TSTP Solution File: KLE119+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : KLE119+1 : TPTP v8.1.0. Released v4.0.0.
% 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 13:00:46 EDT 2022

% Result   : Theorem 1.76s 1.98s
% Output   : Refutation 1.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   28 (  28 unt;   0 nHn;   9 RR)
%            Number of literals    :   28 (  27 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-2 aty)
%            Number of variables   :   24 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    addition(backward_diamond(zero,domain(dollar_c2)),domain(dollar_c1)) != domain(dollar_c1),
    file('KLE119+1.p',unknown),
    [] ).

cnf(4,axiom,
    A = A,
    file('KLE119+1.p',unknown),
    [] ).

cnf(5,axiom,
    addition(A,B) = addition(B,A),
    file('KLE119+1.p',unknown),
    [] ).

cnf(10,axiom,
    addition(A,zero) = A,
    file('KLE119+1.p',unknown),
    [] ).

cnf(16,axiom,
    multiplication(A,one) = A,
    file('KLE119+1.p',unknown),
    [] ).

cnf(19,axiom,
    multiplication(one,A) = A,
    file('KLE119+1.p',unknown),
    [] ).

cnf(24,axiom,
    multiplication(A,zero) = zero,
    file('KLE119+1.p',unknown),
    [] ).

cnf(28,axiom,
    multiplication(antidomain(A),A) = zero,
    file('KLE119+1.p',unknown),
    [] ).

cnf(32,axiom,
    addition(antidomain(antidomain(A)),antidomain(A)) = one,
    file('KLE119+1.p',unknown),
    [] ).

cnf(35,axiom,
    domain(A) = antidomain(antidomain(A)),
    file('KLE119+1.p',unknown),
    [] ).

cnf(36,axiom,
    multiplication(A,coantidomain(A)) = zero,
    file('KLE119+1.p',unknown),
    [] ).

cnf(40,axiom,
    addition(coantidomain(coantidomain(A)),coantidomain(A)) = one,
    file('KLE119+1.p',unknown),
    [] ).

cnf(43,axiom,
    codomain(A) = coantidomain(coantidomain(A)),
    file('KLE119+1.p',unknown),
    [] ).

cnf(47,axiom,
    domain_difference(A,B) = multiplication(domain(A),antidomain(B)),
    file('KLE119+1.p',unknown),
    [] ).

cnf(48,plain,
    multiplication(antidomain(antidomain(A)),antidomain(B)) = domain_difference(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[47]),35])]),
    [iquote('copy,47,demod,35,flip.1')] ).

cnf(53,axiom,
    backward_diamond(A,B) = codomain(multiplication(codomain(B),A)),
    file('KLE119+1.p',unknown),
    [] ).

cnf(54,plain,
    coantidomain(coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = backward_diamond(B,A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[53]),43,43])]),
    [iquote('copy,53,demod,43,43,flip.1')] ).

cnf(62,plain,
    addition(backward_diamond(zero,antidomain(antidomain(dollar_c2))),antidomain(antidomain(dollar_c1))) != antidomain(antidomain(dollar_c1)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),35,35,35]),
    [iquote('back_demod,3,demod,35,35,35')] ).

cnf(69,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(84,plain,
    antidomain(one) = zero,
    inference(para_into,[status(thm),theory(equality)],[28,16]),
    [iquote('para_into,28.1.1,16.1.1')] ).

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(160,plain,
    antidomain(zero) = one,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,84]),84,10]),
    [iquote('para_into,32.1.1.1.1,83.1.1,demod,84,10')] ).

cnf(189,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(256,plain,
    antidomain(A) = domain_difference(one,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,84]),160,19]),
    [iquote('para_into,48.1.1.1.1,83.1.1,demod,160,19')] ).

cnf(324,plain,
    addition(backward_diamond(zero,domain_difference(one,domain_difference(one,dollar_c2))),domain_difference(one,domain_difference(one,dollar_c1))) != domain_difference(one,domain_difference(one,dollar_c1)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[62]),256,256,256,256,256,256]),
    [iquote('back_demod,62,demod,256,256,256,256,256,256')] ).

cnf(357,plain,
    backward_diamond(zero,A) = zero,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[54,24]),189,88])]),
    [iquote('para_into,54.1.1.1.1,24.1.1,demod,189,88,flip.1')] ).

cnf(419,plain,
    domain_difference(one,domain_difference(one,dollar_c1)) != domain_difference(one,domain_difference(one,dollar_c1)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[324]),357,69]),
    [iquote('back_demod,324,demod,357,69')] ).

cnf(420,plain,
    $false,
    inference(binary,[status(thm)],[419,4]),
    [iquote('binary,419.1,4.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KLE119+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n029.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 06:40:44 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.76/1.97  ----- Otter 3.3f, August 2004 -----
% 1.76/1.97  The process was started by sandbox on n029.cluster.edu,
% 1.76/1.97  Wed Jul 27 06:40:44 2022
% 1.76/1.97  The command was "./otter".  The process ID is 30691.
% 1.76/1.97  
% 1.76/1.97  set(prolog_style_variables).
% 1.76/1.97  set(auto).
% 1.76/1.97     dependent: set(auto1).
% 1.76/1.97     dependent: set(process_input).
% 1.76/1.97     dependent: clear(print_kept).
% 1.76/1.97     dependent: clear(print_new_demod).
% 1.76/1.97     dependent: clear(print_back_demod).
% 1.76/1.97     dependent: clear(print_back_sub).
% 1.76/1.97     dependent: set(control_memory).
% 1.76/1.97     dependent: assign(max_mem, 12000).
% 1.76/1.97     dependent: assign(pick_given_ratio, 4).
% 1.76/1.97     dependent: assign(stats_level, 1).
% 1.76/1.97     dependent: assign(max_seconds, 10800).
% 1.76/1.97  clear(print_given).
% 1.76/1.97  
% 1.76/1.97  formula_list(usable).
% 1.76/1.97  all A (A=A).
% 1.76/1.97  all A B (addition(A,B)=addition(B,A)).
% 1.76/1.97  all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.76/1.97  all A (addition(A,zero)=A).
% 1.76/1.97  all A (addition(A,A)=A).
% 1.76/1.97  all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.76/1.97  all A (multiplication(A,one)=A).
% 1.76/1.97  all A (multiplication(one,A)=A).
% 1.76/1.97  all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.76/1.97  all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.76/1.97  all A (multiplication(A,zero)=zero).
% 1.76/1.97  all A (multiplication(zero,A)=zero).
% 1.76/1.97  all A B (le_q(A,B)<->addition(A,B)=B).
% 1.76/1.97  all X0 (multiplication(antidomain(X0),X0)=zero).
% 1.76/1.97  all X0 X1 (addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))=antidomain(multiplication(X0,antidomain(antidomain(X1))))).
% 1.76/1.97  all X0 (addition(antidomain(antidomain(X0)),antidomain(X0))=one).
% 1.76/1.97  all X0 (domain(X0)=antidomain(antidomain(X0))).
% 1.76/1.97  all X0 (multiplication(X0,coantidomain(X0))=zero).
% 1.76/1.97  all X0 X1 (addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))=coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))).
% 1.76/1.97  all X0 (addition(coantidomain(coantidomain(X0)),coantidomain(X0))=one).
% 1.76/1.97  all X0 (codomain(X0)=coantidomain(coantidomain(X0))).
% 1.76/1.97  all X0 (c(X0)=antidomain(domain(X0))).
% 1.76/1.97  all X0 X1 (domain_difference(X0,X1)=multiplication(domain(X0),antidomain(X1))).
% 1.76/1.97  all X0 X1 (forward_diamond(X0,X1)=domain(multiplication(X0,domain(X1)))).
% 1.76/1.97  all X0 X1 (backward_diamond(X0,X1)=codomain(multiplication(codomain(X1),X0))).
% 1.76/1.97  all X0 X1 (forward_box(X0,X1)=c(forward_diamond(X0,c(X1)))).
% 1.76/1.97  all X0 X1 (backward_box(X0,X1)=c(backward_diamond(X0,c(X1)))).
% 1.76/1.97  -(all X0 X1 (addition(backward_diamond(zero,domain(X0)),domain(X1))=domain(X1))).
% 1.76/1.97  end_of_list.
% 1.76/1.97  
% 1.76/1.97  -------> usable clausifies to:
% 1.76/1.97  
% 1.76/1.97  list(usable).
% 1.76/1.97  0 [] A=A.
% 1.76/1.97  0 [] addition(A,B)=addition(B,A).
% 1.76/1.97  0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.76/1.97  0 [] addition(A,zero)=A.
% 1.76/1.97  0 [] addition(A,A)=A.
% 1.76/1.97  0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.76/1.97  0 [] multiplication(A,one)=A.
% 1.76/1.97  0 [] multiplication(one,A)=A.
% 1.76/1.97  0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.76/1.97  0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.76/1.97  0 [] multiplication(A,zero)=zero.
% 1.76/1.97  0 [] multiplication(zero,A)=zero.
% 1.76/1.97  0 [] -le_q(A,B)|addition(A,B)=B.
% 1.76/1.97  0 [] le_q(A,B)|addition(A,B)!=B.
% 1.76/1.97  0 [] multiplication(antidomain(X0),X0)=zero.
% 1.76/1.97  0 [] addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))=antidomain(multiplication(X0,antidomain(antidomain(X1)))).
% 1.76/1.97  0 [] addition(antidomain(antidomain(X0)),antidomain(X0))=one.
% 1.76/1.97  0 [] domain(X0)=antidomain(antidomain(X0)).
% 1.76/1.97  0 [] multiplication(X0,coantidomain(X0))=zero.
% 1.76/1.97  0 [] addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))=coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)).
% 1.76/1.97  0 [] addition(coantidomain(coantidomain(X0)),coantidomain(X0))=one.
% 1.76/1.97  0 [] codomain(X0)=coantidomain(coantidomain(X0)).
% 1.76/1.97  0 [] c(X0)=antidomain(domain(X0)).
% 1.76/1.97  0 [] domain_difference(X0,X1)=multiplication(domain(X0),antidomain(X1)).
% 1.76/1.97  0 [] forward_diamond(X0,X1)=domain(multiplication(X0,domain(X1))).
% 1.76/1.97  0 [] backward_diamond(X0,X1)=codomain(multiplication(codomain(X1),X0)).
% 1.76/1.97  0 [] forward_box(X0,X1)=c(forward_diamond(X0,c(X1))).
% 1.76/1.97  0 [] backward_box(X0,X1)=c(backward_diamond(X0,c(X1))).
% 1.76/1.97  0 [] addition(backward_diamond(zero,domain($c2)),domain($c1))!=domain($c1).
% 1.76/1.97  end_of_list.
% 1.76/1.97  
% 1.76/1.97  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.76/1.97  
% 1.76/1.97  This is a Horn set with equality.  The strategy will be
% 1.76/1.97  Knuth-Bendix and hyper_res, with positive clauses in
% 1.76/1.97  sos and nonpositive clauses in usable.
% 1.76/1.97  
% 1.76/1.97     dependent: set(knuth_bendix).
% 1.76/1.97     dependent: set(anl_eq).
% 1.76/1.97     dependent: set(para_from).
% 1.76/1.97     dependent: set(para_into).
% 1.76/1.97     dependent: clear(para_from_right).
% 1.76/1.97     dependent: clear(para_into_right).
% 1.76/1.97     dependent: set(para_from_vars).
% 1.76/1.97     dependent: set(eq_units_both_ways).
% 1.76/1.97     dependent: set(dynamic_demod_all).
% 1.76/1.97     dependent: set(dynamic_demod).
% 1.76/1.97     dependent: set(order_eq).
% 1.76/1.97     dependent: set(back_demod).
% 1.76/1.97     dependent: set(lrpo).
% 1.76/1.97     dependent: set(hyper_res).
% 1.76/1.97     dependent: clear(order_hyper).
% 1.76/1.97  
% 1.76/1.97  ------------> process usable:
% 1.76/1.97  ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.76/1.97  ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.76/1.97  ** KEPT (pick-wt=10): 3 [] addition(backward_diamond(zero,domain($c2)),domain($c1))!=domain($c1).
% 1.76/1.97  
% 1.76/1.97  ------------> process sos:
% 1.76/1.97  ** KEPT (pick-wt=3): 4 [] A=A.
% 1.76/1.97  ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 1.76/1.97  ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.76/1.97  ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.76/1.97  ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 1.76/1.97  ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 1.76/1.97  ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 1.76/1.97  ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 1.76/1.97  ** KEPT (pick-wt=11): 14 [copy,13,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.76/1.97  ---> New Demodulator: 15 [new_demod,14] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.76/1.97  ** KEPT (pick-wt=5): 16 [] multiplication(A,one)=A.
% 1.76/1.97  ---> New Demodulator: 17 [new_demod,16] multiplication(A,one)=A.
% 1.76/1.97  ** KEPT (pick-wt=5): 18 [] multiplication(one,A)=A.
% 1.76/1.97  ---> New Demodulator: 19 [new_demod,18] multiplication(one,A)=A.
% 1.76/1.97  ** KEPT (pick-wt=13): 20 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.76/1.97  ---> New Demodulator: 21 [new_demod,20] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.76/1.97  ** KEPT (pick-wt=13): 22 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.76/1.97  ---> New Demodulator: 23 [new_demod,22] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.76/1.97  ** KEPT (pick-wt=5): 24 [] multiplication(A,zero)=zero.
% 1.76/1.97  ---> New Demodulator: 25 [new_demod,24] multiplication(A,zero)=zero.
% 1.76/1.97  ** KEPT (pick-wt=5): 26 [] multiplication(zero,A)=zero.
% 1.76/1.97  ---> New Demodulator: 27 [new_demod,26] multiplication(zero,A)=zero.
% 1.76/1.97  ** KEPT (pick-wt=6): 28 [] multiplication(antidomain(A),A)=zero.
% 1.76/1.97  ---> New Demodulator: 29 [new_demod,28] multiplication(antidomain(A),A)=zero.
% 1.76/1.97  ** KEPT (pick-wt=18): 30 [] addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B)))))=antidomain(multiplication(A,antidomain(antidomain(B)))).
% 1.76/1.97  ---> New Demodulator: 31 [new_demod,30] addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B)))))=antidomain(multiplication(A,antidomain(antidomain(B)))).
% 1.76/1.97  ** KEPT (pick-wt=8): 32 [] addition(antidomain(antidomain(A)),antidomain(A))=one.
% 1.76/1.97  ---> New Demodulator: 33 [new_demod,32] addition(antidomain(antidomain(A)),antidomain(A))=one.
% 1.76/1.97  ** KEPT (pick-wt=6): 34 [] domain(A)=antidomain(antidomain(A)).
% 1.76/1.97  ---> New Demodulator: 35 [new_demod,34] domain(A)=antidomain(antidomain(A)).
% 1.76/1.97  ** KEPT (pick-wt=6): 36 [] multiplication(A,coantidomain(A))=zero.
% 1.76/1.97  ---> New Demodulator: 37 [new_demod,36] multiplication(A,coantidomain(A))=zero.
% 1.76/1.97  ** KEPT (pick-wt=18): 38 [] addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=coantidomain(multiplication(coantidomain(coantidomain(A)),B)).
% 1.76/1.97  ---> New Demodulator: 39 [new_demod,38] addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=coantidomain(multiplication(coantidomain(coantidomain(A)),B)).
% 1.76/1.98  ** KEPT (pick-wt=8): 40 [] addition(coantidomain(coantidomain(A)),coantidomain(A))=one.
% 1.76/1.98  ---> New Demodulator: 41 [new_demod,40] addition(coantidomain(coantidomain(A)),coantidomain(A))=one.
% 1.76/1.98  ** KEPT (pick-wt=6): 42 [] codomain(A)=coantidomain(coantidomain(A)).
% 1.76/1.98  ---> New Demodulator: 43 [new_demod,42] codomain(A)=coantidomain(coantidomain(A)).
% 1.76/1.98  ** KEPT (pick-wt=7): 45 [copy,44,demod,35] c(A)=antidomain(antidomain(antidomain(A))).
% 1.76/1.98  ---> New Demodulator: 46 [new_demod,45] c(A)=antidomain(antidomain(antidomain(A))).
% 1.76/1.98  ** KEPT (pick-wt=10): 48 [copy,47,demod,35,flip.1] multiplication(antidomain(antidomain(A)),antidomain(B))=domain_difference(A,B).
% 1.76/1.98  ---> New Demodulator: 49 [new_demod,48] multiplication(antidomain(antidomain(A)),antidomain(B))=domain_difference(A,B).
% 1.76/1.98  ** KEPT (pick-wt=11): 51 [copy,50,demod,35,35,flip.1] antidomain(antidomain(multiplication(A,antidomain(antidomain(B)))))=forward_diamond(A,B).
% 1.76/1.98  ---> New Demodulator: 52 [new_demod,51] antidomain(antidomain(multiplication(A,antidomain(antidomain(B)))))=forward_diamond(A,B).
% 1.76/1.98  ** KEPT (pick-wt=11): 54 [copy,53,demod,43,43,flip.1] coantidomain(coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=backward_diamond(B,A).
% 1.76/1.98  ---> New Demodulator: 55 [new_demod,54] coantidomain(coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=backward_diamond(B,A).
% 1.76/1.98  ** KEPT (pick-wt=13): 57 [copy,56,demod,46,46,flip.1] antidomain(antidomain(antidomain(forward_diamond(A,antidomain(antidomain(antidomain(B)))))))=forward_box(A,B).
% 1.76/1.98  ---> New Demodulator: 58 [new_demod,57] antidomain(antidomain(antidomain(forward_diamond(A,antidomain(antidomain(antidomain(B)))))))=forward_box(A,B).
% 1.76/1.98  ** KEPT (pick-wt=13): 60 [copy,59,demod,46,46,flip.1] antidomain(antidomain(antidomain(backward_diamond(A,antidomain(antidomain(antidomain(B)))))))=backward_box(A,B).
% 1.76/1.98  ---> New Demodulator: 61 [new_demod,60] antidomain(antidomain(antidomain(backward_diamond(A,antidomain(antidomain(antidomain(B)))))))=backward_box(A,B).
% 1.76/1.98    Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.76/1.98    Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] addition(A,B)=addition(B,A).
% 1.76/1.98  >>>> Starting back demodulation with 8.
% 1.76/1.98  >>>> Starting back demodulation with 10.
% 1.76/1.98  >>>> Starting back demodulation with 12.
% 1.76/1.98  >>>> Starting back demodulation with 15.
% 1.76/1.98  >>>> Starting back demodulation with 17.
% 1.76/1.98  >>>> Starting back demodulation with 19.
% 1.76/1.98  >>>> Starting back demodulation with 21.
% 1.76/1.98  >>>> Starting back demodulation with 23.
% 1.76/1.98  >>>> Starting back demodulation with 25.
% 1.76/1.98  >>>> Starting back demodulation with 27.
% 1.76/1.98  >>>> Starting back demodulation with 29.
% 1.76/1.98  >>>> Starting back demodulation with 31.
% 1.76/1.98  >>>> Starting back demodulation with 33.
% 1.76/1.98  >>>> Starting back demodulation with 35.
% 1.76/1.98      >> back demodulating 3 with 35.
% 1.76/1.98  >>>> Starting back demodulation with 37.
% 1.76/1.98  >>>> Starting back demodulation with 39.
% 1.76/1.98  >>>> Starting back demodulation with 41.
% 1.76/1.98  >>>> Starting back demodulation with 43.
% 1.76/1.98  >>>> Starting back demodulation with 46.
% 1.76/1.98  >>>> Starting back demodulation with 49.
% 1.76/1.98  >>>> Starting back demodulation with 52.
% 1.76/1.98  >>>> Starting back demodulation with 55.
% 1.76/1.98  >>>> Starting back demodulation with 58.
% 1.76/1.98  >>>> Starting back demodulation with 61.
% 1.76/1.98  
% 1.76/1.98  ======= end of input processing =======
% 1.76/1.98  
% 1.76/1.98  =========== start of search ===========
% 1.76/1.98  
% 1.76/1.98  -------- PROOF -------- 
% 1.76/1.98  
% 1.76/1.98  ----> UNIT CONFLICT at   0.01 sec ----> 420 [binary,419.1,4.1] $F.
% 1.76/1.98  
% 1.76/1.98  Length of proof is 12.  Level of proof is 5.
% 1.76/1.98  
% 1.76/1.98  ---------------- PROOF ----------------
% 1.76/1.98  % SZS status Theorem
% 1.76/1.98  % SZS output start Refutation
% See solution above
% 1.76/1.98  ------------ end of proof -------------
% 1.76/1.98  
% 1.76/1.98  
% 1.76/1.98  Search stopped by max_proofs option.
% 1.76/1.98  
% 1.76/1.98  
% 1.76/1.98  Search stopped by max_proofs option.
% 1.76/1.98  
% 1.76/1.98  ============ end of search ============
% 1.76/1.98  
% 1.76/1.98  -------------- statistics -------------
% 1.76/1.98  clauses given                 46
% 1.76/1.98  clauses generated            582
% 1.76/1.98  clauses kept                 283
% 1.76/1.98  clauses forward subsumed     433
% 1.76/1.98  clauses back subsumed          8
% 1.76/1.98  Kbytes malloced             3906
% 1.76/1.98  
% 1.76/1.98  ----------- times (seconds) -----------
% 1.76/1.98  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.76/1.98  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.76/1.98  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.76/1.98  
% 1.76/1.98  That finishes the proof of the theorem.
% 1.76/1.98  
% 1.76/1.98  Process 30691 finished Wed Jul 27 06:40:46 2022
% 1.76/1.98  Otter interrupted
% 1.76/1.98  PROOF FOUND
%------------------------------------------------------------------------------