TSTP Solution File: NUN066+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUN066+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 13:10:28 EDT 2022
% Result : Theorem 2.28s 2.49s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of clauses : 55 ( 22 unt; 24 nHn; 11 RR)
% Number of literals : 93 ( 42 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 71 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ r1(A)
| A = dollar_c1 ),
file('NUN066+2.p',unknown),
[] ).
cnf(2,axiom,
( A != dollar_c1
| r1(A) ),
file('NUN066+2.p',unknown),
[] ).
cnf(3,axiom,
( ~ r2(A,B)
| B = dollar_f1(A) ),
file('NUN066+2.p',unknown),
[] ).
cnf(4,axiom,
( A != dollar_f1(B)
| r2(B,A) ),
file('NUN066+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ r2(A,B)
| B != C
| ~ r2(D,C)
| A = D ),
file('NUN066+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ r1(A)
| A != B
| ~ r2(C,B) ),
file('NUN066+2.p',unknown),
[] ).
cnf(12,axiom,
A = A,
file('NUN066+2.p',unknown),
[] ).
cnf(13,axiom,
r2(A,dollar_f4(B,A)),
file('NUN066+2.p',unknown),
[] ).
cnf(21,axiom,
r2(A,dollar_f8(B,A)),
file('NUN066+2.p',unknown),
[] ).
cnf(30,axiom,
dollar_f13(A) = A,
file('NUN066+2.p',unknown),
[] ).
cnf(36,axiom,
( r1(dollar_f17(A))
| r2(dollar_f19(A),dollar_f18(A)) ),
file('NUN066+2.p',unknown),
[] ).
cnf(37,axiom,
( r1(dollar_f17(A))
| A = dollar_f18(A) ),
file('NUN066+2.p',unknown),
[] ).
cnf(38,plain,
( r1(dollar_f17(A))
| dollar_f18(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[37])]),
[iquote('copy,37,flip.2')] ).
cnf(39,axiom,
( A = dollar_f17(A)
| r2(dollar_f19(A),dollar_f18(A)) ),
file('NUN066+2.p',unknown),
[] ).
cnf(40,plain,
( dollar_f17(A) = A
| r2(dollar_f19(A),dollar_f18(A)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[39])]),
[iquote('copy,39,flip.1')] ).
cnf(41,axiom,
( A = dollar_f17(A)
| A = dollar_f18(A) ),
file('NUN066+2.p',unknown),
[] ).
cnf(42,plain,
( dollar_f17(A) = A
| dollar_f18(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[41])])]),
[iquote('copy,41,flip.1,flip.2')] ).
cnf(43,axiom,
( r1(dollar_f20(A))
| r1(dollar_f23(A)) ),
file('NUN066+2.p',unknown),
[] ).
cnf(44,axiom,
( r1(dollar_f20(A))
| A = dollar_f23(A) ),
file('NUN066+2.p',unknown),
[] ).
cnf(45,plain,
( r1(dollar_f20(A))
| dollar_f23(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[44])]),
[iquote('copy,44,flip.2')] ).
cnf(46,axiom,
( r2(dollar_f20(A),dollar_f21(A))
| r1(dollar_f23(A)) ),
file('NUN066+2.p',unknown),
[] ).
cnf(47,axiom,
( r2(dollar_f20(A),dollar_f21(A))
| A = dollar_f23(A) ),
file('NUN066+2.p',unknown),
[] ).
cnf(48,plain,
( r2(dollar_f20(A),dollar_f21(A))
| dollar_f23(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[47])]),
[iquote('copy,47,flip.2')] ).
cnf(49,axiom,
( r2(dollar_f21(A),dollar_f22(A))
| r1(dollar_f23(A)) ),
file('NUN066+2.p',unknown),
[] ).
cnf(50,axiom,
( r2(dollar_f21(A),dollar_f22(A))
| A = dollar_f23(A) ),
file('NUN066+2.p',unknown),
[] ).
cnf(51,plain,
( r2(dollar_f21(A),dollar_f22(A))
| dollar_f23(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[50])]),
[iquote('copy,50,flip.2')] ).
cnf(52,axiom,
( A = dollar_f22(A)
| r1(dollar_f23(A)) ),
file('NUN066+2.p',unknown),
[] ).
cnf(53,plain,
( dollar_f22(A) = A
| r1(dollar_f23(A)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[52])]),
[iquote('copy,52,flip.1')] ).
cnf(54,axiom,
( A = dollar_f22(A)
| A = dollar_f23(A) ),
file('NUN066+2.p',unknown),
[] ).
cnf(55,plain,
( dollar_f22(A) = A
| dollar_f23(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[54])])]),
[iquote('copy,54,flip.1,flip.2')] ).
cnf(61,plain,
r2(A,dollar_f1(A)),
inference(hyper,[status(thm)],[12,4]),
[iquote('hyper,12,4')] ).
cnf(62,plain,
r1(dollar_c1),
inference(hyper,[status(thm)],[12,2]),
[iquote('hyper,12,2')] ).
cnf(78,plain,
dollar_f4(A,B) = dollar_f1(B),
inference(hyper,[status(thm)],[13,3]),
[iquote('hyper,13,3')] ).
cnf(79,plain,
dollar_f1(A) = dollar_f4(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[78])]),
[iquote('copy,78,flip.1')] ).
cnf(88,plain,
( dollar_f1(A) = B
| ~ r2(A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[30,3]),30]),
[iquote('para_into,29.1.1,3.2.1,demod,30')] ).
cnf(89,plain,
( dollar_c1 = A
| ~ r1(A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[30,1]),30]),
[iquote('para_into,29.1.1,1.2.1,demod,30')] ).
cnf(90,plain,
( r2(A,B)
| ~ r2(dollar_f1(A),C)
| C != D
| ~ r2(B,D) ),
inference(para_into,[status(thm),theory(equality)],[61,9]),
[iquote('para_into,61.1.2,9.4.1')] ).
cnf(119,plain,
dollar_f8(A,B) = dollar_f1(B),
inference(hyper,[status(thm)],[21,3]),
[iquote('hyper,21,3')] ).
cnf(120,plain,
dollar_f1(A) = dollar_f8(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[119])]),
[iquote('copy,119,flip.1')] ).
cnf(303,plain,
( r1(dollar_f20(A))
| r1(A) ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[45,43])]),
[iquote('para_from,45.2.1,43.2.1,factor_simp')] ).
cnf(318,plain,
( r1(A)
| r2(dollar_f19(A),dollar_f18(A)) ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[40,36])]),
[iquote('para_from,40.1.1,36.1.1,factor_simp')] ).
cnf(330,plain,
r1(dollar_f20(dollar_f1(A))),
inference(hyper,[status(thm)],[303,10,120,21]),
[iquote('hyper,303,10,120,21')] ).
cnf(346,plain,
dollar_f20(dollar_f1(A)) = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[330,89])]),
[iquote('hyper,330,89,flip.1')] ).
cnf(364,plain,
dollar_f18(dollar_f1(A)) = dollar_f1(A),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[42,10,38,61])]),
[iquote('hyper,42,10,38,61,factor_simp')] ).
cnf(506,plain,
( r2(dollar_f20(A),dollar_f21(A))
| r1(A) ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[48,46])]),
[iquote('para_from,48.2.1,46.2.1,factor_simp')] ).
cnf(849,plain,
( r2(dollar_f21(A),dollar_f22(A))
| r1(A) ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[51,49])]),
[iquote('para_from,51.2.1,49.2.1,factor_simp')] ).
cnf(988,plain,
dollar_f22(dollar_f1(A)) = dollar_f1(A),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[55,10,53,61])]),
[iquote('hyper,55,10,53,61,factor_simp')] ).
cnf(1244,plain,
r2(dollar_f19(dollar_f1(A)),dollar_f1(A)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[318,10,988,61]),988,988,364]),
[iquote('hyper,318,10,987,61,demod,988,988,364')] ).
cnf(1268,plain,
dollar_f19(dollar_f1(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1244,9,61,12])]),
[iquote('hyper,1244,9,61,12,flip.1')] ).
cnf(1282,plain,
dollar_f19(dollar_f4(A,B)) = B,
inference(para_into,[status(thm),theory(equality)],[1268,79]),
[iquote('para_into,1268.1.1.1,79.1.1')] ).
cnf(2511,plain,
r2(dollar_c1,dollar_f21(dollar_f1(A))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[506,10,1282,61]),1282,346,1282]),
[iquote('hyper,506,10,1281,61,demod,1282,346,1282')] ).
cnf(2556,plain,
dollar_f21(dollar_f1(A)) = dollar_f1(dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2511,88])]),
[iquote('hyper,2511,88,flip.1')] ).
cnf(2580,plain,
r2(dollar_f1(dollar_c1),dollar_f1(A)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[849,10,1282,61]),1282,2556,1282,988]),
[iquote('hyper,849,10,1281,61,demod,1282,2556,1282,988')] ).
cnf(2586,plain,
r2(dollar_c1,A),
inference(hyper,[status(thm)],[2580,90,120,21]),
[iquote('hyper,2580,90,120,21')] ).
cnf(2634,plain,
$false,
inference(hyper,[status(thm)],[2586,10,62,12]),
[iquote('hyper,2586,10,62,12')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN066+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.14/0.33 % Computer : n029.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Jul 27 02:48:59 EDT 2022
% 0.14/0.33 % CPUTime :
% 1.78/1.99 ----- Otter 3.3f, August 2004 -----
% 1.78/1.99 The process was started by sandbox2 on n029.cluster.edu,
% 1.78/1.99 Wed Jul 27 02:48:59 2022
% 1.78/1.99 The command was "./otter". The process ID is 13592.
% 1.78/1.99
% 1.78/1.99 set(prolog_style_variables).
% 1.78/1.99 set(auto).
% 1.78/1.99 dependent: set(auto1).
% 1.78/1.99 dependent: set(process_input).
% 1.78/1.99 dependent: clear(print_kept).
% 1.78/1.99 dependent: clear(print_new_demod).
% 1.78/1.99 dependent: clear(print_back_demod).
% 1.78/1.99 dependent: clear(print_back_sub).
% 1.78/1.99 dependent: set(control_memory).
% 1.78/1.99 dependent: assign(max_mem, 12000).
% 1.78/1.99 dependent: assign(pick_given_ratio, 4).
% 1.78/1.99 dependent: assign(stats_level, 1).
% 1.78/1.99 dependent: assign(max_seconds, 10800).
% 1.78/1.99 clear(print_given).
% 1.78/1.99
% 1.78/1.99 formula_list(usable).
% 1.78/1.99 all A (A=A).
% 1.78/1.99 exists Y24 all X19 (-r1(X19)&X19!=Y24|r1(X19)&X19=Y24).
% 1.78/1.99 all X11 exists Y21 all X12 (-r2(X11,X12)&X12!=Y21|r2(X11,X12)&X12=Y21).
% 1.78/1.99 all X13 X14 exists Y22 all X15 (-r3(X13,X14,X15)&X15!=Y22|r3(X13,X14,X15)&X15=Y22).
% 1.78/1.99 all X16 X17 exists Y23 all X18 (-r4(X16,X17,X18)&X18!=Y23|r4(X16,X17,X18)&X18=Y23).
% 1.78/1.99 all X1 X8 exists Y4 ((exists Y5 ((exists Y15 (r2(X8,Y15)&r3(X1,Y15,Y5)))&Y5=Y4))& (exists Y7 (r2(Y7,Y4)&r3(X1,X8,Y7)))).
% 1.78/1.99 all X2 X9 exists Y2 ((exists Y3 ((exists Y14 (r2(X9,Y14)&r4(X2,Y14,Y3)))&Y3=Y2))& (exists Y6 (r3(Y6,X2,Y2)&r4(X2,X9,Y6)))).
% 1.78/1.99 all X3 X10 ((all Y12 ((all Y13 (-r2(X3,Y13)|Y13!=Y12))| -r2(X10,Y12)))|X3=X10).
% 1.78/1.99 all X4 exists Y9 ((exists Y16 (r1(Y16)&r3(X4,Y16,Y9)))&Y9=X4).
% 1.78/1.99 all X5 exists Y8 ((exists Y17 (r1(Y17)&r4(X5,Y17,Y8)))& (exists Y18 (r1(Y18)&Y8=Y18))).
% 1.78/1.99 all X6 ((exists Y19 (r1(Y19)&X6=Y19))| (exists Y1 Y11 (r2(Y1,Y11)&X6=Y11))).
% 1.78/1.99 all X7 Y10 ((all Y20 (-r1(Y20)|Y20!=Y10))| -r2(X7,Y10)).
% 1.78/1.99 -(exists Y1 ((all Y2 ((all Y3 ((all Y4 (-r1(Y4)| -r2(Y4,Y3)))| -r2(Y3,Y2)))|Y1!=Y2))& (all Y5 (-r1(Y5)|Y1!=Y5)))).
% 1.78/1.99 end_of_list.
% 1.78/1.99
% 1.78/1.99 -------> usable clausifies to:
% 1.78/1.99
% 1.78/1.99 list(usable).
% 1.78/1.99 0 [] A=A.
% 1.78/1.99 0 [] -r1(X19)|X19=$c1.
% 1.78/1.99 0 [] X19!=$c1|r1(X19).
% 1.78/1.99 0 [] -r2(X11,X12)|X12=$f1(X11).
% 1.78/1.99 0 [] X12!=$f1(X11)|r2(X11,X12).
% 1.78/1.99 0 [] -r3(X13,X14,X15)|X15=$f2(X13,X14).
% 1.78/1.99 0 [] X15!=$f2(X13,X14)|r3(X13,X14,X15).
% 1.78/1.99 0 [] -r4(X16,X17,X18)|X18=$f3(X16,X17).
% 1.78/1.99 0 [] X18!=$f3(X16,X17)|r4(X16,X17,X18).
% 1.78/1.99 0 [] r2(X8,$f4(X1,X8)).
% 1.78/1.99 0 [] r3(X1,$f4(X1,X8),$f5(X1,X8)).
% 1.78/1.99 0 [] $f5(X1,X8)=$f7(X1,X8).
% 1.78/1.99 0 [] r2($f6(X1,X8),$f7(X1,X8)).
% 1.78/1.99 0 [] r3(X1,X8,$f6(X1,X8)).
% 1.78/1.99 0 [] r2(X9,$f8(X2,X9)).
% 1.78/1.99 0 [] r4(X2,$f8(X2,X9),$f9(X2,X9)).
% 1.78/1.99 0 [] $f9(X2,X9)=$f11(X2,X9).
% 1.78/1.99 0 [] r3($f10(X2,X9),X2,$f11(X2,X9)).
% 1.78/1.99 0 [] r4(X2,X9,$f10(X2,X9)).
% 1.78/1.99 0 [] -r2(X3,Y13)|Y13!=Y12| -r2(X10,Y12)|X3=X10.
% 1.78/1.99 0 [] r1($f12(X4)).
% 1.78/1.99 0 [] r3(X4,$f12(X4),$f13(X4)).
% 1.78/1.99 0 [] $f13(X4)=X4.
% 1.78/1.99 0 [] r1($f14(X5)).
% 1.78/1.99 0 [] r4(X5,$f14(X5),$f16(X5)).
% 1.78/1.99 0 [] r1($f15(X5)).
% 1.78/1.99 0 [] $f16(X5)=$f15(X5).
% 1.78/1.99 0 [] r1($f17(X6))|r2($f19(X6),$f18(X6)).
% 1.78/1.99 0 [] r1($f17(X6))|X6=$f18(X6).
% 1.78/1.99 0 [] X6=$f17(X6)|r2($f19(X6),$f18(X6)).
% 1.78/1.99 0 [] X6=$f17(X6)|X6=$f18(X6).
% 1.78/1.99 0 [] -r1(Y20)|Y20!=Y10| -r2(X7,Y10).
% 1.78/1.99 0 [] r1($f20(Y1))|r1($f23(Y1)).
% 1.78/1.99 0 [] r1($f20(Y1))|Y1=$f23(Y1).
% 1.78/1.99 0 [] r2($f20(Y1),$f21(Y1))|r1($f23(Y1)).
% 1.78/1.99 0 [] r2($f20(Y1),$f21(Y1))|Y1=$f23(Y1).
% 1.78/1.99 0 [] r2($f21(Y1),$f22(Y1))|r1($f23(Y1)).
% 1.78/1.99 0 [] r2($f21(Y1),$f22(Y1))|Y1=$f23(Y1).
% 1.78/1.99 0 [] Y1=$f22(Y1)|r1($f23(Y1)).
% 1.78/1.99 0 [] Y1=$f22(Y1)|Y1=$f23(Y1).
% 1.78/1.99 end_of_list.
% 1.78/1.99
% 1.78/1.99 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.78/1.99
% 1.78/1.99 This ia a non-Horn set with equality. The strategy will be
% 1.78/1.99 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.78/1.99 deletion, with positive clauses in sos and nonpositive
% 1.78/1.99 clauses in usable.
% 1.78/1.99
% 1.78/1.99 dependent: set(knuth_bendix).
% 1.78/1.99 dependent: set(anl_eq).
% 1.78/1.99 dependent: set(para_from).
% 1.78/1.99 dependent: set(para_into).
% 1.78/1.99 dependent: clear(para_from_right).
% 1.78/1.99 dependent: clear(para_into_right).
% 1.78/1.99 dependent: set(para_from_vars).
% 1.78/1.99 dependent: set(eq_units_both_ways).
% 1.78/1.99 dependent: set(dynamic_demod_all).
% 1.78/1.99 dependent: set(dynamic_demod).
% 1.78/1.99 dependent: set(order_eq).
% 1.78/1.99 dependent: set(back_demod).
% 1.78/1.99 dependent: set(lrpo).
% 1.78/1.99 dependent: set(hyper_res).
% 1.78/1.99 dependent: set(unit_deletion).
% 1.78/1.99 dependent: set(factor).
% 1.78/1.99
% 1.78/1.99 ------------> process usable:
% 1.78/1.99 ** KEPT (pick-wt=5): 1 [] -r1(A)|A=$c1.
% 1.78/1.99 ** KEPT (pick-wt=5): 2 [] A!=$c1|r1(A).
% 1.78/1.99 ** KEPT (pick-wt=7): 3 [] -r2(A,B)|B=$f1(A).
% 1.78/1.99 ** KEPT (pick-wt=7): 4 [] A!=$f1(B)|r2(B,A).
% 1.78/1.99 ** KEPT (pick-wt=9): 5 [] -r3(A,B,C)|C=$f2(A,B).
% 1.78/1.99 ** KEPT (pick-wt=9): 6 [] A!=$f2(B,C)|r3(B,C,A).
% 1.78/1.99 ** KEPT (pick-wt=9): 7 [] -r4(A,B,C)|C=$f3(A,B).
% 2.28/2.49 ** KEPT (pick-wt=9): 8 [] A!=$f3(B,C)|r4(B,C,A).
% 2.28/2.49 ** KEPT (pick-wt=12): 9 [] -r2(A,B)|B!=C| -r2(D,C)|A=D.
% 2.28/2.49 ** KEPT (pick-wt=8): 10 [] -r1(A)|A!=B| -r2(C,B).
% 2.28/2.49
% 2.28/2.49 ------------> process sos:
% 2.28/2.49 ** KEPT (pick-wt=3): 12 [] A=A.
% 2.28/2.49 ** KEPT (pick-wt=5): 13 [] r2(A,$f4(B,A)).
% 2.28/2.49 ** KEPT (pick-wt=8): 14 [] r3(A,$f4(A,B),$f5(A,B)).
% 2.28/2.49 ** KEPT (pick-wt=7): 16 [copy,15,flip.1] $f7(A,B)=$f5(A,B).
% 2.28/2.49 ---> New Demodulator: 17 [new_demod,16] $f7(A,B)=$f5(A,B).
% 2.28/2.49 ** KEPT (pick-wt=7): 19 [copy,18,demod,17] r2($f6(A,B),$f5(A,B)).
% 2.28/2.49 ** KEPT (pick-wt=6): 20 [] r3(A,B,$f6(A,B)).
% 2.28/2.49 ** KEPT (pick-wt=5): 21 [] r2(A,$f8(B,A)).
% 2.28/2.49 ** KEPT (pick-wt=8): 22 [] r4(A,$f8(A,B),$f9(A,B)).
% 2.28/2.49 ** KEPT (pick-wt=7): 23 [] $f9(A,B)=$f11(A,B).
% 2.28/2.49 ---> New Demodulator: 24 [new_demod,23] $f9(A,B)=$f11(A,B).
% 2.28/2.49 ** KEPT (pick-wt=8): 25 [] r3($f10(A,B),A,$f11(A,B)).
% 2.28/2.49 ** KEPT (pick-wt=6): 26 [] r4(A,B,$f10(A,B)).
% 2.28/2.49 ** KEPT (pick-wt=3): 27 [] r1($f12(A)).
% 2.28/2.49 ** KEPT (pick-wt=6): 28 [] r3(A,$f12(A),$f13(A)).
% 2.28/2.49 ** KEPT (pick-wt=4): 29 [] $f13(A)=A.
% 2.28/2.49 ---> New Demodulator: 30 [new_demod,29] $f13(A)=A.
% 2.28/2.49 ** KEPT (pick-wt=3): 31 [] r1($f14(A)).
% 2.28/2.49 ** KEPT (pick-wt=6): 32 [] r4(A,$f14(A),$f16(A)).
% 2.28/2.49 ** KEPT (pick-wt=3): 33 [] r1($f15(A)).
% 2.28/2.49 ** KEPT (pick-wt=5): 34 [] $f16(A)=$f15(A).
% 2.28/2.49 ---> New Demodulator: 35 [new_demod,34] $f16(A)=$f15(A).
% 2.28/2.49 ** KEPT (pick-wt=8): 36 [] r1($f17(A))|r2($f19(A),$f18(A)).
% 2.28/2.49 ** KEPT (pick-wt=7): 38 [copy,37,flip.2] r1($f17(A))|$f18(A)=A.
% 2.28/2.49 ** KEPT (pick-wt=9): 40 [copy,39,flip.1] $f17(A)=A|r2($f19(A),$f18(A)).
% 2.28/2.49 ** KEPT (pick-wt=8): 42 [copy,41,flip.1,flip.2] $f17(A)=A|$f18(A)=A.
% 2.28/2.49 ** KEPT (pick-wt=6): 43 [] r1($f20(A))|r1($f23(A)).
% 2.28/2.49 ** KEPT (pick-wt=7): 45 [copy,44,flip.2] r1($f20(A))|$f23(A)=A.
% 2.28/2.49 ** KEPT (pick-wt=8): 46 [] r2($f20(A),$f21(A))|r1($f23(A)).
% 2.28/2.49 ** KEPT (pick-wt=9): 48 [copy,47,flip.2] r2($f20(A),$f21(A))|$f23(A)=A.
% 2.28/2.49 ** KEPT (pick-wt=8): 49 [] r2($f21(A),$f22(A))|r1($f23(A)).
% 2.28/2.49 ** KEPT (pick-wt=9): 51 [copy,50,flip.2] r2($f21(A),$f22(A))|$f23(A)=A.
% 2.28/2.49 ** KEPT (pick-wt=7): 53 [copy,52,flip.1] $f22(A)=A|r1($f23(A)).
% 2.28/2.49 ** KEPT (pick-wt=8): 55 [copy,54,flip.1,flip.2] $f22(A)=A|$f23(A)=A.
% 2.28/2.49 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 2.28/2.49 12 back subsumes 11.
% 2.28/2.49 >>>> Starting back demodulation with 17.
% 2.28/2.49 >>>> Starting back demodulation with 24.
% 2.28/2.49 >> back demodulating 22 with 24.
% 2.28/2.49 >>>> Starting back demodulation with 30.
% 2.28/2.49 >> back demodulating 28 with 30.
% 2.28/2.49 >>>> Starting back demodulation with 35.
% 2.28/2.49 >> back demodulating 32 with 35.
% 2.28/2.49
% 2.28/2.49 ======= end of input processing =======
% 2.28/2.49
% 2.28/2.49 =========== start of search ===========
% 2.28/2.49
% 2.28/2.49
% 2.28/2.49 Resetting weight limit to 8.
% 2.28/2.49
% 2.28/2.49
% 2.28/2.49 Resetting weight limit to 8.
% 2.28/2.49
% 2.28/2.49 sos_size=2205
% 2.28/2.49
% 2.28/2.49 -------- PROOF --------
% 2.28/2.49
% 2.28/2.49 -----> EMPTY CLAUSE at 0.50 sec ----> 2634 [hyper,2586,10,62,12] $F.
% 2.28/2.49
% 2.28/2.49 Length of proof is 32. Level of proof is 9.
% 2.28/2.49
% 2.28/2.49 ---------------- PROOF ----------------
% 2.28/2.49 % SZS status Theorem
% 2.28/2.49 % SZS output start Refutation
% See solution above
% 2.28/2.49 ------------ end of proof -------------
% 2.28/2.49
% 2.28/2.49
% 2.28/2.49 Search stopped by max_proofs option.
% 2.28/2.49
% 2.28/2.49
% 2.28/2.49 Search stopped by max_proofs option.
% 2.28/2.49
% 2.28/2.49 ============ end of search ============
% 2.28/2.49
% 2.28/2.49 -------------- statistics -------------
% 2.28/2.49 clauses given 128
% 2.28/2.49 clauses generated 8233
% 2.28/2.49 clauses kept 2585
% 2.28/2.49 clauses forward subsumed 4866
% 2.28/2.49 clauses back subsumed 167
% 2.28/2.49 Kbytes malloced 4882
% 2.28/2.49
% 2.28/2.49 ----------- times (seconds) -----------
% 2.28/2.49 user CPU time 0.50 (0 hr, 0 min, 0 sec)
% 2.28/2.49 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.28/2.49 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.28/2.49
% 2.28/2.49 That finishes the proof of the theorem.
% 2.28/2.49
% 2.28/2.49 Process 13592 finished Wed Jul 27 02:49:01 2022
% 2.28/2.49 Otter interrupted
% 2.28/2.49 PROOF FOUND
%------------------------------------------------------------------------------