  Found (fun (x4:(forall (Xx:fofType), (cP Xx)))=> (x4 c)) as proof of ((forall (Xx:fofType), (cP Xx))->(cP c))
% 1.69/1.94  Found x40:=(x4 c):(cQ c)
% 1.69/1.94  Found (x4 c) as proof of (cQ c)
% 1.69/1.94  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> (x4 c)) as proof of (cQ c)
% 1.69/1.94  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> (x4 c)) as proof of ((forall (Xx:fofType), (cQ Xx))->(cQ c))
% 1.69/1.94  Found x40:=(x4 c):(cP c)
% 1.69/1.94  Found (x4 c) as proof of (cP c)
% 1.69/1.94  Found (x4 c) as proof of (cP c)
% 1.69/1.94  Found (x30 (x4 c)) as proof of (cR c)
% 1.69/1.94  Found ((x3 c) (x4 c)) as proof of (cR c)
% 1.69/1.94  Found (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c))) as proof of (cR c)
% 1.69/1.94  Found (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c))) as proof of ((forall (Xx:fofType), (cP Xx))->(cR c))
% 1.69/1.94  Found x40:=(x4 c):(cQ c)
% 1.69/1.94  Found (x4 c) as proof of (cQ c)
% 1.69/1.94  Found (x4 c) as proof of (cQ c)
% 1.69/1.94  Found (x10 (x4 c)) as proof of (cR c)
% 1.69/1.94  Found ((x1 c) (x4 c)) as proof of (cR c)
% 1.69/1.94  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))) as proof of (cR c)
% 1.69/1.94  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))) as proof of ((forall (Xx:fofType), (cQ Xx))->(cR c))
% 1.69/1.94  Found ((or_ind00 (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))) as proof of (cR c)
% 1.69/1.94  Found (((or_ind0 (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))) as proof of (cR c)
% 2.32/2.56  Found ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))) as proof of (cR c)
% 2.32/2.56  Found ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))) as proof of (cR c)
% 2.32/2.56  Found x40:=(x4 c):(cQ c)
% 2.32/2.56  Found (x4 c) as proof of (cQ c)
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> (x4 c)) as proof of (cQ c)
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> (x4 c)) as proof of ((forall (Xx:fofType), (cQ Xx))->(cQ c))
% 2.32/2.56  Found x40:=(x4 c):(cP c)
% 2.32/2.56  Found (x4 c) as proof of (cP c)
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cP Xx)))=> (x4 c)) as proof of (cP c)
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cP Xx)))=> (x4 c)) as proof of ((forall (Xx:fofType), (cP Xx))->(cP c))
% 2.32/2.56  Found x40:=(x4 c):(cQ c)
% 2.32/2.56  Found (x4 c) as proof of (cQ c)
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> (x4 c)) as proof of (cQ c)
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> (x4 c)) as proof of ((forall (Xx:fofType), (cQ Xx))->(cQ c))
% 2.32/2.56  Found x40:=(x4 a):(cQ a)
% 2.32/2.56  Found (x4 a) as proof of (cQ a)
% 2.32/2.56  Found (x4 a) as proof of (cQ a)
% 2.32/2.56  Found (x10 (x4 a)) as proof of (cR a)
% 2.32/2.56  Found ((x1 a) (x4 a)) as proof of (cR a)
% 2.32/2.56  Found ((x1 a) (x4 a)) as proof of (cR a)
% 2.32/2.56  Found x40:=(x4 b):(cQ b)
% 2.32/2.56  Found (x4 b) as proof of (cQ b)
% 2.32/2.56  Found (x4 b) as proof of (cQ b)
% 2.32/2.56  Found (x10 (x4 b)) as proof of (cR b)
% 2.32/2.56  Found ((x1 b) (x4 b)) as proof of (cR b)
% 2.32/2.56  Found ((x1 b) (x4 b)) as proof of (cR b)
% 2.32/2.56  Found ((conj10 ((x1 a) (x4 a))) ((x1 b) (x4 b))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found (((conj1 (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))) as proof of ((forall (Xx:fofType), (cQ Xx))->((and (cR a)) (cR b)))
% 2.32/2.56  Found x40:=(x4 b):(cP b)
% 2.32/2.56  Found (x4 b) as proof of (cP b)
% 2.32/2.56  Found (x4 b) as proof of (cP b)
% 2.32/2.56  Found (x30 (x4 b)) as proof of (cR b)
% 2.32/2.56  Found ((x3 b) (x4 b)) as proof of (cR b)
% 2.32/2.56  Found ((x3 b) (x4 b)) as proof of (cR b)
% 2.32/2.56  Found x40:=(x4 a):(cP a)
% 2.32/2.56  Found (x4 a) as proof of (cP a)
% 2.32/2.56  Found (x4 a) as proof of (cP a)
% 2.32/2.56  Found (x30 (x4 a)) as proof of (cR a)
% 2.32/2.56  Found ((x3 a) (x4 a)) as proof of (cR a)
% 2.32/2.56  Found ((x3 a) (x4 a)) as proof of (cR a)
% 2.32/2.56  Found ((conj10 ((x3 a) (x4 a))) ((x3 b) (x4 b))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found (((conj1 (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b)))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b)))) as proof of ((forall (Xx:fofType), (cP Xx))->((and (cR a)) (cR b)))
% 2.32/2.56  Found ((or_ind00 (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b))))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found (((or_ind0 ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b))))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b))))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b))))) as proof of ((and (cR a)) (cR b))
% 2.32/2.56  Found ((conj00 ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.32/2.56  Found (((conj0 (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.32/2.56  Found ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.32/2.56  Found (fun (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.32/2.56  Found (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))))) as proof of ((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->((and ((and (cR a)) (cR b))) (cR c)))
% 2.32/2.56  Found (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))))) as proof of (((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->((and ((and (cR a)) (cR b))) (cR c))))
% 2.32/2.56  Found (and_rect10 (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.32/2.56  Found ((and_rect1 ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.39/2.56  Found (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.39/2.56  Found (fun (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.39/2.56  Found (fun (x0:((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))))))) as proof of ((forall (Xx:fofType), ((cQ Xx)->(cR Xx)))->((and ((and (cR a)) (cR b))) (cR c)))
% 2.39/2.57  Found (fun (x0:((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))))))) as proof of (((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))->((forall (Xx:fofType), ((cQ Xx)->(cR Xx)))->((and ((and (cR a)) (cR b))) (cR c))))
% 2.39/2.57  Found (and_rect00 (fun (x0:((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.39/2.57  Found ((and_rect0 ((and ((and (cR a)) (cR b))) (cR c))) (fun (x0:((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.39/2.57  Found (((fun (P:Type) (x0:(((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))->((forall (Xx:fofType), ((cQ Xx)->(cR Xx)))->P)))=> (((((and_rect ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx)))) P) x0) x)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x0:((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.39/2.57  Found (fun (x:((and ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx)))))=> (((fun (P:Type) (x0:(((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))->((forall (Xx:fofType), ((cQ Xx)->(cR Xx)))->P)))=> (((((and_rect ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx)))) P) x0) x)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x0:((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))))))))) as proof of ((and ((and (cR a)) (cR b))) (cR c))
% 2.39/2.57  Found (fun (x:((and ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx)))))=> (((fun (P:Type) (x0:(((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))->((forall (Xx:fofType), ((cQ Xx)->(cR Xx)))->P)))=> (((((and_rect ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx)))) P) x0) x)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x0:((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c)))))))))) as proof of (((and ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx))))->((and ((and (cR a)) (cR b))) (cR c)))
% 2.39/2.57  Got proof (fun (x:((and ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx)))))=> (((fun (P:Type) (x0:(((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))->((forall (Xx:fofType), ((cQ Xx)->(cR Xx)))->P)))=> (((((and_rect ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx)))) P) x0) x)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x0:((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))))))))
% 2.39/2.60  Time elapsed = 1.960536s
% 2.39/2.60  node=554 cost=717.000000 depth=30
% 2.39/2.60  ::::::::::::::::::::::
% 2.39/2.60  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.39/2.60  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.39/2.60  (fun (x:((and ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx)))))=> (((fun (P:Type) (x0:(((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))->((forall (Xx:fofType), ((cQ Xx)->(cR Xx)))->P)))=> (((((and_rect ((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (forall (Xx:fofType), ((cQ Xx)->(cR Xx)))) P) x0) x)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x0:((and ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx))))) (x1:(forall (Xx:fofType), ((cQ Xx)->(cR Xx))))=> (((fun (P:Type) (x2:(((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))->((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->P)))=> (((((and_rect ((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (forall (Xx:fofType), ((cP Xx)->(cR Xx)))) P) x2) x0)) ((and ((and (cR a)) (cR b))) (cR c))) (fun (x2:((or (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx)))) (x3:(forall (Xx:fofType), ((cP Xx)->(cR Xx))))=> ((((conj ((and (cR a)) (cR b))) (cR c)) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) ((and (cR a)) (cR b))) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((((conj (cR a)) (cR b)) ((x3 a) (x4 a))) ((x3 b) (x4 b))))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((((conj (cR a)) (cR b)) ((x1 a) (x4 a))) ((x1 b) (x4 b)))))) ((((fun (P:Prop) (x4:((forall (Xx:fofType), (cP Xx))->P)) (x5:((forall (Xx:fofType), (cQ Xx))->P))=> ((((((or_ind (forall (Xx:fofType), (cP Xx))) (forall (Xx:fofType), (cQ Xx))) P) x4) x5) x2)) (cR c)) (fun (x4:(forall (Xx:fofType), (cP Xx)))=> ((x3 c) (x4 c)))) (fun (x4:(forall (Xx:fofType), (cQ Xx)))=> ((x1 c) (x4 c))))))))))
% 2.39/2.60  % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------