%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS122+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 : 300s
% DateTime : Wed Jul 27 13:01:12 EDT 2022
% Result : Unsatisfiable 1.99s 2.20s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 22 ( 12 unt; 0 nHn; 22 RR)
% Number of literals : 34 ( 2 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 15 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(22,axiom,
( ~ cUnsatisfiable(A)
| rf(A,dollar_f1(A)) ),
file('KRS122+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ cUnsatisfiable(A)
| ca_Ax2(dollar_f1(A)) ),
file('KRS122+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ cp1(A)
| ~ ra_Px1(A,B) ),
file('KRS122+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ cp1xcomp(A)
| ra_Px1(A,dollar_f3(A)) ),
file('KRS122+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ ca_Ax2(A)
| cp1(A) ),
file('KRS122+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ ca_Ax2(A)
| ~ rinvF(A,B)
| ca_Vx3(B) ),
file('KRS122+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ ca_Vx3(A)
| rf(A,dollar_f5(A)) ),
file('KRS122+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ ca_Vx3(A)
| cp1xcomp(dollar_f5(A)) ),
file('KRS122+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ rf(A,B)
| ~ rf(A,C)
| B = C ),
file('KRS122+1.p',unknown),
[] ).
cnf(37,axiom,
( rinvF(A,B)
| ~ rf(B,A) ),
file('KRS122+1.p',unknown),
[] ).
cnf(46,axiom,
cUnsatisfiable(i2003_11_14_17_21_55116),
file('KRS122+1.p',unknown),
[] ).
cnf(47,plain,
ca_Ax2(dollar_f1(i2003_11_14_17_21_55116)),
inference(hyper,[status(thm)],[46,23]),
[iquote('hyper,46,23')] ).
cnf(48,plain,
rf(i2003_11_14_17_21_55116,dollar_f1(i2003_11_14_17_21_55116)),
inference(hyper,[status(thm)],[46,22]),
[iquote('hyper,46,22')] ).
cnf(50,plain,
cp1(dollar_f1(i2003_11_14_17_21_55116)),
inference(hyper,[status(thm)],[47,28]),
[iquote('hyper,47,28')] ).
cnf(55,plain,
rinvF(dollar_f1(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116),
inference(hyper,[status(thm)],[48,37]),
[iquote('hyper,48,37')] ).
cnf(59,plain,
ca_Vx3(i2003_11_14_17_21_55116),
inference(hyper,[status(thm)],[55,29,47]),
[iquote('hyper,55,29,47')] ).
cnf(63,plain,
cp1xcomp(dollar_f5(i2003_11_14_17_21_55116)),
inference(hyper,[status(thm)],[59,33]),
[iquote('hyper,59,33')] ).
cnf(64,plain,
rf(i2003_11_14_17_21_55116,dollar_f5(i2003_11_14_17_21_55116)),
inference(hyper,[status(thm)],[59,32]),
[iquote('hyper,59,32')] ).
cnf(66,plain,
ra_Px1(dollar_f5(i2003_11_14_17_21_55116),dollar_f3(dollar_f5(i2003_11_14_17_21_55116))),
inference(hyper,[status(thm)],[63,26]),
[iquote('hyper,63,26')] ).
cnf(73,plain,
dollar_f5(i2003_11_14_17_21_55116) = dollar_f1(i2003_11_14_17_21_55116),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[64,35,48])]),
[iquote('hyper,64,35,48,flip.1')] ).
cnf(75,plain,
ra_Px1(dollar_f1(i2003_11_14_17_21_55116),dollar_f3(dollar_f1(i2003_11_14_17_21_55116))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[66]),73,73]),
[iquote('back_demod,66,demod,73,73')] ).
cnf(79,plain,
$false,
inference(hyper,[status(thm)],[75,25,50]),
[iquote('hyper,75,25,50')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS122+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 03:27:01 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.99/2.19 ----- Otter 3.3f, August 2004 -----
% 1.99/2.19 The process was started by sandbox on n006.cluster.edu,
% 1.99/2.19 Wed Jul 27 03:27:02 2022
% 1.99/2.19 The command was "./otter". The process ID is 2828.
% 1.99/2.19
% 1.99/2.19 set(prolog_style_variables).
% 1.99/2.19 set(auto).
% 1.99/2.19 dependent: set(auto1).
% 1.99/2.19 dependent: set(process_input).
% 1.99/2.19 dependent: clear(print_kept).
% 1.99/2.19 dependent: clear(print_new_demod).
% 1.99/2.19 dependent: clear(print_back_demod).
% 1.99/2.19 dependent: clear(print_back_sub).
% 1.99/2.19 dependent: set(control_memory).
% 1.99/2.19 dependent: assign(max_mem, 12000).
% 1.99/2.19 dependent: assign(pick_given_ratio, 4).
% 1.99/2.19 dependent: assign(stats_level, 1).
% 1.99/2.19 dependent: assign(max_seconds, 10800).
% 1.99/2.19 clear(print_given).
% 1.99/2.19
% 1.99/2.19 formula_list(usable).
% 1.99/2.19 all A (A=A).
% 1.99/2.19 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.99/2.19 all A B (A=B&ca_Ax2(A)->ca_Ax2(B)).
% 1.99/2.19 all A B (A=B&ca_Vx3(A)->ca_Vx3(B)).
% 1.99/2.19 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.99/2.19 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.99/2.19 all A B (A=B&cp1(A)->cp1(B)).
% 1.99/2.19 all A B (A=B&cp1xcomp(A)->cp1xcomp(B)).
% 1.99/2.19 all A B C (A=B&ra_Px1(A,C)->ra_Px1(B,C)).
% 1.99/2.19 all A B C (A=B&ra_Px1(C,A)->ra_Px1(C,B)).
% 1.99/2.19 all A B C (A=B&rf(A,C)->rf(B,C)).
% 1.99/2.19 all A B C (A=B&rf(C,A)->rf(C,B)).
% 1.99/2.19 all A B C (A=B&rinvF(A,C)->rinvF(B,C)).
% 1.99/2.19 all A B C (A=B&rinvF(C,A)->rinvF(C,B)).
% 1.99/2.19 all A B C (A=B&rinvR(A,C)->rinvR(B,C)).
% 1.99/2.19 all A B C (A=B&rinvR(C,A)->rinvR(C,B)).
% 1.99/2.19 all A B C (A=B&rr(A,C)->rr(B,C)).
% 1.99/2.19 all A B C (A=B&rr(C,A)->rr(C,B)).
% 1.99/2.19 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.99/2.19 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.99/2.19 all X (cowlThing(X)& -cowlNothing(X)).
% 1.99/2.19 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.99/2.19 all X (cUnsatisfiable(X)<-> (exists Y (rf(X,Y)&ca_Ax2(Y)))).
% 1.99/2.19 all X (cp1(X)<-> -(exists Y ra_Px1(X,Y))).
% 1.99/2.19 all X (cp1xcomp(X)<-> (exists Y0 ra_Px1(X,Y0))).
% 1.99/2.19 all X (ca_Ax2(X)<->cp1(X)& (all Y (rinvF(X,Y)->ca_Vx3(Y)))).
% 1.99/2.19 all X (ca_Vx3(X)<-> (exists Y (rf(X,Y)&cp1xcomp(Y)))).
% 1.99/2.19 all X Y Z (rf(X,Y)&rf(X,Z)->Y=Z).
% 1.99/2.19 all X Y (rinvF(X,Y)<->rf(Y,X)).
% 1.99/2.19 all X Y (rinvR(X,Y)<->rr(Y,X)).
% 1.99/2.19 all X Y Z (rr(X,Y)&rr(Y,Z)->rr(X,Z)).
% 1.99/2.19 cUnsatisfiable(i2003_11_14_17_21_55116).
% 1.99/2.19 end_of_list.
% 1.99/2.19
% 1.99/2.19 -------> usable clausifies to:
% 1.99/2.19
% 1.99/2.19 list(usable).
% 1.99/2.19 0 [] A=A.
% 1.99/2.19 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.99/2.19 0 [] A!=B| -ca_Ax2(A)|ca_Ax2(B).
% 1.99/2.19 0 [] A!=B| -ca_Vx3(A)|ca_Vx3(B).
% 1.99/2.19 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.99/2.19 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.99/2.19 0 [] A!=B| -cp1(A)|cp1(B).
% 1.99/2.19 0 [] A!=B| -cp1xcomp(A)|cp1xcomp(B).
% 1.99/2.19 0 [] A!=B| -ra_Px1(A,C)|ra_Px1(B,C).
% 1.99/2.19 0 [] A!=B| -ra_Px1(C,A)|ra_Px1(C,B).
% 1.99/2.19 0 [] A!=B| -rf(A,C)|rf(B,C).
% 1.99/2.19 0 [] A!=B| -rf(C,A)|rf(C,B).
% 1.99/2.19 0 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 1.99/2.19 0 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 1.99/2.19 0 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 1.99/2.19 0 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 1.99/2.19 0 [] A!=B| -rr(A,C)|rr(B,C).
% 1.99/2.19 0 [] A!=B| -rr(C,A)|rr(C,B).
% 1.99/2.19 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.99/2.19 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.99/2.19 0 [] cowlThing(X).
% 1.99/2.19 0 [] -cowlNothing(X).
% 1.99/2.19 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.99/2.19 0 [] xsd_string(X)|xsd_integer(X).
% 1.99/2.19 0 [] -cUnsatisfiable(X)|rf(X,$f1(X)).
% 1.99/2.19 0 [] -cUnsatisfiable(X)|ca_Ax2($f1(X)).
% 1.99/2.19 0 [] cUnsatisfiable(X)| -rf(X,Y)| -ca_Ax2(Y).
% 1.99/2.19 0 [] -cp1(X)| -ra_Px1(X,Y).
% 1.99/2.19 0 [] cp1(X)|ra_Px1(X,$f2(X)).
% 1.99/2.19 0 [] -cp1xcomp(X)|ra_Px1(X,$f3(X)).
% 1.99/2.19 0 [] cp1xcomp(X)| -ra_Px1(X,Y0).
% 1.99/2.19 0 [] -ca_Ax2(X)|cp1(X).
% 1.99/2.19 0 [] -ca_Ax2(X)| -rinvF(X,Y)|ca_Vx3(Y).
% 1.99/2.19 0 [] ca_Ax2(X)| -cp1(X)|rinvF(X,$f4(X)).
% 1.99/2.19 0 [] ca_Ax2(X)| -cp1(X)| -ca_Vx3($f4(X)).
% 1.99/2.19 0 [] -ca_Vx3(X)|rf(X,$f5(X)).
% 1.99/2.19 0 [] -ca_Vx3(X)|cp1xcomp($f5(X)).
% 1.99/2.19 0 [] ca_Vx3(X)| -rf(X,Y)| -cp1xcomp(Y).
% 1.99/2.19 0 [] -rf(X,Y)| -rf(X,Z)|Y=Z.
% 1.99/2.19 0 [] -rinvF(X,Y)|rf(Y,X).
% 1.99/2.19 0 [] rinvF(X,Y)| -rf(Y,X).
% 1.99/2.19 0 [] -rinvR(X,Y)|rr(Y,X).
% 1.99/2.19 0 [] rinvR(X,Y)| -rr(Y,X).
% 1.99/2.19 0 [] -rr(X,Y)| -rr(Y,Z)|rr(X,Z).
% 1.99/2.19 0 [] cUnsatisfiable(i2003_11_14_17_21_55116).
% 1.99/2.19 end_of_list.
% 1.99/2.19
% 1.99/2.19 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.99/2.19
% 1.99/2.19 This ia a non-Horn set with equality. The strategy will be
% 1.99/2.19 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.99/2.19 deletion, with positive clauses in sos and nonpositive
% 1.99/2.19 clauses in usable.
% 1.99/2.19
% 1.99/2.19 dependent: set(knuth_bendix).
% 1.99/2.19 dependent: set(anl_eq).
% 1.99/2.19 dependent: set(para_from).
% 1.99/2.19 dependent: set(para_into).
% 1.99/2.19 dependent: clear(para_from_right).
% 1.99/2.19 dependent: clear(para_into_right).
% 1.99/2.19 dependent: set(para_from_vars).
% 1.99/2.19 dependent: set(eq_units_both_ways).
% 1.99/2.19 dependent: set(dynamic_demod_all).
% 1.99/2.20 dependent: set(dynamic_demod).
% 1.99/2.20 dependent: set(order_eq).
% 1.99/2.20 dependent: set(back_demod).
% 1.99/2.20 dependent: set(lrpo).
% 1.99/2.20 dependent: set(hyper_res).
% 1.99/2.20 dependent: set(unit_deletion).
% 1.99/2.20 dependent: set(factor).
% 1.99/2.20
% 1.99/2.20 ------------> process usable:
% 1.99/2.20 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.99/2.20 ** KEPT (pick-wt=7): 2 [] A!=B| -ca_Ax2(A)|ca_Ax2(B).
% 1.99/2.20 ** KEPT (pick-wt=7): 3 [] A!=B| -ca_Vx3(A)|ca_Vx3(B).
% 1.99/2.20 ** KEPT (pick-wt=7): 4 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.99/2.20 ** KEPT (pick-wt=7): 5 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.99/2.20 ** KEPT (pick-wt=7): 6 [] A!=B| -cp1(A)|cp1(B).
% 1.99/2.20 ** KEPT (pick-wt=7): 7 [] A!=B| -cp1xcomp(A)|cp1xcomp(B).
% 1.99/2.20 ** KEPT (pick-wt=9): 8 [] A!=B| -ra_Px1(A,C)|ra_Px1(B,C).
% 1.99/2.20 ** KEPT (pick-wt=9): 9 [] A!=B| -ra_Px1(C,A)|ra_Px1(C,B).
% 1.99/2.20 ** KEPT (pick-wt=9): 10 [] A!=B| -rf(A,C)|rf(B,C).
% 1.99/2.20 ** KEPT (pick-wt=9): 11 [] A!=B| -rf(C,A)|rf(C,B).
% 1.99/2.20 ** KEPT (pick-wt=9): 12 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 1.99/2.20 ** KEPT (pick-wt=9): 13 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 1.99/2.20 ** KEPT (pick-wt=9): 14 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 1.99/2.20 ** KEPT (pick-wt=9): 15 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 1.99/2.20 ** KEPT (pick-wt=9): 16 [] A!=B| -rr(A,C)|rr(B,C).
% 1.99/2.20 ** KEPT (pick-wt=9): 17 [] A!=B| -rr(C,A)|rr(C,B).
% 1.99/2.20 ** KEPT (pick-wt=7): 18 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.99/2.20 ** KEPT (pick-wt=7): 19 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.99/2.20 ** KEPT (pick-wt=2): 20 [] -cowlNothing(A).
% 1.99/2.20 ** KEPT (pick-wt=4): 21 [] -xsd_string(A)| -xsd_integer(A).
% 1.99/2.20 ** KEPT (pick-wt=6): 22 [] -cUnsatisfiable(A)|rf(A,$f1(A)).
% 1.99/2.20 ** KEPT (pick-wt=5): 23 [] -cUnsatisfiable(A)|ca_Ax2($f1(A)).
% 1.99/2.20 ** KEPT (pick-wt=7): 24 [] cUnsatisfiable(A)| -rf(A,B)| -ca_Ax2(B).
% 1.99/2.20 ** KEPT (pick-wt=5): 25 [] -cp1(A)| -ra_Px1(A,B).
% 1.99/2.20 ** KEPT (pick-wt=6): 26 [] -cp1xcomp(A)|ra_Px1(A,$f3(A)).
% 1.99/2.20 ** KEPT (pick-wt=5): 27 [] cp1xcomp(A)| -ra_Px1(A,B).
% 1.99/2.20 ** KEPT (pick-wt=4): 28 [] -ca_Ax2(A)|cp1(A).
% 1.99/2.20 ** KEPT (pick-wt=7): 29 [] -ca_Ax2(A)| -rinvF(A,B)|ca_Vx3(B).
% 1.99/2.20 ** KEPT (pick-wt=8): 30 [] ca_Ax2(A)| -cp1(A)|rinvF(A,$f4(A)).
% 1.99/2.20 ** KEPT (pick-wt=7): 31 [] ca_Ax2(A)| -cp1(A)| -ca_Vx3($f4(A)).
% 1.99/2.20 ** KEPT (pick-wt=6): 32 [] -ca_Vx3(A)|rf(A,$f5(A)).
% 1.99/2.20 ** KEPT (pick-wt=5): 33 [] -ca_Vx3(A)|cp1xcomp($f5(A)).
% 1.99/2.20 ** KEPT (pick-wt=7): 34 [] ca_Vx3(A)| -rf(A,B)| -cp1xcomp(B).
% 1.99/2.20 ** KEPT (pick-wt=9): 35 [] -rf(A,B)| -rf(A,C)|B=C.
% 1.99/2.20 ** KEPT (pick-wt=6): 36 [] -rinvF(A,B)|rf(B,A).
% 1.99/2.20 ** KEPT (pick-wt=6): 37 [] rinvF(A,B)| -rf(B,A).
% 1.99/2.20 ** KEPT (pick-wt=6): 38 [] -rinvR(A,B)|rr(B,A).
% 1.99/2.20 ** KEPT (pick-wt=6): 39 [] rinvR(A,B)| -rr(B,A).
% 1.99/2.20 ** KEPT (pick-wt=9): 40 [] -rr(A,B)| -rr(B,C)|rr(A,C).
% 1.99/2.20 20 back subsumes 4.
% 1.99/2.20
% 1.99/2.20 ------------> process sos:
% 1.99/2.20 ** KEPT (pick-wt=3): 42 [] A=A.
% 1.99/2.20 ** KEPT (pick-wt=2): 43 [] cowlThing(A).
% 1.99/2.20 ** KEPT (pick-wt=4): 44 [] xsd_string(A)|xsd_integer(A).
% 1.99/2.20 ** KEPT (pick-wt=6): 45 [] cp1(A)|ra_Px1(A,$f2(A)).
% 1.99/2.20 ** KEPT (pick-wt=2): 46 [] cUnsatisfiable(i2003_11_14_17_21_55116).
% 1.99/2.20 Following clause subsumed by 42 during input processing: 0 [copy,42,flip.1] A=A.
% 1.99/2.20 42 back subsumes 41.
% 1.99/2.20 43 back subsumes 5.
% 1.99/2.20
% 1.99/2.20 ======= end of input processing =======
% 1.99/2.20
% 1.99/2.20 =========== start of search ===========
% 1.99/2.20
% 1.99/2.20 -------- PROOF --------
% 1.99/2.20
% 1.99/2.20 -----> EMPTY CLAUSE at 0.00 sec ----> 79 [hyper,75,25,50] $F.
% 1.99/2.20
% 1.99/2.20 Length of proof is 10. Level of proof is 6.
% 1.99/2.20
% 1.99/2.20 ---------------- PROOF ----------------
% 1.99/2.20 % SZS status Theorem
% 1.99/2.20 % SZS output start Refutation
% See solution above
% 1.99/2.20 ------------ end of proof -------------
% 1.99/2.20
% 1.99/2.20
% 1.99/2.20 Search stopped by max_proofs option.
% 1.99/2.20
% 1.99/2.20
% 1.99/2.20 Search stopped by max_proofs option.
% 1.99/2.20
% 1.99/2.20 ============ end of search ============
% 1.99/2.20
% 1.99/2.20 -------------- statistics -------------
% 1.99/2.20 clauses given 15
% 1.99/2.20 clauses generated 83
% 1.99/2.20 clauses kept 77
% 1.99/2.20 clauses forward subsumed 55
% 1.99/2.20 clauses back subsumed 3
% 1.99/2.20 Kbytes malloced 976
% 1.99/2.20
% 1.99/2.20 ----------- times (seconds) -----------
% 1.99/2.20 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.20 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.20 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.99/2.20
% 1.99/2.20 That finishes the proof of the theorem.
% 1.99/2.20
% 1.99/2.20 Process 2828 finished Wed Jul 27 03:27:03 2022
% 1.99/2.20 Otter interrupted
% 1.99/2.20 PROOF FOUND
%------------------------------------------------------------------------------