TSTP Solution File: KLE017+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE017+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:00:29 EDT 2022
% Result : Theorem 18.95s 19.21s
% Output : Refutation 18.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of clauses : 71 ( 52 unt; 4 nHn; 40 RR)
% Number of literals : 96 ( 50 equ; 22 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 : 75 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE017+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE017+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ test(A)
| complement(dollar_f1(A),A) ),
file('KLE017+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ complement(A,B)
| multiplication(B,A) = zero ),
file('KLE017+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ complement(A,B)
| multiplication(A,B) = zero ),
file('KLE017+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ complement(A,B)
| addition(B,A) = one ),
file('KLE017+1.p',unknown),
[] ).
cnf(8,axiom,
( complement(A,B)
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| addition(B,A) != one ),
file('KLE017+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ test(A)
| c(A) != B
| complement(A,B) ),
file('KLE017+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ test(A)
| c(A) = B
| ~ complement(A,B) ),
file('KLE017+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ le_q(dollar_c1,multiplication(dollar_c3,dollar_c2))
| ~ le_q(dollar_c1,dollar_c3)
| ~ le_q(dollar_c1,dollar_c2) ),
file('KLE017+1.p',unknown),
[] ).
cnf(13,axiom,
A = A,
file('KLE017+1.p',unknown),
[] ).
cnf(14,axiom,
addition(A,B) = addition(B,A),
file('KLE017+1.p',unknown),
[] ).
cnf(15,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE017+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('KLE017+1.p',unknown),
[] ).
cnf(20,axiom,
addition(A,A) = A,
file('KLE017+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE017+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(26,axiom,
multiplication(A,one) = A,
file('KLE017+1.p',unknown),
[] ).
cnf(28,axiom,
multiplication(one,A) = A,
file('KLE017+1.p',unknown),
[] ).
cnf(30,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE017+1.p',unknown),
[] ).
cnf(31,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE017+1.p',unknown),
[] ).
cnf(36,axiom,
multiplication(zero,A) = zero,
file('KLE017+1.p',unknown),
[] ).
cnf(38,axiom,
test(dollar_c3),
file('KLE017+1.p',unknown),
[] ).
cnf(39,axiom,
test(dollar_c2),
file('KLE017+1.p',unknown),
[] ).
cnf(41,axiom,
( le_q(dollar_c1,multiplication(dollar_c3,dollar_c2))
| le_q(dollar_c1,dollar_c3) ),
file('KLE017+1.p',unknown),
[] ).
cnf(42,axiom,
( le_q(dollar_c1,multiplication(dollar_c3,dollar_c2))
| le_q(dollar_c1,dollar_c2) ),
file('KLE017+1.p',unknown),
[] ).
cnf(44,plain,
complement(dollar_c3,c(dollar_c3)),
inference(hyper,[status(thm)],[38,9,13]),
[iquote('hyper,38,9,13')] ).
cnf(45,plain,
complement(dollar_f1(dollar_c3),dollar_c3),
inference(hyper,[status(thm)],[38,3]),
[iquote('hyper,38,3')] ).
cnf(47,plain,
complement(dollar_f1(dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[39,3]),
[iquote('hyper,39,3')] ).
cnf(50,plain,
addition(c(dollar_c3),dollar_c3) = one,
inference(hyper,[status(thm)],[44,7]),
[iquote('hyper,44,7')] ).
cnf(64,plain,
addition(dollar_c3,dollar_f1(dollar_c3)) = one,
inference(hyper,[status(thm)],[45,7]),
[iquote('hyper,45,7')] ).
cnf(66,plain,
multiplication(dollar_f1(dollar_c3),dollar_c3) = zero,
inference(hyper,[status(thm)],[45,6]),
[iquote('hyper,45,6')] ).
cnf(68,plain,
multiplication(dollar_c3,dollar_f1(dollar_c3)) = zero,
inference(hyper,[status(thm)],[45,5]),
[iquote('hyper,45,5')] ).
cnf(80,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(88,plain,
addition(dollar_c2,dollar_f1(dollar_c2)) = one,
inference(hyper,[status(thm)],[47,7]),
[iquote('hyper,47,7')] ).
cnf(110,plain,
addition(zero,A) = A,
inference(para_into,[status(thm),theory(equality)],[19,14]),
[iquote('para_into,18.1.1,14.1.1')] ).
cnf(122,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[20,16])]),
[iquote('para_from,20.1.1,16.1.1.1,flip.1')] ).
cnf(149,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)],[30,1])]),
[iquote('para_into,29.1.1.2,1.2.1,flip.1')] ).
cnf(180,plain,
( le_q(dollar_c1,multiplication(dollar_c3,dollar_c2))
| addition(dollar_c1,dollar_c3) = dollar_c3 ),
inference(hyper,[status(thm)],[41,1]),
[iquote('hyper,41,1')] ).
cnf(188,plain,
addition(multiplication(c(dollar_c3),A),multiplication(dollar_c3,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[50,31]),28])]),
[iquote('para_from,50.1.1,31.1.1.1,demod,28,flip.1')] ).
cnf(204,plain,
( le_q(dollar_c1,multiplication(dollar_c3,dollar_c2))
| addition(dollar_c1,dollar_c2) = dollar_c2 ),
inference(hyper,[status(thm)],[42,1]),
[iquote('hyper,42,1')] ).
cnf(219,plain,
addition(dollar_f1(dollar_c3),dollar_c3) = one,
inference(para_into,[status(thm),theory(equality)],[64,14]),
[iquote('para_into,63.1.1,14.1.1')] ).
cnf(223,plain,
addition(multiplication(dollar_c3,A),multiplication(dollar_f1(dollar_c3),A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[64,31]),28])]),
[iquote('para_from,63.1.1,31.1.1.1,demod,28,flip.1')] ).
cnf(229,plain,
multiplication(dollar_f1(dollar_c3),multiplication(dollar_c3,A)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[66,23]),36])]),
[iquote('para_from,65.1.1,23.1.1.1,demod,36,flip.1')] ).
cnf(230,plain,
complement(dollar_c3,dollar_f1(dollar_c3)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[66,8]),68,219]),13,13,13]),
[iquote('para_from,65.1.1,8.2.1,demod,68,219,unit_del,13,13,13')] ).
cnf(235,plain,
c(dollar_c3) = dollar_f1(dollar_c3),
inference(hyper,[status(thm)],[230,10,38]),
[iquote('hyper,230,10,38')] ).
cnf(256,plain,
addition(multiplication(dollar_f1(dollar_c3),A),multiplication(dollar_c3,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[188]),235]),
[iquote('back_demod,188,demod,235')] ).
cnf(527,plain,
( addition(A,B) = addition(C,B)
| ~ le_q(A,C)
| ~ le_q(C,B) ),
inference(para_into,[status(thm),theory(equality)],[80,1]),
[iquote('para_into,80.1.1.2,1.2.1')] ).
cnf(1496,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[122,2]),
[iquote('hyper,122,2')] ).
cnf(1511,plain,
addition(dollar_c2,one) = one,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[122,88]),88]),
[iquote('para_into,122.1.1.2,87.1.1,demod,88')] ).
cnf(1521,plain,
addition(dollar_c3,one) = one,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[122,64]),64]),
[iquote('para_into,122.1.1.2,63.1.1,demod,64')] ).
cnf(1558,plain,
le_q(addition(A,B),addition(A,addition(B,C))),
inference(para_into,[status(thm),theory(equality)],[1496,16]),
[iquote('para_into,1496.1.2,16.1.1')] ).
cnf(1690,plain,
addition(multiplication(A,dollar_c2),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1511,30]),26,26])]),
[iquote('para_from,1511.1.1,29.1.1.2,demod,26,26,flip.1')] ).
cnf(1715,plain,
addition(multiplication(dollar_c3,A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1521,31]),28,28])]),
[iquote('para_from,1521.1.1,31.1.1.1,demod,28,28,flip.1')] ).
cnf(2829,plain,
( multiplication(dollar_f1(dollar_c3),A) = zero
| ~ le_q(A,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[149,66]),19,66]),
[iquote('para_into,149.1.1.2,65.1.1,demod,19,66')] ).
cnf(2858,plain,
( le_q(multiplication(A,B),multiplication(A,C))
| ~ le_q(B,C) ),
inference(para_from,[status(thm),theory(equality)],[149,1496]),
[iquote('para_from,149.1.1,1496.1.2')] ).
cnf(3032,plain,
le_q(multiplication(dollar_c3,A),A),
inference(para_from,[status(thm),theory(equality)],[223,1496]),
[iquote('para_from,223.1.1,1496.1.2')] ).
cnf(3124,plain,
le_q(multiplication(A,dollar_c2),A),
inference(hyper,[status(thm)],[1690,2]),
[iquote('hyper,1689,2')] ).
cnf(3398,plain,
addition(dollar_c1,dollar_c2) = dollar_c2,
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[527,204,3032]),1715])]),
[iquote('hyper,527,204,3032,demod,1715,factor_simp')] ).
cnf(3400,plain,
addition(dollar_c1,dollar_c3) = dollar_c3,
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[527,180,3124]),1690])]),
[iquote('hyper,527,180,3124,demod,1690,factor_simp')] ).
cnf(3402,plain,
le_q(dollar_c1,dollar_c2),
inference(hyper,[status(thm)],[3398,2]),
[iquote('hyper,3398,2')] ).
cnf(3437,plain,
le_q(dollar_c1,dollar_c3),
inference(hyper,[status(thm)],[3400,2]),
[iquote('hyper,3400,2')] ).
cnf(4648,plain,
le_q(addition(A,dollar_c1),addition(A,dollar_c3)),
inference(para_into,[status(thm),theory(equality)],[1558,3400]),
[iquote('para_into,1558.1.2.2,3400.1.1')] ).
cnf(4651,plain,
le_q(addition(dollar_c1,A),addition(A,dollar_c3)),
inference(para_into,[status(thm),theory(equality)],[4648,14]),
[iquote('para_into,4648.1.1,14.1.1')] ).
cnf(4660,plain,
le_q(addition(dollar_c1,multiplication(dollar_c3,dollar_c2)),dollar_c3),
inference(para_into,[status(thm),theory(equality)],[4651,1690]),
[iquote('para_into,4651.1.2,1689.1.1')] ).
cnf(4778,plain,
multiplication(dollar_f1(dollar_c3),dollar_c1) = zero,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2829,4660]),30,229,19]),
[iquote('hyper,2829,4660,demod,30,229,19')] ).
cnf(4780,plain,
multiplication(dollar_c3,dollar_c1) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[4778,256]),110]),
[iquote('para_from,4778.1.1,256.1.1.1,demod,110')] ).
cnf(4912,plain,
le_q(multiplication(A,dollar_c1),multiplication(A,dollar_c2)),
inference(hyper,[status(thm)],[2858,3402]),
[iquote('hyper,2858,3402')] ).
cnf(4924,plain,
le_q(dollar_c1,multiplication(dollar_c3,dollar_c2)),
inference(para_into,[status(thm),theory(equality)],[4912,4780]),
[iquote('para_into,4912.1.1,4780.1.1')] ).
cnf(4929,plain,
$false,
inference(hyper,[status(thm)],[4924,11,3437,3402]),
[iquote('hyper,4924,11,3437,3402')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE017+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 06:37:48 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.60/1.81 ----- Otter 3.3f, August 2004 -----
% 1.60/1.81 The process was started by sandbox on n028.cluster.edu,
% 1.60/1.81 Wed Jul 27 06:37:49 2022
% 1.60/1.81 The command was "./otter". The process ID is 16305.
% 1.60/1.81
% 1.60/1.81 set(prolog_style_variables).
% 1.60/1.81 set(auto).
% 1.60/1.81 dependent: set(auto1).
% 1.60/1.81 dependent: set(process_input).
% 1.60/1.81 dependent: clear(print_kept).
% 1.60/1.81 dependent: clear(print_new_demod).
% 1.60/1.81 dependent: clear(print_back_demod).
% 1.60/1.81 dependent: clear(print_back_sub).
% 1.60/1.81 dependent: set(control_memory).
% 1.60/1.81 dependent: assign(max_mem, 12000).
% 1.60/1.81 dependent: assign(pick_given_ratio, 4).
% 1.60/1.81 dependent: assign(stats_level, 1).
% 1.60/1.81 dependent: assign(max_seconds, 10800).
% 1.60/1.81 clear(print_given).
% 1.60/1.81
% 1.60/1.81 formula_list(usable).
% 1.60/1.81 all A (A=A).
% 1.60/1.81 all A B (addition(A,B)=addition(B,A)).
% 1.60/1.81 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.60/1.81 all A (addition(A,zero)=A).
% 1.60/1.81 all A (addition(A,A)=A).
% 1.60/1.81 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.60/1.81 all A (multiplication(A,one)=A).
% 1.60/1.81 all A (multiplication(one,A)=A).
% 1.60/1.81 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.60/1.81 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.60/1.81 all A (multiplication(A,zero)=zero).
% 1.60/1.81 all A (multiplication(zero,A)=zero).
% 1.60/1.81 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.60/1.81 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.60/1.81 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.60/1.81 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.60/1.81 all X0 (-test(X0)->c(X0)=zero).
% 1.60/1.81 -(all X0 X1 X2 (test(X0)&test(X1)&test(X2)-> (le_q(X2,multiplication(X0,X1))<->le_q(X2,X0)&le_q(X2,X1)))).
% 1.60/1.81 end_of_list.
% 1.60/1.81
% 1.60/1.81 -------> usable clausifies to:
% 1.60/1.81
% 1.60/1.81 list(usable).
% 1.60/1.81 0 [] A=A.
% 1.60/1.81 0 [] addition(A,B)=addition(B,A).
% 1.60/1.81 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.60/1.81 0 [] addition(A,zero)=A.
% 1.60/1.81 0 [] addition(A,A)=A.
% 1.60/1.81 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.60/1.81 0 [] multiplication(A,one)=A.
% 1.60/1.81 0 [] multiplication(one,A)=A.
% 1.60/1.81 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.60/1.81 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.60/1.81 0 [] multiplication(A,zero)=zero.
% 1.60/1.81 0 [] multiplication(zero,A)=zero.
% 1.60/1.81 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.60/1.81 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.60/1.81 0 [] -test(X0)|complement($f1(X0),X0).
% 1.60/1.81 0 [] test(X0)| -complement(X1,X0).
% 1.60/1.81 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.60/1.81 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.60/1.81 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.60/1.81 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.60/1.81 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.60/1.81 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.60/1.81 0 [] test(X0)|c(X0)=zero.
% 1.60/1.81 0 [] test($c3).
% 1.60/1.81 0 [] test($c2).
% 1.60/1.81 0 [] test($c1).
% 1.60/1.81 0 [] le_q($c1,multiplication($c3,$c2))|le_q($c1,$c3).
% 1.60/1.81 0 [] le_q($c1,multiplication($c3,$c2))|le_q($c1,$c2).
% 1.60/1.81 0 [] -le_q($c1,multiplication($c3,$c2))| -le_q($c1,$c3)| -le_q($c1,$c2).
% 1.60/1.81 end_of_list.
% 1.60/1.81
% 1.60/1.81 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.60/1.81
% 1.60/1.81 This ia a non-Horn set with equality. The strategy will be
% 1.60/1.81 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.60/1.81 deletion, with positive clauses in sos and nonpositive
% 1.60/1.81 clauses in usable.
% 1.60/1.81
% 1.60/1.81 dependent: set(knuth_bendix).
% 1.60/1.81 dependent: set(anl_eq).
% 1.60/1.81 dependent: set(para_from).
% 1.60/1.81 dependent: set(para_into).
% 1.60/1.81 dependent: clear(para_from_right).
% 1.60/1.81 dependent: clear(para_into_right).
% 1.60/1.81 dependent: set(para_from_vars).
% 1.60/1.81 dependent: set(eq_units_both_ways).
% 1.60/1.81 dependent: set(dynamic_demod_all).
% 1.60/1.81 dependent: set(dynamic_demod).
% 1.60/1.81 dependent: set(order_eq).
% 1.60/1.81 dependent: set(back_demod).
% 1.60/1.81 dependent: set(lrpo).
% 1.60/1.81 dependent: set(hyper_res).
% 1.60/1.81 dependent: set(unit_deletion).
% 1.60/1.81 dependent: set(factor).
% 1.60/1.81
% 1.60/1.81 ------------> process usable:
% 1.60/1.81 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.60/1.81 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.60/1.81 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 1.60/1.81 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 1.60/1.81 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 1.60/1.81 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 18.95/19.21 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 18.95/19.21 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 18.95/19.21 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 18.95/19.21 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 18.95/19.21 ** KEPT (pick-wt=11): 11 [] -le_q($c1,multiplication($c3,$c2))| -le_q($c1,$c3)| -le_q($c1,$c2).
% 18.95/19.21
% 18.95/19.21 ------------> process sos:
% 18.95/19.21 ** KEPT (pick-wt=3): 13 [] A=A.
% 18.95/19.21 ** KEPT (pick-wt=7): 14 [] addition(A,B)=addition(B,A).
% 18.95/19.21 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 18.95/19.21 ---> New Demodulator: 17 [new_demod,16] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 18.95/19.21 ** KEPT (pick-wt=5): 18 [] addition(A,zero)=A.
% 18.95/19.21 ---> New Demodulator: 19 [new_demod,18] addition(A,zero)=A.
% 18.95/19.21 ** KEPT (pick-wt=5): 20 [] addition(A,A)=A.
% 18.95/19.21 ---> New Demodulator: 21 [new_demod,20] addition(A,A)=A.
% 18.95/19.21 ** KEPT (pick-wt=11): 23 [copy,22,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 18.95/19.21 ---> New Demodulator: 24 [new_demod,23] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 18.95/19.21 ** KEPT (pick-wt=5): 25 [] multiplication(A,one)=A.
% 18.95/19.21 ---> New Demodulator: 26 [new_demod,25] multiplication(A,one)=A.
% 18.95/19.21 ** KEPT (pick-wt=5): 27 [] multiplication(one,A)=A.
% 18.95/19.21 ---> New Demodulator: 28 [new_demod,27] multiplication(one,A)=A.
% 18.95/19.21 ** KEPT (pick-wt=13): 29 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 18.95/19.21 ---> New Demodulator: 30 [new_demod,29] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 18.95/19.21 ** KEPT (pick-wt=13): 31 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 18.95/19.21 ---> New Demodulator: 32 [new_demod,31] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 18.95/19.21 ** KEPT (pick-wt=5): 33 [] multiplication(A,zero)=zero.
% 18.95/19.21 ---> New Demodulator: 34 [new_demod,33] multiplication(A,zero)=zero.
% 18.95/19.21 ** KEPT (pick-wt=5): 35 [] multiplication(zero,A)=zero.
% 18.95/19.21 ---> New Demodulator: 36 [new_demod,35] multiplication(zero,A)=zero.
% 18.95/19.21 ** KEPT (pick-wt=6): 37 [] test(A)|c(A)=zero.
% 18.95/19.21 ** KEPT (pick-wt=2): 38 [] test($c3).
% 18.95/19.21 ** KEPT (pick-wt=2): 39 [] test($c2).
% 18.95/19.21 ** KEPT (pick-wt=2): 40 [] test($c1).
% 18.95/19.21 ** KEPT (pick-wt=8): 41 [] le_q($c1,multiplication($c3,$c2))|le_q($c1,$c3).
% 18.95/19.21 ** KEPT (pick-wt=8): 42 [] le_q($c1,multiplication($c3,$c2))|le_q($c1,$c2).
% 18.95/19.21 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 18.95/19.21 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] addition(A,B)=addition(B,A).
% 18.95/19.21 >>>> Starting back demodulation with 17.
% 18.95/19.21 >>>> Starting back demodulation with 19.
% 18.95/19.21 >>>> Starting back demodulation with 21.
% 18.95/19.21 >> back demodulating 12 with 21.
% 18.95/19.21 >>>> Starting back demodulation with 24.
% 18.95/19.21 >>>> Starting back demodulation with 26.
% 18.95/19.21 >>>> Starting back demodulation with 28.
% 18.95/19.21 >>>> Starting back demodulation with 30.
% 18.95/19.21 >>>> Starting back demodulation with 32.
% 18.95/19.21 >>>> Starting back demodulation with 34.
% 18.95/19.21 >>>> Starting back demodulation with 36.
% 18.95/19.21
% 18.95/19.21 ======= end of input processing =======
% 18.95/19.21
% 18.95/19.21 =========== start of search ===========
% 18.95/19.21
% 18.95/19.21
% 18.95/19.21 Resetting weight limit to 7.
% 18.95/19.21
% 18.95/19.21
% 18.95/19.21 Resetting weight limit to 7.
% 18.95/19.21
% 18.95/19.21 sos_size=2202
% 18.95/19.21
% 18.95/19.21 -- HEY sandbox, WE HAVE A PROOF!! --
% 18.95/19.21
% 18.95/19.21 -----> EMPTY CLAUSE at 17.39 sec ----> 4929 [hyper,4924,11,3437,3402] $F.
% 18.95/19.21
% 18.95/19.21 Length of proof is 45. Level of proof is 12.
% 18.95/19.21
% 18.95/19.21 ---------------- PROOF ----------------
% 18.95/19.21 % SZS status Theorem
% 18.95/19.21 % SZS output start Refutation
% See solution above
% 18.95/19.21 ------------ end of proof -------------
% 18.95/19.21
% 18.95/19.21
% 18.95/19.21 Search stopped by max_proofs option.
% 18.95/19.21
% 18.95/19.21
% 18.95/19.21 Search stopped by max_proofs option.
% 18.95/19.21
% 18.95/19.21 ============ end of search ============
% 18.95/19.21
% 18.95/19.21 -------------- statistics -------------
% 18.95/19.21 clauses given 2417
% 18.95/19.21 clauses generated 1068680
% 18.95/19.21 clauses kept 4697
% 18.95/19.21 clauses forward subsumed 128451
% 18.95/19.21 clauses back subsumed 1995
% 18.95/19.21 Kbytes malloced 5859
% 18.95/19.21
% 18.95/19.21 ----------- times (seconds) -----------
% 18.95/19.21 user CPU time 17.39 (0 hr, 0 min, 17 sec)
% 18.95/19.21 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 18.95/19.21 wall-clock time 18 (0 hr, 0 min, 18 sec)
% 18.95/19.21
% 18.95/19.21 That finishes the proof of the theorem.
% 18.95/19.21
% 18.95/19.21 Process 16305 finished Wed Jul 27 06:38:07 2022
% 18.95/19.21 Otter interrupted
% 18.95/19.21 PROOF FOUND
%------------------------------------------------------------------------------