TSTP Solution File: KLE110+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE110+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 189.59s 189.81s
% Output : Refutation 196.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of clauses : 150 ( 147 unt; 0 nHn; 150 RR)
% Number of literals : 153 ( 0 equ; 7 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('KLE110+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE110+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE110+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE110+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE110+1.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE110+1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE110+1.p',unknown),
[] ).
cnf(10,axiom,
equal(codomain(u),coantidomain(coantidomain(u))),
file('KLE110+1.p',unknown),
[] ).
cnf(11,axiom,
equal(c(u),antidomain(domain__dfg(u))),
file('KLE110+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE110+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE110+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE110+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE110+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE110+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE110+1.p',unknown),
[] ).
cnf(18,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE110+1.p',unknown),
[] ).
cnf(19,axiom,
equal(codomain(multiplication(codomain(u),v)),backward_diamond(v,u)),
file('KLE110+1.p',unknown),
[] ).
cnf(21,axiom,
equal(c(backward_diamond(u,c(v))),backward_box(u,v)),
file('KLE110+1.p',unknown),
[] ).
cnf(22,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE110+1.p',unknown),
[] ).
cnf(23,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE110+1.p',unknown),
[] ).
cnf(24,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE110+1.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE110+1.p',unknown),
[] ).
cnf(26,axiom,
~ equal(addition(domain__dfg(skc3),backward_box(skc2,forward_diamond(skc2,domain__dfg(skc3)))),backward_box(skc2,forward_diamond(skc2,domain__dfg(skc3)))),
file('KLE110+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('KLE110+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('KLE110+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(skc3)),backward_box(skc2,forward_diamond(skc2,antidomain(antidomain(skc3))))),backward_box(skc2,forward_diamond(skc2,antidomain(antidomain(skc3))))),
inference(rew,[status(thm),theory(equality)],[8,26]),
[iquote('0:Rew:8.0,26.0')] ).
cnf(39,plain,
~ leq(antidomain(antidomain(skc3)),backward_box(skc2,forward_diamond(skc2,antidomain(antidomain(skc3))))),
inference(res,[status(thm),theory(equality)],[15,38]),
[iquote('0:Res:15.1,38.0')] ).
cnf(53,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(57,plain,
equal(coantidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(64,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(73,plain,
equal(addition(zero,coantidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[57,30]),
[iquote('0:SpR:57.0,30.0')] ).
cnf(75,plain,
equal(coantidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[64,73]),
[iquote('0:Rew:64.0,73.0')] ).
cnf(87,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[53,31]),
[iquote('0:SpR:53.0,31.0')] ).
cnf(89,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[64,87]),
[iquote('0:Rew:64.0,87.0')] ).
cnf(268,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(297,plain,
equal(addition(coantidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[30,268]),
[iquote('0:SpR:30.0,268.0')] ).
cnf(298,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[31,268]),
[iquote('0:SpR:31.0,268.0')] ).
cnf(300,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[268,16]),
[iquote('0:SpL:268.0,16.0')] ).
cnf(302,plain,
equal(addition(one,coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,297]),
[iquote('0:Rew:12.0,297.0')] ).
cnf(303,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,298]),
[iquote('0:Rew:12.0,298.0')] ).
cnf(306,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[300]),
[iquote('0:Obv:300.0')] ).
cnf(312,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,306]),
[iquote('0:SpR:12.0,306.0')] ).
cnf(369,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[25,9]),
[iquote('0:SpR:25.0,9.0')] ).
cnf(383,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[30,25]),
[iquote('0:SpR:30.0,25.0')] ).
cnf(384,plain,
equal(addition(multiplication(one,u),multiplication(coantidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[302,25]),
[iquote('0:SpR:302.0,25.0')] ).
cnf(385,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[31,25]),
[iquote('0:SpR:31.0,25.0')] ).
cnf(392,plain,
equal(addition(u,multiplication(coantidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,384]),
[iquote('0:Rew:4.0,384.0')] ).
cnf(397,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,383]),
[iquote('0:Rew:4.0,383.0')] ).
cnf(398,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,385]),
[iquote('0:Rew:4.0,385.0')] ).
cnf(464,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),multiplication(antidomain(addition(u,v)),v)),zero),
inference(spr,[status(thm),theory(equality)],[24,7]),
[iquote('0:SpR:24.0,7.0')] ).
cnf(479,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[30,24]),
[iquote('0:SpR:30.0,24.0')] ).
cnf(481,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[31,24]),
[iquote('0:SpR:31.0,24.0')] ).
cnf(482,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[303,24]),
[iquote('0:SpR:303.0,24.0')] ).
cnf(491,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,482]),
[iquote('0:Rew:3.0,482.0')] ).
cnf(496,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,479]),
[iquote('0:Rew:3.0,479.0')] ).
cnf(497,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,481]),
[iquote('0:Rew:3.0,481.0')] ).
cnf(562,plain,
equal(addition(one,backward_box(u,v)),one),
inference(spr,[status(thm),theory(equality)],[35,303]),
[iquote('0:SpR:35.0,303.0')] ).
cnf(578,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(635,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(657,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
inference(rew,[status(thm),theory(equality)],[302,635,75]),
[iquote('0:Rew:302.0,635.0,75.0,635.0')] ).
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)],[7,27]),
[iquote('0:SpR:7.0,27.0')] ).
cnf(743,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(762,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[303,740,89]),
[iquote('0:Rew:303.0,740.0,89.0,740.0')] ).
cnf(763,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(coantidomain(u))))),one),
inference(rew,[status(thm),theory(equality)],[303,743,89]),
[iquote('0:Rew:303.0,743.0,89.0,743.0')] ).
cnf(940,plain,
equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
inference(spr,[status(thm),theory(equality)],[657,9]),
[iquote('0:SpR:657.0,9.0')] ).
cnf(966,plain,
equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
inference(rew,[status(thm),theory(equality)],[3,940,23]),
[iquote('0:Rew:3.0,940.0,23.0,940.0')] ).
cnf(1196,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[762,7]),
[iquote('0:SpR:762.0,7.0')] ).
cnf(1241,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,1196]),
[iquote('0:Rew:4.0,1196.0')] ).
cnf(1316,plain,
equal(multiplication(one,multiplication(u,antidomain(antidomain(coantidomain(u))))),zero),
inference(spr,[status(thm),theory(equality)],[763,7]),
[iquote('0:SpR:763.0,7.0')] ).
cnf(1356,plain,
equal(multiplication(u,antidomain(antidomain(coantidomain(u)))),zero),
inference(rew,[status(thm),theory(equality)],[4,1316]),
[iquote('0:Rew:4.0,1316.0')] ).
cnf(1637,plain,
leq(multiplication(u,antidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[491,312]),
[iquote('0:SpR:491.0,312.0')] ).
cnf(4145,plain,
equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
inference(spr,[status(thm),theory(equality)],[966,397]),
[iquote('0:SpR:966.0,397.0')] ).
cnf(4148,plain,
equal(addition(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),zero),coantidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[9,397]),
[iquote('0:SpR:9.0,397.0')] ).
cnf(4171,plain,
equal(multiplication(coantidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[64,4145,12]),
[iquote('0:Rew:64.0,4145.0,12.0,4145.0')] ).
cnf(4184,plain,
equal(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[64,4148,12]),
[iquote('0:Rew:64.0,4148.0,12.0,4148.0')] ).
cnf(4377,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1241,398]),
[iquote('0:SpR:1241.0,398.0')] ).
cnf(4383,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),u)),u),
inference(spr,[status(thm),theory(equality)],[7,398]),
[iquote('0:SpR:7.0,398.0')] ).
cnf(4393,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),antidomain(antidomain(u)))),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[1241,398]),
[iquote('0:SpR:1241.0,398.0')] ).
cnf(4401,plain,
equal(multiplication(antidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[64,4383]),
[iquote('0:Rew:64.0,4383.0')] ).
cnf(4415,plain,
equal(domain_difference(u,antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[64,4393,37]),
[iquote('0:Rew:64.0,4393.0,37.0,4393.0')] ).
cnf(4418,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[64,4377,12]),
[iquote('0:Rew:64.0,4377.0,12.0,4377.0')] ).
cnf(4458,plain,
equal(domain_difference(antidomain(u),u),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[4401,37]),
[iquote('0:SpR:4401.0,37.0')] ).
cnf(4525,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)],[35,4458]),
[iquote('0:SpR:35.0,4458.0')] ).
cnf(4637,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)],[4401,496]),
[iquote('0:SpR:4401.0,496.0')] ).
cnf(4649,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[9,496]),
[iquote('0:SpR:9.0,496.0')] ).
cnf(4663,plain,
equal(multiplication(u,coantidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[64,4649]),
[iquote('0:Rew:64.0,4649.0')] ).
cnf(4664,plain,
equal(coantidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4663,4184]),
[iquote('0:Rew:4663.0,4184.0')] ).
cnf(4726,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)],[12,4637]),
[iquote('0:Rew:12.0,4637.0')] ).
cnf(4914,plain,
equal(addition(multiplication(u,antidomain(coantidomain(u))),zero),u),
inference(spr,[status(thm),theory(equality)],[1356,497]),
[iquote('0:SpR:1356.0,497.0')] ).
cnf(4922,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)],[4171,497]),
[iquote('0:SpR:4171.0,497.0')] ).
cnf(4934,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1241,497]),
[iquote('0:SpR:1241.0,497.0')] ).
cnf(4947,plain,
equal(multiplication(u,antidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[64,4914,12]),
[iquote('0:Rew:64.0,4914.0,12.0,4914.0')] ).
cnf(4958,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[64,4934]),
[iquote('0:Rew:64.0,4934.0')] ).
cnf(4959,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4418,4958]),
[iquote('0:Rew:4418.0,4958.0')] ).
cnf(4960,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(u))))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4959,35]),
[iquote('0:Rew:4959.0,35.0')] ).
cnf(5008,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)],[4959,4525]),
[iquote('0:Rew:4959.0,4525.0')] ).
cnf(5037,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)],[4959,578]),
[iquote('0:Rew:4959.0,578.0')] ).
cnf(5086,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4959,4960]),
[iquote('0:Rew:4959.0,4960.0')] ).
cnf(5130,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)],[12,4922]),
[iquote('0:Rew:12.0,4922.0')] ).
cnf(5131,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4959,5130]),
[iquote('0:Rew:4959.0,5130.0')] ).
cnf(5136,plain,
equal(antidomain(antidomain(backward_box(u,v))),backward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4415,5008,5086]),
[iquote('0:Rew:4415.0,5008.0,5086.0,5008.0')] ).
cnf(5147,plain,
equal(backward_box(u,multiplication(v,antidomain(antidomain(w)))),backward_box(u,forward_diamond(v,w))),
inference(rew,[status(thm),theory(equality)],[5086,5037]),
[iquote('0:Rew:5086.0,5037.0')] ).
cnf(5252,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4959,36]),
[iquote('0:SpR:4959.0,36.0')] ).
cnf(5328,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[5252,36]),
[iquote('0:Rew:5252.0,36.0')] ).
cnf(5332,plain,
~ leq(antidomain(antidomain(skc3)),backward_box(skc2,forward_diamond(skc2,skc3))),
inference(rew,[status(thm),theory(equality)],[5328,39]),
[iquote('0:Rew:5328.0,39.0')] ).
cnf(5849,plain,
equal(backward_box(u,u),antidomain(coantidomain(coantidomain(zero)))),
inference(spr,[status(thm),theory(equality)],[966,5086]),
[iquote('0:SpR:966.0,5086.0')] ).
cnf(5862,plain,
equal(backward_box(u,u),one),
inference(rew,[status(thm),theory(equality)],[89,5849,57,75]),
[iquote('0:Rew:89.0,5849.0,57.0,5849.0,75.0,5849.0')] ).
cnf(7107,plain,
equal(backward_box(u,multiplication(v,antidomain(w))),backward_box(u,forward_diamond(v,antidomain(w)))),
inference(spr,[status(thm),theory(equality)],[4959,5147]),
[iquote('0:SpR:4959.0,5147.0')] ).
cnf(10034,plain,
equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[491,369]),
[iquote('0:SpR:491.0,369.0')] ).
cnf(10155,plain,
equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[64,10034,9,23]),
[iquote('0:Rew:64.0,10034.0,9.0,10034.0,23.0,10034.0')] ).
cnf(11398,plain,
equal(addition(multiplication(antidomain(u),u),multiplication(antidomain(u),multiplication(coantidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[392,464]),
[iquote('0:SpR:392.0,464.0')] ).
cnf(11516,plain,
equal(multiplication(antidomain(u),multiplication(coantidomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[64,11398,7]),
[iquote('0:Rew:64.0,11398.0,7.0,11398.0')] ).
cnf(15537,plain,
equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4663,10155]),
[iquote('0:SpR:4663.0,10155.0')] ).
cnf(15548,plain,
equal(addition(antidomain(antidomain(u)),zero),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[15537,5131]),
[iquote('0:Rew:15537.0,5131.0')] ).
cnf(15550,plain,
equal(coantidomain(antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[64,15548,12]),
[iquote('0:Rew:64.0,15548.0,12.0,15548.0')] ).
cnf(15563,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(antidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[15550,5086]),
[iquote('0:Rew:15550.0,5086.0')] ).
cnf(15922,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[15550,15563]),
[iquote('0:Rew:15550.0,15563.0')] ).
cnf(15923,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(antidomain(u),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4959,15922]),
[iquote('0:Rew:4959.0,15922.0')] ).
cnf(18211,plain,
equal(multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4947,11516]),
[iquote('0:SpR:4947.0,11516.0')] ).
cnf(18242,plain,
equal(addition(coantidomain(coantidomain(u)),zero),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[18211,4726]),
[iquote('0:Rew:18211.0,4726.0')] ).
cnf(18245,plain,
equal(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[64,18242,12]),
[iquote('0:Rew:64.0,18242.0,12.0,18242.0')] ).
cnf(18280,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(u)),v)))),backward_box(v,antidomain(coantidomain(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[18245,15923]),
[iquote('0:SpR:18245.0,15923.0')] ).
cnf(18311,plain,
equal(coantidomain(coantidomain(coantidomain(u))),antidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[18245,15550]),
[iquote('0:SpR:18245.0,15550.0')] ).
cnf(18414,plain,
equal(antidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4664,18311]),
[iquote('0:Rew:4664.0,18311.0')] ).
cnf(18415,plain,
equal(coantidomain(multiplication(antidomain(u),v)),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[18414,15923]),
[iquote('0:Rew:18414.0,15923.0')] ).
cnf(18552,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(u)),v)),backward_box(v,coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[18414,18280]),
[iquote('0:Rew:18414.0,18280.0,18414.0,18280.0')] ).
cnf(18553,plain,
equal(addition(coantidomain(multiplication(u,v)),backward_box(v,coantidomain(u))),backward_box(v,coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[18552,28]),
[iquote('0:Rew:18552.0,28.0')] ).
cnf(18583,plain,
equal(addition(backward_box(u,coantidomain(v)),coantidomain(multiplication(v,u))),backward_box(u,coantidomain(v))),
inference(rew,[status(thm),theory(equality)],[12,18553]),
[iquote('0:Rew:12.0,18553.0')] ).
cnf(19144,plain,
equal(multiplication(multiplication(antidomain(u),v),backward_box(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[18415,9]),
[iquote('0:SpR:18415.0,9.0')] ).
cnf(19257,plain,
equal(multiplication(antidomain(u),multiplication(v,backward_box(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[23,19144]),
[iquote('0:Rew:23.0,19144.0')] ).
cnf(19887,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)],[18415,18583]),
[iquote('0:SpR:18415.0,18583.0')] ).
cnf(19947,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)],[18415,19887,23]),
[iquote('0:Rew:18415.0,19887.0,23.0,19887.0')] ).
cnf(23727,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)],[5862,19947]),
[iquote('0:SpR:5862.0,19947.0')] ).
cnf(23822,plain,
equal(backward_box(u,backward_box(v,multiplication(v,u))),one),
inference(rew,[status(thm),theory(equality)],[562,23727,12]),
[iquote('0:Rew:562.0,23727.0,12.0,23727.0')] ).
cnf(47118,plain,
equal(multiplication(antidomain(backward_box(u,multiplication(u,v))),multiplication(v,one)),zero),
inference(spr,[status(thm),theory(equality)],[23822,19257]),
[iquote('0:SpR:23822.0,19257.0')] ).
cnf(47270,plain,
equal(multiplication(antidomain(backward_box(u,multiplication(u,v))),v),zero),
inference(rew,[status(thm),theory(equality)],[3,47118]),
[iquote('0:Rew:3.0,47118.0')] ).
cnf(221930,plain,
equal(addition(zero,multiplication(antidomain(antidomain(backward_box(u,multiplication(u,v)))),v)),v),
inference(spr,[status(thm),theory(equality)],[47270,398]),
[iquote('0:SpR:47270.0,398.0')] ).
cnf(222229,plain,
equal(multiplication(backward_box(u,multiplication(u,v)),v),v),
inference(rew,[status(thm),theory(equality)],[64,221930,5136]),
[iquote('0:Rew:64.0,221930.0,5136.0,221930.0')] ).
cnf(222414,plain,
leq(antidomain(u),backward_box(v,multiplication(v,antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[222229,1637]),
[iquote('0:SpR:222229.0,1637.0')] ).
cnf(222684,plain,
leq(antidomain(u),backward_box(v,forward_diamond(v,antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[7107,222414]),
[iquote('0:Rew:7107.0,222414.0')] ).
cnf(224055,plain,
leq(antidomain(antidomain(u)),backward_box(v,forward_diamond(v,u))),
inference(spr,[status(thm),theory(equality)],[5328,222684]),
[iquote('0:SpR:5328.0,222684.0')] ).
cnf(224151,plain,
$false,
inference(unc,[status(thm)],[224055,5332]),
[iquote('0:UnC:224055.0,5332.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE110+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 13:39:04 EDT 2022
% 0.13/0.33 % CPUTime :
% 189.59/189.81
% 189.59/189.81 SPASS V 3.9
% 189.59/189.81 SPASS beiseite: Proof found.
% 189.59/189.81 % SZS status Theorem
% 189.59/189.81 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 189.59/189.81 SPASS derived 145586 clauses, backtracked 0 clauses, performed 0 splits and kept 17065 clauses.
% 189.59/189.81 SPASS allocated 239265 KBytes.
% 189.59/189.81 SPASS spent 0:03:09.22 on the problem.
% 189.59/189.81 0:00:00.04 for the input.
% 189.59/189.81 0:00:00.03 for the FLOTTER CNF translation.
% 189.59/189.81 0:00:00.93 for inferences.
% 189.59/189.81 0:00:00.00 for the backtracking.
% 189.59/189.81 0:03:07.77 for the reduction.
% 189.59/189.81
% 189.59/189.81
% 189.59/189.81 Here is a proof with depth 8, length 150 :
% 189.59/189.81 % SZS output start Refutation
% See solution above
% 196.24/196.41 Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity domain1 domain4 codomain1 codomain4 complement additive_commutativity domain3 codomain3 order domain_difference forward_diamond backward_diamond backward_box additive_associativity multiplicative_associativity right_distributivity left_distributivity goals domain2 codomain2
% 196.24/196.41
%------------------------------------------------------------------------------