%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG227+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 12:46:23 EDT 2022
% Result : Theorem 1.74s 1.98s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of clauses : 17 ( 13 unt; 3 nHn; 16 RR)
% Number of literals : 32 ( 12 equ; 15 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ v1_xboole_0(dollar_c3),
file('ALG227+1.p',unknown),
[] ).
cnf(2,axiom,
~ r2_hidden(dollar_c1,k1_closure3(dollar_c3,dollar_c2)),
file('ALG227+1.p',unknown),
[] ).
cnf(3,axiom,
k1_funct_1(dollar_c2,dollar_c1) != k1_xboole_0,
file('ALG227+1.p',unknown),
[] ).
cnf(10,axiom,
( v1_xboole_0(A)
| ~ m1_pboole(B,A)
| C = k1_closure3(A,B)
| C != a_2_0_closure3(A,B) ),
file('ALG227+1.p',unknown),
[] ).
cnf(17,axiom,
( v1_xboole_0(A)
| ~ m1_pboole(B,A)
| r2_hidden(C,a_2_0_closure3(A,B))
| ~ m1_subset_1(D,A)
| C != D
| k1_funct_1(B,D) = k1_xboole_0 ),
file('ALG227+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ v1_xboole_0(A)
| A = B
| ~ v1_xboole_0(B) ),
file('ALG227+1.p',unknown),
[] ).
cnf(29,axiom,
A = A,
file('ALG227+1.p',unknown),
[] ).
cnf(30,axiom,
m1_pboole(dollar_c2,dollar_c3),
file('ALG227+1.p',unknown),
[] ).
cnf(31,axiom,
m1_subset_1(dollar_c1,dollar_c3),
file('ALG227+1.p',unknown),
[] ).
cnf(34,axiom,
v1_xboole_0(k1_xboole_0),
file('ALG227+1.p',unknown),
[] ).
cnf(35,axiom,
v1_xboole_0(dollar_c4),
file('ALG227+1.p',unknown),
[] ).
cnf(59,plain,
k1_xboole_0 = dollar_c4,
inference(hyper,[status(thm)],[35,25,34]),
[iquote('hyper,35,25,34')] ).
cnf(64,plain,
( v1_xboole_0(A)
| ~ m1_pboole(B,A)
| r2_hidden(C,a_2_0_closure3(A,B))
| ~ m1_subset_1(D,A)
| C != D
| k1_funct_1(B,D) = dollar_c4 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),59]),
[iquote('back_demod,17,demod,59')] ).
cnf(66,plain,
k1_funct_1(dollar_c2,dollar_c1) != dollar_c4,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),59]),
[iquote('back_demod,3,demod,59')] ).
cnf(77,plain,
k1_closure3(dollar_c3,dollar_c2) = a_2_0_closure3(dollar_c3,dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[30,10,29]),1])]),
[iquote('hyper,30,10,29,unit_del,1,flip.1')] ).
cnf(78,plain,
~ r2_hidden(dollar_c1,a_2_0_closure3(dollar_c3,dollar_c2)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),77]),
[iquote('back_demod,2,demod,77')] ).
cnf(447,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[64,30,31,29]),1,78,66]),
[iquote('hyper,64,30,31,29,unit_del,1,78,66')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG227+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 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 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 03:34:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.96 ----- Otter 3.3f, August 2004 -----
% 1.74/1.96 The process was started by sandbox on n010.cluster.edu,
% 1.74/1.96 Wed Jul 27 03:34:25 2022
% 1.74/1.96 The command was "./otter". The process ID is 22344.
% 1.74/1.96
% 1.74/1.96 set(prolog_style_variables).
% 1.74/1.96 set(auto).
% 1.74/1.96 dependent: set(auto1).
% 1.74/1.96 dependent: set(process_input).
% 1.74/1.96 dependent: clear(print_kept).
% 1.74/1.96 dependent: clear(print_new_demod).
% 1.74/1.96 dependent: clear(print_back_demod).
% 1.74/1.96 dependent: clear(print_back_sub).
% 1.74/1.96 dependent: set(control_memory).
% 1.74/1.96 dependent: assign(max_mem, 12000).
% 1.74/1.96 dependent: assign(pick_given_ratio, 4).
% 1.74/1.96 dependent: assign(stats_level, 1).
% 1.74/1.96 dependent: assign(max_seconds, 10800).
% 1.74/1.96 clear(print_given).
% 1.74/1.96
% 1.74/1.96 formula_list(usable).
% 1.74/1.96 all A (A=A).
% 1.74/1.96 -(all A (-v1_xboole_0(A)-> (all B (m1_pboole(B,A)-> (all C (m1_subset_1(C,A)-> (-r2_hidden(C,k1_closure3(A,B))->k1_funct_1(B,C)=k1_xboole_0))))))).
% 1.74/1.96 all A B (r2_hidden(A,B)-> -r2_hidden(B,A)).
% 1.74/1.96 all A (v1_xboole_0(A)->v1_fraenkel(A)).
% 1.74/1.96 all A (v1_xboole_0(A)->v1_finset_1(A)).
% 1.74/1.96 all A (v1_xboole_0(A)->v1_funct_1(A)).
% 1.74/1.96 all A (v1_relat_1(A)&v1_xboole_0(A)&v1_funct_1(A)->v1_relat_1(A)&v1_funct_1(A)&v2_funct_1(A)).
% 1.74/1.96 all A (-v1_xboole_0(A)-> (all B (m1_pboole(B,A)-> (all C (C=k1_closure3(A,B)<->C=a_2_0_closure3(A,B)))))).
% 1.74/1.96 $T.
% 1.74/1.96 $T.
% 1.74/1.96 $T.
% 1.74/1.96 all A B (m1_pboole(B,A)->v1_relat_1(B)&v1_funct_1(B)).
% 1.74/1.96 $T.
% 1.74/1.96 all A exists B m1_pboole(B,A).
% 1.74/1.96 all A exists B m1_subset_1(B,A).
% 1.74/1.96 v1_xboole_0(k1_xboole_0).
% 1.74/1.96 all A B C (-v1_xboole_0(B)&m1_pboole(C,B)-> (r2_hidden(A,a_2_0_closure3(B,C))<-> (exists D (m1_subset_1(D,B)&A=D&k1_funct_1(C,D)!=k1_xboole_0)))).
% 1.74/1.96 exists A (v1_xboole_0(A)&v1_relat_1(A)&v1_funct_1(A)&v2_funct_1(A)&v1_finset_1(A)&v1_fraenkel(A)).
% 1.74/1.96 exists A (-v1_xboole_0(A)&v1_finset_1(A)).
% 1.74/1.96 exists A (v1_relat_1(A)&v1_funct_1(A)).
% 1.74/1.96 exists A v1_xboole_0(A).
% 1.74/1.96 exists A (v1_relat_1(A)&v1_xboole_0(A)&v1_funct_1(A)).
% 1.74/1.96 exists A (-v1_xboole_0(A)).
% 1.74/1.96 exists A (v1_relat_1(A)&v1_funct_1(A)&v2_funct_1(A)).
% 1.74/1.96 all A B (r2_hidden(A,B)->m1_subset_1(A,B)).
% 1.74/1.96 all A B (m1_subset_1(A,B)->v1_xboole_0(B)|r2_hidden(A,B)).
% 1.74/1.96 all A B ((all C (r2_hidden(C,A)<->r2_hidden(C,B)))->A=B).
% 1.74/1.96 all A (v1_xboole_0(A)->A=k1_xboole_0).
% 1.74/1.96 all A B (-(r2_hidden(A,B)&v1_xboole_0(B))).
% 1.74/1.96 all A B (-(v1_xboole_0(A)&A!=B&v1_xboole_0(B))).
% 1.74/1.96 end_of_list.
% 1.74/1.96
% 1.74/1.96 -------> usable clausifies to:
% 1.74/1.96
% 1.74/1.96 list(usable).
% 1.74/1.96 0 [] A=A.
% 1.74/1.96 0 [] -v1_xboole_0($c3).
% 1.74/1.96 0 [] m1_pboole($c2,$c3).
% 1.74/1.96 0 [] m1_subset_1($c1,$c3).
% 1.74/1.96 0 [] -r2_hidden($c1,k1_closure3($c3,$c2)).
% 1.74/1.96 0 [] k1_funct_1($c2,$c1)!=k1_xboole_0.
% 1.74/1.96 0 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 1.74/1.96 0 [] -v1_xboole_0(A)|v1_fraenkel(A).
% 1.74/1.96 0 [] -v1_xboole_0(A)|v1_finset_1(A).
% 1.74/1.96 0 [] -v1_xboole_0(A)|v1_funct_1(A).
% 1.74/1.96 0 [] -v1_relat_1(A)| -v1_xboole_0(A)| -v1_funct_1(A)|v2_funct_1(A).
% 1.74/1.96 0 [] v1_xboole_0(A)| -m1_pboole(B,A)|C!=k1_closure3(A,B)|C=a_2_0_closure3(A,B).
% 1.74/1.96 0 [] v1_xboole_0(A)| -m1_pboole(B,A)|C=k1_closure3(A,B)|C!=a_2_0_closure3(A,B).
% 1.74/1.96 0 [] $T.
% 1.74/1.96 0 [] $T.
% 1.74/1.96 0 [] $T.
% 1.74/1.96 0 [] -m1_pboole(B,A)|v1_relat_1(B).
% 1.74/1.96 0 [] -m1_pboole(B,A)|v1_funct_1(B).
% 1.74/1.96 0 [] $T.
% 1.74/1.96 0 [] m1_pboole($f1(A),A).
% 1.74/1.96 0 [] m1_subset_1($f2(A),A).
% 1.74/1.96 0 [] v1_xboole_0(k1_xboole_0).
% 1.74/1.96 0 [] v1_xboole_0(B)| -m1_pboole(C,B)| -r2_hidden(A,a_2_0_closure3(B,C))|m1_subset_1($f3(A,B,C),B).
% 1.74/1.96 0 [] v1_xboole_0(B)| -m1_pboole(C,B)| -r2_hidden(A,a_2_0_closure3(B,C))|A=$f3(A,B,C).
% 1.74/1.96 0 [] v1_xboole_0(B)| -m1_pboole(C,B)| -r2_hidden(A,a_2_0_closure3(B,C))|k1_funct_1(C,$f3(A,B,C))!=k1_xboole_0.
% 1.74/1.96 0 [] v1_xboole_0(B)| -m1_pboole(C,B)|r2_hidden(A,a_2_0_closure3(B,C))| -m1_subset_1(D,B)|A!=D|k1_funct_1(C,D)=k1_xboole_0.
% 1.74/1.96 0 [] v1_xboole_0($c4).
% 1.74/1.96 0 [] v1_relat_1($c4).
% 1.74/1.96 0 [] v1_funct_1($c4).
% 1.74/1.96 0 [] v2_funct_1($c4).
% 1.74/1.96 0 [] v1_finset_1($c4).
% 1.74/1.96 0 [] v1_fraenkel($c4).
% 1.74/1.96 0 [] -v1_xboole_0($c5).
% 1.74/1.96 0 [] v1_finset_1($c5).
% 1.74/1.96 0 [] v1_relat_1($c6).
% 1.74/1.96 0 [] v1_funct_1($c6).
% 1.74/1.96 0 [] v1_xboole_0($c7).
% 1.74/1.96 0 [] v1_relat_1($c8).
% 1.74/1.96 0 [] v1_xboole_0($c8).
% 1.74/1.96 0 [] v1_funct_1($c8).
% 1.74/1.96 0 [] -v1_xboole_0($c9).
% 1.74/1.96 0 [] v1_relat_1($c10).
% 1.74/1.96 0 [] v1_funct_1($c10).
% 1.74/1.96 0 [] v2_funct_1($c10).
% 1.74/1.96 0 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 1.74/1.96 0 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 1.74/1.96 0 [] r2_hidden($f4(A,B),A)|r2_hidden($f4(A,B),B)|A=B.
% 1.74/1.96 0 [] -r2_hidden($f4(A,B),A)| -r2_hidden($f4(A,B),B)|A=B.
% 1.74/1.96 0 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 1.74/1.96 0 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 1.74/1.96 0 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 1.74/1.96 end_of_list.
% 1.74/1.96
% 1.74/1.96 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.74/1.98
% 1.74/1.98 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.98 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.98 deletion, with positive clauses in sos and nonpositive
% 1.74/1.98 clauses in usable.
% 1.74/1.98
% 1.74/1.98 dependent: set(knuth_bendix).
% 1.74/1.98 dependent: set(anl_eq).
% 1.74/1.98 dependent: set(para_from).
% 1.74/1.98 dependent: set(para_into).
% 1.74/1.98 dependent: clear(para_from_right).
% 1.74/1.98 dependent: clear(para_into_right).
% 1.74/1.98 dependent: set(para_from_vars).
% 1.74/1.98 dependent: set(eq_units_both_ways).
% 1.74/1.98 dependent: set(dynamic_demod_all).
% 1.74/1.98 dependent: set(dynamic_demod).
% 1.74/1.98 dependent: set(order_eq).
% 1.74/1.98 dependent: set(back_demod).
% 1.74/1.98 dependent: set(lrpo).
% 1.74/1.98 dependent: set(hyper_res).
% 1.74/1.98 dependent: set(unit_deletion).
% 1.74/1.98 dependent: set(factor).
% 1.74/1.98
% 1.74/1.98 ------------> process usable:
% 1.74/1.98 ** KEPT (pick-wt=2): 1 [] -v1_xboole_0($c3).
% 1.74/1.98 ** KEPT (pick-wt=5): 2 [] -r2_hidden($c1,k1_closure3($c3,$c2)).
% 1.74/1.98 ** KEPT (pick-wt=5): 3 [] k1_funct_1($c2,$c1)!=k1_xboole_0.
% 1.74/1.98 ** KEPT (pick-wt=6): 4 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 1.74/1.98 ** KEPT (pick-wt=4): 5 [] -v1_xboole_0(A)|v1_fraenkel(A).
% 1.74/1.98 ** KEPT (pick-wt=4): 6 [] -v1_xboole_0(A)|v1_finset_1(A).
% 1.74/1.98 ** KEPT (pick-wt=4): 7 [] -v1_xboole_0(A)|v1_funct_1(A).
% 1.74/1.98 ** KEPT (pick-wt=8): 8 [] -v1_relat_1(A)| -v1_xboole_0(A)| -v1_funct_1(A)|v2_funct_1(A).
% 1.74/1.98 ** KEPT (pick-wt=15): 9 [] v1_xboole_0(A)| -m1_pboole(B,A)|C!=k1_closure3(A,B)|C=a_2_0_closure3(A,B).
% 1.74/1.98 ** KEPT (pick-wt=15): 10 [] v1_xboole_0(A)| -m1_pboole(B,A)|C=k1_closure3(A,B)|C!=a_2_0_closure3(A,B).
% 1.74/1.98 ** KEPT (pick-wt=5): 11 [] -m1_pboole(A,B)|v1_relat_1(A).
% 1.74/1.98 ** KEPT (pick-wt=5): 12 [] -m1_pboole(A,B)|v1_funct_1(A).
% 1.74/1.98 ** KEPT (pick-wt=16): 13 [] v1_xboole_0(A)| -m1_pboole(B,A)| -r2_hidden(C,a_2_0_closure3(A,B))|m1_subset_1($f3(C,A,B),A).
% 1.74/1.98 ** KEPT (pick-wt=16): 15 [copy,14,flip.4] v1_xboole_0(A)| -m1_pboole(B,A)| -r2_hidden(C,a_2_0_closure3(A,B))|$f3(C,A,B)=C.
% 1.74/1.98 ** KEPT (pick-wt=18): 16 [] v1_xboole_0(A)| -m1_pboole(B,A)| -r2_hidden(C,a_2_0_closure3(A,B))|k1_funct_1(B,$f3(C,A,B))!=k1_xboole_0.
% 1.74/1.98 ** KEPT (pick-wt=21): 17 [] v1_xboole_0(A)| -m1_pboole(B,A)|r2_hidden(C,a_2_0_closure3(A,B))| -m1_subset_1(D,A)|C!=D|k1_funct_1(B,D)=k1_xboole_0.
% 1.74/1.98 ** KEPT (pick-wt=2): 18 [] -v1_xboole_0($c5).
% 1.74/1.98 ** KEPT (pick-wt=2): 19 [] -v1_xboole_0($c9).
% 1.74/1.98 ** KEPT (pick-wt=6): 20 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 1.74/1.98 ** KEPT (pick-wt=8): 21 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 1.74/1.98 ** KEPT (pick-wt=13): 22 [] -r2_hidden($f4(A,B),A)| -r2_hidden($f4(A,B),B)|A=B.
% 1.74/1.98 ** KEPT (pick-wt=5): 23 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 1.74/1.98 ** KEPT (pick-wt=5): 24 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 1.74/1.98 ** KEPT (pick-wt=7): 25 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 1.74/1.98
% 1.74/1.98 ------------> process sos:
% 1.74/1.98 ** KEPT (pick-wt=3): 29 [] A=A.
% 1.74/1.98 ** KEPT (pick-wt=3): 30 [] m1_pboole($c2,$c3).
% 1.74/1.98 ** KEPT (pick-wt=3): 31 [] m1_subset_1($c1,$c3).
% 1.74/1.98 ** KEPT (pick-wt=4): 32 [] m1_pboole($f1(A),A).
% 1.74/1.98 ** KEPT (pick-wt=4): 33 [] m1_subset_1($f2(A),A).
% 1.74/1.98 ** KEPT (pick-wt=2): 34 [] v1_xboole_0(k1_xboole_0).
% 1.74/1.98 ** KEPT (pick-wt=2): 35 [] v1_xboole_0($c4).
% 1.74/1.98 ** KEPT (pick-wt=2): 36 [] v1_relat_1($c4).
% 1.74/1.98 ** KEPT (pick-wt=2): 37 [] v1_funct_1($c4).
% 1.74/1.98 ** KEPT (pick-wt=2): 38 [] v2_funct_1($c4).
% 1.74/1.98 ** KEPT (pick-wt=2): 39 [] v1_finset_1($c4).
% 1.74/1.98 ** KEPT (pick-wt=2): 40 [] v1_fraenkel($c4).
% 1.74/1.98 ** KEPT (pick-wt=2): 41 [] v1_finset_1($c5).
% 1.74/1.98 ** KEPT (pick-wt=2): 42 [] v1_relat_1($c6).
% 1.74/1.98 ** KEPT (pick-wt=2): 43 [] v1_funct_1($c6).
% 1.74/1.98 ** KEPT (pick-wt=2): 44 [] v1_xboole_0($c7).
% 1.74/1.98 ** KEPT (pick-wt=2): 45 [] v1_relat_1($c8).
% 1.74/1.98 ** KEPT (pick-wt=2): 46 [] v1_xboole_0($c8).
% 1.74/1.98 ** KEPT (pick-wt=2): 47 [] v1_funct_1($c8).
% 1.74/1.98 ** KEPT (pick-wt=2): 48 [] v1_relat_1($c10).
% 1.74/1.98 ** KEPT (pick-wt=2): 49 [] v1_funct_1($c10).
% 1.74/1.98 ** KEPT (pick-wt=2): 50 [] v2_funct_1($c10).
% 1.74/1.98 ** KEPT (pick-wt=13): 51 [] r2_hidden($f4(A,B),A)|r2_hidden($f4(A,B),B)|A=B.
% 1.74/1.98 Following clause subsumed by 29 during input processing: 0 [copy,29,flip.1] A=A.
% 1.74/1.98 29 back subsumes 28.
% 1.74/1.98 29 back subsumes 27.
% 1.74/1.98
% 1.74/1.98 ======= end of input processing =======
% 1.74/1.98
% 1.74/1.98 =========== start of search ===========
% 1.74/1.98
% 1.74/1.98 -------- PROOF --------
% 1.74/1.98
% 1.74/1.98 -----> EMPTY CLAUSE at 0.02 sec ----> 447 [hyper,64,30,31,29,unit_del,1,78,66] $F.
% 1.74/1.98
% 1.74/1.98 Length of proof is 5. Level of proof is 2.
% 1.74/1.98
% 1.74/1.98 ---------------- PROOF ----------------
% 1.74/1.98 % SZS status Theorem
% 1.74/1.98 % SZS output start Refutation
% See solution above
% 1.74/1.98 ------------ end of proof -------------
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Search stopped by max_proofs option.
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Search stopped by max_proofs option.
% 1.74/1.98
% 1.74/1.98 ============ end of search ============
% 1.74/1.98
% 1.74/1.98 -------------- statistics -------------
% 1.74/1.98 clauses given 46
% 1.74/1.98 clauses generated 753
% 1.74/1.98 clauses kept 441
% 1.74/1.98 clauses forward subsumed 371
% 1.74/1.98 clauses back subsumed 4
% 1.74/1.98 Kbytes malloced 1953
% 1.74/1.98
% 1.74/1.98 ----------- times (seconds) -----------
% 1.74/1.98 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.74/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.98
% 1.74/1.98 That finishes the proof of the theorem.
% 1.74/1.98
% 1.74/1.98 Process 22344 finished Wed Jul 27 03:34:26 2022
% 1.74/1.98 Otter interrupted
% 1.74/1.98 PROOF FOUND
%------------------------------------------------------------------------------