TSTP Solution File: KLE008+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE008+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:00:27 EDT 2022
% Result : Theorem 84.93s 85.13s
% Output : Refutation 84.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of clauses : 60 ( 38 unt; 4 nHn; 34 RR)
% Number of literals : 89 ( 43 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 74 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE008+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE008+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ test(A)
| complement(dollar_f1(A),A) ),
file('KLE008+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ complement(A,B)
| multiplication(B,A) = zero ),
file('KLE008+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ complement(A,B)
| multiplication(A,B) = zero ),
file('KLE008+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ complement(A,B)
| addition(B,A) = one ),
file('KLE008+1.p',unknown),
[] ).
cnf(8,axiom,
( complement(A,B)
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| addition(B,A) != one ),
file('KLE008+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ test(A)
| c(A) != B
| complement(A,B) ),
file('KLE008+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ test(A)
| c(A) = B
| ~ complement(A,B) ),
file('KLE008+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ le_q(dollar_c3,multiplication(dollar_c1,dollar_c2))
| ~ le_q(dollar_c3,dollar_c2)
| ~ le_q(multiplication(c(dollar_c1),dollar_c3),zero) ),
file('KLE008+1.p',unknown),
[] ).
cnf(13,axiom,
A = A,
file('KLE008+1.p',unknown),
[] ).
cnf(14,axiom,
addition(A,B) = addition(B,A),
file('KLE008+1.p',unknown),
[] ).
cnf(15,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE008+1.p',unknown),
[] ).
cnf(16,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(19,axiom,
addition(A,zero) = A,
file('KLE008+1.p',unknown),
[] ).
cnf(20,axiom,
addition(A,A) = A,
file('KLE008+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE008+1.p',unknown),
[] ).
cnf(23,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22])]),
[iquote('copy,22,flip.1')] ).
cnf(28,axiom,
multiplication(one,A) = A,
file('KLE008+1.p',unknown),
[] ).
cnf(29,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE008+1.p',unknown),
[] ).
cnf(31,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE008+1.p',unknown),
[] ).
cnf(36,axiom,
multiplication(zero,A) = zero,
file('KLE008+1.p',unknown),
[] ).
cnf(38,axiom,
test(dollar_c1),
file('KLE008+1.p',unknown),
[] ).
cnf(39,axiom,
( le_q(dollar_c3,multiplication(dollar_c1,dollar_c2))
| le_q(dollar_c3,dollar_c2) ),
file('KLE008+1.p',unknown),
[] ).
cnf(40,axiom,
( le_q(dollar_c3,multiplication(dollar_c1,dollar_c2))
| le_q(multiplication(c(dollar_c1),dollar_c3),zero) ),
file('KLE008+1.p',unknown),
[] ).
cnf(42,plain,
complement(dollar_c1,c(dollar_c1)),
inference(hyper,[status(thm)],[38,9,13]),
[iquote('hyper,38,9,13')] ).
cnf(43,plain,
complement(dollar_f1(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[38,3]),
[iquote('hyper,38,3')] ).
cnf(44,plain,
addition(c(dollar_c1),dollar_c1) = one,
inference(hyper,[status(thm)],[42,7]),
[iquote('hyper,42,7')] ).
cnf(54,plain,
addition(dollar_c1,dollar_f1(dollar_c1)) = one,
inference(hyper,[status(thm)],[43,7]),
[iquote('hyper,43,7')] ).
cnf(55,plain,
multiplication(dollar_f1(dollar_c1),dollar_c1) = zero,
inference(hyper,[status(thm)],[43,6]),
[iquote('hyper,43,6')] ).
cnf(58,plain,
multiplication(dollar_c1,dollar_f1(dollar_c1)) = zero,
inference(hyper,[status(thm)],[43,5]),
[iquote('hyper,43,5')] ).
cnf(65,plain,
addition(zero,A) = A,
inference(para_into,[status(thm),theory(equality)],[19,14]),
[iquote('para_into,18.1.1,14.1.1')] ).
cnf(72,plain,
le_q(A,A),
inference(hyper,[status(thm)],[20,2]),
[iquote('hyper,20,2')] ).
cnf(75,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,20])]),
[iquote('para_into,16.1.1.1,20.1.1,flip.1')] ).
cnf(79,plain,
( addition(A,addition(B,C)) = addition(B,C)
| ~ le_q(A,B) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,1])]),
[iquote('para_into,16.1.1.1,1.2.1,flip.1')] ).
cnf(99,plain,
( multiplication(A,multiplication(B,C)) = zero
| ~ complement(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,5]),36])]),
[iquote('para_into,23.1.1.1,5.2.1,demod,36,flip.1')] ).
cnf(120,plain,
( addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,C)
| ~ le_q(B,C) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,1])]),
[iquote('para_into,29.1.1.2,1.2.1,flip.1')] ).
cnf(146,plain,
addition(multiplication(c(dollar_c1),A),multiplication(dollar_c1,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[44,31]),28])]),
[iquote('para_from,44.1.1,31.1.1.1,demod,28,flip.1')] ).
cnf(177,plain,
addition(dollar_f1(dollar_c1),dollar_c1) = one,
inference(para_into,[status(thm),theory(equality)],[54,14]),
[iquote('para_into,53.1.1,14.1.1')] ).
cnf(187,plain,
( le_q(dollar_c3,multiplication(dollar_c1,dollar_c2))
| multiplication(c(dollar_c1),dollar_c3) = zero ),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[40,1]),19]),
[iquote('hyper,40,1,demod,19')] ).
cnf(192,plain,
multiplication(dollar_f1(dollar_c1),multiplication(dollar_c1,A)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[55,23]),36])]),
[iquote('para_from,55.1.1,23.1.1.1,demod,36,flip.1')] ).
cnf(193,plain,
complement(dollar_c1,dollar_f1(dollar_c1)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[55,8]),58,177]),13,13,13]),
[iquote('para_from,55.1.1,8.2.1,demod,58,177,unit_del,13,13,13')] ).
cnf(195,plain,
c(dollar_c1) = dollar_f1(dollar_c1),
inference(hyper,[status(thm)],[193,10,38]),
[iquote('hyper,193,10,38')] ).
cnf(199,plain,
( le_q(dollar_c3,multiplication(dollar_c1,dollar_c2))
| multiplication(dollar_f1(dollar_c1),dollar_c3) = zero ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[187]),195]),
[iquote('back_demod,187,demod,195')] ).
cnf(220,plain,
addition(multiplication(dollar_f1(dollar_c1),A),multiplication(dollar_c1,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[146]),195]),
[iquote('back_demod,146,demod,195')] ).
cnf(227,plain,
( ~ le_q(dollar_c3,multiplication(dollar_c1,dollar_c2))
| ~ le_q(dollar_c3,dollar_c2)
| ~ le_q(multiplication(dollar_f1(dollar_c1),dollar_c3),zero) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),195]),
[iquote('back_demod,11,demod,195')] ).
cnf(577,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[75,2]),
[iquote('hyper,75,2')] ).
cnf(584,plain,
addition(dollar_c1,one) = one,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[75,54]),54]),
[iquote('para_into,75.1.1.2,53.1.1,demod,54')] ).
cnf(627,plain,
addition(multiplication(dollar_c1,A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[584,31]),28,28])]),
[iquote('para_from,584.1.1,31.1.1.1,demod,28,28,flip.1')] ).
cnf(847,plain,
( le_q(A,addition(B,C))
| ~ le_q(A,B) ),
inference(para_from,[status(thm),theory(equality)],[79,577]),
[iquote('para_from,79.1.1,577.1.2')] ).
cnf(2963,plain,
( multiplication(A,B) = multiplication(A,multiplication(C,D))
| ~ le_q(B,multiplication(C,D))
| ~ complement(C,A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[120,99]),19]),
[iquote('para_into,120.1.1.2,99.1.1,demod,19')] ).
cnf(3001,plain,
( le_q(multiplication(A,B),multiplication(A,C))
| ~ le_q(B,C) ),
inference(para_from,[status(thm),theory(equality)],[120,577]),
[iquote('para_from,120.1.1,577.1.2')] ).
cnf(3929,plain,
( le_q(A,B)
| ~ le_q(A,multiplication(dollar_c1,B)) ),
inference(para_into,[status(thm),theory(equality)],[847,627]),
[iquote('para_into,847.1.2,627.1.1')] ).
cnf(4002,plain,
le_q(dollar_c3,dollar_c2),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3929,39])]),
[iquote('hyper,3929,39,factor_simp')] ).
cnf(5707,plain,
le_q(multiplication(A,dollar_c3),multiplication(A,dollar_c2)),
inference(hyper,[status(thm)],[3001,4002]),
[iquote('hyper,3001,4002')] ).
cnf(6410,plain,
multiplication(dollar_f1(dollar_c1),dollar_c3) = zero,
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2963,199,193]),192])]),
[iquote('hyper,2963,199,193,demod,192,factor_simp')] ).
cnf(6411,plain,
~ le_q(dollar_c3,multiplication(dollar_c1,dollar_c2)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[227]),6410]),4002,72]),
[iquote('back_demod,227,demod,6410,unit_del,4002,72')] ).
cnf(6425,plain,
multiplication(dollar_c1,dollar_c3) = dollar_c3,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[6410,220]),65]),
[iquote('para_from,6409.1.1,220.1.1.1,demod,65')] ).
cnf(6455,plain,
le_q(dollar_c3,multiplication(dollar_c1,dollar_c2)),
inference(para_from,[status(thm),theory(equality)],[6425,5707]),
[iquote('para_from,6425.1.1,5707.1.1')] ).
cnf(6456,plain,
$false,
inference(binary,[status(thm)],[6455,6411]),
[iquote('binary,6455.1,6411.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE008+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.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 06:27:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.15 ----- Otter 3.3f, August 2004 -----
% 1.96/2.15 The process was started by sandbox on n013.cluster.edu,
% 1.96/2.15 Wed Jul 27 06:27:45 2022
% 1.96/2.15 The command was "./otter". The process ID is 30631.
% 1.96/2.15
% 1.96/2.15 set(prolog_style_variables).
% 1.96/2.15 set(auto).
% 1.96/2.15 dependent: set(auto1).
% 1.96/2.15 dependent: set(process_input).
% 1.96/2.15 dependent: clear(print_kept).
% 1.96/2.15 dependent: clear(print_new_demod).
% 1.96/2.15 dependent: clear(print_back_demod).
% 1.96/2.15 dependent: clear(print_back_sub).
% 1.96/2.15 dependent: set(control_memory).
% 1.96/2.15 dependent: assign(max_mem, 12000).
% 1.96/2.15 dependent: assign(pick_given_ratio, 4).
% 1.96/2.15 dependent: assign(stats_level, 1).
% 1.96/2.15 dependent: assign(max_seconds, 10800).
% 1.96/2.15 clear(print_given).
% 1.96/2.15
% 1.96/2.15 formula_list(usable).
% 1.96/2.15 all A (A=A).
% 1.96/2.15 all A B (addition(A,B)=addition(B,A)).
% 1.96/2.15 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.96/2.15 all A (addition(A,zero)=A).
% 1.96/2.15 all A (addition(A,A)=A).
% 1.96/2.15 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.96/2.15 all A (multiplication(A,one)=A).
% 1.96/2.15 all A (multiplication(one,A)=A).
% 1.96/2.15 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.96/2.15 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.96/2.15 all A (multiplication(A,zero)=zero).
% 1.96/2.15 all A (multiplication(zero,A)=zero).
% 1.96/2.15 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.96/2.15 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.96/2.15 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.96/2.15 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.96/2.15 all X0 (-test(X0)->c(X0)=zero).
% 1.96/2.15 -(all X0 X1 X2 (test(X2)-> (le_q(X0,multiplication(X2,X1))<->le_q(X0,X1)&le_q(multiplication(c(X2),X0),zero)))).
% 1.96/2.15 end_of_list.
% 1.96/2.15
% 1.96/2.15 -------> usable clausifies to:
% 1.96/2.15
% 1.96/2.15 list(usable).
% 1.96/2.15 0 [] A=A.
% 1.96/2.15 0 [] addition(A,B)=addition(B,A).
% 1.96/2.15 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.96/2.15 0 [] addition(A,zero)=A.
% 1.96/2.15 0 [] addition(A,A)=A.
% 1.96/2.15 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.96/2.15 0 [] multiplication(A,one)=A.
% 1.96/2.15 0 [] multiplication(one,A)=A.
% 1.96/2.15 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.96/2.15 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.96/2.15 0 [] multiplication(A,zero)=zero.
% 1.96/2.15 0 [] multiplication(zero,A)=zero.
% 1.96/2.15 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.96/2.15 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.96/2.15 0 [] -test(X0)|complement($f1(X0),X0).
% 1.96/2.15 0 [] test(X0)| -complement(X1,X0).
% 1.96/2.15 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.96/2.15 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.96/2.15 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.96/2.15 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.96/2.15 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.96/2.15 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.96/2.15 0 [] test(X0)|c(X0)=zero.
% 1.96/2.15 0 [] test($c1).
% 1.96/2.15 0 [] le_q($c3,multiplication($c1,$c2))|le_q($c3,$c2).
% 1.96/2.15 0 [] le_q($c3,multiplication($c1,$c2))|le_q(multiplication(c($c1),$c3),zero).
% 1.96/2.15 0 [] -le_q($c3,multiplication($c1,$c2))| -le_q($c3,$c2)| -le_q(multiplication(c($c1),$c3),zero).
% 1.96/2.15 end_of_list.
% 1.96/2.15
% 1.96/2.15 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.96/2.15
% 1.96/2.15 This ia a non-Horn set with equality. The strategy will be
% 1.96/2.15 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.96/2.15 deletion, with positive clauses in sos and nonpositive
% 1.96/2.15 clauses in usable.
% 1.96/2.15
% 1.96/2.15 dependent: set(knuth_bendix).
% 1.96/2.15 dependent: set(anl_eq).
% 1.96/2.15 dependent: set(para_from).
% 1.96/2.15 dependent: set(para_into).
% 1.96/2.15 dependent: clear(para_from_right).
% 1.96/2.15 dependent: clear(para_into_right).
% 1.96/2.15 dependent: set(para_from_vars).
% 1.96/2.15 dependent: set(eq_units_both_ways).
% 1.96/2.15 dependent: set(dynamic_demod_all).
% 1.96/2.15 dependent: set(dynamic_demod).
% 1.96/2.15 dependent: set(order_eq).
% 1.96/2.15 dependent: set(back_demod).
% 1.96/2.15 dependent: set(lrpo).
% 1.96/2.15 dependent: set(hyper_res).
% 1.96/2.15 dependent: set(unit_deletion).
% 1.96/2.15 dependent: set(factor).
% 1.96/2.15
% 1.96/2.15 ------------> process usable:
% 1.96/2.15 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.96/2.15 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.96/2.15 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 1.96/2.15 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 1.96/2.15 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 1.96/2.15 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 84.93/85.13 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 84.93/85.13 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 84.93/85.13 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 84.93/85.13 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 84.93/85.13 ** KEPT (pick-wt=14): 11 [] -le_q($c3,multiplication($c1,$c2))| -le_q($c3,$c2)| -le_q(multiplication(c($c1),$c3),zero).
% 84.93/85.13
% 84.93/85.13 ------------> process sos:
% 84.93/85.13 ** KEPT (pick-wt=3): 13 [] A=A.
% 84.93/85.13 ** KEPT (pick-wt=7): 14 [] addition(A,B)=addition(B,A).
% 84.93/85.13 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 84.93/85.13 ---> New Demodulator: 17 [new_demod,16] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 84.93/85.13 ** KEPT (pick-wt=5): 18 [] addition(A,zero)=A.
% 84.93/85.13 ---> New Demodulator: 19 [new_demod,18] addition(A,zero)=A.
% 84.93/85.13 ** KEPT (pick-wt=5): 20 [] addition(A,A)=A.
% 84.93/85.13 ---> New Demodulator: 21 [new_demod,20] addition(A,A)=A.
% 84.93/85.13 ** KEPT (pick-wt=11): 23 [copy,22,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 84.93/85.13 ---> New Demodulator: 24 [new_demod,23] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 84.93/85.13 ** KEPT (pick-wt=5): 25 [] multiplication(A,one)=A.
% 84.93/85.13 ---> New Demodulator: 26 [new_demod,25] multiplication(A,one)=A.
% 84.93/85.13 ** KEPT (pick-wt=5): 27 [] multiplication(one,A)=A.
% 84.93/85.13 ---> New Demodulator: 28 [new_demod,27] multiplication(one,A)=A.
% 84.93/85.13 ** KEPT (pick-wt=13): 29 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 84.93/85.13 ---> New Demodulator: 30 [new_demod,29] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 84.93/85.13 ** KEPT (pick-wt=13): 31 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 84.93/85.13 ---> New Demodulator: 32 [new_demod,31] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 84.93/85.13 ** KEPT (pick-wt=5): 33 [] multiplication(A,zero)=zero.
% 84.93/85.13 ---> New Demodulator: 34 [new_demod,33] multiplication(A,zero)=zero.
% 84.93/85.13 ** KEPT (pick-wt=5): 35 [] multiplication(zero,A)=zero.
% 84.93/85.13 ---> New Demodulator: 36 [new_demod,35] multiplication(zero,A)=zero.
% 84.93/85.13 ** KEPT (pick-wt=6): 37 [] test(A)|c(A)=zero.
% 84.93/85.13 ** KEPT (pick-wt=2): 38 [] test($c1).
% 84.93/85.13 ** KEPT (pick-wt=8): 39 [] le_q($c3,multiplication($c1,$c2))|le_q($c3,$c2).
% 84.93/85.13 ** KEPT (pick-wt=11): 40 [] le_q($c3,multiplication($c1,$c2))|le_q(multiplication(c($c1),$c3),zero).
% 84.93/85.13 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 84.93/85.13 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] addition(A,B)=addition(B,A).
% 84.93/85.13 >>>> Starting back demodulation with 17.
% 84.93/85.13 >>>> Starting back demodulation with 19.
% 84.93/85.13 >>>> Starting back demodulation with 21.
% 84.93/85.13 >> back demodulating 12 with 21.
% 84.93/85.13 >>>> Starting back demodulation with 24.
% 84.93/85.13 >>>> Starting back demodulation with 26.
% 84.93/85.13 >>>> Starting back demodulation with 28.
% 84.93/85.13 >>>> Starting back demodulation with 30.
% 84.93/85.13 >>>> Starting back demodulation with 32.
% 84.93/85.13 >>>> Starting back demodulation with 34.
% 84.93/85.13 >>>> Starting back demodulation with 36.
% 84.93/85.13
% 84.93/85.13 ======= end of input processing =======
% 84.93/85.13
% 84.93/85.13 =========== start of search ===========
% 84.93/85.13
% 84.93/85.13
% 84.93/85.13 Resetting weight limit to 8.
% 84.93/85.13
% 84.93/85.13
% 84.93/85.13 Resetting weight limit to 8.
% 84.93/85.13
% 84.93/85.13 sos_size=2869
% 84.93/85.13
% 84.93/85.13 -- HEY sandbox, WE HAVE A PROOF!! --
% 84.93/85.13
% 84.93/85.13 ----> UNIT CONFLICT at 82.97 sec ----> 6456 [binary,6455.1,6411.1] $F.
% 84.93/85.13
% 84.93/85.13 Length of proof is 36. Level of proof is 9.
% 84.93/85.13
% 84.93/85.13 ---------------- PROOF ----------------
% 84.93/85.13 % SZS status Theorem
% 84.93/85.13 % SZS output start Refutation
% See solution above
% 84.93/85.13 ------------ end of proof -------------
% 84.93/85.13
% 84.93/85.13
% 84.93/85.13 Search stopped by max_proofs option.
% 84.93/85.13
% 84.93/85.13
% 84.93/85.13 Search stopped by max_proofs option.
% 84.93/85.13
% 84.93/85.13 ============ end of search ============
% 84.93/85.13
% 84.93/85.13 -------------- statistics -------------
% 84.93/85.13 clauses given 3863
% 84.93/85.13 clauses generated 2600857
% 84.93/85.13 clauses kept 6351
% 84.93/85.13 clauses forward subsumed 137112
% 84.93/85.13 clauses back subsumed 2944
% 84.93/85.13 Kbytes malloced 6835
% 84.93/85.13
% 84.93/85.13 ----------- times (seconds) -----------
% 84.93/85.13 user CPU time 82.97 (0 hr, 1 min, 22 sec)
% 84.93/85.13 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 84.93/85.13 wall-clock time 84 (0 hr, 1 min, 24 sec)
% 84.93/85.13
% 84.93/85.13 That finishes the proof of the theorem.
% 84.93/85.13
% 84.93/85.13 Process 30631 finished Wed Jul 27 06:29:09 2022
% 84.93/85.13 Otter interrupted
% 84.93/85.13 PROOF FOUND
%------------------------------------------------------------------------------