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
%------------------------------------------------------------------------------