TSTP Solution File: KLE084-10 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE084-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 : Sun Jul 17 02:28:25 EDT 2022
% Result : Unsatisfiable 280.60s 281.04s
% Output : Refutation 288.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of clauses : 125 ( 125 unt; 0 nHn; 125 RR)
% Number of literals : 125 ( 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 : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE084-10.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE084-10.p',unknown),
[] ).
cnf(5,axiom,
equal(addition(u,zero),u),
file('KLE084-10.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,u),u),
file('KLE084-10.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE084-10.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(u,one),u),
file('KLE084-10.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(one,u),u),
file('KLE084-10.p',unknown),
[] ).
cnf(10,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE084-10.p',unknown),
[] ).
cnf(11,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE084-10.p',unknown),
[] ).
cnf(13,axiom,
equal(multiplication(zero,u),zero),
file('KLE084-10.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE084-10.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE084-10.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE084-10.p',unknown),
[] ).
cnf(19,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE084-10.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE084-10.p',unknown),
[] ).
cnf(21,axiom,
equal(addition(coantidomain(multiplication(u,v)),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),
file('KLE084-10.p',unknown),
[] ).
cnf(22,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE084-10.p',unknown),
[] ).
cnf(24,axiom,
~ equal(domain__dfg(multiplication(sK2_goals_X0,domain__dfg(sK1_goals_X1))),domain__dfg(multiplication(sK2_goals_X0,sK1_goals_X1))),
file('KLE084-10.p',unknown),
[] ).
cnf(25,plain,
equal(addition(coantidomain(u),coantidomain(coantidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[3,22]),
[iquote('0:Rew:3.0,22.0')] ).
cnf(26,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[3,18]),
[iquote('0:Rew:3.0,18.0')] ).
cnf(27,plain,
~ equal(antidomain(antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1))))),antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1)))),
inference(rew,[status(thm),theory(equality)],[19,24]),
[iquote('0:Rew:19.0,24.0,19.0,24.0,19.0,24.0')] ).
cnf(41,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[16,8]),
[iquote('0:SpR:16.0,8.0')] ).
cnf(45,plain,
equal(coantidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[20,9]),
[iquote('0:SpR:20.0,9.0')] ).
cnf(51,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(67,plain,
equal(addition(zero,coantidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[45,25]),
[iquote('0:SpR:45.0,25.0')] ).
cnf(69,plain,
equal(coantidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[51,67]),
[iquote('0:Rew:51.0,67.0')] ).
cnf(76,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[41,26]),
[iquote('0:SpR:41.0,26.0')] ).
cnf(78,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[51,76]),
[iquote('0:Rew:51.0,76.0')] ).
cnf(139,plain,
equal(multiplication(u,multiplication(v,coantidomain(multiplication(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[7,20]),
[iquote('0:SpR:7.0,20.0')] ).
cnf(144,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),multiplication(zero,v)),
inference(spr,[status(thm),theory(equality)],[16,7]),
[iquote('0:SpR:16.0,7.0')] ).
cnf(153,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),zero),
inference(rew,[status(thm),theory(equality)],[13,144]),
[iquote('0:Rew:13.0,144.0')] ).
cnf(165,plain,
equal(multiplication(antidomain(multiplication(u,v)),multiplication(u,multiplication(v,w))),zero),
inference(spr,[status(thm),theory(equality)],[7,153]),
[iquote('0:SpR:7.0,153.0')] ).
cnf(181,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(220,plain,
equal(addition(coantidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[25,181]),
[iquote('0:SpR:25.0,181.0')] ).
cnf(221,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[26,181]),
[iquote('0:SpR:26.0,181.0')] ).
cnf(223,plain,
equal(addition(one,coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[3,220]),
[iquote('0:Rew:3.0,220.0')] ).
cnf(224,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[3,221]),
[iquote('0:Rew:3.0,221.0')] ).
cnf(251,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[11,20]),
[iquote('0:SpR:11.0,20.0')] ).
cnf(262,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[25,11]),
[iquote('0:SpR:25.0,11.0')] ).
cnf(263,plain,
equal(addition(multiplication(one,u),multiplication(coantidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[223,11]),
[iquote('0:SpR:223.0,11.0')] ).
cnf(264,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[26,11]),
[iquote('0:SpR:26.0,11.0')] ).
cnf(271,plain,
equal(addition(u,multiplication(coantidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[9,263]),
[iquote('0:Rew:9.0,263.0')] ).
cnf(276,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[9,262]),
[iquote('0:Rew:9.0,262.0')] ).
cnf(277,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[9,264]),
[iquote('0:Rew:9.0,264.0')] ).
cnf(341,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),multiplication(antidomain(addition(u,v)),v)),zero),
inference(spr,[status(thm),theory(equality)],[10,16]),
[iquote('0:SpR:10.0,16.0')] ).
cnf(354,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[25,10]),
[iquote('0:SpR:25.0,10.0')] ).
cnf(356,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[26,10]),
[iquote('0:SpR:26.0,10.0')] ).
cnf(357,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[224,10]),
[iquote('0:SpR:224.0,10.0')] ).
cnf(365,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[8,357]),
[iquote('0:Rew:8.0,357.0')] ).
cnf(369,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[8,354]),
[iquote('0:Rew:8.0,354.0')] ).
cnf(370,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[8,356]),
[iquote('0:Rew:8.0,356.0')] ).
cnf(585,plain,
equal(addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u))),coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u))),
inference(spr,[status(thm),theory(equality)],[16,21]),
[iquote('0:SpR:16.0,21.0')] ).
cnf(604,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
inference(rew,[status(thm),theory(equality)],[223,585,69]),
[iquote('0:Rew:223.0,585.0,69.0,585.0')] ).
cnf(612,plain,
equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
inference(spr,[status(thm),theory(equality)],[604,20]),
[iquote('0:SpR:604.0,20.0')] ).
cnf(638,plain,
equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
inference(rew,[status(thm),theory(equality)],[8,612,7]),
[iquote('0:Rew:8.0,612.0,7.0,612.0')] ).
cnf(725,plain,
equal(addition(multiplication(antidomain(multiplication(u,v)),w),multiplication(antidomain(multiplication(u,antidomain(antidomain(v)))),w)),multiplication(antidomain(multiplication(u,antidomain(antidomain(v)))),w)),
inference(spr,[status(thm),theory(equality)],[17,11]),
[iquote('0:SpR:17.0,11.0')] ).
cnf(740,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[16,17]),
[iquote('0:SpR:16.0,17.0')] ).
cnf(744,plain,
equal(addition(antidomain(zero),antidomain(multiplication(u,antidomain(antidomain(coantidomain(u)))))),antidomain(multiplication(u,antidomain(antidomain(coantidomain(u)))))),
inference(spr,[status(thm),theory(equality)],[20,17]),
[iquote('0:SpR:20.0,17.0')] ).
cnf(761,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[224,740,78]),
[iquote('0:Rew:224.0,740.0,78.0,740.0')] ).
cnf(762,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(coantidomain(u))))),one),
inference(rew,[status(thm),theory(equality)],[224,744,78]),
[iquote('0:Rew:224.0,744.0,78.0,744.0')] ).
cnf(773,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[761,16]),
[iquote('0:SpR:761.0,16.0')] ).
cnf(802,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[9,773]),
[iquote('0:Rew:9.0,773.0')] ).
cnf(828,plain,
equal(multiplication(one,multiplication(u,antidomain(antidomain(coantidomain(u))))),zero),
inference(spr,[status(thm),theory(equality)],[762,16]),
[iquote('0:SpR:762.0,16.0')] ).
cnf(858,plain,
equal(multiplication(u,antidomain(antidomain(coantidomain(u)))),zero),
inference(rew,[status(thm),theory(equality)],[9,828]),
[iquote('0:Rew:9.0,828.0')] ).
cnf(2650,plain,
equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
inference(spr,[status(thm),theory(equality)],[638,276]),
[iquote('0:SpR:638.0,276.0')] ).
cnf(2653,plain,
equal(addition(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),zero),coantidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[20,276]),
[iquote('0:SpR:20.0,276.0')] ).
cnf(2679,plain,
equal(multiplication(coantidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[51,2650,3]),
[iquote('0:Rew:51.0,2650.0,3.0,2650.0')] ).
cnf(2691,plain,
equal(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[51,2653,3]),
[iquote('0:Rew:51.0,2653.0,3.0,2653.0')] ).
cnf(2881,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[802,277]),
[iquote('0:SpR:802.0,277.0')] ).
cnf(2884,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),u)),u),
inference(spr,[status(thm),theory(equality)],[16,277]),
[iquote('0:SpR:16.0,277.0')] ).
cnf(2900,plain,
equal(multiplication(antidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[51,2884]),
[iquote('0:Rew:51.0,2884.0')] ).
cnf(2914,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[51,2881,3]),
[iquote('0:Rew:51.0,2881.0,3.0,2881.0')] ).
cnf(3075,plain,
equal(addition(multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u)),coantidomain(coantidomain(u))),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[2900,369]),
[iquote('0:SpR:2900.0,369.0')] ).
cnf(3093,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[20,369]),
[iquote('0:SpR:20.0,369.0')] ).
cnf(3102,plain,
equal(multiplication(u,coantidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[51,3093]),
[iquote('0:Rew:51.0,3093.0')] ).
cnf(3103,plain,
equal(coantidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[3102,2691]),
[iquote('0:Rew:3102.0,2691.0')] ).
cnf(3164,plain,
equal(addition(coantidomain(coantidomain(u)),multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u))),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[3,3075]),
[iquote('0:Rew:3.0,3075.0')] ).
cnf(3327,plain,
equal(addition(multiplication(u,multiplication(v,antidomain(w))),multiplication(u,multiplication(v,antidomain(antidomain(w))))),multiplication(u,v)),
inference(spr,[status(thm),theory(equality)],[370,10]),
[iquote('0:SpR:370.0,10.0')] ).
cnf(3340,plain,
equal(addition(multiplication(u,antidomain(coantidomain(u))),zero),u),
inference(spr,[status(thm),theory(equality)],[858,370]),
[iquote('0:SpR:858.0,370.0')] ).
cnf(3345,plain,
equal(addition(multiplication(coantidomain(antidomain(antidomain(antidomain(u)))),antidomain(u)),antidomain(antidomain(u))),coantidomain(antidomain(antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[2679,370]),
[iquote('0:SpR:2679.0,370.0')] ).
cnf(3358,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[802,370]),
[iquote('0:SpR:802.0,370.0')] ).
cnf(3364,plain,
equal(multiplication(u,antidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[51,3340,3]),
[iquote('0:Rew:51.0,3340.0,3.0,3340.0')] ).
cnf(3373,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[51,3358]),
[iquote('0:Rew:51.0,3358.0')] ).
cnf(3374,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[2914,3373]),
[iquote('0:Rew:2914.0,3373.0')] ).
cnf(3433,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(antidomain(antidomain(u)))),antidomain(u))),coantidomain(antidomain(antidomain(antidomain(u))))),
inference(rew,[status(thm),theory(equality)],[3,3345]),
[iquote('0:Rew:3.0,3345.0')] ).
cnf(3434,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[3374,3433]),
[iquote('0:Rew:3374.0,3433.0')] ).
cnf(3873,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),zero),zero),
inference(spr,[status(thm),theory(equality)],[251,181]),
[iquote('0:SpR:251.0,181.0')] ).
cnf(3901,plain,
equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[365,251]),
[iquote('0:SpR:365.0,251.0')] ).
cnf(3974,plain,
equal(multiplication(u,coantidomain(addition(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[51,3873,3]),
[iquote('0:Rew:51.0,3873.0,3.0,3873.0')] ).
cnf(4004,plain,
equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[51,3901,20,7]),
[iquote('0:Rew:51.0,3901.0,20.0,3901.0,7.0,3901.0')] ).
cnf(4596,plain,
equal(addition(multiplication(antidomain(u),u),multiplication(antidomain(u),multiplication(coantidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[271,341]),
[iquote('0:SpR:271.0,341.0')] ).
cnf(4697,plain,
equal(multiplication(antidomain(u),multiplication(coantidomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[51,4596,16]),
[iquote('0:Rew:51.0,4596.0,16.0,4596.0')] ).
cnf(5407,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(addition(u,v))))),u),
inference(spr,[status(thm),theory(equality)],[3974,369]),
[iquote('0:SpR:3974.0,369.0')] ).
cnf(5482,plain,
equal(multiplication(u,coantidomain(coantidomain(addition(u,v)))),u),
inference(rew,[status(thm),theory(equality)],[51,5407]),
[iquote('0:Rew:51.0,5407.0')] ).
cnf(6055,plain,
equal(addition(multiplication(antidomain(u),multiplication(antidomain(v),coantidomain(antidomain(antidomain(u))))),zero),multiplication(antidomain(v),coantidomain(antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[4004,277]),
[iquote('0:SpR:4004.0,277.0')] ).
cnf(6079,plain,
equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[3102,4004]),
[iquote('0:SpR:3102.0,4004.0')] ).
cnf(6090,plain,
equal(addition(antidomain(antidomain(u)),zero),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[6079,3434]),
[iquote('0:Rew:6079.0,3434.0')] ).
cnf(6092,plain,
equal(coantidomain(antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[51,6090,3]),
[iquote('0:Rew:51.0,6090.0,3.0,6090.0')] ).
cnf(6279,plain,
equal(multiplication(antidomain(u),multiplication(antidomain(v),coantidomain(antidomain(antidomain(u))))),multiplication(antidomain(v),coantidomain(antidomain(antidomain(u))))),
inference(rew,[status(thm),theory(equality)],[51,6055,3]),
[iquote('0:Rew:51.0,6055.0,3.0,6055.0')] ).
cnf(6280,plain,
equal(multiplication(antidomain(u),multiplication(antidomain(v),antidomain(antidomain(antidomain(u))))),multiplication(antidomain(v),antidomain(antidomain(antidomain(u))))),
inference(rew,[status(thm),theory(equality)],[6092,6279]),
[iquote('0:Rew:6092.0,6279.0')] ).
cnf(6281,plain,
equal(multiplication(antidomain(u),multiplication(antidomain(v),antidomain(u))),multiplication(antidomain(v),antidomain(u))),
inference(rew,[status(thm),theory(equality)],[3374,6280]),
[iquote('0:Rew:3374.0,6280.0')] ).
cnf(6349,plain,
equal(multiplication(antidomain(u),multiplication(antidomain(v),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[6092,4004]),
[iquote('0:SpR:6092.0,4004.0')] ).
cnf(6425,plain,
equal(multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[3364,4697]),
[iquote('0:SpR:3364.0,4697.0')] ).
cnf(6448,plain,
equal(addition(coantidomain(coantidomain(u)),zero),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[6425,3164]),
[iquote('0:Rew:6425.0,3164.0')] ).
cnf(6450,plain,
equal(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[51,6448,3]),
[iquote('0:Rew:51.0,6448.0,3.0,6448.0')] ).
cnf(6566,plain,
equal(antidomain(antidomain(coantidomain(u))),coantidomain(u)),
inference(spr,[status(thm),theory(equality)],[3103,6450]),
[iquote('0:SpR:3103.0,6450.0')] ).
cnf(6648,plain,
equal(coantidomain(coantidomain(u)),antidomain(coantidomain(u))),
inference(spr,[status(thm),theory(equality)],[6566,6092]),
[iquote('0:SpR:6566.0,6092.0')] ).
cnf(6706,plain,
equal(multiplication(u,antidomain(coantidomain(addition(u,v)))),u),
inference(rew,[status(thm),theory(equality)],[6648,5482]),
[iquote('0:Rew:6648.0,5482.0')] ).
cnf(7525,plain,
equal(multiplication(antidomain(multiplication(u,v)),antidomain(coantidomain(antidomain(multiplication(u,antidomain(antidomain(v))))))),antidomain(multiplication(u,v))),
inference(spr,[status(thm),theory(equality)],[17,6706]),
[iquote('0:SpR:17.0,6706.0')] ).
cnf(7565,plain,
equal(multiplication(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,v))),
inference(rew,[status(thm),theory(equality)],[3374,7525,6092]),
[iquote('0:Rew:3374.0,7525.0,6092.0,7525.0')] ).
cnf(10125,plain,
equal(addition(multiplication(antidomain(multiplication(u,v)),multiplication(u,antidomain(antidomain(v)))),zero),zero),
inference(spr,[status(thm),theory(equality)],[16,725]),
[iquote('0:SpR:16.0,725.0')] ).
cnf(10202,plain,
equal(multiplication(antidomain(multiplication(u,v)),multiplication(u,antidomain(antidomain(v)))),zero),
inference(rew,[status(thm),theory(equality)],[51,10125,3]),
[iquote('0:Rew:51.0,10125.0,3.0,10125.0')] ).
cnf(25560,plain,
equal(multiplication(antidomain(zero),multiplication(u,antidomain(antidomain(multiplication(v,coantidomain(multiplication(u,v))))))),zero),
inference(spr,[status(thm),theory(equality)],[139,10202]),
[iquote('0:SpR:139.0,10202.0')] ).
cnf(25670,plain,
equal(multiplication(u,antidomain(antidomain(multiplication(v,coantidomain(multiplication(u,v)))))),zero),
inference(rew,[status(thm),theory(equality)],[9,25560,78]),
[iquote('0:Rew:9.0,25560.0,78.0,25560.0')] ).
cnf(27025,plain,
equal(multiplication(antidomain(multiplication(u,antidomain(antidomain(v)))),multiplication(u,v)),zero),
inference(spr,[status(thm),theory(equality)],[2900,165]),
[iquote('0:SpR:2900.0,165.0')] ).
cnf(119352,plain,
equal(addition(multiplication(antidomain(u),multiplication(antidomain(v),antidomain(u))),zero),multiplication(antidomain(u),antidomain(v))),
inference(spr,[status(thm),theory(equality)],[6349,3327]),
[iquote('0:SpR:6349.0,3327.0')] ).
cnf(119632,plain,
equal(multiplication(antidomain(u),multiplication(antidomain(v),antidomain(u))),multiplication(antidomain(u),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[51,119352,3]),
[iquote('0:Rew:51.0,119352.0,3.0,119352.0')] ).
cnf(119633,plain,
equal(multiplication(antidomain(u),antidomain(v)),multiplication(antidomain(v),antidomain(u))),
inference(rew,[status(thm),theory(equality)],[6281,119632]),
[iquote('0:Rew:6281.0,119632.0')] ).
cnf(211115,plain,
equal(addition(multiplication(u,antidomain(multiplication(v,coantidomain(multiplication(u,v))))),zero),u),
inference(spr,[status(thm),theory(equality)],[25670,370]),
[iquote('0:SpR:25670.0,370.0')] ).
cnf(211462,plain,
equal(multiplication(u,antidomain(multiplication(v,coantidomain(multiplication(u,v))))),u),
inference(rew,[status(thm),theory(equality)],[51,211115,3]),
[iquote('0:Rew:51.0,211115.0,3.0,211115.0')] ).
cnf(214960,plain,
equal(multiplication(antidomain(multiplication(u,antidomain(antidomain(v)))),antidomain(multiplication(multiplication(u,v),coantidomain(zero)))),antidomain(multiplication(u,antidomain(antidomain(v))))),
inference(spr,[status(thm),theory(equality)],[27025,211462]),
[iquote('0:SpR:27025.0,211462.0')] ).
cnf(215490,plain,
equal(multiplication(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
inference(rew,[status(thm),theory(equality)],[119633,214960,8,7,69]),
[iquote('0:Rew:119633.0,214960.0,8.0,214960.0,7.0,214960.0,69.0,214960.0')] ).
cnf(215491,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(v)))),antidomain(multiplication(u,v))),
inference(rew,[status(thm),theory(equality)],[7565,215490]),
[iquote('0:Rew:7565.0,215490.0')] ).
cnf(215500,plain,
~ equal(antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))),antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1)))),
inference(rew,[status(thm),theory(equality)],[215491,27]),
[iquote('0:Rew:215491.0,27.0')] ).
cnf(216090,plain,
$false,
inference(obv,[status(thm),theory(equality)],[215500]),
[iquote('0:Obv:215500.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE084-10 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 16 10:09:17 EDT 2022
% 0.14/0.35 % CPUTime :
% 280.60/281.04
% 280.60/281.04 SPASS V 3.9
% 280.60/281.04 SPASS beiseite: Proof found.
% 280.60/281.04 % SZS status Theorem
% 280.60/281.04 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 280.60/281.04 SPASS derived 131999 clauses, backtracked 0 clauses, performed 0 splits and kept 16436 clauses.
% 280.60/281.04 SPASS allocated 252337 KBytes.
% 280.60/281.04 SPASS spent 0:4:40.40 on the problem.
% 280.60/281.04 0:00:00.03 for the input.
% 280.60/281.04 0:00:00.00 for the FLOTTER CNF translation.
% 280.60/281.04 0:00:00.87 for inferences.
% 280.60/281.04 0:00:00.00 for the backtracking.
% 280.60/281.04 0:4:39.23 for the reduction.
% 280.60/281.04
% 280.60/281.04
% 280.60/281.04 Here is a proof with depth 6, length 125 :
% 280.60/281.04 % SZS output start Refutation
% See solution above
% 288.98/289.47 Formulae used in the proof : additive_commutativity additive_associativity additive_identity additive_idempotence multiplicative_associativity multiplicative_right_identity multiplicative_left_identity right_distributivity left_distributivity left_annihilation domain1 domain2 domain3 domain4 codomain1 codomain2 codomain3 goals
% 288.98/289.47
%------------------------------------------------------------------------------