TSTP Solution File: KLE090+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE090+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:00:43 EDT 2022
% Result : Theorem 2.03s 2.29s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of clauses : 61 ( 58 unt; 0 nHn; 17 RR)
% Number of literals : 64 ( 56 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE090+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE090+1.p',unknown),
[] ).
cnf(3,axiom,
addition(antidomain(dollar_c1),antidomain(dollar_c2)) != antidomain(dollar_c2),
file('KLE090+1.p',unknown),
[] ).
cnf(5,axiom,
addition(A,B) = addition(B,A),
file('KLE090+1.p',unknown),
[] ).
cnf(6,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE090+1.p',unknown),
[] ).
cnf(7,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(10,axiom,
addition(A,zero) = A,
file('KLE090+1.p',unknown),
[] ).
cnf(11,axiom,
addition(A,A) = A,
file('KLE090+1.p',unknown),
[] ).
cnf(13,axiom,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE090+1.p',unknown),
[] ).
cnf(14,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(17,axiom,
multiplication(A,one) = A,
file('KLE090+1.p',unknown),
[] ).
cnf(19,axiom,
multiplication(one,A) = A,
file('KLE090+1.p',unknown),
[] ).
cnf(20,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE090+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE090+1.p',unknown),
[] ).
cnf(27,axiom,
multiplication(zero,A) = zero,
file('KLE090+1.p',unknown),
[] ).
cnf(29,axiom,
multiplication(antidomain(A),A) = zero,
file('KLE090+1.p',unknown),
[] ).
cnf(30,axiom,
addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
file('KLE090+1.p',unknown),
[] ).
cnf(32,axiom,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
file('KLE090+1.p',unknown),
[] ).
cnf(36,axiom,
multiplication(A,coantidomain(A)) = zero,
file('KLE090+1.p',unknown),
[] ).
cnf(38,axiom,
addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)),
file('KLE090+1.p',unknown),
[] ).
cnf(40,axiom,
addition(coantidomain(coantidomain(A)),coantidomain(A)) = one,
file('KLE090+1.p',unknown),
[] ).
cnf(44,axiom,
addition(dollar_c2,dollar_c1) = dollar_c1,
file('KLE090+1.p',unknown),
[] ).
cnf(52,plain,
addition(zero,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,10])]),
[iquote('para_into,5.1.1,9.1.1,flip.1')] ).
cnf(53,plain,
( addition(A,B) = A
| ~ le_q(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,1])]),
[iquote('para_into,5.1.1,1.2.1,flip.1')] ).
cnf(54,plain,
addition(antidomain(dollar_c2),antidomain(dollar_c1)) != antidomain(dollar_c2),
inference(para_from,[status(thm),theory(equality)],[5,3]),
[iquote('para_from,5.1.1,3.1.1')] ).
cnf(56,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,11])]),
[iquote('para_into,7.1.1.1,11.1.1,flip.1')] ).
cnf(67,plain,
addition(dollar_c1,dollar_c2) = dollar_c1,
inference(para_into,[status(thm),theory(equality)],[44,5]),
[iquote('para_into,44.1.1,5.1.1')] ).
cnf(77,plain,
antidomain(one) = zero,
inference(para_into,[status(thm),theory(equality)],[29,17]),
[iquote('para_into,28.1.1,16.1.1')] ).
cnf(78,plain,
multiplication(antidomain(A),multiplication(A,B)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[29,14]),27])]),
[iquote('para_from,28.1.1,14.1.1.1,demod,27,flip.1')] ).
cnf(80,plain,
addition(multiplication(A,dollar_c1),multiplication(A,dollar_c2)) = multiplication(A,dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,67])]),
[iquote('para_into,20.1.1.2,67.1.1,flip.1')] ).
cnf(88,plain,
coantidomain(one) = zero,
inference(para_into,[status(thm),theory(equality)],[36,19]),
[iquote('para_into,36.1.1,18.1.1')] ).
cnf(89,plain,
multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero,
inference(para_into,[status(thm),theory(equality)],[36,14]),
[iquote('para_into,36.1.1,14.1.1')] ).
cnf(171,plain,
antidomain(zero) = one,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,77]),77,10]),
[iquote('para_into,32.1.1.1.1,76.1.1,demod,77,10')] ).
cnf(189,plain,
addition(multiplication(A,antidomain(antidomain(B))),multiplication(A,antidomain(B))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[32,20]),17])]),
[iquote('para_from,32.1.1,20.1.1.2,demod,17,flip.1')] ).
cnf(191,plain,
addition(multiplication(antidomain(antidomain(A)),B),multiplication(antidomain(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[32,22]),19])]),
[iquote('para_from,32.1.1,22.1.1.1,demod,19,flip.1')] ).
cnf(212,plain,
addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)),
inference(para_into,[status(thm),theory(equality)],[38,29]),
[iquote('para_into,38.1.1.1.1,28.1.1')] ).
cnf(242,plain,
coantidomain(zero) = one,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[40,88]),88,10]),
[iquote('para_into,40.1.1.1.1,87.1.1,demod,88,10')] ).
cnf(253,plain,
addition(one,coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[212]),242]),
[iquote('back_demod,212,demod,242')] ).
cnf(258,plain,
addition(multiplication(A,coantidomain(coantidomain(B))),multiplication(A,coantidomain(B))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[40,20]),17])]),
[iquote('para_from,40.1.1,20.1.1.2,demod,17,flip.1')] ).
cnf(260,plain,
addition(multiplication(coantidomain(coantidomain(A)),B),multiplication(coantidomain(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[40,22]),19])]),
[iquote('para_from,40.1.1,22.1.1.1,demod,19,flip.1')] ).
cnf(310,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[56,2]),
[iquote('hyper,56,2')] ).
cnf(326,plain,
le_q(A,addition(B,A)),
inference(para_into,[status(thm),theory(equality)],[310,5]),
[iquote('para_into,310.1.2,5.1.1')] ).
cnf(332,plain,
le_q(coantidomain(A),one),
inference(para_into,[status(thm),theory(equality)],[326,40]),
[iquote('para_into,326.1.2,40.1.1')] ).
cnf(333,plain,
le_q(antidomain(A),one),
inference(para_into,[status(thm),theory(equality)],[326,32]),
[iquote('para_into,326.1.2,32.1.1')] ).
cnf(363,plain,
addition(one,coantidomain(A)) = one,
inference(hyper,[status(thm)],[332,53]),
[iquote('hyper,332,53')] ).
cnf(373,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[253]),363])]),
[iquote('back_demod,253,demod,363,flip.1')] ).
cnf(378,plain,
addition(one,antidomain(A)) = one,
inference(hyper,[status(thm)],[333,53]),
[iquote('hyper,333,53')] ).
cnf(441,plain,
addition(A,multiplication(antidomain(B),A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[378,22]),19,19])]),
[iquote('para_from,377.1.1,22.1.1.1,demod,19,19,flip.1')] ).
cnf(767,plain,
multiplication(antidomain(dollar_c1),dollar_c2) = zero,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[80,29]),52,29]),
[iquote('para_into,80.1.1.1,28.1.1,demod,52,29')] ).
cnf(792,plain,
antidomain(multiplication(antidomain(dollar_c1),antidomain(antidomain(dollar_c2)))) = one,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[767,30]),171,378])]),
[iquote('para_from,767.1.1,30.1.1.1.1,demod,171,378,flip.1')] ).
cnf(1142,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[191,29]),10]),
[iquote('para_into,191.1.1.2,28.1.1,demod,10')] ).
cnf(1150,plain,
antidomain(antidomain(antidomain(A))) = antidomain(A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1142,189]),29,52])]),
[iquote('para_from,1142.1.1,189.1.1.2,demod,29,52,flip.1')] ).
cnf(1194,plain,
multiplication(A,coantidomain(coantidomain(A))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[258,36]),10]),
[iquote('para_into,258.1.1.2,36.1.1,demod,10')] ).
cnf(1200,plain,
coantidomain(coantidomain(coantidomain(A))) = coantidomain(A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[260,36]),1194,52])]),
[iquote('para_into,260.1.1.1,36.1.1,demod,1194,52,flip.1')] ).
cnf(1221,plain,
multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[373,89]),17]),
[iquote('para_from,373.1.1,89.1.1.2.2,demod,17')] ).
cnf(1224,plain,
multiplication(coantidomain(antidomain(A)),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1221,260]),1200,10]),
[iquote('para_from,1221.1.1,260.1.1.2,demod,1200,10')] ).
cnf(1234,plain,
multiplication(antidomain(coantidomain(antidomain(A))),A) = zero,
inference(para_from,[status(thm),theory(equality)],[1224,78]),
[iquote('para_from,1224.1.1,78.1.1.2')] ).
cnf(1276,plain,
multiplication(antidomain(dollar_c1),antidomain(antidomain(dollar_c2))) = zero,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[792,1234]),88,171,19]),
[iquote('para_from,792.1.1,1234.1.1.1.1.1,demod,88,171,19')] ).
cnf(1279,plain,
multiplication(antidomain(dollar_c1),antidomain(dollar_c2)) = antidomain(dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1276,189]),1150,10]),
[iquote('para_from,1276.1.1,189.1.1.2,demod,1150,10')] ).
cnf(1285,plain,
addition(antidomain(dollar_c2),antidomain(dollar_c1)) = antidomain(dollar_c2),
inference(para_from,[status(thm),theory(equality)],[1279,441]),
[iquote('para_from,1279.1.1,441.1.1.2')] ).
cnf(1287,plain,
$false,
inference(binary,[status(thm)],[1285,54]),
[iquote('binary,1285.1,54.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE090+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n021.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 06:27:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.92 ----- Otter 3.3f, August 2004 -----
% 1.71/1.92 The process was started by sandbox on n021.cluster.edu,
% 1.71/1.92 Wed Jul 27 06:27:53 2022
% 1.71/1.92 The command was "./otter". The process ID is 2445.
% 1.71/1.92
% 1.71/1.92 set(prolog_style_variables).
% 1.71/1.92 set(auto).
% 1.71/1.92 dependent: set(auto1).
% 1.71/1.92 dependent: set(process_input).
% 1.71/1.92 dependent: clear(print_kept).
% 1.71/1.92 dependent: clear(print_new_demod).
% 1.71/1.92 dependent: clear(print_back_demod).
% 1.71/1.92 dependent: clear(print_back_sub).
% 1.71/1.92 dependent: set(control_memory).
% 1.71/1.92 dependent: assign(max_mem, 12000).
% 1.71/1.92 dependent: assign(pick_given_ratio, 4).
% 1.71/1.92 dependent: assign(stats_level, 1).
% 1.71/1.92 dependent: assign(max_seconds, 10800).
% 1.71/1.92 clear(print_given).
% 1.71/1.92
% 1.71/1.92 formula_list(usable).
% 1.71/1.92 all A (A=A).
% 1.71/1.92 all A B (addition(A,B)=addition(B,A)).
% 1.71/1.92 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.71/1.92 all A (addition(A,zero)=A).
% 1.71/1.92 all A (addition(A,A)=A).
% 1.71/1.92 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.71/1.92 all A (multiplication(A,one)=A).
% 1.71/1.92 all A (multiplication(one,A)=A).
% 1.71/1.92 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.71/1.92 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.71/1.92 all A (multiplication(A,zero)=zero).
% 1.71/1.92 all A (multiplication(zero,A)=zero).
% 1.71/1.92 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.71/1.92 all X0 (multiplication(antidomain(X0),X0)=zero).
% 1.71/1.92 all X0 X1 (addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))=antidomain(multiplication(X0,antidomain(antidomain(X1))))).
% 1.71/1.92 all X0 (addition(antidomain(antidomain(X0)),antidomain(X0))=one).
% 1.71/1.92 all X0 (domain(X0)=antidomain(antidomain(X0))).
% 1.71/1.92 all X0 (multiplication(X0,coantidomain(X0))=zero).
% 1.71/1.92 all X0 X1 (addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))=coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))).
% 1.71/1.92 all X0 (addition(coantidomain(coantidomain(X0)),coantidomain(X0))=one).
% 1.71/1.92 all X0 (codomain(X0)=coantidomain(coantidomain(X0))).
% 1.71/1.92 -(all X0 X1 (addition(X0,X1)=X1->addition(antidomain(X1),antidomain(X0))=antidomain(X0))).
% 1.71/1.92 end_of_list.
% 1.71/1.92
% 1.71/1.92 -------> usable clausifies to:
% 1.71/1.92
% 1.71/1.92 list(usable).
% 1.71/1.92 0 [] A=A.
% 1.71/1.92 0 [] addition(A,B)=addition(B,A).
% 1.71/1.92 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.71/1.92 0 [] addition(A,zero)=A.
% 1.71/1.92 0 [] addition(A,A)=A.
% 1.71/1.92 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.71/1.92 0 [] multiplication(A,one)=A.
% 1.71/1.92 0 [] multiplication(one,A)=A.
% 1.71/1.92 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.71/1.92 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.71/1.92 0 [] multiplication(A,zero)=zero.
% 1.71/1.92 0 [] multiplication(zero,A)=zero.
% 1.71/1.92 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.71/1.92 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.71/1.92 0 [] multiplication(antidomain(X0),X0)=zero.
% 1.71/1.92 0 [] addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))=antidomain(multiplication(X0,antidomain(antidomain(X1)))).
% 1.71/1.92 0 [] addition(antidomain(antidomain(X0)),antidomain(X0))=one.
% 1.71/1.92 0 [] domain(X0)=antidomain(antidomain(X0)).
% 1.71/1.92 0 [] multiplication(X0,coantidomain(X0))=zero.
% 1.71/1.92 0 [] addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))=coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)).
% 1.71/1.92 0 [] addition(coantidomain(coantidomain(X0)),coantidomain(X0))=one.
% 1.71/1.92 0 [] codomain(X0)=coantidomain(coantidomain(X0)).
% 1.71/1.92 0 [] addition($c2,$c1)=$c1.
% 1.71/1.92 0 [] addition(antidomain($c1),antidomain($c2))!=antidomain($c2).
% 1.71/1.92 end_of_list.
% 1.71/1.92
% 1.71/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.71/1.92
% 1.71/1.92 This is a Horn set with equality. The strategy will be
% 1.71/1.92 Knuth-Bendix and hyper_res, with positive clauses in
% 1.71/1.92 sos and nonpositive clauses in usable.
% 1.71/1.92
% 1.71/1.92 dependent: set(knuth_bendix).
% 1.71/1.92 dependent: set(anl_eq).
% 1.71/1.92 dependent: set(para_from).
% 1.71/1.92 dependent: set(para_into).
% 1.71/1.92 dependent: clear(para_from_right).
% 1.71/1.92 dependent: clear(para_into_right).
% 1.71/1.92 dependent: set(para_from_vars).
% 1.71/1.92 dependent: set(eq_units_both_ways).
% 1.71/1.92 dependent: set(dynamic_demod_all).
% 1.71/1.92 dependent: set(dynamic_demod).
% 1.71/1.92 dependent: set(order_eq).
% 1.71/1.92 dependent: set(back_demod).
% 1.71/1.92 dependent: set(lrpo).
% 1.71/1.92 dependent: set(hyper_res).
% 1.71/1.92 dependent: clear(order_hyper).
% 1.71/1.92
% 1.71/1.92 ------------> process usable:
% 1.71/1.92 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.71/1.92 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.71/1.92 ** KEPT (pick-wt=8): 3 [] addition(antidomain($c1),antidomain($c2))!=antidomain($c2).
% 1.71/1.92
% 1.71/1.92 ------------> process sos:
% 1.71/1.92 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.71/1.92 ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 1.71/1.92 ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.71/1.92 ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.71/1.92 ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 1.71/1.92 ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 1.71/1.92 ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 1.71/1.92 ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 1.71/1.92 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.71/1.92 ---> New Demodulator: 15 [new_demod,14] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.71/1.92 ** KEPT (pick-wt=5): 16 [] multiplication(A,one)=A.
% 1.71/1.92 ---> New Demodulator: 17 [new_demod,16] multiplication(A,one)=A.
% 1.71/1.92 ** KEPT (pick-wt=5): 18 [] multiplication(one,A)=A.
% 1.71/1.92 ---> New Demodulator: 19 [new_demod,18] multiplication(one,A)=A.
% 1.71/1.92 ** KEPT (pick-wt=13): 20 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.71/1.92 ---> New Demodulator: 21 [new_demod,20] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.71/1.92 ** KEPT (pick-wt=13): 22 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.71/1.92 ---> New Demodulator: 23 [new_demod,22] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.71/1.92 ** KEPT (pick-wt=5): 24 [] multiplication(A,zero)=zero.
% 1.71/1.92 ---> New Demodulator: 25 [new_demod,24] multiplication(A,zero)=zero.
% 1.71/1.92 ** KEPT (pick-wt=5): 26 [] multiplication(zero,A)=zero.
% 1.71/1.92 ---> New Demodulator: 27 [new_demod,26] multiplication(zero,A)=zero.
% 1.71/1.92 ** KEPT (pick-wt=6): 28 [] multiplication(antidomain(A),A)=zero.
% 1.71/1.92 ---> New Demodulator: 29 [new_demod,28] multiplication(antidomain(A),A)=zero.
% 1.71/1.92 ** KEPT (pick-wt=18): 30 [] addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B)))))=antidomain(multiplication(A,antidomain(antidomain(B)))).
% 1.71/1.92 ---> New Demodulator: 31 [new_demod,30] addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B)))))=antidomain(multiplication(A,antidomain(antidomain(B)))).
% 1.71/1.92 ** KEPT (pick-wt=8): 32 [] addition(antidomain(antidomain(A)),antidomain(A))=one.
% 1.71/1.92 ---> New Demodulator: 33 [new_demod,32] addition(antidomain(antidomain(A)),antidomain(A))=one.
% 1.71/1.92 ** KEPT (pick-wt=6): 34 [] domain(A)=antidomain(antidomain(A)).
% 1.71/1.92 ---> New Demodulator: 35 [new_demod,34] domain(A)=antidomain(antidomain(A)).
% 1.71/1.92 ** KEPT (pick-wt=6): 36 [] multiplication(A,coantidomain(A))=zero.
% 1.71/1.92 ---> New Demodulator: 37 [new_demod,36] multiplication(A,coantidomain(A))=zero.
% 1.71/1.92 ** KEPT (pick-wt=18): 38 [] addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=coantidomain(multiplication(coantidomain(coantidomain(A)),B)).
% 1.71/1.92 ---> New Demodulator: 39 [new_demod,38] addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=coantidomain(multiplication(coantidomain(coantidomain(A)),B)).
% 1.71/1.92 ** KEPT (pick-wt=8): 40 [] addition(coantidomain(coantidomain(A)),coantidomain(A))=one.
% 1.71/1.92 ---> New Demodulator: 41 [new_demod,40] addition(coantidomain(coantidomain(A)),coantidomain(A))=one.
% 1.71/1.92 ** KEPT (pick-wt=6): 42 [] codomain(A)=coantidomain(coantidomain(A)).
% 1.71/1.92 ---> New Demodulator: 43 [new_demod,42] codomain(A)=coantidomain(coantidomain(A)).
% 1.71/1.92 ** KEPT (pick-wt=5): 44 [] addition($c2,$c1)=$c1.
% 1.71/1.92 ---> New Demodulator: 45 [new_demod,44] addition($c2,$c1)=$c1.
% 1.71/1.92 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.71/1.92 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] addition(A,B)=addition(B,A).
% 1.71/1.92 >>>> Starting back demodulation with 8.
% 2.03/2.29 >>>> Starting back demodulation with 10.
% 2.03/2.29 >>>> Starting back demodulation with 12.
% 2.03/2.29 >>>> Starting back demodulation with 15.
% 2.03/2.29 >>>> Starting back demodulation with 17.
% 2.03/2.29 >>>> Starting back demodulation with 19.
% 2.03/2.29 >>>> Starting back demodulation with 21.
% 2.03/2.29 >>>> Starting back demodulation with 23.
% 2.03/2.29 >>>> Starting back demodulation with 25.
% 2.03/2.29 >>>> Starting back demodulation with 27.
% 2.03/2.29 >>>> Starting back demodulation with 29.
% 2.03/2.29 >>>> Starting back demodulation with 31.
% 2.03/2.29 >>>> Starting back demodulation with 33.
% 2.03/2.29 >>>> Starting back demodulation with 35.
% 2.03/2.29 >>>> Starting back demodulation with 37.
% 2.03/2.29 >>>> Starting back demodulation with 39.
% 2.03/2.29 >>>> Starting back demodulation with 41.
% 2.03/2.29 >>>> Starting back demodulation with 43.
% 2.03/2.29 >>>> Starting back demodulation with 45.
% 2.03/2.29
% 2.03/2.29 ======= end of input processing =======
% 2.03/2.29
% 2.03/2.29 =========== start of search ===========
% 2.03/2.29
% 2.03/2.29
% 2.03/2.29 Resetting weight limit to 8.
% 2.03/2.29
% 2.03/2.29
% 2.03/2.29 Resetting weight limit to 8.
% 2.03/2.29
% 2.03/2.29 sos_size=563
% 2.03/2.29
% 2.03/2.29 -------- PROOF --------
% 2.03/2.29
% 2.03/2.29 ----> UNIT CONFLICT at 0.37 sec ----> 1287 [binary,1285.1,54.1] $F.
% 2.03/2.29
% 2.03/2.29 Length of proof is 40. Level of proof is 13.
% 2.03/2.29
% 2.03/2.29 ---------------- PROOF ----------------
% 2.03/2.29 % SZS status Theorem
% 2.03/2.29 % SZS output start Refutation
% See solution above
% 2.03/2.29 ------------ end of proof -------------
% 2.03/2.29
% 2.03/2.29
% 2.03/2.29 Search stopped by max_proofs option.
% 2.03/2.29
% 2.03/2.29
% 2.03/2.29 Search stopped by max_proofs option.
% 2.03/2.29
% 2.03/2.29 ============ end of search ============
% 2.03/2.29
% 2.03/2.29 -------------- statistics -------------
% 2.03/2.29 clauses given 530
% 2.03/2.29 clauses generated 73468
% 2.03/2.29 clauses kept 1054
% 2.03/2.29 clauses forward subsumed 16807
% 2.03/2.29 clauses back subsumed 79
% 2.03/2.29 Kbytes malloced 6835
% 2.03/2.29
% 2.03/2.29 ----------- times (seconds) -----------
% 2.03/2.29 user CPU time 0.37 (0 hr, 0 min, 0 sec)
% 2.03/2.29 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.03/2.29 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.03/2.29
% 2.03/2.29 That finishes the proof of the theorem.
% 2.03/2.29
% 2.03/2.29 Process 2445 finished Wed Jul 27 06:27:55 2022
% 2.03/2.29 Otter interrupted
% 2.03/2.29 PROOF FOUND
%------------------------------------------------------------------------------