TSTP Solution File: KLE132+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE132+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 02:28:40 EDT 2022
% Result : Theorem 17.63s 17.83s
% Output : Refutation 18.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of clauses : 139 ( 127 unt; 0 nHn; 139 RR)
% Number of literals : 151 ( 0 equ; 19 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(domain__dfg(skc3),zero),
file('KLE132+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE132+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE132+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE132+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE132+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(u,zero),zero),
file('KLE132+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE132+1.p',unknown),
[] ).
cnf(9,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE132+1.p',unknown),
[] ).
cnf(10,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE132+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE132+1.p',unknown),
[] ).
cnf(15,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE132+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE132+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE132+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE132+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE132+1.p',unknown),
[] ).
cnf(20,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE132+1.p',unknown),
[] ).
cnf(24,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE132+1.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE132+1.p',unknown),
[] ).
cnf(26,axiom,
equal(addition(domain__dfg(skc3),forward_diamond(skc2,domain__dfg(skc3))),forward_diamond(skc2,domain__dfg(skc3))),
file('KLE132+1.p',unknown),
[] ).
cnf(27,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE132+1.p',unknown),
[] ).
cnf(28,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE132+1.p',unknown),
[] ).
cnf(29,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE132+1.p',unknown),
[] ).
cnf(30,axiom,
equal(addition(coantidomain(multiplication(u,v)),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),
file('KLE132+1.p',unknown),
[] ).
cnf(31,axiom,
equal(addition(forward_diamond(skc2,domain__dfg(u)),forward_diamond(star(skc2),domain_difference(domain__dfg(u),forward_diamond(skc2,domain__dfg(u))))),forward_diamond(star(skc2),domain_difference(domain__dfg(u),forward_diamond(skc2,domain__dfg(u))))),
file('KLE132+1.p',unknown),
[] ).
cnf(34,plain,
~ equal(antidomain(antidomain(skc3)),zero),
inference(rew,[status(thm),theory(equality)],[9,1]),
[iquote('0:Rew:9.0,1.0')] ).
cnf(35,plain,
equal(addition(coantidomain(u),coantidomain(coantidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[13,16]),
[iquote('0:Rew:13.0,16.0')] ).
cnf(36,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[13,15]),
[iquote('0:Rew:13.0,15.0')] ).
cnf(41,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[9,20]),
[iquote('0:Rew:9.0,20.0,9.0,20.0')] ).
cnf(42,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[9,19]),
[iquote('0:Rew:9.0,19.0')] ).
cnf(43,plain,
equal(addition(antidomain(antidomain(skc3)),forward_diamond(skc2,antidomain(antidomain(skc3)))),forward_diamond(skc2,antidomain(antidomain(skc3)))),
inference(rew,[status(thm),theory(equality)],[9,26]),
[iquote('0:Rew:9.0,26.0')] ).
cnf(44,plain,
equal(addition(forward_diamond(skc2,antidomain(antidomain(u))),forward_diamond(star(skc2),domain_difference(antidomain(antidomain(u)),forward_diamond(skc2,antidomain(antidomain(u)))))),forward_diamond(star(skc2),domain_difference(antidomain(antidomain(u)),forward_diamond(skc2,antidomain(antidomain(u)))))),
inference(rew,[status(thm),theory(equality)],[9,31]),
[iquote('0:Rew:9.0,31.0')] ).
cnf(61,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(65,plain,
equal(coantidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[10,5]),
[iquote('0:SpR:10.0,5.0')] ).
cnf(73,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[13,2]),
[iquote('0:SpR:13.0,2.0')] ).
cnf(87,plain,
equal(addition(zero,coantidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[65,35]),
[iquote('0:SpR:65.0,35.0')] ).
cnf(89,plain,
equal(coantidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[73,87]),
[iquote('0:Rew:73.0,87.0')] ).
cnf(96,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[61,36]),
[iquote('0:SpR:61.0,36.0')] ).
cnf(98,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[73,96]),
[iquote('0:Rew:73.0,96.0')] ).
cnf(117,plain,
( ~ equal(u,u)
| leq(zero,u) ),
inference(spl,[status(thm),theory(equality)],[73,18]),
[iquote('0:SpL:73.0,18.0')] ).
cnf(121,plain,
leq(zero,u),
inference(obv,[status(thm),theory(equality)],[117]),
[iquote('0:Obv:117.0')] ).
cnf(130,plain,
equal(multiplication(antidomain(zero),antidomain(u)),domain_difference(one,u)),
inference(spr,[status(thm),theory(equality)],[61,42]),
[iquote('0:SpR:61.0,42.0')] ).
cnf(134,plain,
equal(domain_difference(one,u),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[5,130,98]),
[iquote('0:Rew:5.0,130.0,98.0,130.0')] ).
cnf(189,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(zero)))),forward_diamond(u,one)),
inference(spr,[status(thm),theory(equality)],[61,41]),
[iquote('0:SpR:61.0,41.0')] ).
cnf(190,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(one)))),forward_diamond(u,zero)),
inference(spr,[status(thm),theory(equality)],[98,41]),
[iquote('0:SpR:98.0,41.0')] ).
cnf(196,plain,
equal(forward_diamond(u,one),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4,189,98]),
[iquote('0:Rew:4.0,189.0,98.0,189.0')] ).
cnf(197,plain,
equal(forward_diamond(u,zero),zero),
inference(rew,[status(thm),theory(equality)],[61,190,98,6]),
[iquote('0:Rew:61.0,190.0,98.0,190.0,6.0,190.0,61.0,190.0')] ).
cnf(287,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,24]),
[iquote('0:SpR:3.0,24.0')] ).
cnf(288,plain,
( ~ leq(u,v)
| equal(addition(u,addition(v,w)),addition(v,w)) ),
inference(spr,[status(thm),theory(equality)],[17,24]),
[iquote('0:SpR:17.1,24.0')] ).
cnf(338,plain,
equal(addition(coantidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[35,287]),
[iquote('0:SpR:35.0,287.0')] ).
cnf(339,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[36,287]),
[iquote('0:SpR:36.0,287.0')] ).
cnf(344,plain,
equal(addition(one,coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[13,338]),
[iquote('0:Rew:13.0,338.0')] ).
cnf(345,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[13,339]),
[iquote('0:Rew:13.0,339.0')] ).
cnf(373,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[28,10]),
[iquote('0:SpR:28.0,10.0')] ).
cnf(374,plain,
equal(antidomain(antidomain(addition(multiplication(u,antidomain(antidomain(v))),multiplication(w,antidomain(antidomain(v)))))),forward_diamond(addition(u,w),v)),
inference(spr,[status(thm),theory(equality)],[28,41]),
[iquote('0:SpR:28.0,41.0')] ).
cnf(387,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[35,28]),
[iquote('0:SpR:35.0,28.0')] ).
cnf(388,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[36,28]),
[iquote('0:SpR:36.0,28.0')] ).
cnf(398,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[5,387]),
[iquote('0:Rew:5.0,387.0')] ).
cnf(399,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[5,388]),
[iquote('0:Rew:5.0,388.0')] ).
cnf(438,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),multiplication(antidomain(addition(u,v)),v)),zero),
inference(spr,[status(thm),theory(equality)],[27,8]),
[iquote('0:SpR:27.0,8.0')] ).
cnf(453,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[35,27]),
[iquote('0:SpR:35.0,27.0')] ).
cnf(454,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[36,27]),
[iquote('0:SpR:36.0,27.0')] ).
cnf(467,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[4,453]),
[iquote('0:Rew:4.0,453.0')] ).
cnf(468,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[4,454]),
[iquote('0:Rew:4.0,454.0')] ).
cnf(498,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[345,27]),
[iquote('0:SpR:345.0,27.0')] ).
cnf(508,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[4,498]),
[iquote('0:Rew:4.0,498.0')] ).
cnf(549,plain,
equal(addition(multiplication(antidomain(antidomain(skc3)),u),multiplication(forward_diamond(skc2,antidomain(antidomain(skc3))),u)),multiplication(forward_diamond(skc2,antidomain(antidomain(skc3))),u)),
inference(spr,[status(thm),theory(equality)],[43,28]),
[iquote('0:SpR:43.0,28.0')] ).
cnf(552,plain,
equal(addition(multiplication(u,antidomain(antidomain(skc3))),multiplication(u,forward_diamond(skc2,antidomain(antidomain(skc3))))),multiplication(u,forward_diamond(skc2,antidomain(antidomain(skc3))))),
inference(spr,[status(thm),theory(equality)],[43,27]),
[iquote('0:SpR:43.0,27.0')] ).
cnf(686,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)],[8,30]),
[iquote('0:SpR:8.0,30.0')] ).
cnf(708,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
inference(rew,[status(thm),theory(equality)],[344,686,89]),
[iquote('0:Rew:344.0,686.0,89.0,686.0')] ).
cnf(817,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)],[8,29]),
[iquote('0:SpR:8.0,29.0')] ).
cnf(820,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)],[10,29]),
[iquote('0:SpR:10.0,29.0')] ).
cnf(839,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[345,817,98]),
[iquote('0:Rew:345.0,817.0,98.0,817.0')] ).
cnf(840,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(coantidomain(u))))),one),
inference(rew,[status(thm),theory(equality)],[345,820,98]),
[iquote('0:Rew:345.0,820.0,98.0,820.0')] ).
cnf(1155,plain,
equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
inference(spr,[status(thm),theory(equality)],[708,10]),
[iquote('0:SpR:708.0,10.0')] ).
cnf(1183,plain,
equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
inference(rew,[status(thm),theory(equality)],[4,1155,25]),
[iquote('0:Rew:4.0,1155.0,25.0,1155.0')] ).
cnf(1404,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[839,8]),
[iquote('0:SpR:839.0,8.0')] ).
cnf(1424,plain,
equal(forward_diamond(antidomain(u),u),antidomain(one)),
inference(spr,[status(thm),theory(equality)],[839,41]),
[iquote('0:SpR:839.0,41.0')] ).
cnf(1444,plain,
equal(forward_diamond(antidomain(u),u),zero),
inference(rew,[status(thm),theory(equality)],[61,1424]),
[iquote('0:Rew:61.0,1424.0')] ).
cnf(1452,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[5,1404]),
[iquote('0:Rew:5.0,1404.0')] ).
cnf(1530,plain,
equal(multiplication(one,multiplication(u,antidomain(antidomain(coantidomain(u))))),zero),
inference(spr,[status(thm),theory(equality)],[840,8]),
[iquote('0:SpR:840.0,8.0')] ).
cnf(1571,plain,
equal(multiplication(u,antidomain(antidomain(coantidomain(u)))),zero),
inference(rew,[status(thm),theory(equality)],[5,1530]),
[iquote('0:Rew:5.0,1530.0')] ).
cnf(4122,plain,
equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
inference(spr,[status(thm),theory(equality)],[1183,398]),
[iquote('0:SpR:1183.0,398.0')] ).
cnf(4149,plain,
equal(multiplication(coantidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[73,4122,13]),
[iquote('0:Rew:73.0,4122.0,13.0,4122.0')] ).
cnf(4295,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1452,399]),
[iquote('0:SpR:1452.0,399.0')] ).
cnf(4337,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[73,4295,13]),
[iquote('0:Rew:73.0,4295.0,13.0,4295.0')] ).
cnf(4470,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[10,467]),
[iquote('0:SpR:10.0,467.0')] ).
cnf(4483,plain,
equal(multiplication(u,coantidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[73,4470]),
[iquote('0:Rew:73.0,4470.0')] ).
cnf(4748,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)],[4149,468]),
[iquote('0:SpR:4149.0,468.0')] ).
cnf(4761,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1452,468]),
[iquote('0:SpR:1452.0,468.0')] ).
cnf(4785,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[73,4761]),
[iquote('0:Rew:73.0,4761.0')] ).
cnf(4786,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4337,4785]),
[iquote('0:Rew:4337.0,4785.0')] ).
cnf(4850,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)],[13,4748]),
[iquote('0:Rew:13.0,4748.0')] ).
cnf(4851,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4786,4850]),
[iquote('0:Rew:4786.0,4850.0')] ).
cnf(4865,plain,
equal(multiplication(antidomain(u),antidomain(v)),domain_difference(antidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[4786,42]),
[iquote('0:SpR:4786.0,42.0')] ).
cnf(4876,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4786,41]),
[iquote('0:SpR:4786.0,41.0')] ).
cnf(4931,plain,
equal(antidomain(antidomain(forward_diamond(u,v))),forward_diamond(u,v)),
inference(spr,[status(thm),theory(equality)],[41,4786]),
[iquote('0:SpR:41.0,4786.0')] ).
cnf(4936,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(v)))),antidomain(forward_diamond(u,v))),
inference(spr,[status(thm),theory(equality)],[41,4786]),
[iquote('0:SpR:41.0,4786.0')] ).
cnf(4957,plain,
equal(domain_difference(antidomain(antidomain(u)),v),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4865,42]),
[iquote('0:Rew:4865.0,42.0')] ).
cnf(4971,plain,
equal(addition(forward_diamond(skc2,antidomain(antidomain(u))),forward_diamond(star(skc2),domain_difference(u,forward_diamond(skc2,antidomain(antidomain(u)))))),forward_diamond(star(skc2),domain_difference(u,forward_diamond(skc2,antidomain(antidomain(u)))))),
inference(rew,[status(thm),theory(equality)],[4957,44]),
[iquote('0:Rew:4957.0,44.0')] ).
cnf(4989,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[4876,41]),
[iquote('0:Rew:4876.0,41.0')] ).
cnf(5019,plain,
equal(addition(multiplication(u,antidomain(antidomain(skc3))),multiplication(u,forward_diamond(skc2,skc3))),multiplication(u,forward_diamond(skc2,skc3))),
inference(rew,[status(thm),theory(equality)],[4989,552]),
[iquote('0:Rew:4989.0,552.0')] ).
cnf(5020,plain,
equal(addition(multiplication(antidomain(antidomain(skc3)),u),multiplication(forward_diamond(skc2,skc3),u)),multiplication(forward_diamond(skc2,skc3),u)),
inference(rew,[status(thm),theory(equality)],[4989,549]),
[iquote('0:Rew:4989.0,549.0')] ).
cnf(5154,plain,
equal(addition(forward_diamond(skc2,u),forward_diamond(star(skc2),domain_difference(u,forward_diamond(skc2,u)))),forward_diamond(star(skc2),domain_difference(u,forward_diamond(skc2,u)))),
inference(rew,[status(thm),theory(equality)],[4989,4971]),
[iquote('0:Rew:4989.0,4971.0')] ).
cnf(6792,plain,
( ~ leq(u,zero)
| equal(addition(u,v),v) ),
inference(spr,[status(thm),theory(equality)],[73,288]),
[iquote('0:SpR:73.0,288.1')] ).
cnf(8615,plain,
equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[508,373]),
[iquote('0:SpR:508.0,373.0')] ).
cnf(8752,plain,
equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[73,8615,10,25]),
[iquote('0:Rew:73.0,8615.0,10.0,8615.0,25.0,8615.0')] ).
cnf(9863,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),zero),zero),
inference(spr,[status(thm),theory(equality)],[438,287]),
[iquote('0:SpR:438.0,287.0')] ).
cnf(9990,plain,
equal(multiplication(antidomain(addition(u,v)),u),zero),
inference(rew,[status(thm),theory(equality)],[73,9863,13]),
[iquote('0:Rew:73.0,9863.0,13.0,9863.0')] ).
cnf(9991,plain,
equal(addition(zero,multiplication(antidomain(addition(u,v)),v)),zero),
inference(rew,[status(thm),theory(equality)],[9990,438]),
[iquote('0:Rew:9990.0,438.0')] ).
cnf(9998,plain,
equal(multiplication(antidomain(addition(u,v)),v),zero),
inference(rew,[status(thm),theory(equality)],[73,9991]),
[iquote('0:Rew:73.0,9991.0')] ).
cnf(11746,plain,
equal(addition(multiplication(antidomain(addition(u,forward_diamond(skc2,skc3))),antidomain(antidomain(skc3))),zero),zero),
inference(spr,[status(thm),theory(equality)],[9998,5019]),
[iquote('0:SpR:9998.0,5019.0')] ).
cnf(11781,plain,
equal(multiplication(antidomain(addition(u,forward_diamond(skc2,skc3))),antidomain(antidomain(skc3))),zero),
inference(rew,[status(thm),theory(equality)],[73,11746,13]),
[iquote('0:Rew:73.0,11746.0,13.0,11746.0')] ).
cnf(11782,plain,
equal(domain_difference(antidomain(addition(u,forward_diamond(skc2,skc3))),antidomain(skc3)),zero),
inference(rew,[status(thm),theory(equality)],[4865,11781]),
[iquote('0:Rew:4865.0,11781.0')] ).
cnf(12225,plain,
equal(addition(multiplication(antidomain(antidomain(skc3)),antidomain(antidomain(coantidomain(forward_diamond(skc2,skc3))))),zero),zero),
inference(spr,[status(thm),theory(equality)],[1571,5020]),
[iquote('0:SpR:1571.0,5020.0')] ).
cnf(12262,plain,
equal(multiplication(antidomain(antidomain(skc3)),antidomain(antidomain(coantidomain(forward_diamond(skc2,skc3))))),zero),
inference(rew,[status(thm),theory(equality)],[73,12225,13]),
[iquote('0:Rew:73.0,12225.0,13.0,12225.0')] ).
cnf(12263,plain,
equal(domain_difference(antidomain(antidomain(skc3)),antidomain(coantidomain(forward_diamond(skc2,skc3)))),zero),
inference(rew,[status(thm),theory(equality)],[4865,12262]),
[iquote('0:Rew:4865.0,12262.0')] ).
cnf(12264,plain,
equal(domain_difference(skc3,antidomain(coantidomain(forward_diamond(skc2,skc3)))),zero),
inference(rew,[status(thm),theory(equality)],[4957,12263]),
[iquote('0:Rew:4957.0,12263.0')] ).
cnf(12985,plain,
equal(antidomain(antidomain(addition(multiplication(u,antidomain(antidomain(v))),zero))),forward_diamond(addition(u,antidomain(antidomain(antidomain(v)))),v)),
inference(spr,[status(thm),theory(equality)],[8,374]),
[iquote('0:SpR:8.0,374.0')] ).
cnf(13069,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(addition(u,antidomain(v)),v)),
inference(rew,[status(thm),theory(equality)],[73,12985,13,4786]),
[iquote('0:Rew:73.0,12985.0,13.0,12985.0,4786.0,12985.0')] ).
cnf(13070,plain,
equal(forward_diamond(addition(u,antidomain(v)),v),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[4931,13069,4936]),
[iquote('0:Rew:4931.0,13069.0,4936.0,13069.0')] ).
cnf(20333,plain,
equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4483,8752]),
[iquote('0:SpR:4483.0,8752.0')] ).
cnf(20344,plain,
equal(addition(antidomain(antidomain(u)),zero),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[20333,4851]),
[iquote('0:Rew:20333.0,4851.0')] ).
cnf(20346,plain,
equal(coantidomain(antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[73,20344,13]),
[iquote('0:Rew:73.0,20344.0,13.0,20344.0')] ).
cnf(46732,plain,
( ~ leq(u,zero)
| equal(forward_diamond(antidomain(v),v),forward_diamond(u,v)) ),
inference(spr,[status(thm),theory(equality)],[6792,13070]),
[iquote('0:SpR:6792.1,13070.0')] ).
cnf(46766,plain,
( ~ leq(u,zero)
| equal(forward_diamond(u,v),zero) ),
inference(rew,[status(thm),theory(equality)],[1444,46732]),
[iquote('0:Rew:1444.0,46732.1')] ).
cnf(46829,plain,
( ~ leq(u,zero)
| equal(antidomain(antidomain(u)),zero) ),
inference(spr,[status(thm),theory(equality)],[46766,196]),
[iquote('0:SpR:46766.1,196.0')] ).
cnf(47008,plain,
( ~ leq(u,zero)
| equal(antidomain(zero),antidomain(u)) ),
inference(spr,[status(thm),theory(equality)],[46829,4786]),
[iquote('0:SpR:46829.1,4786.0')] ).
cnf(47198,plain,
( ~ leq(u,zero)
| equal(antidomain(u),one) ),
inference(rew,[status(thm),theory(equality)],[98,47008]),
[iquote('0:Rew:98.0,47008.1')] ).
cnf(48070,plain,
( ~ leq(addition(u,forward_diamond(skc2,skc3)),zero)
| equal(domain_difference(one,antidomain(skc3)),zero) ),
inference(spr,[status(thm),theory(equality)],[47198,11782]),
[iquote('0:SpR:47198.1,11782.0')] ).
cnf(48266,plain,
( ~ leq(addition(u,forward_diamond(skc2,skc3)),zero)
| equal(antidomain(antidomain(skc3)),zero) ),
inference(rew,[status(thm),theory(equality)],[134,48070]),
[iquote('0:Rew:134.0,48070.1')] ).
cnf(48267,plain,
~ leq(addition(u,forward_diamond(skc2,skc3)),zero),
inference(mrr,[status(thm)],[48266,34]),
[iquote('0:MRR:48266.1,34.0')] ).
cnf(48579,plain,
~ leq(addition(forward_diamond(skc2,skc3),u),zero),
inference(spl,[status(thm),theory(equality)],[13,48267]),
[iquote('0:SpL:13.0,48267.0')] ).
cnf(48941,plain,
~ leq(forward_diamond(star(skc2),domain_difference(skc3,forward_diamond(skc2,skc3))),zero),
inference(spl,[status(thm),theory(equality)],[5154,48579]),
[iquote('0:SpL:5154.0,48579.0')] ).
cnf(53422,plain,
equal(coantidomain(forward_diamond(u,v)),antidomain(forward_diamond(u,v))),
inference(spr,[status(thm),theory(equality)],[4931,20346]),
[iquote('0:SpR:4931.0,20346.0')] ).
cnf(53698,plain,
equal(domain_difference(skc3,antidomain(antidomain(forward_diamond(skc2,skc3)))),zero),
inference(rew,[status(thm),theory(equality)],[53422,12264]),
[iquote('0:Rew:53422.0,12264.0')] ).
cnf(53813,plain,
equal(domain_difference(skc3,forward_diamond(skc2,skc3)),zero),
inference(rew,[status(thm),theory(equality)],[4931,53698]),
[iquote('0:Rew:4931.0,53698.0')] ).
cnf(53822,plain,
~ leq(forward_diamond(star(skc2),zero),zero),
inference(rew,[status(thm),theory(equality)],[53813,48941]),
[iquote('0:Rew:53813.0,48941.0')] ).
cnf(53824,plain,
~ leq(zero,zero),
inference(rew,[status(thm),theory(equality)],[197,53822]),
[iquote('0:Rew:197.0,53822.0')] ).
cnf(53825,plain,
$false,
inference(mrr,[status(thm)],[53824,121]),
[iquote('0:MRR:53824.0,121.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : KLE132+1 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.10 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Thu Jun 16 13:04:00 EDT 2022
% 0.09/0.30 % CPUTime :
% 17.63/17.83
% 17.63/17.83 SPASS V 3.9
% 17.63/17.83 SPASS beiseite: Proof found.
% 17.63/17.83 % SZS status Theorem
% 17.63/17.83 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.63/17.83 SPASS derived 35155 clauses, backtracked 0 clauses, performed 0 splits and kept 6189 clauses.
% 17.63/17.83 SPASS allocated 135754 KBytes.
% 17.63/17.83 SPASS spent 0:0:17.48 on the problem.
% 17.63/17.83 0:00:00.03 for the input.
% 17.63/17.83 0:00:00.02 for the FLOTTER CNF translation.
% 17.63/17.83 0:00:00.22 for inferences.
% 17.63/17.83 0:00:00.00 for the backtracking.
% 17.63/17.83 0:0:17.14 for the reduction.
% 17.63/17.83
% 17.63/17.83
% 17.63/17.83 Here is a proof with depth 8, length 139 :
% 17.63/17.83 % SZS output start Refutation
% See solution above
% 18.05/18.24 Formulae used in the proof : goals additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity right_annihilation domain1 domain4 codomain1 additive_commutativity domain3 codomain3 order domain_difference forward_diamond additive_associativity multiplicative_associativity right_distributivity left_distributivity domain2 codomain2
% 18.05/18.24
%------------------------------------------------------------------------------