TSTP Solution File: KLE009+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE009+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 4.59s 4.76s
% Output : Refutation 4.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of clauses : 78 ( 66 unt; 0 nHn; 68 RR)
% Number of literals : 96 ( 63 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ test(A)
| complement(dollar_f1(A),A) ),
file('KLE009+2.p',unknown),
[] ).
cnf(4,axiom,
( test(A)
| ~ complement(B,A) ),
file('KLE009+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ complement(A,B)
| multiplication(B,A) = zero ),
file('KLE009+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ complement(A,B)
| multiplication(A,B) = zero ),
file('KLE009+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ complement(A,B)
| addition(B,A) = one ),
file('KLE009+2.p',unknown),
[] ).
cnf(8,axiom,
( complement(A,B)
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| addition(B,A) != one ),
file('KLE009+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ test(A)
| c(A) != B
| complement(A,B) ),
file('KLE009+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ test(A)
| c(A) = B
| ~ complement(A,B) ),
file('KLE009+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ test(A)
| ~ test(B)
| c(addition(A,B)) = multiplication(c(A),c(B)) ),
file('KLE009+2.p',unknown),
[] ).
cnf(13,axiom,
one != addition(addition(addition(multiplication(dollar_c2,dollar_c1),multiplication(dollar_c2,c(dollar_c1))),multiplication(c(dollar_c2),dollar_c1)),multiplication(c(dollar_c2),c(dollar_c1))),
file('KLE009+2.p',unknown),
[] ).
cnf(14,plain,
addition(addition(addition(multiplication(dollar_c2,dollar_c1),multiplication(dollar_c2,c(dollar_c1))),multiplication(c(dollar_c2),dollar_c1)),multiplication(c(dollar_c2),c(dollar_c1))) != one,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(18,axiom,
A = A,
file('KLE009+2.p',unknown),
[] ).
cnf(19,axiom,
addition(A,B) = addition(B,A),
file('KLE009+2.p',unknown),
[] ).
cnf(20,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE009+2.p',unknown),
[] ).
cnf(22,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(31,axiom,
multiplication(A,one) = A,
file('KLE009+2.p',unknown),
[] ).
cnf(33,axiom,
multiplication(one,A) = A,
file('KLE009+2.p',unknown),
[] ).
cnf(34,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE009+2.p',unknown),
[] ).
cnf(36,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE009+2.p',unknown),
[] ).
cnf(43,axiom,
test(dollar_c1),
file('KLE009+2.p',unknown),
[] ).
cnf(44,axiom,
test(dollar_c2),
file('KLE009+2.p',unknown),
[] ).
cnf(45,plain,
addition(multiplication(dollar_c2,dollar_c1),addition(multiplication(dollar_c2,c(dollar_c1)),addition(multiplication(c(dollar_c2),dollar_c1),multiplication(c(dollar_c2),c(dollar_c1))))) != one,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[14]),22,22,22]),
[iquote('back_demod,14,demod,22,22,22')] ).
cnf(53,plain,
complement(dollar_c1,c(dollar_c1)),
inference(hyper,[status(thm)],[43,9,18]),
[iquote('hyper,43,9,18')] ).
cnf(54,plain,
complement(dollar_f1(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[43,3]),
[iquote('hyper,43,3')] ).
cnf(67,plain,
complement(dollar_c2,c(dollar_c2)),
inference(hyper,[status(thm)],[44,9,18]),
[iquote('hyper,44,9,18')] ).
cnf(68,plain,
complement(dollar_f1(dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[44,3]),
[iquote('hyper,44,3')] ).
cnf(69,plain,
addition(c(dollar_c1),dollar_c1) = one,
inference(hyper,[status(thm)],[53,7]),
[iquote('hyper,53,7')] ).
cnf(71,plain,
multiplication(dollar_c1,c(dollar_c1)) = zero,
inference(hyper,[status(thm)],[53,6]),
[iquote('hyper,53,6')] ).
cnf(74,plain,
multiplication(c(dollar_c1),dollar_c1) = zero,
inference(hyper,[status(thm)],[53,5]),
[iquote('hyper,53,5')] ).
cnf(75,plain,
test(c(dollar_c1)),
inference(hyper,[status(thm)],[53,4]),
[iquote('hyper,53,4')] ).
cnf(86,plain,
c(addition(dollar_c2,c(dollar_c1))) = multiplication(c(dollar_c2),c(c(dollar_c1))),
inference(hyper,[status(thm)],[75,11,44]),
[iquote('hyper,75,11,44')] ).
cnf(96,plain,
( addition(A,B) = one
| ~ complement(A,B) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,7])]),
[iquote('para_into,19.1.1,7.2.1,flip.1')] ).
cnf(99,plain,
( ~ test(A)
| ~ test(B)
| c(addition(B,A)) = multiplication(c(A),c(B)) ),
inference(para_from,[status(thm),theory(equality)],[19,11]),
[iquote('para_from,19.1.1,11.3.1.1')] ).
cnf(101,plain,
addition(dollar_c1,dollar_f1(dollar_c1)) = one,
inference(hyper,[status(thm)],[54,7]),
[iquote('hyper,54,7')] ).
cnf(103,plain,
multiplication(dollar_f1(dollar_c1),dollar_c1) = zero,
inference(hyper,[status(thm)],[54,6]),
[iquote('hyper,54,6')] ).
cnf(106,plain,
multiplication(dollar_c1,dollar_f1(dollar_c1)) = zero,
inference(hyper,[status(thm)],[54,5]),
[iquote('hyper,54,5')] ).
cnf(107,plain,
addition(c(dollar_c2),dollar_c2) = one,
inference(hyper,[status(thm)],[67,7]),
[iquote('hyper,67,7')] ).
cnf(109,plain,
multiplication(dollar_c2,c(dollar_c2)) = zero,
inference(hyper,[status(thm)],[67,6]),
[iquote('hyper,67,6')] ).
cnf(112,plain,
multiplication(c(dollar_c2),dollar_c2) = zero,
inference(hyper,[status(thm)],[67,5]),
[iquote('hyper,67,5')] ).
cnf(113,plain,
test(c(dollar_c2)),
inference(hyper,[status(thm)],[67,4]),
[iquote('hyper,67,4')] ).
cnf(128,plain,
c(addition(c(dollar_c1),c(dollar_c2))) = multiplication(c(c(dollar_c1)),c(c(dollar_c2))),
inference(hyper,[status(thm)],[113,11,75]),
[iquote('hyper,113,11,75')] ).
cnf(142,plain,
addition(dollar_c2,dollar_f1(dollar_c2)) = one,
inference(hyper,[status(thm)],[68,7]),
[iquote('hyper,68,7')] ).
cnf(144,plain,
multiplication(dollar_f1(dollar_c2),dollar_c2) = zero,
inference(hyper,[status(thm)],[68,6]),
[iquote('hyper,68,6')] ).
cnf(147,plain,
multiplication(dollar_c2,dollar_f1(dollar_c2)) = zero,
inference(hyper,[status(thm)],[68,5]),
[iquote('hyper,68,5')] ).
cnf(380,plain,
addition(dollar_c1,c(dollar_c1)) = one,
inference(para_into,[status(thm),theory(equality)],[69,19]),
[iquote('para_into,69.1.1,19.1.1')] ).
cnf(393,plain,
complement(c(dollar_c1),dollar_c1),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[71,8]),74,380]),18,18,18]),
[iquote('para_from,71.1.1,8.2.1,demod,74,380,unit_del,18,18,18')] ).
cnf(395,plain,
c(c(dollar_c1)) = dollar_c1,
inference(hyper,[status(thm)],[393,10,75]),
[iquote('hyper,393,10,75')] ).
cnf(406,plain,
c(addition(c(dollar_c1),c(dollar_c2))) = multiplication(dollar_c1,c(c(dollar_c2))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[128]),395]),
[iquote('back_demod,128,demod,395')] ).
cnf(414,plain,
c(addition(dollar_c2,c(dollar_c1))) = multiplication(c(dollar_c2),dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[86]),395]),
[iquote('back_demod,86,demod,395')] ).
cnf(442,plain,
addition(multiplication(dollar_c2,dollar_c1),addition(multiplication(c(dollar_c2),dollar_c1),addition(multiplication(c(dollar_c2),c(dollar_c1)),multiplication(dollar_c2,c(dollar_c1))))) != one,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[45,19]),22]),
[iquote('para_into,45.1.1.2,19.1.1,demod,22')] ).
cnf(484,plain,
addition(dollar_f1(dollar_c1),dollar_c1) = one,
inference(para_into,[status(thm),theory(equality)],[101,19]),
[iquote('para_into,101.1.1,19.1.1')] ).
cnf(497,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)],[103,8]),106,484]),18,18,18]),
[iquote('para_from,103.1.1,8.2.1,demod,106,484,unit_del,18,18,18')] ).
cnf(510,plain,
c(dollar_c1) = dollar_f1(dollar_c1),
inference(hyper,[status(thm)],[497,10,43]),
[iquote('hyper,497,10,43')] ).
cnf(511,plain,
test(dollar_f1(dollar_c1)),
inference(hyper,[status(thm)],[497,4]),
[iquote('hyper,497,4')] ).
cnf(530,plain,
addition(multiplication(dollar_c2,dollar_c1),addition(multiplication(c(dollar_c2),dollar_c1),addition(multiplication(c(dollar_c2),dollar_f1(dollar_c1)),multiplication(dollar_c2,dollar_f1(dollar_c1))))) != one,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[442]),510,510]),
[iquote('back_demod,442,demod,510,510')] ).
cnf(553,plain,
c(addition(dollar_c2,dollar_f1(dollar_c1))) = multiplication(c(dollar_c2),dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[414]),510]),
[iquote('back_demod,414,demod,510')] ).
cnf(561,plain,
c(addition(dollar_f1(dollar_c1),c(dollar_c2))) = multiplication(dollar_c1,c(c(dollar_c2))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[406]),510]),
[iquote('back_demod,406,demod,510')] ).
cnf(570,plain,
c(dollar_f1(dollar_c1)) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[395]),510]),
[iquote('back_demod,394,demod,510')] ).
cnf(616,plain,
addition(dollar_c2,c(dollar_c2)) = one,
inference(para_into,[status(thm),theory(equality)],[107,19]),
[iquote('para_into,107.1.1,19.1.1')] ).
cnf(623,plain,
addition(multiplication(c(dollar_c2),A),multiplication(dollar_c2,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[107,36]),33])]),
[iquote('para_from,107.1.1,36.1.1.1,demod,33,flip.1')] ).
cnf(627,plain,
addition(multiplication(dollar_c2,dollar_c1),addition(multiplication(c(dollar_c2),dollar_c1),dollar_f1(dollar_c1))) != one,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[530]),623]),
[iquote('back_demod,530,demod,623')] ).
cnf(630,plain,
complement(c(dollar_c2),dollar_c2),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[109,8]),112,616]),18,18,18]),
[iquote('para_from,109.1.1,8.2.1,demod,112,616,unit_del,18,18,18')] ).
cnf(632,plain,
c(c(dollar_c2)) = dollar_c2,
inference(hyper,[status(thm)],[630,10,113]),
[iquote('hyper,630,10,113')] ).
cnf(643,plain,
c(addition(dollar_f1(dollar_c1),c(dollar_c2))) = multiplication(dollar_c1,dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[561]),632]),
[iquote('back_demod,561,demod,632')] ).
cnf(687,plain,
addition(dollar_f1(dollar_c2),dollar_c2) = one,
inference(hyper,[status(thm)],[96,68]),
[iquote('hyper,96,68')] ).
cnf(688,plain,
( addition(A,addition(B,C)) = one
| ~ complement(addition(A,B),C) ),
inference(para_into,[status(thm),theory(equality)],[96,22]),
[iquote('para_into,96.1.1,21.1.1')] ).
cnf(717,plain,
addition(multiplication(A,dollar_c2),multiplication(A,dollar_f1(dollar_c2))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[142,34]),31])]),
[iquote('para_from,142.1.1,34.1.1.2,demod,31,flip.1')] ).
cnf(739,plain,
complement(dollar_c2,dollar_f1(dollar_c2)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[144,8]),147,687]),18,18,18]),
[iquote('para_from,144.1.1,8.2.1,demod,147,687,unit_del,18,18,18')] ).
cnf(741,plain,
c(dollar_c2) = dollar_f1(dollar_c2),
inference(hyper,[status(thm)],[739,10,44]),
[iquote('hyper,739,10,44')] ).
cnf(742,plain,
test(dollar_f1(dollar_c2)),
inference(hyper,[status(thm)],[739,4]),
[iquote('hyper,739,4')] ).
cnf(776,plain,
c(addition(dollar_f1(dollar_c1),dollar_f1(dollar_c2))) = multiplication(dollar_c1,dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[643]),741]),
[iquote('back_demod,643,demod,741')] ).
cnf(788,plain,
c(dollar_f1(dollar_c2)) = dollar_c2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[632]),741]),
[iquote('back_demod,631,demod,741')] ).
cnf(791,plain,
addition(multiplication(dollar_c2,dollar_c1),addition(multiplication(dollar_f1(dollar_c2),dollar_c1),dollar_f1(dollar_c1))) != one,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[627]),741]),
[iquote('back_demod,627,demod,741')] ).
cnf(810,plain,
c(addition(dollar_c2,dollar_f1(dollar_c1))) = multiplication(dollar_f1(dollar_c2),dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[553]),741]),
[iquote('back_demod,553,demod,741')] ).
cnf(886,plain,
multiplication(dollar_c2,dollar_c1) = multiplication(dollar_c1,dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[99,742,511]),776,788,570])]),
[iquote('hyper,99,742,511,demod,776,788,570,flip.1')] ).
cnf(891,plain,
multiplication(dollar_f1(dollar_c2),dollar_c1) = multiplication(dollar_c1,dollar_f1(dollar_c2)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[99,511,44]),810,570,741]),
[iquote('hyper,99,511,44,demod,810,570,741')] ).
cnf(920,plain,
addition(multiplication(dollar_c1,dollar_c2),addition(multiplication(dollar_c1,dollar_f1(dollar_c2)),dollar_f1(dollar_c1))) != one,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[791]),886,891]),
[iquote('back_demod,791,demod,886,891')] ).
cnf(3074,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[920,688]),717]),18,497]),
[iquote('para_into,920.1.1,688.1.1,demod,717,unit_del,18,497')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE009+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 06:32:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.93 ----- Otter 3.3f, August 2004 -----
% 1.73/1.93 The process was started by sandbox on n005.cluster.edu,
% 1.73/1.93 Wed Jul 27 06:32:20 2022
% 1.73/1.93 The command was "./otter". The process ID is 9355.
% 1.73/1.93
% 1.73/1.93 set(prolog_style_variables).
% 1.73/1.93 set(auto).
% 1.73/1.93 dependent: set(auto1).
% 1.73/1.93 dependent: set(process_input).
% 1.73/1.93 dependent: clear(print_kept).
% 1.73/1.93 dependent: clear(print_new_demod).
% 1.73/1.93 dependent: clear(print_back_demod).
% 1.73/1.93 dependent: clear(print_back_sub).
% 1.73/1.93 dependent: set(control_memory).
% 1.73/1.93 dependent: assign(max_mem, 12000).
% 1.73/1.93 dependent: assign(pick_given_ratio, 4).
% 1.73/1.93 dependent: assign(stats_level, 1).
% 1.73/1.93 dependent: assign(max_seconds, 10800).
% 1.73/1.93 clear(print_given).
% 1.73/1.93
% 1.73/1.93 formula_list(usable).
% 1.73/1.93 all A (A=A).
% 1.73/1.93 all A B (addition(A,B)=addition(B,A)).
% 1.73/1.93 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.73/1.93 all A (addition(A,zero)=A).
% 1.73/1.93 all A (addition(A,A)=A).
% 1.73/1.93 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.73/1.93 all A (multiplication(A,one)=A).
% 1.73/1.93 all A (multiplication(one,A)=A).
% 1.73/1.93 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.73/1.93 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.73/1.93 all A (multiplication(A,zero)=zero).
% 1.73/1.93 all A (multiplication(zero,A)=zero).
% 1.73/1.93 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.73/1.93 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.73/1.93 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.73/1.93 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.73/1.93 all X0 (-test(X0)->c(X0)=zero).
% 1.73/1.93 all X0 X1 (test(X0)&test(X1)->c(addition(X0,X1))=multiplication(c(X0),c(X1))).
% 1.73/1.93 all X0 X1 (test(X0)&test(X1)->c(multiplication(X0,X1))=addition(c(X0),c(X1))).
% 1.73/1.93 -(all X0 X1 (test(X1)&test(X0)->one=addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))).
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 -------> usable clausifies to:
% 1.73/1.93
% 1.73/1.93 list(usable).
% 1.73/1.93 0 [] A=A.
% 1.73/1.93 0 [] addition(A,B)=addition(B,A).
% 1.73/1.93 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.73/1.93 0 [] addition(A,zero)=A.
% 1.73/1.93 0 [] addition(A,A)=A.
% 1.73/1.93 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.73/1.93 0 [] multiplication(A,one)=A.
% 1.73/1.93 0 [] multiplication(one,A)=A.
% 1.73/1.93 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.73/1.93 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.73/1.93 0 [] multiplication(A,zero)=zero.
% 1.73/1.93 0 [] multiplication(zero,A)=zero.
% 1.73/1.93 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.73/1.93 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.73/1.93 0 [] -test(X0)|complement($f1(X0),X0).
% 1.73/1.93 0 [] test(X0)| -complement(X1,X0).
% 1.73/1.93 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.73/1.93 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.73/1.93 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.73/1.93 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.73/1.93 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.73/1.93 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.73/1.93 0 [] test(X0)|c(X0)=zero.
% 1.73/1.93 0 [] -test(X0)| -test(X1)|c(addition(X0,X1))=multiplication(c(X0),c(X1)).
% 1.73/1.93 0 [] -test(X0)| -test(X1)|c(multiplication(X0,X1))=addition(c(X0),c(X1)).
% 1.73/1.93 0 [] test($c1).
% 1.73/1.93 0 [] test($c2).
% 1.73/1.93 0 [] one!=addition(addition(addition(multiplication($c2,$c1),multiplication($c2,c($c1))),multiplication(c($c2),$c1)),multiplication(c($c2),c($c1))).
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.73/1.93
% 1.73/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.73/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.73/1.93 deletion, with positive clauses in sos and nonpositive
% 1.73/1.93 clauses in usable.
% 1.73/1.93
% 1.73/1.93 dependent: set(knuth_bendix).
% 1.73/1.93 dependent: set(anl_eq).
% 1.73/1.93 dependent: set(para_from).
% 1.73/1.93 dependent: set(para_into).
% 1.73/1.93 dependent: clear(para_from_right).
% 1.73/1.93 dependent: clear(para_into_right).
% 1.73/1.93 dependent: set(para_from_vars).
% 1.73/1.93 dependent: set(eq_units_both_ways).
% 1.73/1.93 dependent: set(dynamic_demod_all).
% 1.73/1.93 dependent: set(dynamic_demod).
% 1.73/1.93 dependent: set(order_eq).
% 1.73/1.93 dependent: set(back_demod).
% 1.73/1.93 dependent: set(lrpo).
% 1.73/1.93 dependent: set(hyper_res).
% 1.73/1.93 dependent: set(unit_deletion).
% 1.73/1.93 dependent: set(factor).
% 1.73/1.93
% 1.73/1.93 ------------> process usable:
% 4.59/4.76 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 4.59/4.76 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 4.59/4.76 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 4.59/4.76 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 4.59/4.76 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 4.59/4.76 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 4.59/4.76 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 4.59/4.76 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 4.59/4.76 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 4.59/4.76 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 4.59/4.76 ** KEPT (pick-wt=14): 11 [] -test(A)| -test(B)|c(addition(A,B))=multiplication(c(A),c(B)).
% 4.59/4.76 ** KEPT (pick-wt=14): 12 [] -test(A)| -test(B)|c(multiplication(A,B))=addition(c(A),c(B)).
% 4.59/4.76 ** KEPT (pick-wt=21): 14 [copy,13,flip.1] addition(addition(addition(multiplication($c2,$c1),multiplication($c2,c($c1))),multiplication(c($c2),$c1)),multiplication(c($c2),c($c1)))!=one.
% 4.59/4.76
% 4.59/4.76 ------------> process sos:
% 4.59/4.76 ** KEPT (pick-wt=3): 18 [] A=A.
% 4.59/4.76 ** KEPT (pick-wt=7): 19 [] addition(A,B)=addition(B,A).
% 4.59/4.76 ** KEPT (pick-wt=11): 21 [copy,20,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 4.59/4.76 ---> New Demodulator: 22 [new_demod,21] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 4.59/4.76 ** KEPT (pick-wt=5): 23 [] addition(A,zero)=A.
% 4.59/4.76 ---> New Demodulator: 24 [new_demod,23] addition(A,zero)=A.
% 4.59/4.76 ** KEPT (pick-wt=5): 25 [] addition(A,A)=A.
% 4.59/4.76 ---> New Demodulator: 26 [new_demod,25] addition(A,A)=A.
% 4.59/4.76 ** KEPT (pick-wt=11): 28 [copy,27,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 4.59/4.76 ---> New Demodulator: 29 [new_demod,28] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 4.59/4.76 ** KEPT (pick-wt=5): 30 [] multiplication(A,one)=A.
% 4.59/4.76 ---> New Demodulator: 31 [new_demod,30] multiplication(A,one)=A.
% 4.59/4.76 ** KEPT (pick-wt=5): 32 [] multiplication(one,A)=A.
% 4.59/4.76 ---> New Demodulator: 33 [new_demod,32] multiplication(one,A)=A.
% 4.59/4.76 ** KEPT (pick-wt=13): 34 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 4.59/4.76 ---> New Demodulator: 35 [new_demod,34] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 4.59/4.76 ** KEPT (pick-wt=13): 36 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 4.59/4.76 ---> New Demodulator: 37 [new_demod,36] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 4.59/4.76 ** KEPT (pick-wt=5): 38 [] multiplication(A,zero)=zero.
% 4.59/4.76 ---> New Demodulator: 39 [new_demod,38] multiplication(A,zero)=zero.
% 4.59/4.76 ** KEPT (pick-wt=5): 40 [] multiplication(zero,A)=zero.
% 4.59/4.76 ---> New Demodulator: 41 [new_demod,40] multiplication(zero,A)=zero.
% 4.59/4.76 ** KEPT (pick-wt=6): 42 [] test(A)|c(A)=zero.
% 4.59/4.76 ** KEPT (pick-wt=2): 43 [] test($c1).
% 4.59/4.76 ** KEPT (pick-wt=2): 44 [] test($c2).
% 4.59/4.76 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 4.59/4.76 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] addition(A,B)=addition(B,A).
% 4.59/4.76 >>>> Starting back demodulation with 22.
% 4.59/4.76 >> back demodulating 14 with 22.
% 4.59/4.76 >>>> Starting back demodulation with 24.
% 4.59/4.76 >>>> Starting back demodulation with 26.
% 4.59/4.76 >> back demodulating 17 with 26.
% 4.59/4.76 >> back demodulating 16 with 26.
% 4.59/4.76 >> back demodulating 15 with 26.
% 4.59/4.76 >>>> Starting back demodulation with 29.
% 4.59/4.76 >>>> Starting back demodulation with 31.
% 4.59/4.76 >>>> Starting back demodulation with 33.
% 4.59/4.76 >>>> Starting back demodulation with 35.
% 4.59/4.76 >>>> Starting back demodulation with 37.
% 4.59/4.76 >>>> Starting back demodulation with 39.
% 4.59/4.76 >>>> Starting back demodulation with 41.
% 4.59/4.76
% 4.59/4.76 ======= end of input processing =======
% 4.59/4.76
% 4.59/4.76 =========== start of search ===========
% 4.59/4.76
% 4.59/4.76
% 4.59/4.76 Resetting weight limit to 7.
% 4.59/4.76
% 4.59/4.76
% 4.59/4.76 Resetting weight limit to 7.
% 4.59/4.76
% 4.59/4.76 sos_size=1710
% 4.59/4.76
% 4.59/4.76 -------- PROOF --------
% 4.59/4.76
% 4.59/4.76 -----> EMPTY CLAUSE at 2.83 sec ----> 3074 [para_into,920.1.1,688.1.1,demod,717,unit_del,18,497] $F.
% 4.59/4.76
% 4.59/4.76 Length of proof is 58. Level of proof is 11.
% 4.59/4.76
% 4.59/4.76 ---------------- PROOF ----------------
% 4.59/4.76 % SZS status Theorem
% 4.59/4.76 % SZS output start Refutation
% See solution above
% 4.59/4.76 ------------ end of proof -------------
% 4.59/4.76
% 4.59/4.76
% 4.59/4.76 Search stopped by max_proofs option.
% 4.59/4.76
% 4.59/4.76
% 4.59/4.76 Search stopped by max_proofs option.
% 4.59/4.76
% 4.59/4.76 ============ end of search ============
% 4.59/4.76
% 4.59/4.76 -------------- statistics -------------
% 4.59/4.76 clauses given 996
% 4.59/4.76 clauses generated 211473
% 4.59/4.76 clauses kept 2777
% 4.59/4.76 clauses forward subsumed 29877
% 4.59/4.76 clauses back subsumed 747
% 4.59/4.76 Kbytes malloced 5859
% 4.59/4.76
% 4.59/4.76 ----------- times (seconds) -----------
% 4.59/4.76 user CPU time 2.83 (0 hr, 0 min, 2 sec)
% 4.59/4.76 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 4.59/4.76 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 4.59/4.76
% 4.59/4.76 That finishes the proof of the theorem.
% 4.59/4.76
% 4.59/4.76 Process 9355 finished Wed Jul 27 06:32:25 2022
% 4.59/4.76 Otter interrupted
% 4.59/4.76 PROOF FOUND
%------------------------------------------------------------------------------