TSTP Solution File: RNG025-4 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG025-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %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 : 600s
% DateTime : Mon Jul 18 20:41:14 EDT 2022
% Result : Unsatisfiable 0.45s 0.62s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of clauses : 84 ( 84 unt; 0 nHn; 84 RR)
% Number of literals : 84 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(add(associator(x__dfg,y__dfg,z__dfg),associator(x__dfg,z__dfg,y__dfg)),additive_identity),
file('RNG025-4.p',unknown),
[] ).
cnf(2,axiom,
equal(add(additive_identity,u),u),
file('RNG025-4.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,additive_identity),u),
file('RNG025-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(additive_identity,u),additive_identity),
file('RNG025-4.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(u,additive_identity),additive_identity),
file('RNG025-4.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG025-4.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG025-4.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG025-4.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG025-4.p',unknown),
[] ).
cnf(11,axiom,
equal(add(u,v),add(v,u)),
file('RNG025-4.p',unknown),
[] ).
cnf(12,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG025-4.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(multiply(u,v),v),multiply(u,multiply(v,v))),
file('RNG025-4.p',unknown),
[] ).
cnf(15,axiom,
equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
file('RNG025-4.p',unknown),
[] ).
cnf(16,axiom,
equal(add(multiply(u,v),additive_inverse(multiply(v,u))),commutator(v,u)),
file('RNG025-4.p',unknown),
[] ).
cnf(18,plain,
equal(add(additive_inverse(multiply(u,multiply(v,w))),multiply(multiply(u,v),w)),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[11,15]),
[iquote('0:Rew:11.0,15.0')] ).
cnf(27,plain,
equal(additive_inverse(additive_identity),additive_identity),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(64,plain,
equal(add(u,add(v,additive_inverse(add(u,v)))),additive_identity),
inference(spr,[status(thm),theory(equality)],[12,7]),
[iquote('0:SpR:12.0,7.0')] ).
cnf(69,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[11,12]),
[iquote('0:SpR:11.0,12.0')] ).
cnf(71,plain,
equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[7,12]),
[iquote('0:SpR:7.0,12.0')] ).
cnf(75,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[2,71]),
[iquote('0:Rew:2.0,71.0')] ).
cnf(76,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[12,69]),
[iquote('0:Rew:12.0,69.0')] ).
cnf(120,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),add(v,additive_identity)),
inference(spr,[status(thm),theory(equality)],[64,75]),
[iquote('0:SpR:64.0,75.0')] ).
cnf(136,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[3,120]),
[iquote('0:Rew:3.0,120.0')] ).
cnf(152,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[8,136]),
[iquote('0:SpR:8.0,136.0')] ).
cnf(181,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[152,75]),
[iquote('0:SpR:152.0,75.0')] ).
cnf(184,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[11,152]),
[iquote('0:SpR:11.0,152.0')] ).
cnf(190,plain,
equal(add(u,additive_inverse(add(v,add(w,u)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[12,152]),
[iquote('0:SpR:12.0,152.0')] ).
cnf(236,plain,
equal(add(additive_inverse(u),v),additive_inverse(add(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[181,11]),
[iquote('0:SpR:181.0,11.0')] ).
cnf(263,plain,
equal(add(u,additive_inverse(add(v,w))),additive_inverse(add(v,add(w,additive_inverse(u))))),
inference(spr,[status(thm),theory(equality)],[12,181]),
[iquote('0:SpR:12.0,181.0')] ).
cnf(275,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(multiply(multiply(u,v),w)))),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[236,18]),
[iquote('0:Rew:236.0,18.0')] ).
cnf(317,plain,
equal(add(additive_inverse(multiply(u,v)),multiply(v,u)),commutator(u,v)),
inference(spr,[status(thm),theory(equality)],[16,11]),
[iquote('0:SpR:16.0,11.0')] ).
cnf(323,plain,
equal(add(multiply(u,v),additive_inverse(commutator(v,u))),additive_inverse(additive_inverse(multiply(v,u)))),
inference(spr,[status(thm),theory(equality)],[16,184]),
[iquote('0:SpR:16.0,184.0')] ).
cnf(338,plain,
equal(additive_inverse(add(multiply(u,v),additive_inverse(multiply(v,u)))),commutator(u,v)),
inference(rew,[status(thm),theory(equality)],[236,317]),
[iquote('0:Rew:236.0,317.0')] ).
cnf(339,plain,
equal(additive_inverse(commutator(u,v)),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[16,338]),
[iquote('0:Rew:16.0,338.0')] ).
cnf(347,plain,
equal(add(additive_inverse(commutator(u,v)),multiply(v,u)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[11,323,8]),
[iquote('0:Rew:11.0,323.0,8.0,323.0')] ).
cnf(348,plain,
equal(additive_inverse(add(commutator(u,v),additive_inverse(multiply(v,u)))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[236,347]),
[iquote('0:Rew:236.0,347.0')] ).
cnf(349,plain,
equal(additive_inverse(add(commutator(multiply(u,v),v),additive_inverse(multiply(v,multiply(u,v))))),multiply(u,multiply(v,v))),
inference(rew,[status(thm),theory(equality)],[348,13]),
[iquote('0:Rew:348.0,13.0')] ).
cnf(354,plain,
equal(additive_inverse(additive_inverse(add(commutator(u,multiply(v,u)),additive_inverse(additive_inverse(multiply(u,multiply(v,u))))))),multiply(v,multiply(u,u))),
inference(rew,[status(thm),theory(equality)],[236,349,339]),
[iquote('0:Rew:236.0,349.0,339.0,349.0')] ).
cnf(355,plain,
equal(add(commutator(u,multiply(v,u)),multiply(u,multiply(v,u))),multiply(v,multiply(u,u))),
inference(rew,[status(thm),theory(equality)],[8,354]),
[iquote('0:Rew:8.0,354.0,8.0,354.0')] ).
cnf(392,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),multiply(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[7,10]),
[iquote('0:SpR:7.0,10.0')] ).
cnf(402,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),additive_identity),
inference(rew,[status(thm),theory(equality)],[4,392]),
[iquote('0:Rew:4.0,392.0')] ).
cnf(540,plain,
equal(add(multiply(additive_inverse(u),v),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[402,152]),
[iquote('0:SpR:402.0,152.0')] ).
cnf(561,plain,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,540,11,27]),
[iquote('0:Rew:2.0,540.0,11.0,540.0,27.0,540.0')] ).
cnf(601,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[7,9]),
[iquote('0:SpR:7.0,9.0')] ).
cnf(613,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
inference(rew,[status(thm),theory(equality)],[5,601]),
[iquote('0:Rew:5.0,601.0')] ).
cnf(647,plain,
equal(add(multiply(u,additive_inverse(v)),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[613,152]),
[iquote('0:SpR:613.0,152.0')] ).
cnf(674,plain,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,647,11,27]),
[iquote('0:Rew:2.0,647.0,11.0,647.0,27.0,647.0')] ).
cnf(1020,plain,
equal(add(u,additive_inverse(add(v,add(u,w)))),additive_inverse(add(v,w))),
inference(spr,[status(thm),theory(equality)],[76,184]),
[iquote('0:SpR:76.0,184.0')] ).
cnf(1204,plain,
equal(additive_inverse(additive_inverse(multiply(multiply(u,v),w))),add(multiply(u,multiply(v,w)),associator(u,v,w))),
inference(spr,[status(thm),theory(equality)],[275,184]),
[iquote('0:SpR:275.0,184.0')] ).
cnf(1221,plain,
equal(additive_inverse(add(multiply(u,add(multiply(v,w),multiply(v,x))),additive_inverse(multiply(multiply(u,v),add(w,x))))),associator(u,v,add(w,x))),
inference(spr,[status(thm),theory(equality)],[9,275]),
[iquote('0:SpR:9.0,275.0')] ).
cnf(1222,plain,
equal(additive_inverse(add(multiply(u,additive_inverse(multiply(v,w))),additive_inverse(multiply(multiply(u,v),additive_inverse(w))))),associator(u,v,additive_inverse(w))),
inference(spr,[status(thm),theory(equality)],[674,275]),
[iquote('0:SpR:674.0,275.0')] ).
cnf(1224,plain,
equal(additive_inverse(add(multiply(u,additive_inverse(multiply(v,w))),additive_inverse(multiply(multiply(u,additive_inverse(v)),w)))),associator(u,additive_inverse(v),w)),
inference(spr,[status(thm),theory(equality)],[561,275]),
[iquote('0:SpR:561.0,275.0')] ).
cnf(1225,plain,
equal(additive_inverse(add(multiply(u,add(multiply(v,w),multiply(x,w))),additive_inverse(multiply(multiply(u,add(v,x)),w)))),associator(u,add(v,x),w)),
inference(spr,[status(thm),theory(equality)],[10,275]),
[iquote('0:SpR:10.0,275.0')] ).
cnf(1231,plain,
equal(additive_inverse(add(add(commutator(u,multiply(v,u)),multiply(u,multiply(v,u))),additive_inverse(multiply(multiply(v,u),u)))),associator(v,u,u)),
inference(spr,[status(thm),theory(equality)],[355,275]),
[iquote('0:SpR:355.0,275.0')] ).
cnf(1242,plain,
equal(multiply(multiply(u,v),w),add(associator(u,v,w),multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[8,1204,11]),
[iquote('0:Rew:8.0,1204.0,11.0,1204.0')] ).
cnf(1260,plain,
equal(add(multiply(u,multiply(v,w)),additive_inverse(multiply(multiply(u,v),w))),associator(u,additive_inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[8,1224,236,674,561]),
[iquote('0:Rew:8.0,1224.0,236.0,1224.0,674.0,1224.0,8.0,1224.0,561.0,1224.0,674.0,1224.0')] ).
cnf(1261,plain,
equal(additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),additive_inverse(multiply(u,multiply(v,w)))))),associator(u,additive_inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[263,1260,1242]),
[iquote('0:Rew:263.0,1260.0,1242.0,1260.0')] ).
cnf(1262,plain,
equal(associator(u,additive_inverse(v),w),additive_inverse(associator(u,v,w))),
inference(rew,[status(thm),theory(equality)],[2,1261,11,7]),
[iquote('0:Rew:2.0,1261.0,11.0,1261.0,7.0,1261.0')] ).
cnf(1263,plain,
equal(add(multiply(u,multiply(v,w)),additive_inverse(multiply(multiply(u,v),w))),associator(u,v,additive_inverse(w))),
inference(rew,[status(thm),theory(equality)],[8,1222,236,674]),
[iquote('0:Rew:8.0,1222.0,236.0,1222.0,674.0,1222.0,8.0,1222.0,674.0,1222.0')] ).
cnf(1264,plain,
equal(additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),additive_inverse(multiply(u,multiply(v,w)))))),associator(u,v,additive_inverse(w))),
inference(rew,[status(thm),theory(equality)],[263,1263,1242]),
[iquote('0:Rew:263.0,1263.0,1242.0,1263.0')] ).
cnf(1265,plain,
equal(associator(u,v,additive_inverse(w)),additive_inverse(associator(u,v,w))),
inference(rew,[status(thm),theory(equality)],[2,1264,11,7]),
[iquote('0:Rew:2.0,1264.0,11.0,1264.0,7.0,1264.0')] ).
cnf(1306,plain,
equal(associator(u,v,v),additive_identity),
inference(rew,[status(thm),theory(equality)],[27,1231,7,339,16,12]),
[iquote('0:Rew:27.0,1231.0,7.0,1231.0,339.0,1231.0,16.0,1231.0,12.0,1231.0')] ).
cnf(1315,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),add(multiply(u,multiply(x,w)),additive_inverse(add(multiply(multiply(u,v),w),multiply(multiply(u,x),w)))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[12,1225,9,10]),
[iquote('0:Rew:12.0,1225.0,9.0,1225.0,10.0,1225.0,9.0,1225.0')] ).
cnf(1316,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(add(associator(u,v,w),multiply(u,multiply(v,w))),associator(u,x,w))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[190,1315,1242]),
[iquote('0:Rew:190.0,1315.0,1242.0,1315.0,1242.0,1315.0')] ).
cnf(1317,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),associator(u,x,w)))))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[12,1316]),
[iquote('0:Rew:12.0,1316.0')] ).
cnf(1318,plain,
equal(additive_inverse(additive_inverse(add(associator(u,v,w),associator(u,x,w)))),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[1020,1317]),
[iquote('0:Rew:1020.0,1317.0')] ).
cnf(1319,plain,
equal(add(associator(u,v,w),associator(u,x,w)),associator(u,add(v,x),w)),
inference(rew,[status(thm),theory(equality)],[8,1318]),
[iquote('0:Rew:8.0,1318.0')] ).
cnf(1320,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),add(multiply(u,multiply(v,x)),additive_inverse(add(multiply(multiply(u,v),w),multiply(multiply(u,v),x)))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[12,1221,9]),
[iquote('0:Rew:12.0,1221.0,9.0,1221.0,9.0,1221.0')] ).
cnf(1321,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(add(associator(u,v,w),multiply(u,multiply(v,w))),associator(u,v,x))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[190,1320,1242]),
[iquote('0:Rew:190.0,1320.0,1242.0,1320.0,1242.0,1320.0')] ).
cnf(1322,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(add(associator(u,v,w),add(multiply(u,multiply(v,w)),associator(u,v,x)))))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[12,1321]),
[iquote('0:Rew:12.0,1321.0')] ).
cnf(1323,plain,
equal(additive_inverse(additive_inverse(add(associator(u,v,w),associator(u,v,x)))),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[1020,1322]),
[iquote('0:Rew:1020.0,1322.0')] ).
cnf(1324,plain,
equal(add(associator(u,v,w),associator(u,v,x)),associator(u,v,add(w,x))),
inference(rew,[status(thm),theory(equality)],[8,1323]),
[iquote('0:Rew:8.0,1323.0')] ).
cnf(1824,plain,
equal(add(associator(u,v,w),additive_identity),associator(u,add(v,w),w)),
inference(spr,[status(thm),theory(equality)],[1306,1319]),
[iquote('0:SpR:1306.0,1319.0')] ).
cnf(1834,plain,
equal(associator(u,add(v,w),w),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[2,1824,11]),
[iquote('0:Rew:2.0,1824.0,11.0,1824.0')] ).
cnf(1999,plain,
equal(add(associator(u,v,w),additive_identity),associator(u,v,add(w,v))),
inference(spr,[status(thm),theory(equality)],[1306,1324]),
[iquote('0:SpR:1306.0,1324.0')] ).
cnf(2008,plain,
equal(add(additive_identity,associator(u,v,w)),associator(u,v,add(v,w))),
inference(spr,[status(thm),theory(equality)],[1306,1324]),
[iquote('0:SpR:1306.0,1324.0')] ).
cnf(2014,plain,
equal(associator(u,v,add(w,v)),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[2,1999,11]),
[iquote('0:Rew:2.0,1999.0,11.0,1999.0')] ).
cnf(2019,plain,
equal(associator(u,v,add(v,w)),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[2,2008]),
[iquote('0:Rew:2.0,2008.0')] ).
cnf(2111,plain,
equal(associator(u,additive_inverse(v),additive_inverse(add(v,w))),associator(u,w,additive_inverse(add(v,w)))),
inference(spr,[status(thm),theory(equality)],[152,1834]),
[iquote('0:SpR:152.0,1834.0')] ).
cnf(2140,plain,
equal(associator(u,v,add(v,w)),additive_inverse(associator(u,w,add(v,w)))),
inference(rew,[status(thm),theory(equality)],[8,2111,1265,1262]),
[iquote('0:Rew:8.0,2111.0,1265.0,2111.0,1262.0,2111.0,1265.0,2111.0')] ).
cnf(2141,plain,
equal(associator(u,v,w),additive_inverse(associator(u,w,v))),
inference(rew,[status(thm),theory(equality)],[2019,2140,2014]),
[iquote('0:Rew:2019.0,2140.0,2014.0,2140.0')] ).
cnf(2143,plain,
~ equal(add(associator(x__dfg,y__dfg,z__dfg),additive_inverse(associator(x__dfg,y__dfg,z__dfg))),additive_identity),
inference(rew,[status(thm),theory(equality)],[2141,1]),
[iquote('0:Rew:2141.0,1.0')] ).
cnf(2149,plain,
~ equal(additive_identity,additive_identity),
inference(rew,[status(thm),theory(equality)],[7,2143]),
[iquote('0:Rew:7.0,2143.0')] ).
cnf(2150,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2149]),
[iquote('0:Obv:2149.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG025-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon May 30 21:00:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.45/0.62
% 0.45/0.62 SPASS V 3.9
% 0.45/0.62 SPASS beiseite: Proof found.
% 0.45/0.62 % SZS status Theorem
% 0.45/0.62 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.62 SPASS derived 1175 clauses, backtracked 0 clauses, performed 0 splits and kept 285 clauses.
% 0.45/0.62 SPASS allocated 65944 KBytes.
% 0.45/0.62 SPASS spent 0:00:00.26 on the problem.
% 0.45/0.62 0:00:00.04 for the input.
% 0.45/0.62 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.62 0:00:00.01 for inferences.
% 0.45/0.62 0:00:00.00 for the backtracking.
% 0.45/0.62 0:00:00.19 for the reduction.
% 0.45/0.62
% 0.45/0.62
% 0.45/0.62 Here is a proof with depth 5, length 84 :
% 0.45/0.62 % SZS output start Refutation
% See solution above
% 0.47/0.63 Formulae used in the proof : prove_equation left_additive_identity right_additive_identity left_multiplicative_zero right_multiplicative_zero right_additive_inverse additive_inverse_additive_inverse distribute1 distribute2 commutativity_for_addition associativity_for_addition right_alternative associator commutator
% 0.47/0.63
%------------------------------------------------------------------------------