TSTP Solution File: KLE109+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE109+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 02:28:34 EDT 2022
% Result : Theorem 185.91s 186.10s
% Output : Refutation 193.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 26
% Syntax : Number of clauses : 184 ( 179 unt; 0 nHn; 184 RR)
% Number of literals : 189 ( 0 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE109+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE109+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE109+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE109+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(zero,u),zero),
file('KLE109+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE109+1.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE109+1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE109+1.p',unknown),
[] ).
cnf(10,axiom,
equal(codomain(u),coantidomain(coantidomain(u))),
file('KLE109+1.p',unknown),
[] ).
cnf(11,axiom,
equal(c(u),antidomain(domain__dfg(u))),
file('KLE109+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE109+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE109+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE109+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE109+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE109+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE109+1.p',unknown),
[] ).
cnf(18,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE109+1.p',unknown),
[] ).
cnf(19,axiom,
equal(codomain(multiplication(codomain(u),v)),backward_diamond(v,u)),
file('KLE109+1.p',unknown),
[] ).
cnf(21,axiom,
equal(c(backward_diamond(u,c(v))),backward_box(u,v)),
file('KLE109+1.p',unknown),
[] ).
cnf(22,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE109+1.p',unknown),
[] ).
cnf(23,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE109+1.p',unknown),
[] ).
cnf(24,axiom,
~ equal(addition(forward_diamond(skc3,backward_box(skc3,domain__dfg(skc2))),domain__dfg(skc2)),domain__dfg(skc2)),
file('KLE109+1.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE109+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE109+1.p',unknown),
[] ).
cnf(27,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE109+1.p',unknown),
[] ).
cnf(28,axiom,
equal(addition(coantidomain(multiplication(u,v)),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),
file('KLE109+1.p',unknown),
[] ).
cnf(29,plain,
equal(c(u),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[8,11]),
[iquote('0:Rew:8.0,11.0')] ).
cnf(30,plain,
equal(addition(coantidomain(u),coantidomain(coantidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[12,14]),
[iquote('0:Rew:12.0,14.0')] ).
cnf(31,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[12,13]),
[iquote('0:Rew:12.0,13.0')] ).
cnf(32,plain,
equal(antidomain(antidomain(antidomain(backward_diamond(u,antidomain(antidomain(antidomain(v))))))),backward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[29,21]),
[iquote('0:Rew:29.0,21.0,29.0,21.0')] ).
cnf(34,plain,
equal(backward_diamond(u,v),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(v)),u)))),
inference(rew,[status(thm),theory(equality)],[10,19]),
[iquote('0:Rew:10.0,19.0,10.0,19.0')] ).
cnf(35,plain,
equal(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(u))))),v)))))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[34,32]),
[iquote('0:Rew:34.0,32.0')] ).
cnf(36,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[8,18]),
[iquote('0:Rew:8.0,18.0,8.0,18.0')] ).
cnf(37,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[8,17]),
[iquote('0:Rew:8.0,17.0')] ).
cnf(38,plain,
~ equal(addition(antidomain(antidomain(skc2)),forward_diamond(skc3,backward_box(skc3,antidomain(antidomain(skc2))))),antidomain(antidomain(skc2))),
inference(rew,[status(thm),theory(equality)],[12,24,8]),
[iquote('0:Rew:12.0,24.0,8.0,24.0')] ).
cnf(52,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(56,plain,
equal(coantidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(63,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(72,plain,
equal(addition(zero,coantidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[56,30]),
[iquote('0:SpR:56.0,30.0')] ).
cnf(74,plain,
equal(coantidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[63,72]),
[iquote('0:Rew:63.0,72.0')] ).
cnf(86,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[52,31]),
[iquote('0:SpR:52.0,31.0')] ).
cnf(88,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[63,86]),
[iquote('0:Rew:63.0,86.0')] ).
cnf(96,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[15,12]),
[iquote('0:SpR:15.1,12.0')] ).
cnf(167,plain,
equal(antidomain(antidomain(domain_difference(u,antidomain(v)))),forward_diamond(antidomain(antidomain(u)),v)),
inference(spr,[status(thm),theory(equality)],[37,36]),
[iquote('0:SpR:37.0,36.0')] ).
cnf(197,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),multiplication(zero,v)),
inference(spr,[status(thm),theory(equality)],[7,23]),
[iquote('0:SpR:7.0,23.0')] ).
cnf(207,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),zero),
inference(rew,[status(thm),theory(equality)],[6,197]),
[iquote('0:Rew:6.0,197.0')] ).
cnf(267,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,22]),
[iquote('0:SpR:2.0,22.0')] ).
cnf(296,plain,
equal(addition(coantidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[30,267]),
[iquote('0:SpR:30.0,267.0')] ).
cnf(297,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[31,267]),
[iquote('0:SpR:31.0,267.0')] ).
cnf(299,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[267,16]),
[iquote('0:SpL:267.0,16.0')] ).
cnf(301,plain,
equal(addition(one,coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,296]),
[iquote('0:Rew:12.0,296.0')] ).
cnf(302,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,297]),
[iquote('0:Rew:12.0,297.0')] ).
cnf(305,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[299]),
[iquote('0:Obv:299.0')] ).
cnf(311,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,305]),
[iquote('0:SpR:12.0,305.0')] ).
cnf(368,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[26,9]),
[iquote('0:SpR:26.0,9.0')] ).
cnf(382,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[30,26]),
[iquote('0:SpR:30.0,26.0')] ).
cnf(383,plain,
equal(addition(multiplication(one,u),multiplication(coantidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[301,26]),
[iquote('0:SpR:301.0,26.0')] ).
cnf(384,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[31,26]),
[iquote('0:SpR:31.0,26.0')] ).
cnf(391,plain,
equal(addition(u,multiplication(coantidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,383]),
[iquote('0:Rew:4.0,383.0')] ).
cnf(396,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,382]),
[iquote('0:Rew:4.0,382.0')] ).
cnf(397,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,384]),
[iquote('0:Rew:4.0,384.0')] ).
cnf(463,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),multiplication(antidomain(addition(u,v)),v)),zero),
inference(spr,[status(thm),theory(equality)],[25,7]),
[iquote('0:SpR:25.0,7.0')] ).
cnf(478,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[30,25]),
[iquote('0:SpR:30.0,25.0')] ).
cnf(480,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[31,25]),
[iquote('0:SpR:31.0,25.0')] ).
cnf(481,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[302,25]),
[iquote('0:SpR:302.0,25.0')] ).
cnf(490,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,481]),
[iquote('0:Rew:3.0,481.0')] ).
cnf(495,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,478]),
[iquote('0:Rew:3.0,478.0')] ).
cnf(496,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,480]),
[iquote('0:Rew:3.0,480.0')] ).
cnf(555,plain,
( ~ leq(forward_diamond(skc3,backward_box(skc3,antidomain(antidomain(skc2)))),antidomain(antidomain(skc2)))
| ~ equal(antidomain(antidomain(skc2)),antidomain(antidomain(skc2))) ),
inference(spl,[status(thm),theory(equality)],[96,38]),
[iquote('0:SpL:96.1,38.0')] ).
cnf(556,plain,
~ leq(forward_diamond(skc3,backward_box(skc3,antidomain(antidomain(skc2)))),antidomain(antidomain(skc2))),
inference(obv,[status(thm),theory(equality)],[555]),
[iquote('0:Obv:555.1')] ).
cnf(626,plain,
equal(addition(one,backward_box(u,v)),one),
inference(spr,[status(thm),theory(equality)],[35,302]),
[iquote('0:SpR:35.0,302.0')] ).
cnf(636,plain,
equal(antidomain(antidomain(multiplication(u,backward_box(v,w)))),forward_diamond(u,antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(w))))),v)))))),
inference(spr,[status(thm),theory(equality)],[35,36]),
[iquote('0:SpR:35.0,36.0')] ).
cnf(641,plain,
equal(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(one)))),u)))))),backward_box(u,zero)),
inference(spr,[status(thm),theory(equality)],[88,35]),
[iquote('0:SpR:88.0,35.0')] ).
cnf(642,plain,
equal(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(forward_diamond(u,v)))),w)))))),backward_box(w,multiplication(u,antidomain(antidomain(v))))),
inference(spr,[status(thm),theory(equality)],[36,35]),
[iquote('0:SpR:36.0,35.0')] ).
cnf(657,plain,
equal(backward_box(u,zero),antidomain(antidomain(antidomain(coantidomain(coantidomain(u)))))),
inference(rew,[status(thm),theory(equality)],[4,641,74,56,88,52]),
[iquote('0:Rew:4.0,641.0,74.0,641.0,56.0,641.0,88.0,641.0,52.0,641.0')] ).
cnf(713,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)],[7,28]),
[iquote('0:SpR:7.0,28.0')] ).
cnf(738,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
inference(rew,[status(thm),theory(equality)],[301,713,74]),
[iquote('0:Rew:301.0,713.0,74.0,713.0')] ).
cnf(844,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)],[7,27]),
[iquote('0:SpR:7.0,27.0')] ).
cnf(847,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)],[9,27]),
[iquote('0:SpR:9.0,27.0')] ).
cnf(851,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v)))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v)))))),
inference(spr,[status(thm),theory(equality)],[207,27]),
[iquote('0:SpR:207.0,27.0')] ).
cnf(866,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[302,844,88]),
[iquote('0:Rew:302.0,844.0,88.0,844.0')] ).
cnf(867,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(coantidomain(u))))),one),
inference(rew,[status(thm),theory(equality)],[302,847,88]),
[iquote('0:Rew:302.0,847.0,88.0,847.0')] ).
cnf(868,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v))))),one),
inference(rew,[status(thm),theory(equality)],[302,851,88]),
[iquote('0:Rew:302.0,851.0,88.0,851.0')] ).
cnf(925,plain,
equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
inference(spr,[status(thm),theory(equality)],[738,9]),
[iquote('0:SpR:738.0,9.0')] ).
cnf(951,plain,
equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
inference(rew,[status(thm),theory(equality)],[3,925,23]),
[iquote('0:Rew:3.0,925.0,23.0,925.0')] ).
cnf(1181,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[866,7]),
[iquote('0:SpR:866.0,7.0')] ).
cnf(1226,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,1181]),
[iquote('0:Rew:4.0,1181.0')] ).
cnf(1301,plain,
equal(multiplication(one,multiplication(u,antidomain(antidomain(coantidomain(u))))),zero),
inference(spr,[status(thm),theory(equality)],[867,7]),
[iquote('0:SpR:867.0,7.0')] ).
cnf(1341,plain,
equal(multiplication(u,antidomain(antidomain(coantidomain(u)))),zero),
inference(rew,[status(thm),theory(equality)],[4,1301]),
[iquote('0:Rew:4.0,1301.0')] ).
cnf(1622,plain,
leq(multiplication(u,antidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[490,311]),
[iquote('0:SpR:490.0,311.0')] ).
cnf(4009,plain,
equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
inference(spr,[status(thm),theory(equality)],[951,396]),
[iquote('0:SpR:951.0,396.0')] ).
cnf(4012,plain,
equal(addition(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),zero),coantidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[9,396]),
[iquote('0:SpR:9.0,396.0')] ).
cnf(4035,plain,
equal(multiplication(coantidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[63,4009,12]),
[iquote('0:Rew:63.0,4009.0,12.0,4009.0')] ).
cnf(4048,plain,
equal(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[63,4012,12]),
[iquote('0:Rew:63.0,4012.0,12.0,4012.0')] ).
cnf(4230,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1226,397]),
[iquote('0:SpR:1226.0,397.0')] ).
cnf(4236,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),u)),u),
inference(spr,[status(thm),theory(equality)],[7,397]),
[iquote('0:SpR:7.0,397.0')] ).
cnf(4246,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),antidomain(antidomain(u)))),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[1226,397]),
[iquote('0:SpR:1226.0,397.0')] ).
cnf(4254,plain,
equal(multiplication(antidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[63,4236]),
[iquote('0:Rew:63.0,4236.0')] ).
cnf(4268,plain,
equal(domain_difference(u,antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[63,4246,37]),
[iquote('0:Rew:63.0,4246.0,37.0,4246.0')] ).
cnf(4271,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[63,4230,12]),
[iquote('0:Rew:63.0,4230.0,12.0,4230.0')] ).
cnf(4311,plain,
equal(domain_difference(antidomain(u),u),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[4254,37]),
[iquote('0:SpR:4254.0,37.0')] ).
cnf(4372,plain,
equal(domain_difference(backward_box(u,v),antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(v))))),u)))))),backward_box(u,v)),
inference(spr,[status(thm),theory(equality)],[35,4311]),
[iquote('0:SpR:35.0,4311.0')] ).
cnf(4475,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)],[4254,495]),
[iquote('0:SpR:4254.0,495.0')] ).
cnf(4487,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[9,495]),
[iquote('0:SpR:9.0,495.0')] ).
cnf(4501,plain,
equal(multiplication(u,coantidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[63,4487]),
[iquote('0:Rew:63.0,4487.0')] ).
cnf(4502,plain,
equal(coantidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4501,4048]),
[iquote('0:Rew:4501.0,4048.0')] ).
cnf(4564,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)],[12,4475]),
[iquote('0:Rew:12.0,4475.0')] ).
cnf(4751,plain,
equal(addition(multiplication(u,antidomain(coantidomain(u))),zero),u),
inference(spr,[status(thm),theory(equality)],[1341,496]),
[iquote('0:SpR:1341.0,496.0')] ).
cnf(4759,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)],[4035,496]),
[iquote('0:SpR:4035.0,496.0')] ).
cnf(4771,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1226,496]),
[iquote('0:SpR:1226.0,496.0')] ).
cnf(4784,plain,
equal(multiplication(u,antidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[63,4751,12]),
[iquote('0:Rew:63.0,4751.0,12.0,4751.0')] ).
cnf(4795,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[63,4771]),
[iquote('0:Rew:63.0,4771.0')] ).
cnf(4796,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4271,4795]),
[iquote('0:Rew:4271.0,4795.0')] ).
cnf(4797,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(u))))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4796,35]),
[iquote('0:Rew:4796.0,35.0')] ).
cnf(4823,plain,
equal(antidomain(antidomain(multiplication(u,backward_box(v,w)))),forward_diamond(u,antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(w))),v)))))),
inference(rew,[status(thm),theory(equality)],[4796,636]),
[iquote('0:Rew:4796.0,636.0')] ).
cnf(4845,plain,
equal(domain_difference(backward_box(u,v),antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(v))),u)))))),backward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4796,4372]),
[iquote('0:Rew:4796.0,4372.0')] ).
cnf(4874,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(forward_diamond(u,v)))),w)))),backward_box(w,multiplication(u,antidomain(antidomain(v))))),
inference(rew,[status(thm),theory(equality)],[4796,642]),
[iquote('0:Rew:4796.0,642.0')] ).
cnf(4875,plain,
equal(backward_box(u,zero),antidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[4796,657]),
[iquote('0:Rew:4796.0,657.0')] ).
cnf(4923,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4796,4797]),
[iquote('0:Rew:4796.0,4797.0')] ).
cnf(4967,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)],[12,4759]),
[iquote('0:Rew:12.0,4759.0')] ).
cnf(4968,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4796,4967]),
[iquote('0:Rew:4796.0,4967.0')] ).
cnf(4973,plain,
equal(antidomain(antidomain(backward_box(u,v))),backward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4268,4845,4923]),
[iquote('0:Rew:4268.0,4845.0,4923.0,4845.0')] ).
cnf(4982,plain,
equal(antidomain(antidomain(multiplication(u,backward_box(v,w)))),forward_diamond(u,backward_box(v,w))),
inference(rew,[status(thm),theory(equality)],[4923,4823]),
[iquote('0:Rew:4923.0,4823.0')] ).
cnf(4984,plain,
equal(backward_box(u,multiplication(v,antidomain(antidomain(w)))),backward_box(u,forward_diamond(v,w))),
inference(rew,[status(thm),theory(equality)],[4923,4874]),
[iquote('0:Rew:4923.0,4874.0')] ).
cnf(5073,plain,
equal(multiplication(antidomain(u),antidomain(v)),domain_difference(antidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[4796,37]),
[iquote('0:SpR:4796.0,37.0')] ).
cnf(5086,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4796,36]),
[iquote('0:SpR:4796.0,36.0')] ).
cnf(5112,plain,
equal(antidomain(antidomain(forward_diamond(u,v))),forward_diamond(u,v)),
inference(spr,[status(thm),theory(equality)],[36,4796]),
[iquote('0:SpR:36.0,4796.0')] ).
cnf(5116,plain,
equal(antidomain(domain_difference(u,antidomain(v))),antidomain(forward_diamond(antidomain(antidomain(u)),v))),
inference(spr,[status(thm),theory(equality)],[167,4796]),
[iquote('0:SpR:167.0,4796.0')] ).
cnf(5150,plain,
equal(antidomain(domain_difference(antidomain(u),antidomain(multiplication(u,v)))),one),
inference(rew,[status(thm),theory(equality)],[5073,868]),
[iquote('0:Rew:5073.0,868.0')] ).
cnf(5159,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[5086,36]),
[iquote('0:Rew:5086.0,36.0')] ).
cnf(5223,plain,
equal(antidomain(forward_diamond(antidomain(antidomain(antidomain(u))),multiplication(u,v))),one),
inference(rew,[status(thm),theory(equality)],[5116,5150]),
[iquote('0:Rew:5116.0,5150.0')] ).
cnf(5255,plain,
equal(antidomain(forward_diamond(antidomain(u),multiplication(u,v))),one),
inference(rew,[status(thm),theory(equality)],[4796,5223]),
[iquote('0:Rew:4796.0,5223.0')] ).
cnf(5686,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),v)))),backward_box(v,antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[4796,4923]),
[iquote('0:SpR:4796.0,4923.0')] ).
cnf(5688,plain,
equal(backward_box(u,u),antidomain(coantidomain(coantidomain(zero)))),
inference(spr,[status(thm),theory(equality)],[951,4923]),
[iquote('0:SpR:951.0,4923.0')] ).
cnf(5701,plain,
equal(backward_box(u,u),one),
inference(rew,[status(thm),theory(equality)],[88,5688,56,74]),
[iquote('0:Rew:88.0,5688.0,56.0,5688.0,74.0,5688.0')] ).
cnf(5713,plain,
equal(backward_box(u,antidomain(antidomain(v))),backward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4923,5686]),
[iquote('0:Rew:4923.0,5686.0')] ).
cnf(5716,plain,
~ leq(forward_diamond(skc3,backward_box(skc3,skc2)),antidomain(antidomain(skc2))),
inference(rew,[status(thm),theory(equality)],[5713,556]),
[iquote('0:Rew:5713.0,556.0')] ).
cnf(6550,plain,
equal(antidomain(multiplication(u,backward_box(v,w))),antidomain(forward_diamond(u,backward_box(v,w)))),
inference(spr,[status(thm),theory(equality)],[4982,4796]),
[iquote('0:SpR:4982.0,4796.0')] ).
cnf(6793,plain,
equal(backward_box(u,multiplication(v,antidomain(w))),backward_box(u,forward_diamond(v,antidomain(w)))),
inference(spr,[status(thm),theory(equality)],[4796,4984]),
[iquote('0:SpR:4796.0,4984.0')] ).
cnf(8812,plain,
equal(multiplication(one,forward_diamond(antidomain(u),multiplication(u,v))),zero),
inference(spr,[status(thm),theory(equality)],[5255,7]),
[iquote('0:SpR:5255.0,7.0')] ).
cnf(8987,plain,
equal(forward_diamond(antidomain(u),multiplication(u,v)),zero),
inference(rew,[status(thm),theory(equality)],[4,8812]),
[iquote('0:Rew:4.0,8812.0')] ).
cnf(9668,plain,
equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[490,368]),
[iquote('0:SpR:490.0,368.0')] ).
cnf(9789,plain,
equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[63,9668,9,23]),
[iquote('0:Rew:63.0,9668.0,9.0,9668.0,23.0,9668.0')] ).
cnf(11017,plain,
equal(addition(multiplication(antidomain(u),u),multiplication(antidomain(u),multiplication(coantidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[391,463]),
[iquote('0:SpR:391.0,463.0')] ).
cnf(11135,plain,
equal(multiplication(antidomain(u),multiplication(coantidomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[63,11017,7]),
[iquote('0:Rew:63.0,11017.0,7.0,11017.0')] ).
cnf(14490,plain,
equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4501,9789]),
[iquote('0:SpR:4501.0,9789.0')] ).
cnf(14501,plain,
equal(addition(antidomain(antidomain(u)),zero),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[14490,4968]),
[iquote('0:Rew:14490.0,4968.0')] ).
cnf(14503,plain,
equal(coantidomain(antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[63,14501,12]),
[iquote('0:Rew:63.0,14501.0,12.0,14501.0')] ).
cnf(14512,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(antidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[14503,4923]),
[iquote('0:Rew:14503.0,4923.0')] ).
cnf(14849,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[14503,14512]),
[iquote('0:Rew:14503.0,14512.0')] ).
cnf(14850,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(antidomain(u),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4796,14849]),
[iquote('0:Rew:4796.0,14849.0')] ).
cnf(17039,plain,
equal(multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4784,11135]),
[iquote('0:SpR:4784.0,11135.0')] ).
cnf(17069,plain,
equal(addition(coantidomain(coantidomain(u)),zero),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[17039,4564]),
[iquote('0:Rew:17039.0,4564.0')] ).
cnf(17072,plain,
equal(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[63,17069,12]),
[iquote('0:Rew:63.0,17069.0,12.0,17069.0')] ).
cnf(17296,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(u)),v)))),backward_box(v,antidomain(coantidomain(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[17072,14850]),
[iquote('0:SpR:17072.0,14850.0')] ).
cnf(17324,plain,
equal(coantidomain(coantidomain(coantidomain(u))),antidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[17072,14503]),
[iquote('0:SpR:17072.0,14503.0')] ).
cnf(17424,plain,
equal(antidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4502,17324]),
[iquote('0:Rew:4502.0,17324.0')] ).
cnf(17426,plain,
equal(coantidomain(multiplication(antidomain(u),v)),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[17424,14850]),
[iquote('0:Rew:17424.0,14850.0')] ).
cnf(17428,plain,
equal(backward_box(u,zero),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[17424,4875]),
[iquote('0:Rew:17424.0,4875.0')] ).
cnf(17594,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(u)),v)),backward_box(v,coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[17424,17296]),
[iquote('0:Rew:17424.0,17296.0,17424.0,17296.0')] ).
cnf(17595,plain,
equal(addition(coantidomain(multiplication(u,v)),backward_box(v,coantidomain(u))),backward_box(v,coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[17594,28]),
[iquote('0:Rew:17594.0,28.0')] ).
cnf(17625,plain,
equal(addition(backward_box(u,coantidomain(v)),coantidomain(multiplication(v,u))),backward_box(u,coantidomain(v))),
inference(rew,[status(thm),theory(equality)],[12,17595]),
[iquote('0:Rew:12.0,17595.0')] ).
cnf(18195,plain,
equal(multiplication(multiplication(antidomain(u),v),backward_box(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[17426,9]),
[iquote('0:SpR:17426.0,9.0')] ).
cnf(18307,plain,
equal(multiplication(antidomain(u),multiplication(v,backward_box(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[23,18195]),
[iquote('0:Rew:23.0,18195.0')] ).
cnf(18908,plain,
equal(addition(backward_box(u,backward_box(v,w)),coantidomain(multiplication(multiplication(antidomain(w),v),u))),backward_box(u,backward_box(v,w))),
inference(spr,[status(thm),theory(equality)],[17426,17625]),
[iquote('0:SpR:17426.0,17625.0')] ).
cnf(18968,plain,
equal(addition(backward_box(u,backward_box(v,w)),backward_box(multiplication(v,u),w)),backward_box(u,backward_box(v,w))),
inference(rew,[status(thm),theory(equality)],[17426,18908,23]),
[iquote('0:Rew:17426.0,18908.0,23.0,18908.0')] ).
cnf(22733,plain,
equal(addition(backward_box(u,backward_box(v,multiplication(v,u))),one),backward_box(u,backward_box(v,multiplication(v,u)))),
inference(spr,[status(thm),theory(equality)],[5701,18968]),
[iquote('0:SpR:5701.0,18968.0')] ).
cnf(22828,plain,
equal(backward_box(u,backward_box(v,multiplication(v,u))),one),
inference(rew,[status(thm),theory(equality)],[626,22733,12]),
[iquote('0:Rew:626.0,22733.0,12.0,22733.0')] ).
cnf(45956,plain,
equal(multiplication(antidomain(backward_box(u,multiplication(u,v))),multiplication(v,one)),zero),
inference(spr,[status(thm),theory(equality)],[22828,18307]),
[iquote('0:SpR:22828.0,18307.0')] ).
cnf(46106,plain,
equal(multiplication(antidomain(backward_box(u,multiplication(u,v))),v),zero),
inference(rew,[status(thm),theory(equality)],[3,45956]),
[iquote('0:Rew:3.0,45956.0')] ).
cnf(220522,plain,
equal(addition(zero,multiplication(antidomain(antidomain(backward_box(u,multiplication(u,v)))),v)),v),
inference(spr,[status(thm),theory(equality)],[46106,397]),
[iquote('0:SpR:46106.0,397.0')] ).
cnf(220821,plain,
equal(multiplication(backward_box(u,multiplication(u,v)),v),v),
inference(rew,[status(thm),theory(equality)],[63,220522,4973]),
[iquote('0:Rew:63.0,220522.0,4973.0,220522.0')] ).
cnf(221006,plain,
leq(antidomain(u),backward_box(v,multiplication(v,antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[220821,1622]),
[iquote('0:SpR:220821.0,1622.0')] ).
cnf(221276,plain,
leq(antidomain(u),backward_box(v,forward_diamond(v,antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[6793,221006]),
[iquote('0:Rew:6793.0,221006.0')] ).
cnf(223146,plain,
leq(antidomain(antidomain(u)),backward_box(v,forward_diamond(v,u))),
inference(spr,[status(thm),theory(equality)],[5159,221276]),
[iquote('0:SpR:5159.0,221276.0')] ).
cnf(227987,plain,
leq(antidomain(antidomain(multiplication(u,v))),backward_box(antidomain(u),zero)),
inference(spr,[status(thm),theory(equality)],[8987,223146]),
[iquote('0:SpR:8987.0,223146.0')] ).
cnf(228103,plain,
leq(antidomain(antidomain(multiplication(u,v))),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[14503,227987,17428]),
[iquote('0:Rew:14503.0,227987.0,17428.0,227987.0')] ).
cnf(228535,plain,
leq(antidomain(antidomain(u)),antidomain(antidomain(backward_box(v,multiplication(v,u))))),
inference(spr,[status(thm),theory(equality)],[220821,228103]),
[iquote('0:SpR:220821.0,228103.0')] ).
cnf(228638,plain,
leq(antidomain(antidomain(u)),backward_box(v,multiplication(v,u))),
inference(rew,[status(thm),theory(equality)],[4973,228535]),
[iquote('0:Rew:4973.0,228535.0')] ).
cnf(235224,plain,
leq(antidomain(antidomain(multiplication(u,backward_box(u,v)))),backward_box(antidomain(v),zero)),
inference(spr,[status(thm),theory(equality)],[18307,228638]),
[iquote('0:SpR:18307.0,228638.0')] ).
cnf(235397,plain,
leq(antidomain(antidomain(multiplication(u,backward_box(u,v)))),antidomain(antidomain(v))),
inference(rew,[status(thm),theory(equality)],[14503,235224,17428]),
[iquote('0:Rew:14503.0,235224.0,17428.0,235224.0')] ).
cnf(235398,plain,
leq(antidomain(antidomain(forward_diamond(u,backward_box(u,v)))),antidomain(antidomain(v))),
inference(rew,[status(thm),theory(equality)],[6550,235397]),
[iquote('0:Rew:6550.0,235397.0')] ).
cnf(235399,plain,
leq(forward_diamond(u,backward_box(u,v)),antidomain(antidomain(v))),
inference(rew,[status(thm),theory(equality)],[5112,235398]),
[iquote('0:Rew:5112.0,235398.0')] ).
cnf(235400,plain,
$false,
inference(unc,[status(thm)],[235399,5716]),
[iquote('0:UnC:235399.0,5716.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE109+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 11:14:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 185.91/186.10
% 185.91/186.10 SPASS V 3.9
% 185.91/186.10 SPASS beiseite: Proof found.
% 185.91/186.10 % SZS status Theorem
% 185.91/186.10 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 185.91/186.10 SPASS derived 152951 clauses, backtracked 0 clauses, performed 0 splits and kept 17891 clauses.
% 185.91/186.10 SPASS allocated 245693 KBytes.
% 185.91/186.10 SPASS spent 0:03:05.48 on the problem.
% 185.91/186.10 0:00:00.03 for the input.
% 185.91/186.10 0:00:00.03 for the FLOTTER CNF translation.
% 185.91/186.10 0:00:00.90 for inferences.
% 185.91/186.10 0:00:00.00 for the backtracking.
% 185.91/186.10 0:03:04.14 for the reduction.
% 185.91/186.10
% 185.91/186.10
% 185.91/186.10 Here is a proof with depth 11, length 184 :
% 185.91/186.10 % SZS output start Refutation
% See solution above
% 193.66/193.84 Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation domain1 domain4 codomain1 codomain4 complement additive_commutativity domain3 codomain3 order domain_difference forward_diamond backward_diamond backward_box additive_associativity multiplicative_associativity goals right_distributivity left_distributivity domain2 codomain2
% 193.66/193.84
%------------------------------------------------------------------------------