TSTP Solution File: FLD029-3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD029-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 12:53:45 EDT 2022
% Result : Unsatisfiable 53.72s 53.99s
% Output : Refutation 53.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 24
% Syntax : Number of clauses : 80 ( 58 unt; 2 nHn; 80 RR)
% Number of literals : 125 ( 0 equ; 45 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 : 10 ( 10 usr; 6 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('FLD029-3.p',unknown),
[] ).
cnf(3,axiom,
( sum(additive_identity,A,A)
| ~ defined(A) ),
file('FLD029-3.p',unknown),
[] ).
cnf(4,axiom,
( sum(additive_inverse(A),A,additive_identity)
| ~ defined(A) ),
file('FLD029-3.p',unknown),
[] ).
cnf(5,axiom,
( sum(A,B,C)
| ~ sum(B,A,C) ),
file('FLD029-3.p',unknown),
[] ).
cnf(6,axiom,
( product(A,B,C)
| ~ product(A,D,E)
| ~ product(D,F,B)
| ~ product(E,F,C) ),
file('FLD029-3.p',unknown),
[] ).
cnf(7,axiom,
( product(A,B,C)
| ~ product(D,E,A)
| ~ product(E,B,F)
| ~ product(D,F,C) ),
file('FLD029-3.p',unknown),
[] ).
cnf(8,axiom,
( product(multiplicative_identity,A,A)
| ~ defined(A) ),
file('FLD029-3.p',unknown),
[] ).
cnf(9,axiom,
( product(multiplicative_inverse(A),A,multiplicative_identity)
| sum(additive_identity,A,additive_identity)
| ~ defined(A) ),
file('FLD029-3.p',unknown),
[] ).
cnf(10,axiom,
( product(A,B,C)
| ~ product(B,A,C) ),
file('FLD029-3.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('FLD029-3.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('FLD029-3.p',unknown),
[] ).
cnf(14,axiom,
( defined(additive_inverse(A))
| ~ defined(A) ),
file('FLD029-3.p',unknown),
[] ).
cnf(15,axiom,
( defined(multiply(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD029-3.p',unknown),
[] ).
cnf(17,axiom,
( sum(A,B,add(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD029-3.p',unknown),
[] ).
cnf(18,axiom,
( product(A,B,multiply(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD029-3.p',unknown),
[] ).
cnf(25,axiom,
~ sum(additive_identity,b,additive_identity),
file('FLD029-3.p',unknown),
[] ).
cnf(26,axiom,
~ product(multiplicative_identity,u,v),
file('FLD029-3.p',unknown),
[] ).
cnf(28,plain,
( sum(A,B,B)
| ~ sum(A,C,C)
| ~ sum(C,D,B) ),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.3.4')] ).
cnf(35,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(36,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(39,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(41,plain,
( defined(multiply(A,A))
| ~ defined(A) ),
inference(factor,[status(thm)],[15]),
[iquote('factor,15.2.3')] ).
cnf(43,plain,
( product(A,A,multiply(A,A))
| ~ defined(A) ),
inference(factor,[status(thm)],[18]),
[iquote('factor,18.2.3')] ).
cnf(50,axiom,
defined(additive_identity),
file('FLD029-3.p',unknown),
[] ).
cnf(51,axiom,
defined(multiplicative_identity),
file('FLD029-3.p',unknown),
[] ).
cnf(52,axiom,
defined(a),
file('FLD029-3.p',unknown),
[] ).
cnf(53,axiom,
defined(b),
file('FLD029-3.p',unknown),
[] ).
cnf(55,axiom,
defined(v),
file('FLD029-3.p',unknown),
[] ).
cnf(56,axiom,
product(a,u,b),
file('FLD029-3.p',unknown),
[] ).
cnf(57,axiom,
product(a,v,b),
file('FLD029-3.p',unknown),
[] ).
cnf(59,plain,
product(additive_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[50,43]),
[iquote('hyper,50,43')] ).
cnf(61,plain,
defined(multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[50,41]),
[iquote('hyper,50,41')] ).
cnf(64,plain,
defined(additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[50,14]),
[iquote('hyper,50,14')] ).
cnf(66,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[50,8]),
[iquote('hyper,50,8')] ).
cnf(67,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(hyper,[status(thm)],[50,4]),
[iquote('hyper,50,4')] ).
cnf(68,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[50,3]),
[iquote('hyper,50,3')] ).
cnf(86,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(hyper,[status(thm)],[51,8]),
[iquote('hyper,51,8')] ).
cnf(88,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(hyper,[status(thm)],[51,3]),
[iquote('hyper,51,3')] ).
cnf(114,plain,
( product(multiplicative_inverse(a),a,multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(hyper,[status(thm)],[52,9]),
[iquote('hyper,52,9')] ).
cnf(115,plain,
product(multiplicative_identity,a,a),
inference(hyper,[status(thm)],[52,8]),
[iquote('hyper,52,8')] ).
cnf(117,plain,
sum(additive_identity,a,a),
inference(hyper,[status(thm)],[52,3]),
[iquote('hyper,52,3')] ).
cnf(154,plain,
sum(additive_inverse(b),b,additive_identity),
inference(hyper,[status(thm)],[53,4]),
[iquote('hyper,53,4')] ).
cnf(217,plain,
product(additive_identity,v,multiply(additive_identity,v)),
inference(hyper,[status(thm)],[55,18,50]),
[iquote('hyper,55,18,50')] ).
cnf(220,plain,
product(v,a,multiply(v,a)),
inference(hyper,[status(thm)],[55,18,52]),
[iquote('hyper,55,18,52')] ).
cnf(221,plain,
product(v,multiplicative_identity,multiply(v,multiplicative_identity)),
inference(hyper,[status(thm)],[55,18,51]),
[iquote('hyper,55,18,51')] ).
cnf(232,plain,
sum(v,additive_identity,add(v,additive_identity)),
inference(hyper,[status(thm)],[55,17,50]),
[iquote('hyper,55,17,50')] ).
cnf(256,plain,
product(multiplicative_identity,v,v),
inference(hyper,[status(thm)],[55,8]),
[iquote('hyper,55,8')] ).
cnf(258,plain,
sum(additive_identity,v,v),
inference(hyper,[status(thm)],[55,3]),
[iquote('hyper,55,3')] ).
cnf(323,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[64,3]),
[iquote('hyper,64,3')] ).
cnf(574,plain,
product(v,a,b),
inference(hyper,[status(thm)],[57,10]),
[iquote('hyper,57,10')] ).
cnf(1032,plain,
sum(additive_identity,multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[61,3]),
[iquote('hyper,61,3')] ).
cnf(1170,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[66,10]),
[iquote('hyper,66,10')] ).
cnf(1643,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[67,5]),
[iquote('hyper,67,5')] ).
cnf(2199,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(hyper,[status(thm)],[88,5]),
[iquote('hyper,88,5')] ).
cnf(4612,plain,
product(a,multiplicative_identity,a),
inference(hyper,[status(thm)],[115,10]),
[iquote('hyper,115,10')] ).
cnf(10550,plain,
product(v,multiplicative_identity,v),
inference(hyper,[status(thm)],[256,10]),
[iquote('hyper,256,10')] ).
cnf(10555,plain,
sum(v,additive_identity,v),
inference(hyper,[status(thm)],[258,5]),
[iquote('hyper,258,5')] ).
cnf(10803,plain,
sum(b,additive_inverse(b),additive_identity),
inference(hyper,[status(thm)],[154,5]),
[iquote('hyper,154,5')] ).
cnf(11113,plain,
sum(multiply(additive_identity,v),b,b),
inference(hyper,[status(thm)],[217,36,117,57]),
[iquote('hyper,217,36,117,57')] ).
cnf(11117,plain,
product(v,additive_identity,multiply(additive_identity,v)),
inference(hyper,[status(thm)],[217,10]),
[iquote('hyper,217,10')] ).
cnf(11131,plain,
product(a,v,multiply(v,a)),
inference(hyper,[status(thm)],[220,10]),
[iquote('hyper,220,10')] ).
cnf(11133,plain,
product(multiply(v,a),multiplicative_identity,b),
inference(hyper,[status(thm)],[220,7,4612,574]),
[iquote('hyper,220,7,4612,574')] ).
cnf(11149,plain,
product(multiplicative_identity,v,multiply(v,multiplicative_identity)),
inference(hyper,[status(thm)],[221,10]),
[iquote('hyper,221,10')] ).
cnf(11151,plain,
product(multiply(v,multiplicative_identity),multiplicative_identity,v),
inference(hyper,[status(thm)],[221,7,86,10550]),
[iquote('hyper,221,7,86,10550')] ).
cnf(11211,plain,
product(v,multiplicative_identity,add(v,additive_identity)),
inference(hyper,[status(thm)],[232,12,10555,10550,1170]),
[iquote('hyper,232,12,10555,10550,1170')] ).
cnf(11232,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[323,1,68,1643]),
[iquote('hyper,323,1,68,1643')] ).
cnf(11238,plain,
product(additive_identity,multiplicative_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[11232,39,68,1170]),
[iquote('hyper,11232,39,68,1170')] ).
cnf(11249,plain,
product(multiplicative_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[11238,6,66,1170]),
[iquote('hyper,11238,6,66,1170')] ).
cnf(11348,plain,
product(multiplicative_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[1032,12,2199,66,59]),
[iquote('hyper,1032,12,2199,66,59')] ).
cnf(11472,plain,
sum(multiply(additive_identity,v),additive_identity,additive_identity),
inference(hyper,[status(thm)],[11113,28,10803]),
[iquote('hyper,11113,28,10803')] ).
cnf(11491,plain,
product(multiplicative_identity,add(v,additive_identity),v),
inference(hyper,[status(thm)],[11211,6,11149,11151]),
[iquote('hyper,11211,6,11149,11151')] ).
cnf(11492,plain,
product(a,add(v,additive_identity),b),
inference(hyper,[status(thm)],[11211,6,11131,11133]),
[iquote('hyper,11211,6,11131,11133')] ).
cnf(11518,plain,
product(multiply(additive_identity,additive_identity),multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[11348,7,11238,11249]),
[iquote('hyper,11348,7,11238,11249')] ).
cnf(11575,plain,
product(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[11518,6,59,1170]),
[iquote('hyper,11518,6,59,1170')] ).
cnf(11604,plain,
product(v,additive_identity,additive_identity),
inference(hyper,[status(thm)],[11575,12,10555,11117,11472]),
[iquote('hyper,11575,12,10555,11117,11472')] ).
cnf(11629,plain,
product(additive_identity,v,additive_identity),
inference(hyper,[status(thm)],[11604,10]),
[iquote('hyper,11604,10')] ).
cnf(11778,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[11629,35,114,57]),25]),
[iquote('hyper,11629,35,114,57,unit_del,25')] ).
cnf(11953,plain,
product(multiplicative_inverse(a),b,v),
inference(hyper,[status(thm)],[11778,6,11492,11491]),
[iquote('hyper,11778,6,11492,11491')] ).
cnf(11975,plain,
product(multiplicative_identity,u,v),
inference(hyper,[status(thm)],[11953,7,11778,56]),
[iquote('hyper,11953,7,11778,56')] ).
cnf(11976,plain,
$false,
inference(binary,[status(thm)],[11975,26]),
[iquote('binary,11975.1,26.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD029-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 03:20:07 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 sandbox2 on n019.cluster.edu,
% 1.73/1.93 Wed Jul 27 03:20:07 2022
% 1.73/1.93 The command was "./otter". The process ID is 25599.
% 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 list(usable).
% 1.73/1.93 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.73/1.93 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.73/1.93 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.73/1.93 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.73/1.93 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.73/1.93 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.73/1.93 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.73/1.93 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.73/1.93 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.73/1.93 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.73/1.93 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.73/1.93 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.73/1.93 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.73/1.93 0 [] defined(additive_identity).
% 1.73/1.93 0 [] defined(additive_inverse(X))| -defined(X).
% 1.73/1.93 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.73/1.93 0 [] defined(multiplicative_identity).
% 1.73/1.93 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.73/1.93 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.73/1.93 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.73/1.93 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.73/1.93 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.73/1.93 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.73/1.93 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.73/1.93 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).
% 1.73/1.93 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.73/1.93 0 [] defined(a).
% 1.73/1.93 0 [] defined(b).
% 1.73/1.93 0 [] defined(u).
% 1.73/1.93 0 [] defined(v).
% 1.73/1.93 0 [] -sum(additive_identity,b,additive_identity).
% 1.73/1.93 0 [] product(a,u,b).
% 1.73/1.93 0 [] product(a,v,b).
% 1.73/1.93 0 [] -product(multiplicative_identity,u,v).
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.73/1.93
% 1.73/1.93 This is a non-Horn set without equality. The strategy will
% 1.73/1.93 be ordered hyper_res, unit deletion, and factoring, with
% 1.73/1.93 satellites in sos and with nuclei in usable.
% 1.73/1.93
% 1.73/1.93 dependent: set(hyper_res).
% 1.73/1.93 dependent: set(factor).
% 1.73/1.93 dependent: set(unit_deletion).
% 1.73/1.93
% 1.73/1.93 ------------> process usable:
% 1.73/1.93 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.73/1.93 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.73/1.93 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.73/1.93 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.73/1.93 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.73/1.93 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.73/1.93 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.73/1.93 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.73/1.93 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.73/1.93 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** 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).
% 1.73/1.93 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 1.73/1.93 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 53.72/53.99 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 53.72/53.99 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 53.72/53.99 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 53.72/53.99 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 53.72/53.99 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 53.72/53.99 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 53.72/53.99 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 53.72/53.99 ** 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).
% 53.72/53.99 ** 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).
% 53.72/53.99 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 53.72/53.99 ** KEPT (pick-wt=4): 25 [] -sum(additive_identity,b,additive_identity).
% 53.72/53.99 ** KEPT (pick-wt=4): 26 [] -product(multiplicative_identity,u,v).
% 53.72/53.99
% 53.72/53.99 ------------> process sos:
% 53.72/53.99 ** KEPT (pick-wt=2): 50 [] defined(additive_identity).
% 53.72/53.99 ** KEPT (pick-wt=2): 51 [] defined(multiplicative_identity).
% 53.72/53.99 ** KEPT (pick-wt=2): 52 [] defined(a).
% 53.72/53.99 ** KEPT (pick-wt=2): 53 [] defined(b).
% 53.72/53.99 ** KEPT (pick-wt=2): 54 [] defined(u).
% 53.72/53.99 ** KEPT (pick-wt=2): 55 [] defined(v).
% 53.72/53.99 ** KEPT (pick-wt=4): 56 [] product(a,u,b).
% 53.72/53.99 ** KEPT (pick-wt=4): 57 [] product(a,v,b).
% 53.72/53.99
% 53.72/53.99 ======= end of input processing =======
% 53.72/53.99
% 53.72/53.99 =========== start of search ===========
% 53.72/53.99
% 53.72/53.99
% 53.72/53.99 Resetting weight limit to 6.
% 53.72/53.99
% 53.72/53.99
% 53.72/53.99 Resetting weight limit to 6.
% 53.72/53.99
% 53.72/53.99 sos_size=9400
% 53.72/53.99
% 53.72/53.99 -- HEY sandbox2, WE HAVE A PROOF!! --
% 53.72/53.99
% 53.72/53.99 ----> UNIT CONFLICT at 52.05 sec ----> 11976 [binary,11975.1,26.1] $F.
% 53.72/53.99
% 53.72/53.99 Length of proof is 55. Level of proof is 12.
% 53.72/53.99
% 53.72/53.99 ---------------- PROOF ----------------
% 53.72/53.99 % SZS status Unsatisfiable
% 53.72/53.99 % SZS output start Refutation
% See solution above
% 53.72/53.99 ------------ end of proof -------------
% 53.72/53.99
% 53.72/53.99
% 53.72/53.99 Search stopped by max_proofs option.
% 53.72/53.99
% 53.72/53.99
% 53.72/53.99 Search stopped by max_proofs option.
% 53.72/53.99
% 53.72/53.99 ============ end of search ============
% 53.72/53.99
% 53.72/53.99 -------------- statistics -------------
% 53.72/53.99 clauses given 4088
% 53.72/53.99 clauses generated 36543091
% 53.72/53.99 clauses kept 11975
% 53.72/53.99 clauses forward subsumed 36967
% 53.72/53.99 clauses back subsumed 45
% 53.72/53.99 Kbytes malloced 6835
% 53.72/53.99
% 53.72/53.99 ----------- times (seconds) -----------
% 53.72/53.99 user CPU time 52.05 (0 hr, 0 min, 52 sec)
% 53.72/53.99 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 53.72/53.99 wall-clock time 53 (0 hr, 0 min, 53 sec)
% 53.72/53.99
% 53.72/53.99 That finishes the proof of the theorem.
% 53.72/53.99
% 53.72/53.99 Process 25599 finished Wed Jul 27 03:21:00 2022
% 53.72/53.99 Otter interrupted
% 53.72/53.99 PROOF FOUND
%------------------------------------------------------------------------------