TSTP Solution File: FLD054-4 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD054-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 12:53:51 EDT 2022
% Result : Unsatisfiable 125.02s 125.29s
% Output : Refutation 125.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 27
% Syntax : Number of clauses : 97 ( 75 unt; 2 nHn; 97 RR)
% Number of literals : 142 ( 0 equ; 46 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( sum(A,B,C)
| ~ sum(A,D,E)
| ~ sum(D,F,B)
| ~ sum(E,F,C) ),
file('FLD054-4.p',unknown),
[] ).
cnf(3,axiom,
( sum(additive_identity,A,A)
| ~ defined(A) ),
file('FLD054-4.p',unknown),
[] ).
cnf(4,axiom,
( sum(additive_inverse(A),A,additive_identity)
| ~ defined(A) ),
file('FLD054-4.p',unknown),
[] ).
cnf(5,axiom,
( sum(A,B,C)
| ~ sum(B,A,C) ),
file('FLD054-4.p',unknown),
[] ).
cnf(6,axiom,
( product(A,B,C)
| ~ product(A,D,E)
| ~ product(D,F,B)
| ~ product(E,F,C) ),
file('FLD054-4.p',unknown),
[] ).
cnf(7,axiom,
( product(A,B,C)
| ~ product(D,E,A)
| ~ product(E,B,F)
| ~ product(D,F,C) ),
file('FLD054-4.p',unknown),
[] ).
cnf(8,axiom,
( product(multiplicative_identity,A,A)
| ~ defined(A) ),
file('FLD054-4.p',unknown),
[] ).
cnf(9,axiom,
( product(multiplicative_inverse(A),A,multiplicative_identity)
| sum(additive_identity,A,additive_identity)
| ~ defined(A) ),
file('FLD054-4.p',unknown),
[] ).
cnf(10,axiom,
( product(A,B,C)
| ~ product(B,A,C) ),
file('FLD054-4.p',unknown),
[] ).
cnf(11,axiom,
( sum(A,B,C)
| ~ sum(D,E,F)
| ~ product(F,G,C)
| ~ product(D,G,A)
| ~ product(E,G,B) ),
file('FLD054-4.p',unknown),
[] ).
cnf(12,axiom,
( product(A,B,C)
| ~ sum(D,E,A)
| ~ product(D,B,F)
| ~ product(E,B,G)
| ~ sum(F,G,C) ),
file('FLD054-4.p',unknown),
[] ).
cnf(14,axiom,
( defined(additive_inverse(A))
| ~ defined(A) ),
file('FLD054-4.p',unknown),
[] ).
cnf(15,axiom,
( defined(multiply(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD054-4.p',unknown),
[] ).
cnf(17,axiom,
( sum(A,B,add(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD054-4.p',unknown),
[] ).
cnf(18,axiom,
( product(A,B,multiply(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD054-4.p',unknown),
[] ).
cnf(25,axiom,
~ sum(additive_identity,a,additive_identity),
file('FLD054-4.p',unknown),
[] ).
cnf(26,axiom,
~ sum(additive_identity,b,additive_identity),
file('FLD054-4.p',unknown),
[] ).
cnf(27,axiom,
~ product(k,multiplicative_inverse(l),u),
file('FLD054-4.p',unknown),
[] ).
cnf(29,plain,
( sum(A,B,B)
| ~ sum(A,C,C)
| ~ sum(C,D,B) ),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.3.4')] ).
cnf(36,plain,
( sum(A,B,A)
| ~ sum(C,D,C)
| ~ product(C,E,A)
| ~ product(D,E,B) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.3.4')] ).
cnf(37,plain,
( sum(A,B,B)
| ~ sum(C,D,D)
| ~ product(D,E,B)
| ~ product(C,E,A) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.3.5')] ).
cnf(40,plain,
( product(A,B,C)
| ~ sum(D,D,A)
| ~ product(D,B,E)
| ~ sum(E,E,C) ),
inference(factor,[status(thm)],[12]),
[iquote('factor,12.3.4')] ).
cnf(42,plain,
( defined(multiply(A,A))
| ~ defined(A) ),
inference(factor,[status(thm)],[15]),
[iquote('factor,15.2.3')] ).
cnf(44,plain,
( product(A,A,multiply(A,A))
| ~ defined(A) ),
inference(factor,[status(thm)],[18]),
[iquote('factor,18.2.3')] ).
cnf(51,axiom,
defined(additive_identity),
file('FLD054-4.p',unknown),
[] ).
cnf(52,axiom,
defined(multiplicative_identity),
file('FLD054-4.p',unknown),
[] ).
cnf(53,axiom,
defined(a),
file('FLD054-4.p',unknown),
[] ).
cnf(54,axiom,
defined(b),
file('FLD054-4.p',unknown),
[] ).
cnf(55,axiom,
defined(u),
file('FLD054-4.p',unknown),
[] ).
cnf(57,axiom,
defined(l),
file('FLD054-4.p',unknown),
[] ).
cnf(58,axiom,
sum(multiplicative_inverse(a),multiplicative_inverse(b),u),
file('FLD054-4.p',unknown),
[] ).
cnf(59,axiom,
sum(a,b,k),
file('FLD054-4.p',unknown),
[] ).
cnf(60,axiom,
product(a,b,l),
file('FLD054-4.p',unknown),
[] ).
cnf(62,plain,
product(additive_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[51,44]),
[iquote('hyper,51,44')] ).
cnf(64,plain,
defined(multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[51,42]),
[iquote('hyper,51,42')] ).
cnf(67,plain,
defined(additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[51,14]),
[iquote('hyper,51,14')] ).
cnf(69,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[51,8]),
[iquote('hyper,51,8')] ).
cnf(70,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(hyper,[status(thm)],[51,4]),
[iquote('hyper,51,4')] ).
cnf(71,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[51,3]),
[iquote('hyper,51,3')] ).
cnf(91,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(hyper,[status(thm)],[52,3]),
[iquote('hyper,52,3')] ).
cnf(117,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[53,9]),25]),
[iquote('hyper,53,9,unit_del,25')] ).
cnf(118,plain,
product(multiplicative_identity,a,a),
inference(hyper,[status(thm)],[53,8]),
[iquote('hyper,53,8')] ).
cnf(120,plain,
sum(additive_identity,a,a),
inference(hyper,[status(thm)],[53,3]),
[iquote('hyper,53,3')] ).
cnf(131,plain,
product(additive_identity,b,multiply(additive_identity,b)),
inference(hyper,[status(thm)],[54,18,51]),
[iquote('hyper,54,18,51')] ).
cnf(155,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[54,9]),26]),
[iquote('hyper,54,9,unit_del,26')] ).
cnf(156,plain,
product(multiplicative_identity,b,b),
inference(hyper,[status(thm)],[54,8]),
[iquote('hyper,54,8')] ).
cnf(158,plain,
sum(additive_identity,b,b),
inference(hyper,[status(thm)],[54,3]),
[iquote('hyper,54,3')] ).
cnf(183,plain,
sum(u,additive_identity,add(u,additive_identity)),
inference(hyper,[status(thm)],[55,17,51]),
[iquote('hyper,55,17,51')] ).
cnf(203,plain,
product(multiplicative_identity,u,u),
inference(hyper,[status(thm)],[55,8]),
[iquote('hyper,55,8')] ).
cnf(205,plain,
sum(additive_identity,u,u),
inference(hyper,[status(thm)],[55,3]),
[iquote('hyper,55,3')] ).
cnf(278,plain,
product(additive_identity,l,multiply(additive_identity,l)),
inference(hyper,[status(thm)],[57,18,51]),
[iquote('hyper,57,18,51')] ).
cnf(323,plain,
( product(multiplicative_inverse(l),l,multiplicative_identity)
| sum(additive_identity,l,additive_identity) ),
inference(hyper,[status(thm)],[57,9]),
[iquote('hyper,57,9')] ).
cnf(324,plain,
product(multiplicative_identity,l,l),
inference(hyper,[status(thm)],[57,8]),
[iquote('hyper,57,8')] ).
cnf(325,plain,
sum(additive_inverse(l),l,additive_identity),
inference(hyper,[status(thm)],[57,4]),
[iquote('hyper,57,4')] ).
cnf(326,plain,
sum(additive_identity,l,l),
inference(hyper,[status(thm)],[57,3]),
[iquote('hyper,57,3')] ).
cnf(400,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[67,3]),
[iquote('hyper,67,3')] ).
cnf(678,plain,
sum(b,a,k),
inference(hyper,[status(thm)],[59,5]),
[iquote('hyper,59,5')] ).
cnf(908,plain,
product(b,a,l),
inference(hyper,[status(thm)],[60,10]),
[iquote('hyper,60,10')] ).
cnf(1474,plain,
sum(additive_identity,multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[64,3]),
[iquote('hyper,64,3')] ).
cnf(1639,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[69,10]),
[iquote('hyper,69,10')] ).
cnf(2193,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[70,5]),
[iquote('hyper,70,5')] ).
cnf(2830,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(hyper,[status(thm)],[91,5]),
[iquote('hyper,91,5')] ).
cnf(9236,plain,
product(b,multiplicative_identity,b),
inference(hyper,[status(thm)],[156,10]),
[iquote('hyper,156,10')] ).
cnf(9239,plain,
sum(b,additive_identity,b),
inference(hyper,[status(thm)],[158,5]),
[iquote('hyper,158,5')] ).
cnf(9765,plain,
product(u,multiplicative_identity,u),
inference(hyper,[status(thm)],[203,10]),
[iquote('hyper,203,10')] ).
cnf(9768,plain,
sum(u,additive_identity,u),
inference(hyper,[status(thm)],[205,5]),
[iquote('hyper,205,5')] ).
cnf(10865,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(hyper,[status(thm)],[117,10]),
[iquote('hyper,117,10')] ).
cnf(10866,plain,
product(multiplicative_inverse(a),l,b),
inference(hyper,[status(thm)],[117,6,60,156]),
[iquote('hyper,117,6,60,156')] ).
cnf(11193,plain,
sum(l,additive_identity,l),
inference(hyper,[status(thm)],[326,5]),
[iquote('hyper,326,5')] ).
cnf(11537,plain,
sum(multiply(additive_identity,b),l,l),
inference(hyper,[status(thm)],[131,37,120,60]),
[iquote('hyper,131,37,120,60')] ).
cnf(11541,plain,
product(b,additive_identity,multiply(additive_identity,b)),
inference(hyper,[status(thm)],[131,10]),
[iquote('hyper,131,10')] ).
cnf(11543,plain,
product(multiplicative_inverse(b),l,a),
inference(hyper,[status(thm)],[155,6,908,118]),
[iquote('hyper,155,6,908,118')] ).
cnf(11553,plain,
sum(l,additive_inverse(l),additive_identity),
inference(hyper,[status(thm)],[325,5]),
[iquote('hyper,325,5')] ).
cnf(11751,plain,
product(u,multiplicative_identity,add(u,additive_identity)),
inference(hyper,[status(thm)],[183,12,9768,9765,1639]),
[iquote('hyper,183,12,9768,9765,1639')] ).
cnf(11752,plain,
product(add(u,additive_identity),multiplicative_identity,u),
inference(hyper,[status(thm)],[183,12,9765,1639,9768]),
[iquote('hyper,183,12,9765,1639,9768')] ).
cnf(11987,plain,
sum(multiply(additive_identity,l),l,l),
inference(hyper,[status(thm)],[278,37,91,324]),
[iquote('hyper,278,37,91,324')] ).
cnf(11989,plain,
product(l,additive_identity,multiply(additive_identity,l)),
inference(hyper,[status(thm)],[278,10]),
[iquote('hyper,278,10')] ).
cnf(12084,plain,
product(l,multiplicative_inverse(a),b),
inference(hyper,[status(thm)],[10865,7,908,9236]),
[iquote('hyper,10865,7,908,9236')] ).
cnf(12115,plain,
product(u,l,k),
inference(hyper,[status(thm)],[11543,12,58,10866,678]),
[iquote('hyper,11543,12,58,10866,678')] ).
cnf(12164,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[400,1,71,2193]),
[iquote('hyper,400,1,71,2193')] ).
cnf(12170,plain,
product(additive_identity,multiplicative_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[12164,40,71,1639]),
[iquote('hyper,12164,40,71,1639')] ).
cnf(12182,plain,
product(multiplicative_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[12170,6,69,1639]),
[iquote('hyper,12170,6,69,1639')] ).
cnf(12323,plain,
product(multiplicative_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[1474,12,2830,69,62]),
[iquote('hyper,1474,12,2830,69,62')] ).
cnf(12389,plain,
sum(multiply(additive_identity,b),additive_identity,additive_identity),
inference(hyper,[status(thm)],[11537,29,11553]),
[iquote('hyper,11537,29,11553')] ).
cnf(12439,plain,
product(add(u,additive_identity),l,k),
inference(hyper,[status(thm)],[11751,7,324,12115]),
[iquote('hyper,11751,7,324,12115')] ).
cnf(12470,plain,
sum(multiply(additive_identity,l),additive_identity,additive_identity),
inference(hyper,[status(thm)],[11987,29,11553]),
[iquote('hyper,11987,29,11553')] ).
cnf(12548,plain,
product(multiply(additive_identity,additive_identity),multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[12323,7,12170,12182]),
[iquote('hyper,12323,7,12170,12182')] ).
cnf(12620,plain,
product(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[12548,6,62,1639]),
[iquote('hyper,12548,6,62,1639')] ).
cnf(12653,plain,
product(l,additive_identity,additive_identity),
inference(hyper,[status(thm)],[12620,12,11193,11989,12470]),
[iquote('hyper,12620,12,11193,11989,12470')] ).
cnf(12657,plain,
product(b,additive_identity,additive_identity),
inference(hyper,[status(thm)],[12620,12,9239,11541,12389]),
[iquote('hyper,12620,12,9239,11541,12389')] ).
cnf(12683,plain,
product(additive_identity,l,additive_identity),
inference(hyper,[status(thm)],[12653,10]),
[iquote('hyper,12653,10')] ).
cnf(12797,plain,
product(additive_identity,b,additive_identity),
inference(hyper,[status(thm)],[12657,10]),
[iquote('hyper,12657,10')] ).
cnf(13039,plain,
product(additive_identity,multiplicative_inverse(a),additive_identity),
inference(hyper,[status(thm)],[12797,7,12683,12084]),
[iquote('hyper,12797,7,12683,12084')] ).
cnf(13143,plain,
product(multiplicative_inverse(l),l,multiplicative_identity),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[13039,36,323,12084]),26]),
[iquote('hyper,13039,36,323,12084,unit_del,26')] ).
cnf(13144,plain,
product(l,multiplicative_inverse(l),multiplicative_identity),
inference(hyper,[status(thm)],[13143,10]),
[iquote('hyper,13143,10')] ).
cnf(13154,plain,
product(k,multiplicative_inverse(l),u),
inference(hyper,[status(thm)],[13144,7,12439,11752]),
[iquote('hyper,13144,7,12439,11752')] ).
cnf(13155,plain,
$false,
inference(binary,[status(thm)],[13154,27]),
[iquote('binary,13154.1,27.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD054-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n018.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 03:10:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.39/1.93 ----- Otter 3.3f, August 2004 -----
% 1.39/1.93 The process was started by sandbox on n018.cluster.edu,
% 1.39/1.93 Wed Jul 27 03:10:46 2022
% 1.39/1.93 The command was "./otter". The process ID is 2414.
% 1.39/1.93
% 1.39/1.93 set(prolog_style_variables).
% 1.39/1.93 set(auto).
% 1.39/1.93 dependent: set(auto1).
% 1.39/1.93 dependent: set(process_input).
% 1.39/1.93 dependent: clear(print_kept).
% 1.39/1.93 dependent: clear(print_new_demod).
% 1.39/1.93 dependent: clear(print_back_demod).
% 1.39/1.93 dependent: clear(print_back_sub).
% 1.39/1.93 dependent: set(control_memory).
% 1.39/1.93 dependent: assign(max_mem, 12000).
% 1.39/1.93 dependent: assign(pick_given_ratio, 4).
% 1.39/1.93 dependent: assign(stats_level, 1).
% 1.39/1.93 dependent: assign(max_seconds, 10800).
% 1.39/1.93 clear(print_given).
% 1.39/1.93
% 1.39/1.93 list(usable).
% 1.39/1.93 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.39/1.93 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.39/1.93 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.39/1.93 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.39/1.93 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.39/1.93 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.39/1.93 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.39/1.93 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.39/1.93 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.39/1.93 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.39/1.93 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.39/1.93 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.39/1.93 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.39/1.93 0 [] defined(additive_identity).
% 1.39/1.93 0 [] defined(additive_inverse(X))| -defined(X).
% 1.39/1.93 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.39/1.93 0 [] defined(multiplicative_identity).
% 1.39/1.93 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.39/1.93 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.39/1.93 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.39/1.93 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.39/1.93 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.39/1.93 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.39/1.93 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.39/1.93 0 [] less_or_e_qual(additive_identity,Z)| -less_or_e_qual(additive_identity,X)| -less_or_e_qual(additive_identity,Y)| -product(X,Y,Z).
% 1.39/1.93 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.39/1.93 0 [] defined(a).
% 1.39/1.93 0 [] defined(b).
% 1.39/1.93 0 [] defined(u).
% 1.39/1.93 0 [] defined(k).
% 1.39/1.93 0 [] defined(l).
% 1.39/1.93 0 [] -sum(additive_identity,a,additive_identity).
% 1.39/1.93 0 [] -sum(additive_identity,b,additive_identity).
% 1.39/1.93 0 [] sum(multiplicative_inverse(a),multiplicative_inverse(b),u).
% 1.39/1.93 0 [] sum(a,b,k).
% 1.39/1.93 0 [] product(a,b,l).
% 1.39/1.93 0 [] -product(k,multiplicative_inverse(l),u).
% 1.39/1.93 end_of_list.
% 1.39/1.93
% 1.39/1.93 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.39/1.93
% 1.39/1.93 This is a non-Horn set without equality. The strategy will
% 1.39/1.93 be ordered hyper_res, unit deletion, and factoring, with
% 1.39/1.93 satellites in sos and with nuclei in usable.
% 1.39/1.93
% 1.39/1.93 dependent: set(hyper_res).
% 1.39/1.93 dependent: set(factor).
% 1.39/1.93 dependent: set(unit_deletion).
% 1.39/1.93
% 1.39/1.93 ------------> process usable:
% 1.39/1.93 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.39/1.93 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.39/1.93 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.39/1.93 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.39/1.93 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.39/1.93 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.39/1.93 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.39/1.93 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.39/1.93 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.39/1.93 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.39/1.93 ** KEPT (pick-wt=20): 11 [] sum(A,B,C)| -sum(D,E,F)| -product(F,G,C)| -product(D,G,A)| -product(E,G,B).
% 1.39/1.93 ** KEPT (pick-wt=20): 12 [] product(A,B,C)| -sum(D,E,A)| -product(D,B,F)| -product(E,B,G)| -sum(F,G,C).
% 1.39/1.93 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 125.02/125.29 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 125.02/125.29 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 125.02/125.29 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 125.02/125.29 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 125.02/125.29 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 125.02/125.29 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 125.02/125.29 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 125.02/125.29 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 125.02/125.29 ** KEPT (pick-wt=14): 22 [] less_or_e_qual(A,B)| -less_or_e_qual(C,D)| -sum(C,E,A)| -sum(D,E,B).
% 125.02/125.29 ** KEPT (pick-wt=13): 23 [] less_or_e_qual(additive_identity,A)| -less_or_e_qual(additive_identity,B)| -less_or_e_qual(additive_identity,C)| -product(B,C,A).
% 125.02/125.29 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 125.02/125.29 ** KEPT (pick-wt=4): 25 [] -sum(additive_identity,a,additive_identity).
% 125.02/125.29 ** KEPT (pick-wt=4): 26 [] -sum(additive_identity,b,additive_identity).
% 125.02/125.29 ** KEPT (pick-wt=5): 27 [] -product(k,multiplicative_inverse(l),u).
% 125.02/125.29
% 125.02/125.29 ------------> process sos:
% 125.02/125.29 ** KEPT (pick-wt=2): 51 [] defined(additive_identity).
% 125.02/125.29 ** KEPT (pick-wt=2): 52 [] defined(multiplicative_identity).
% 125.02/125.29 ** KEPT (pick-wt=2): 53 [] defined(a).
% 125.02/125.29 ** KEPT (pick-wt=2): 54 [] defined(b).
% 125.02/125.29 ** KEPT (pick-wt=2): 55 [] defined(u).
% 125.02/125.29 ** KEPT (pick-wt=2): 56 [] defined(k).
% 125.02/125.29 ** KEPT (pick-wt=2): 57 [] defined(l).
% 125.02/125.29 ** KEPT (pick-wt=6): 58 [] sum(multiplicative_inverse(a),multiplicative_inverse(b),u).
% 125.02/125.29 ** KEPT (pick-wt=4): 59 [] sum(a,b,k).
% 125.02/125.29 ** KEPT (pick-wt=4): 60 [] product(a,b,l).
% 125.02/125.29
% 125.02/125.29 ======= end of input processing =======
% 125.02/125.29
% 125.02/125.29 =========== start of search ===========
% 125.02/125.29
% 125.02/125.29
% 125.02/125.29 Resetting weight limit to 6.
% 125.02/125.29
% 125.02/125.29
% 125.02/125.29 Resetting weight limit to 6.
% 125.02/125.29
% 125.02/125.29 sos_size=8989
% 125.02/125.29
% 125.02/125.29 -- HEY sandbox, WE HAVE A PROOF!! --
% 125.02/125.29
% 125.02/125.29 ----> UNIT CONFLICT at 123.32 sec ----> 13155 [binary,13154.1,27.1] $F.
% 125.02/125.29
% 125.02/125.29 Length of proof is 69. Level of proof is 13.
% 125.02/125.29
% 125.02/125.29 ---------------- PROOF ----------------
% 125.02/125.29 % SZS status Unsatisfiable
% 125.02/125.29 % SZS output start Refutation
% See solution above
% 125.02/125.29 ------------ end of proof -------------
% 125.02/125.29
% 125.02/125.29
% 125.02/125.29 Search stopped by max_proofs option.
% 125.02/125.29
% 125.02/125.29
% 125.02/125.29 Search stopped by max_proofs option.
% 125.02/125.29
% 125.02/125.29 ============ end of search ============
% 125.02/125.29
% 125.02/125.29 -------------- statistics -------------
% 125.02/125.29 clauses given 6143
% 125.02/125.29 clauses generated 88077434
% 125.02/125.29 clauses kept 13154
% 125.02/125.29 clauses forward subsumed 51883
% 125.02/125.29 clauses back subsumed 44
% 125.02/125.29 Kbytes malloced 6835
% 125.02/125.29
% 125.02/125.29 ----------- times (seconds) -----------
% 125.02/125.29 user CPU time 123.32 (0 hr, 2 min, 3 sec)
% 125.02/125.29 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 125.02/125.29 wall-clock time 125 (0 hr, 2 min, 5 sec)
% 125.02/125.29
% 125.02/125.29 That finishes the proof of the theorem.
% 125.02/125.29
% 125.02/125.29 Process 2414 finished Wed Jul 27 03:12:51 2022
% 125.02/125.29 Otter interrupted
% 125.02/125.29 PROOF FOUND
%------------------------------------------------------------------------------