TSTP Solution File: SYO128^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO128^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n022.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 00:50:42 EDT 2022
% Result : Theorem 2.32s 2.58s
% Output : Proof 2.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SYO128^5 : TPTP v7.5.0. Released v4.0.0.
% 0.10/0.14 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35 % Computer : n022.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % RAMPerCPU : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % DateTime : Fri Mar 11 16:09:12 EST 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.36 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.36 Python 2.7.5
% 1.72/1.98 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 1.72/1.98 FOF formula (<kernel.Constant object at 0x1d43950>, <kernel.Sort object at 0x2b97b7ef9638>) of role type named r
% 1.72/1.98 Using role type
% 1.72/1.98 Declaring r:Prop
% 1.72/1.98 FOF formula (<kernel.Constant object at 0x1d439e0>, <kernel.Sort object at 0x2b97b7ef9638>) of role type named p
% 1.72/1.98 Using role type
% 1.72/1.98 Declaring p:Prop
% 1.72/1.98 FOF formula (<kernel.Constant object at 0x1d43290>, <kernel.Sort object at 0x2b97b7ef9638>) of role type named q
% 1.72/1.98 Using role type
% 1.72/1.98 Declaring q:Prop
% 1.72/1.98 FOF formula (((and p) ((or q) r))->((or ((and p) q)) ((and p) r))) of role conjecture named cDISJ_BUG_2
% 1.72/1.98 Conjecture to prove = (((and p) ((or q) r))->((or ((and p) q)) ((and p) r))):Prop
% 1.72/1.98 We need to prove ['(((and p) ((or q) r))->((or ((and p) q)) ((and p) r)))']
% 1.72/1.98 Parameter r:Prop.
% 1.72/1.98 Parameter p:Prop.
% 1.72/1.98 Parameter q:Prop.
% 1.72/1.98 Trying to prove (((and p) ((or q) r))->((or ((and p) q)) ((and p) r)))
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found conj000:=(conj00 r):(r->((and p) r))
% 1.72/1.98 Found (conj00 r) as proof of (r->((and p) r))
% 1.72/1.98 Found ((fun (B:Prop)=> ((conj0 B) x0)) r) as proof of (r->((and p) r))
% 1.72/1.98 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 1.72/1.98 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found conj000:=(conj00 q):(q->((and p) q))
% 1.72/1.98 Found (conj00 q) as proof of (q->((and p) q))
% 1.72/1.98 Found ((fun (B:Prop)=> ((conj0 B) x0)) q) as proof of (q->((and p) q))
% 1.72/1.98 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 1.72/1.98 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found conj000:=(conj00 r):(r->((and p) r))
% 1.72/1.98 Found (conj00 r) as proof of (r->((and p) r))
% 1.72/1.98 Found ((fun (B:Prop)=> ((conj0 B) x0)) r) as proof of (r->((and p) r))
% 1.72/1.98 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 1.72/1.98 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 1.72/1.98 Found conj000:=(conj00 q):(q->((and p) q))
% 1.72/1.98 Found (conj00 q) as proof of (q->((and p) q))
% 1.72/1.98 Found ((fun (B:Prop)=> ((conj0 B) x0)) q) as proof of (q->((and p) q))
% 1.72/1.98 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 1.72/1.98 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x2:r
% 1.72/1.98 Found (fun (x2:r)=> x2) as proof of r
% 1.72/1.98 Found (fun (x2:r)=> x2) as proof of (r->r)
% 1.72/1.98 Found x2:q
% 1.72/1.98 Found (fun (x2:q)=> x2) as proof of q
% 1.72/1.98 Found (fun (x2:q)=> x2) as proof of (q->q)
% 1.72/1.98 Found x2:r
% 1.72/1.98 Found (fun (x2:r)=> x2) as proof of r
% 1.72/1.98 Found (fun (x2:r)=> x2) as proof of (r->r)
% 1.72/1.98 Found x2:q
% 1.72/1.98 Found (fun (x2:q)=> x2) as proof of q
% 1.72/1.98 Found (fun (x2:q)=> x2) as proof of (q->q)
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found x0 as proof of p
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found (fun (x1:((or q) r))=> x0) as proof of p
% 1.72/1.98 Found (fun (x0:p) (x1:((or q) r))=> x0) as proof of (((or q) r)->p)
% 1.72/1.98 Found (fun (x0:p) (x1:((or q) r))=> x0) as proof of (p->(((or q) r)->p))
% 1.72/1.98 Found (and_rect00 (fun (x0:p) (x1:((or q) r))=> x0)) as proof of p
% 1.72/1.98 Found ((and_rect0 p) (fun (x0:p) (x1:((or q) r))=> x0)) as proof of p
% 1.72/1.98 Found (((fun (P:Type) (x0:(p->(((or q) r)->P)))=> (((((and_rect p) ((or q) r)) P) x0) x)) p) (fun (x0:p) (x1:((or q) r))=> x0)) as proof of p
% 1.72/1.98 Found (((fun (P:Type) (x0:(p->(((or q) r)->P)))=> (((((and_rect p) ((or q) r)) P) x0) x)) p) (fun (x0:p) (x1:((or q) r))=> x0)) as proof of p
% 1.72/1.98 Found x2:r
% 1.72/1.98 Found (fun (x2:r)=> x2) as proof of r
% 1.72/1.98 Found (fun (x2:r)=> x2) as proof of (r->r)
% 1.72/1.98 Found x0:p
% 1.72/1.98 Found (fun (x1:((or q) r))=> x0) as proof of p
% 1.72/1.98 Found (fun (x0:p) (x1:((or q) r))=> x0) as proof of (((or q) r)->p)
% 1.72/1.98 Found (fun (x0:p) (x1:((or q) r))=> x0) as proof of (p->(((or q) r)->p))
% 1.72/1.98 Found (and_rect00 (fun (x0:p) (x1:((or q) r))=> x0)) as proof of p
% 1.72/1.98 Found ((and_rect0 p) (fun (x0:p) (x1:((or q) r))=> x0)) as proof of p
% 1.72/1.98 Found (((fun (P:Type) (x0:(p->(((or q) r)->P)))=> (((((and_rect p) ((or q) r)) P) x0) x)) p) (fun (x0:p) (x1:((or q) r))=> x0)) as proof of p
% 2.32/2.51 Found (((fun (P:Type) (x0:(p->(((or q) r)->P)))=> (((((and_rect p) ((or q) r)) P) x0) x)) p) (fun (x0:p) (x1:((or q) r))=> x0)) as proof of p
% 2.32/2.51 Found x2:q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of (q->q)
% 2.32/2.51 Found x2:r
% 2.32/2.51 Found (fun (x2:r)=> x2) as proof of r
% 2.32/2.51 Found (fun (x2:r)=> x2) as proof of (r->r)
% 2.32/2.51 Found x2:q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of (q->q)
% 2.32/2.51 Found x2:q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of (q->q)
% 2.32/2.51 Found x2:r
% 2.32/2.51 Found (fun (x2:r)=> x2) as proof of r
% 2.32/2.51 Found (fun (x2:r)=> x2) as proof of (r->r)
% 2.32/2.51 Found x2:q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of (q->q)
% 2.32/2.51 Found x2:r
% 2.32/2.51 Found (fun (x2:r)=> x2) as proof of r
% 2.32/2.51 Found (fun (x2:r)=> x2) as proof of (r->r)
% 2.32/2.51 Found x2:q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of q
% 2.32/2.51 Found (fun (x2:q)=> x2) as proof of (q->q)
% 2.32/2.51 Found x2:r
% 2.32/2.51 Found (fun (x2:r)=> x2) as proof of r
% 2.32/2.51 Found (fun (x2:r)=> x2) as proof of (r->r)
% 2.32/2.51 Found conj000:=(conj00 r):(r->((and p) r))
% 2.32/2.51 Found (conj00 r) as proof of (r->((and p) r))
% 2.32/2.51 Found ((fun (B:Prop)=> ((conj0 B) x0)) r) as proof of (r->((and p) r))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 2.32/2.51 Found conj000:=(conj00 q):(q->((and p) q))
% 2.32/2.51 Found (conj00 q) as proof of (q->((and p) q))
% 2.32/2.51 Found ((fun (B:Prop)=> ((conj0 B) x0)) q) as proof of (q->((and p) q))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 2.32/2.51 Found conj000:=(conj00 r):(r->((and p) r))
% 2.32/2.51 Found (conj00 r) as proof of (r->((and p) r))
% 2.32/2.51 Found ((fun (B:Prop)=> ((conj0 B) x0)) r) as proof of (r->((and p) r))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 2.32/2.51 Found conj000:=(conj00 q):(q->((and p) q))
% 2.32/2.51 Found (conj00 q) as proof of (q->((and p) q))
% 2.32/2.51 Found ((fun (B:Prop)=> ((conj0 B) x0)) q) as proof of (q->((and p) q))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 2.32/2.51 Found conj000:=(conj00 r):(r->((and p) r))
% 2.32/2.51 Found (conj00 r) as proof of (r->((and p) r))
% 2.32/2.51 Found ((fun (B:Prop)=> ((conj0 B) x0)) r) as proof of (r->((and p) r))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) r) as proof of (r->((and p) r))
% 2.32/2.51 Found conj000:=(conj00 q):(q->((and p) q))
% 2.32/2.51 Found (conj00 q) as proof of (q->((and p) q))
% 2.32/2.51 Found ((fun (B:Prop)=> ((conj0 B) x0)) q) as proof of (q->((and p) q))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 2.32/2.51 Found ((fun (B:Prop)=> (((conj p) B) x0)) q) as proof of (q->((and p) q))
% 2.32/2.51 Found x0:p
% 2.32/2.51 Found x0 as proof of p
% 2.32/2.51 Found x0:p
% 2.32/2.51 Found x0 as proof of p
% 2.32/2.51 Found x0:p
% 2.32/2.51 Found x0 as proof of p
% 2.32/2.51 Found x0:p
% 2.32/2.51 Found x0 as proof of p
% 2.32/2.51 Found x0:p
% 2.32/2.51 Found x0 as proof of p
% 2.32/2.51 Found x0:p
% 2.32/2.51 Found x0 as proof of p
% 2.32/2.51 Found conj0000:=(conj000 x2):((and p) q)
% 2.32/2.51 Found (conj000 x2) as proof of ((and p) q)
% 2.32/2.51 Found ((conj00 q) x2) as proof of ((and p) q)
% 2.32/2.51 Found (((fun (B:Prop)=> ((conj0 B) x0)) q) x2) as proof of ((and p) q)
% 2.32/2.51 Found (((fun (B:Prop)=> (((conj p) B) x0)) q) x2) as proof of ((and p) q)
% 2.32/2.51 Found (((fun (B:Prop)=> (((conj p) B) x0)) q) x2) as proof of ((and p) q)
% 2.32/2.51 Found (or_introl00 (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.51 Found ((or_introl0 ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.51 Found (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.51 Found (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.51 Found (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2))) as proof of (q->((or ((and p) q)) ((and p) r)))
% 2.32/2.53 Found conj0000:=(conj000 x2):((and p) r)
% 2.32/2.53 Found (conj000 x2) as proof of ((and p) r)
% 2.32/2.53 Found ((conj00 r) x2) as proof of ((and p) r)
% 2.32/2.53 Found (((fun (B:Prop)=> ((conj0 B) x0)) r) x2) as proof of ((and p) r)
% 2.32/2.53 Found (((fun (B:Prop)=> (((conj p) B) x0)) r) x2) as proof of ((and p) r)
% 2.32/2.53 Found (((fun (B:Prop)=> (((conj p) B) x0)) r) x2) as proof of ((and p) r)
% 2.32/2.53 Found (or_intror00 (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found ((or_intror0 ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2))) as proof of (r->((or ((and p) q)) ((and p) r)))
% 2.32/2.53 Found ((or_ind00 (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found (((or_ind0 ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found (fun (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2))))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found (fun (x0:p) (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2))))) as proof of (((or q) r)->((or ((and p) q)) ((and p) r)))
% 2.32/2.53 Found (fun (x0:p) (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2))))) as proof of (p->(((or q) r)->((or ((and p) q)) ((and p) r))))
% 2.32/2.53 Found (and_rect00 (fun (x0:p) (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)))))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found ((and_rect0 ((or ((and p) q)) ((and p) r))) (fun (x0:p) (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)))))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.53 Found (((fun (P:Type) (x0:(p->(((or q) r)->P)))=> (((((and_rect p) ((or q) r)) P) x0) x)) ((or ((and p) q)) ((and p) r))) (fun (x0:p) (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)))))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.58 Found (fun (x:((and p) ((or q) r)))=> (((fun (P:Type) (x0:(p->(((or q) r)->P)))=> (((((and_rect p) ((or q) r)) P) x0) x)) ((or ((and p) q)) ((and p) r))) (fun (x0:p) (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2))))))) as proof of ((or ((and p) q)) ((and p) r))
% 2.32/2.58 Found (fun (x:((and p) ((or q) r)))=> (((fun (P:Type) (x0:(p->(((or q) r)->P)))=> (((((and_rect p) ((or q) r)) P) x0) x)) ((or ((and p) q)) ((and p) r))) (fun (x0:p) (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2))))))) as proof of (((and p) ((or q) r))->((or ((and p) q)) ((and p) r)))
% 2.32/2.58 Got proof (fun (x:((and p) ((or q) r)))=> (((fun (P:Type) (x0:(p->(((or q) r)->P)))=> (((((and_rect p) ((or q) r)) P) x0) x)) ((or ((and p) q)) ((and p) r))) (fun (x0:p) (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)))))))
% 2.32/2.58 Time elapsed = 1.910678s
% 2.32/2.58 node=868 cost=486.000000 depth=20
% 2.32/2.58 ::::::::::::::::::::::
% 2.32/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.32/2.58 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.32/2.58 (fun (x:((and p) ((or q) r)))=> (((fun (P:Type) (x0:(p->(((or q) r)->P)))=> (((((and_rect p) ((or q) r)) P) x0) x)) ((or ((and p) q)) ((and p) r))) (fun (x0:p) (x1:((or q) r))=> ((((fun (P:Prop) (x2:(q->P)) (x3:(r->P))=> ((((((or_ind q) r) P) x2) x3) x1)) ((or ((and p) q)) ((and p) r))) (fun (x2:q)=> (((or_introl ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) q) x2)))) (fun (x2:r)=> (((or_intror ((and p) q)) ((and p) r)) (((fun (B:Prop)=> (((conj p) B) x0)) r) x2)))))))
% 2.32/2.58 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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