%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : FLD012-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 12:53:42 EDT 2022
% Result : Unsatisfiable 58.46s 58.65s
% Output : Refutation 58.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 27
% Syntax : Number of clauses : 98 ( 74 unt; 2 nHn; 98 RR)
% Number of literals : 148 ( 0 equ; 51 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 : 80 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( sum(A,B,C)
| ~ sum(A,D,E)
| ~ sum(D,F,B)
| ~ sum(E,F,C) ),
file('FLD012-4.p',unknown),
[] ).
cnf(2,axiom,
( sum(A,B,C)
| ~ sum(D,E,A)
| ~ sum(E,B,F)
| ~ sum(D,F,C) ),
file('FLD012-4.p',unknown),
[] ).
cnf(3,axiom,
( sum(additive_identity,A,A)
| ~ defined(A) ),
file('FLD012-4.p',unknown),
[] ).
cnf(4,axiom,
( sum(additive_inverse(A),A,additive_identity)
| ~ defined(A) ),
file('FLD012-4.p',unknown),
[] ).
cnf(5,axiom,
( sum(A,B,C)
| ~ sum(B,A,C) ),
file('FLD012-4.p',unknown),
[] ).
cnf(6,axiom,
( product(A,B,C)
| ~ product(A,D,E)
| ~ product(D,F,B)
| ~ product(E,F,C) ),
file('FLD012-4.p',unknown),
[] ).
cnf(7,axiom,
( product(A,B,C)
| ~ product(D,E,A)
| ~ product(E,B,F)
| ~ product(D,F,C) ),
file('FLD012-4.p',unknown),
[] ).
cnf(8,axiom,
( product(multiplicative_identity,A,A)
| ~ defined(A) ),
file('FLD012-4.p',unknown),
[] ).
cnf(9,axiom,
( product(multiplicative_inverse(A),A,multiplicative_identity)
| sum(additive_identity,A,additive_identity)
| ~ defined(A) ),
file('FLD012-4.p',unknown),
[] ).
cnf(10,axiom,
( product(A,B,C)
| ~ product(B,A,C) ),
file('FLD012-4.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('FLD012-4.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('FLD012-4.p',unknown),
[] ).
cnf(14,axiom,
( defined(additive_inverse(A))
| ~ defined(A) ),
file('FLD012-4.p',unknown),
[] ).
cnf(15,axiom,
( defined(multiply(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD012-4.p',unknown),
[] ).
cnf(17,axiom,
( sum(A,B,add(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD012-4.p',unknown),
[] ).
cnf(18,axiom,
( product(A,B,multiply(A,B))
| ~ defined(A)
| ~ defined(B) ),
file('FLD012-4.p',unknown),
[] ).
cnf(25,axiom,
~ sum(additive_identity,a,additive_identity),
file('FLD012-4.p',unknown),
[] ).
cnf(26,axiom,
~ sum(additive_identity,b,additive_identity),
file('FLD012-4.p',unknown),
[] ).
cnf(27,axiom,
~ product(multiplicative_identity,multiplicative_inverse(u),v),
file('FLD012-4.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(30,plain,
( sum(A,B,A)
| ~ sum(C,D,A)
| ~ sum(D,B,D) ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.2.4')] ).
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('FLD012-4.p',unknown),
[] ).
cnf(52,axiom,
defined(multiplicative_identity),
file('FLD012-4.p',unknown),
[] ).
cnf(53,axiom,
defined(a),
file('FLD012-4.p',unknown),
[] ).
cnf(54,axiom,
defined(b),
file('FLD012-4.p',unknown),
[] ).
cnf(55,axiom,
defined(u),
file('FLD012-4.p',unknown),
[] ).
cnf(56,axiom,
defined(v),
file('FLD012-4.p',unknown),
[] ).
cnf(57,axiom,
product(a,b,u),
file('FLD012-4.p',unknown),
[] ).
cnf(58,axiom,
product(multiplicative_inverse(a),multiplicative_inverse(b),v),
file('FLD012-4.p',unknown),
[] ).
cnf(60,plain,
product(additive_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[51,44]),
[iquote('hyper,51,44')] ).
cnf(62,plain,
defined(multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[51,42]),
[iquote('hyper,51,42')] ).
cnf(65,plain,
defined(additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[51,14]),
[iquote('hyper,51,14')] ).
cnf(67,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[51,8]),
[iquote('hyper,51,8')] ).
cnf(68,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(hyper,[status(thm)],[51,4]),
[iquote('hyper,51,4')] ).
cnf(69,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[51,3]),
[iquote('hyper,51,3')] ).
cnf(89,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(hyper,[status(thm)],[52,3]),
[iquote('hyper,52,3')] ).
cnf(115,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(116,plain,
product(multiplicative_identity,a,a),
inference(hyper,[status(thm)],[53,8]),
[iquote('hyper,53,8')] ).
cnf(118,plain,
sum(additive_identity,a,a),
inference(hyper,[status(thm)],[53,3]),
[iquote('hyper,53,3')] ).
cnf(129,plain,
product(additive_identity,b,multiply(additive_identity,b)),
inference(hyper,[status(thm)],[54,18,51]),
[iquote('hyper,54,18,51')] ).
cnf(153,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(154,plain,
product(multiplicative_identity,b,b),
inference(hyper,[status(thm)],[54,8]),
[iquote('hyper,54,8')] ).
cnf(156,plain,
sum(additive_identity,b,b),
inference(hyper,[status(thm)],[54,3]),
[iquote('hyper,54,3')] ).
cnf(169,plain,
product(additive_identity,u,multiply(additive_identity,u)),
inference(hyper,[status(thm)],[55,18,51]),
[iquote('hyper,55,18,51')] ).
cnf(200,plain,
( product(multiplicative_inverse(u),u,multiplicative_identity)
| sum(additive_identity,u,additive_identity) ),
inference(hyper,[status(thm)],[55,9]),
[iquote('hyper,55,9')] ).
cnf(201,plain,
product(multiplicative_identity,u,u),
inference(hyper,[status(thm)],[55,8]),
[iquote('hyper,55,8')] ).
cnf(202,plain,
sum(additive_inverse(u),u,additive_identity),
inference(hyper,[status(thm)],[55,4]),
[iquote('hyper,55,4')] ).
cnf(218,plain,
product(additive_identity,v,multiply(additive_identity,v)),
inference(hyper,[status(thm)],[56,18,51]),
[iquote('hyper,56,18,51')] ).
cnf(233,plain,
sum(v,additive_identity,add(v,additive_identity)),
inference(hyper,[status(thm)],[56,17,51]),
[iquote('hyper,56,17,51')] ).
cnf(257,plain,
product(multiplicative_identity,v,v),
inference(hyper,[status(thm)],[56,8]),
[iquote('hyper,56,8')] ).
cnf(258,plain,
sum(additive_inverse(v),v,additive_identity),
inference(hyper,[status(thm)],[56,4]),
[iquote('hyper,56,4')] ).
cnf(259,plain,
sum(additive_identity,v,v),
inference(hyper,[status(thm)],[56,3]),
[iquote('hyper,56,3')] ).
cnf(324,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[65,3]),
[iquote('hyper,65,3')] ).
cnf(399,plain,
product(b,a,u),
inference(hyper,[status(thm)],[57,10]),
[iquote('hyper,57,10')] ).
cnf(1170,plain,
sum(additive_identity,multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[62,3]),
[iquote('hyper,62,3')] ).
cnf(1317,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[67,10]),
[iquote('hyper,67,10')] ).
cnf(1644,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[68,5]),
[iquote('hyper,68,5')] ).
cnf(2400,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(hyper,[status(thm)],[89,5]),
[iquote('hyper,89,5')] ).
cnf(9555,plain,
product(b,multiplicative_identity,b),
inference(hyper,[status(thm)],[154,10]),
[iquote('hyper,154,10')] ).
cnf(9558,plain,
sum(b,additive_identity,b),
inference(hyper,[status(thm)],[156,5]),
[iquote('hyper,156,5')] ).
cnf(10576,plain,
product(v,multiplicative_identity,v),
inference(hyper,[status(thm)],[257,10]),
[iquote('hyper,257,10')] ).
cnf(10579,plain,
sum(v,additive_identity,v),
inference(hyper,[status(thm)],[259,5]),
[iquote('hyper,259,5')] ).
cnf(10836,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(hyper,[status(thm)],[115,10]),
[iquote('hyper,115,10')] ).
cnf(10852,plain,
product(multiplicative_inverse(b),u,a),
inference(hyper,[status(thm)],[153,6,399,116]),
[iquote('hyper,153,6,399,116')] ).
cnf(10854,plain,
sum(u,additive_inverse(u),additive_identity),
inference(hyper,[status(thm)],[202,5]),
[iquote('hyper,202,5')] ).
cnf(10855,plain,
sum(v,additive_inverse(v),additive_identity),
inference(hyper,[status(thm)],[258,5]),
[iquote('hyper,258,5')] ).
cnf(10891,plain,
sum(multiply(additive_identity,b),u,u),
inference(hyper,[status(thm)],[129,37,118,57]),
[iquote('hyper,129,37,118,57')] ).
cnf(10895,plain,
product(b,additive_identity,multiply(additive_identity,b)),
inference(hyper,[status(thm)],[129,10]),
[iquote('hyper,129,10')] ).
cnf(11010,plain,
sum(u,multiply(additive_identity,u),u),
inference(hyper,[status(thm)],[169,36,2400,201]),
[iquote('hyper,169,36,2400,201')] ).
cnf(11148,plain,
sum(multiply(additive_identity,v),v,v),
inference(hyper,[status(thm)],[218,37,89,257]),
[iquote('hyper,218,37,89,257')] ).
cnf(11241,plain,
product(v,multiplicative_identity,add(v,additive_identity)),
inference(hyper,[status(thm)],[233,12,10579,10576,1317]),
[iquote('hyper,233,12,10579,10576,1317')] ).
cnf(11242,plain,
product(add(v,additive_identity),multiplicative_identity,v),
inference(hyper,[status(thm)],[233,12,10576,1317,10579]),
[iquote('hyper,233,12,10576,1317,10579')] ).
cnf(11271,plain,
product(u,multiplicative_inverse(a),b),
inference(hyper,[status(thm)],[10836,7,399,9555]),
[iquote('hyper,10836,7,399,9555')] ).
cnf(11273,plain,
product(v,u,multiplicative_identity),
inference(hyper,[status(thm)],[10852,7,58,115]),
[iquote('hyper,10852,7,58,115')] ).
cnf(11282,plain,
product(multiply(additive_identity,v),u,additive_identity),
inference(hyper,[status(thm)],[11273,7,218,1317]),
[iquote('hyper,11273,7,218,1317')] ).
cnf(11333,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[324,1,69,1644]),
[iquote('hyper,324,1,69,1644')] ).
cnf(11340,plain,
product(additive_identity,multiplicative_identity,additive_inverse(additive_identity)),
inference(hyper,[status(thm)],[11333,40,69,1317]),
[iquote('hyper,11333,40,69,1317')] ).
cnf(11351,plain,
product(multiplicative_identity,additive_inverse(additive_identity),additive_identity),
inference(hyper,[status(thm)],[11340,6,67,1317]),
[iquote('hyper,11340,6,67,1317')] ).
cnf(11480,plain,
product(multiplicative_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(hyper,[status(thm)],[1170,12,2400,67,60]),
[iquote('hyper,1170,12,2400,67,60')] ).
cnf(11539,plain,
sum(multiply(additive_identity,b),additive_identity,additive_identity),
inference(hyper,[status(thm)],[10891,29,10854]),
[iquote('hyper,10891,29,10854')] ).
cnf(11563,plain,
sum(additive_identity,multiply(additive_identity,u),additive_identity),
inference(hyper,[status(thm)],[11010,30,202]),
[iquote('hyper,11010,30,202')] ).
cnf(11596,plain,
sum(multiply(additive_identity,v),additive_identity,additive_identity),
inference(hyper,[status(thm)],[11148,29,10855]),
[iquote('hyper,11148,29,10855')] ).
cnf(11617,plain,
product(add(v,additive_identity),u,multiplicative_identity),
inference(hyper,[status(thm)],[11241,7,201,11273]),
[iquote('hyper,11241,7,201,11273')] ).
cnf(11664,plain,
product(multiply(additive_identity,additive_identity),multiplicative_identity,additive_identity),
inference(hyper,[status(thm)],[11480,7,11340,11351]),
[iquote('hyper,11480,7,11340,11351')] ).
cnf(11698,plain,
product(additive_identity,u,additive_identity),
inference(hyper,[status(thm)],[11596,12,11282,169,11563]),
[iquote('hyper,11596,12,11282,169,11563')] ).
cnf(11844,plain,
product(additive_identity,additive_identity,additive_identity),
inference(hyper,[status(thm)],[11664,6,60,1317]),
[iquote('hyper,11664,6,60,1317')] ).
cnf(11863,plain,
product(b,additive_identity,additive_identity),
inference(hyper,[status(thm)],[11844,12,9558,10895,11539]),
[iquote('hyper,11844,12,9558,10895,11539')] ).
cnf(11892,plain,
product(additive_identity,b,additive_identity),
inference(hyper,[status(thm)],[11863,10]),
[iquote('hyper,11863,10')] ).
cnf(12003,plain,
product(additive_identity,multiplicative_inverse(a),additive_identity),
inference(hyper,[status(thm)],[11892,7,11698,11271]),
[iquote('hyper,11892,7,11698,11271')] ).
cnf(12082,plain,
product(multiplicative_inverse(u),u,multiplicative_identity),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[12003,36,200,11271]),26]),
[iquote('hyper,12003,36,200,11271,unit_del,26')] ).
cnf(12083,plain,
product(u,multiplicative_inverse(u),multiplicative_identity),
inference(hyper,[status(thm)],[12082,10]),
[iquote('hyper,12082,10')] ).
cnf(12093,plain,
product(multiplicative_identity,multiplicative_inverse(u),v),
inference(hyper,[status(thm)],[12083,7,11617,11242]),
[iquote('hyper,12083,7,11617,11242')] ).
cnf(12094,plain,
$false,
inference(binary,[status(thm)],[12093,27]),
[iquote('binary,12093.1,27.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD012-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 03:26:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.14 ----- Otter 3.3f, August 2004 -----
% 1.96/2.14 The process was started by sandbox2 on n015.cluster.edu,
% 1.96/2.14 Wed Jul 27 03:26:26 2022
% 1.96/2.14 The command was "./otter". The process ID is 13025.
% 1.96/2.14
% 1.96/2.14 set(prolog_style_variables).
% 1.96/2.14 set(auto).
% 1.96/2.14 dependent: set(auto1).
% 1.96/2.14 dependent: set(process_input).
% 1.96/2.14 dependent: clear(print_kept).
% 1.96/2.14 dependent: clear(print_new_demod).
% 1.96/2.14 dependent: clear(print_back_demod).
% 1.96/2.14 dependent: clear(print_back_sub).
% 1.96/2.14 dependent: set(control_memory).
% 1.96/2.14 dependent: assign(max_mem, 12000).
% 1.96/2.14 dependent: assign(pick_given_ratio, 4).
% 1.96/2.14 dependent: assign(stats_level, 1).
% 1.96/2.14 dependent: assign(max_seconds, 10800).
% 1.96/2.14 clear(print_given).
% 1.96/2.14
% 1.96/2.14 list(usable).
% 1.96/2.14 0 [] sum(X,V,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W).
% 1.96/2.14 0 [] sum(U,Z,W)| -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W).
% 1.96/2.14 0 [] sum(additive_identity,X,X)| -defined(X).
% 1.96/2.14 0 [] sum(additive_inverse(X),X,additive_identity)| -defined(X).
% 1.96/2.14 0 [] sum(Y,X,Z)| -sum(X,Y,Z).
% 1.96/2.14 0 [] product(X,V,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W).
% 1.96/2.14 0 [] product(U,Z,W)| -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W).
% 1.96/2.14 0 [] product(multiplicative_identity,X,X)| -defined(X).
% 1.96/2.14 0 [] product(multiplicative_inverse(X),X,multiplicative_identity)|sum(additive_identity,X,additive_identity)| -defined(X).
% 1.96/2.14 0 [] product(Y,X,Z)| -product(X,Y,Z).
% 1.96/2.14 0 [] sum(C,D,B)| -sum(X,Y,A)| -product(A,Z,B)| -product(X,Z,C)| -product(Y,Z,D).
% 1.96/2.14 0 [] product(A,Z,B)| -sum(X,Y,A)| -product(X,Z,C)| -product(Y,Z,D)| -sum(C,D,B).
% 1.96/2.14 0 [] defined(add(X,Y))| -defined(X)| -defined(Y).
% 1.96/2.14 0 [] defined(additive_identity).
% 1.96/2.14 0 [] defined(additive_inverse(X))| -defined(X).
% 1.96/2.14 0 [] defined(multiply(X,Y))| -defined(X)| -defined(Y).
% 1.96/2.14 0 [] defined(multiplicative_identity).
% 1.96/2.14 0 [] defined(multiplicative_inverse(X))| -defined(X)|sum(additive_identity,X,additive_identity).
% 1.96/2.14 0 [] sum(X,Y,add(X,Y))| -defined(X)| -defined(Y).
% 1.96/2.14 0 [] product(X,Y,multiply(X,Y))| -defined(X)| -defined(Y).
% 1.96/2.14 0 [] sum(additive_identity,X,Y)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,X).
% 1.96/2.14 0 [] less_or_e_qual(X,Z)| -less_or_e_qual(X,Y)| -less_or_e_qual(Y,Z).
% 1.96/2.14 0 [] less_or_e_qual(X,Y)|less_or_e_qual(Y,X)| -defined(X)| -defined(Y).
% 1.96/2.14 0 [] less_or_e_qual(U,V)| -less_or_e_qual(X,Y)| -sum(X,Z,U)| -sum(Y,Z,V).
% 1.96/2.14 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).
% 1.96/2.14 0 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 1.96/2.14 0 [] defined(a).
% 1.96/2.14 0 [] defined(b).
% 1.96/2.14 0 [] defined(u).
% 1.96/2.14 0 [] defined(v).
% 1.96/2.14 0 [] -sum(additive_identity,a,additive_identity).
% 1.96/2.14 0 [] -sum(additive_identity,b,additive_identity).
% 1.96/2.14 0 [] product(a,b,u).
% 1.96/2.14 0 [] product(multiplicative_inverse(a),multiplicative_inverse(b),v).
% 1.96/2.14 0 [] -product(multiplicative_identity,multiplicative_inverse(u),v).
% 1.96/2.14 end_of_list.
% 1.96/2.14
% 1.96/2.14 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.96/2.14
% 1.96/2.14 This is a non-Horn set without equality. The strategy will
% 1.96/2.14 be ordered hyper_res, unit deletion, and factoring, with
% 1.96/2.14 satellites in sos and with nuclei in usable.
% 1.96/2.14
% 1.96/2.14 dependent: set(hyper_res).
% 1.96/2.14 dependent: set(factor).
% 1.96/2.14 dependent: set(unit_deletion).
% 1.96/2.14
% 1.96/2.14 ------------> process usable:
% 1.96/2.14 ** KEPT (pick-wt=16): 1 [] sum(A,B,C)| -sum(A,D,E)| -sum(D,F,B)| -sum(E,F,C).
% 1.96/2.14 ** KEPT (pick-wt=16): 2 [] sum(A,B,C)| -sum(D,E,A)| -sum(E,B,F)| -sum(D,F,C).
% 1.96/2.14 ** KEPT (pick-wt=6): 3 [] sum(additive_identity,A,A)| -defined(A).
% 1.96/2.14 ** KEPT (pick-wt=7): 4 [] sum(additive_inverse(A),A,additive_identity)| -defined(A).
% 1.96/2.14 ** KEPT (pick-wt=8): 5 [] sum(A,B,C)| -sum(B,A,C).
% 1.96/2.14 ** KEPT (pick-wt=16): 6 [] product(A,B,C)| -product(A,D,E)| -product(D,F,B)| -product(E,F,C).
% 1.96/2.14 ** KEPT (pick-wt=16): 7 [] product(A,B,C)| -product(D,E,A)| -product(E,B,F)| -product(D,F,C).
% 1.96/2.14 ** KEPT (pick-wt=6): 8 [] product(multiplicative_identity,A,A)| -defined(A).
% 1.96/2.14 ** KEPT (pick-wt=11): 9 [] product(multiplicative_inverse(A),A,multiplicative_identity)|sum(additive_identity,A,additive_identity)| -defined(A).
% 1.96/2.14 ** KEPT (pick-wt=8): 10 [] product(A,B,C)| -product(B,A,C).
% 1.96/2.14 ** 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).
% 1.96/2.14 ** 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).
% 1.96/2.14 ** KEPT (pick-wt=8): 13 [] defined(add(A,B))| -defined(A)| -defined(B).
% 58.46/58.65 ** KEPT (pick-wt=5): 14 [] defined(additive_inverse(A))| -defined(A).
% 58.46/58.65 ** KEPT (pick-wt=8): 15 [] defined(multiply(A,B))| -defined(A)| -defined(B).
% 58.46/58.65 ** KEPT (pick-wt=9): 16 [] defined(multiplicative_inverse(A))| -defined(A)|sum(additive_identity,A,additive_identity).
% 58.46/58.65 ** KEPT (pick-wt=10): 17 [] sum(A,B,add(A,B))| -defined(A)| -defined(B).
% 58.46/58.65 ** KEPT (pick-wt=10): 18 [] product(A,B,multiply(A,B))| -defined(A)| -defined(B).
% 58.46/58.65 ** KEPT (pick-wt=10): 19 [] sum(additive_identity,A,B)| -less_or_e_qual(A,B)| -less_or_e_qual(B,A).
% 58.46/58.65 ** KEPT (pick-wt=9): 20 [] less_or_e_qual(A,B)| -less_or_e_qual(A,C)| -less_or_e_qual(C,B).
% 58.46/58.65 ** KEPT (pick-wt=10): 21 [] less_or_e_qual(A,B)|less_or_e_qual(B,A)| -defined(A)| -defined(B).
% 58.46/58.65 ** 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).
% 58.46/58.65 ** 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).
% 58.46/58.65 ** KEPT (pick-wt=4): 24 [] -sum(additive_identity,additive_identity,multiplicative_identity).
% 58.46/58.65 ** KEPT (pick-wt=4): 25 [] -sum(additive_identity,a,additive_identity).
% 58.46/58.65 ** KEPT (pick-wt=4): 26 [] -sum(additive_identity,b,additive_identity).
% 58.46/58.65 ** KEPT (pick-wt=5): 27 [] -product(multiplicative_identity,multiplicative_inverse(u),v).
% 58.46/58.65
% 58.46/58.65 ------------> process sos:
% 58.46/58.65 ** KEPT (pick-wt=2): 51 [] defined(additive_identity).
% 58.46/58.65 ** KEPT (pick-wt=2): 52 [] defined(multiplicative_identity).
% 58.46/58.65 ** KEPT (pick-wt=2): 53 [] defined(a).
% 58.46/58.65 ** KEPT (pick-wt=2): 54 [] defined(b).
% 58.46/58.65 ** KEPT (pick-wt=2): 55 [] defined(u).
% 58.46/58.65 ** KEPT (pick-wt=2): 56 [] defined(v).
% 58.46/58.65 ** KEPT (pick-wt=4): 57 [] product(a,b,u).
% 58.46/58.65 ** KEPT (pick-wt=6): 58 [] product(multiplicative_inverse(a),multiplicative_inverse(b),v).
% 58.46/58.65
% 58.46/58.65 ======= end of input processing =======
% 58.46/58.65
% 58.46/58.65 =========== start of search ===========
% 58.46/58.65
% 58.46/58.65
% 58.46/58.65 Resetting weight limit to 6.
% 58.46/58.65
% 58.46/58.65
% 58.46/58.65 Resetting weight limit to 6.
% 58.46/58.65
% 58.46/58.65 sos_size=9400
% 58.46/58.65
% 58.46/58.65 -- HEY sandbox2, WE HAVE A PROOF!! --
% 58.46/58.65
% 58.46/58.65 ----> UNIT CONFLICT at 56.50 sec ----> 12094 [binary,12093.1,27.1] $F.
% 58.46/58.65
% 58.46/58.65 Length of proof is 70. Level of proof is 13.
% 58.46/58.65
% 58.46/58.65 ---------------- PROOF ----------------
% 58.46/58.65 % SZS status Unsatisfiable
% 58.46/58.65 % SZS output start Refutation
% See solution above
% 58.46/58.65 ------------ end of proof -------------
% 58.46/58.65
% 58.46/58.65
% 58.46/58.65 Search stopped by max_proofs option.
% 58.46/58.65
% 58.46/58.65
% 58.46/58.65 Search stopped by max_proofs option.
% 58.46/58.65
% 58.46/58.65 ============ end of search ============
% 58.46/58.65
% 58.46/58.65 -------------- statistics -------------
% 58.46/58.65 clauses given 4308
% 58.46/58.65 clauses generated 39444612
% 58.46/58.65 clauses kept 12093
% 58.46/58.65 clauses forward subsumed 44152
% 58.46/58.65 clauses back subsumed 44
% 58.46/58.65 Kbytes malloced 6835
% 58.46/58.65
% 58.46/58.65 ----------- times (seconds) -----------
% 58.46/58.65 user CPU time 56.50 (0 hr, 0 min, 56 sec)
% 58.46/58.65 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 58.46/58.65 wall-clock time 59 (0 hr, 0 min, 59 sec)
% 58.46/58.65
% 58.46/58.65 That finishes the proof of the theorem.
% 58.46/58.65
% 58.46/58.65 Process 13025 finished Wed Jul 27 03:27:25 2022
% 58.46/58.65 Otter interrupted
% 58.46/58.65 PROOF FOUND
%------------------------------------------------------------------------------