TSTP Solution File: KLE106+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE106+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 02:28:33 EDT 2022
% Result : Theorem 116.48s 116.67s
% Output : Refutation 120.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 28
% Syntax : Number of clauses : 283 ( 278 unt; 0 nHn; 283 RR)
% Number of literals : 288 ( 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 : 19 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE106+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE106+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE106+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE106+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,zero),zero),
file('KLE106+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(zero,u),zero),
file('KLE106+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE106+1.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE106+1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE106+1.p',unknown),
[] ).
cnf(10,axiom,
equal(codomain(u),coantidomain(coantidomain(u))),
file('KLE106+1.p',unknown),
[] ).
cnf(11,axiom,
equal(c(u),antidomain(domain__dfg(u))),
file('KLE106+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE106+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE106+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE106+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE106+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE106+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE106+1.p',unknown),
[] ).
cnf(18,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE106+1.p',unknown),
[] ).
cnf(19,axiom,
equal(codomain(multiplication(codomain(u),v)),backward_diamond(v,u)),
file('KLE106+1.p',unknown),
[] ).
cnf(21,axiom,
equal(c(backward_diamond(u,c(v))),backward_box(u,v)),
file('KLE106+1.p',unknown),
[] ).
cnf(22,axiom,
~ equal(addition(forward_diamond(skc3,domain__dfg(skc4)),domain__dfg(skc5)),domain__dfg(skc5)),
file('KLE106+1.p',unknown),
[] ).
cnf(23,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE106+1.p',unknown),
[] ).
cnf(24,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE106+1.p',unknown),
[] ).
cnf(25,axiom,
equal(addition(domain__dfg(skc4),backward_box(skc3,domain__dfg(skc5))),backward_box(skc3,domain__dfg(skc5))),
file('KLE106+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE106+1.p',unknown),
[] ).
cnf(27,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE106+1.p',unknown),
[] ).
cnf(28,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE106+1.p',unknown),
[] ).
cnf(29,axiom,
equal(addition(coantidomain(multiplication(u,v)),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),
file('KLE106+1.p',unknown),
[] ).
cnf(30,plain,
equal(c(u),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[8,11]),
[iquote('0:Rew:8.0,11.0')] ).
cnf(31,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(32,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(33,plain,
equal(antidomain(antidomain(antidomain(backward_diamond(u,antidomain(antidomain(antidomain(v))))))),backward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[30,21]),
[iquote('0:Rew:30.0,21.0,30.0,21.0')] ).
cnf(35,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(36,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)],[35,33]),
[iquote('0:Rew:35.0,33.0')] ).
cnf(37,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(38,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(39,plain,
~ equal(addition(antidomain(antidomain(skc5)),forward_diamond(skc3,antidomain(antidomain(skc4)))),antidomain(antidomain(skc5))),
inference(rew,[status(thm),theory(equality)],[12,22,8]),
[iquote('0:Rew:12.0,22.0,8.0,22.0,8.0,22.0')] ).
cnf(40,plain,
equal(addition(antidomain(antidomain(skc4)),backward_box(skc3,antidomain(antidomain(skc5)))),backward_box(skc3,antidomain(antidomain(skc5)))),
inference(rew,[status(thm),theory(equality)],[8,25]),
[iquote('0:Rew:8.0,25.0,8.0,25.0')] ).
cnf(55,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(59,plain,
equal(coantidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(66,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(75,plain,
equal(addition(zero,coantidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[59,31]),
[iquote('0:SpR:59.0,31.0')] ).
cnf(77,plain,
equal(coantidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[66,75]),
[iquote('0:Rew:66.0,75.0')] ).
cnf(89,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[55,32]),
[iquote('0:SpR:55.0,32.0')] ).
cnf(91,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[66,89]),
[iquote('0:Rew:66.0,89.0')] ).
cnf(99,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(116,plain,
equal(domain_difference(u,u),zero),
inference(spr,[status(thm),theory(equality)],[38,7]),
[iquote('0:SpR:38.0,7.0')] ).
cnf(153,plain,
equal(multiplication(antidomain(antidomain(u)),forward_diamond(v,w)),domain_difference(u,antidomain(multiplication(v,antidomain(antidomain(w)))))),
inference(spr,[status(thm),theory(equality)],[37,38]),
[iquote('0:SpR:37.0,38.0')] ).
cnf(160,plain,
equal(antidomain(antidomain(domain_difference(u,antidomain(v)))),forward_diamond(antidomain(antidomain(u)),v)),
inference(spr,[status(thm),theory(equality)],[38,37]),
[iquote('0:SpR:38.0,37.0')] ).
cnf(185,plain,
equal(antidomain(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w)))))),forward_diamond(multiplication(u,v),w)),
inference(spr,[status(thm),theory(equality)],[24,37]),
[iquote('0:SpR:24.0,37.0')] ).
cnf(193,plain,
equal(multiplication(u,multiplication(coantidomain(u),v)),multiplication(zero,v)),
inference(spr,[status(thm),theory(equality)],[9,24]),
[iquote('0:SpR:9.0,24.0')] ).
cnf(194,plain,
equal(multiplication(domain_difference(u,v),w),multiplication(antidomain(antidomain(u)),multiplication(antidomain(v),w))),
inference(spr,[status(thm),theory(equality)],[38,24]),
[iquote('0:SpR:38.0,24.0')] ).
cnf(201,plain,
equal(multiplication(u,multiplication(coantidomain(u),v)),zero),
inference(rew,[status(thm),theory(equality)],[6,193]),
[iquote('0:Rew:6.0,193.0')] ).
cnf(259,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,23]),
[iquote('0:SpR:2.0,23.0')] ).
cnf(299,plain,
equal(addition(coantidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[31,259]),
[iquote('0:SpR:31.0,259.0')] ).
cnf(300,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[32,259]),
[iquote('0:SpR:32.0,259.0')] ).
cnf(302,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[259,16]),
[iquote('0:SpL:259.0,16.0')] ).
cnf(304,plain,
equal(addition(one,coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,299]),
[iquote('0:Rew:12.0,299.0')] ).
cnf(305,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,300]),
[iquote('0:Rew:12.0,300.0')] ).
cnf(308,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[302]),
[iquote('0:Obv:302.0')] ).
cnf(314,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,308]),
[iquote('0:SpR:12.0,308.0')] ).
cnf(358,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[27,9]),
[iquote('0:SpR:27.0,9.0')] ).
cnf(372,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[31,27]),
[iquote('0:SpR:31.0,27.0')] ).
cnf(373,plain,
equal(addition(multiplication(one,u),multiplication(coantidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[304,27]),
[iquote('0:SpR:304.0,27.0')] ).
cnf(374,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[32,27]),
[iquote('0:SpR:32.0,27.0')] ).
cnf(380,plain,
equal(addition(u,multiplication(coantidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,373]),
[iquote('0:Rew:4.0,373.0')] ).
cnf(384,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,372]),
[iquote('0:Rew:4.0,372.0')] ).
cnf(385,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,374]),
[iquote('0:Rew:4.0,374.0')] ).
cnf(393,plain,
equal(addition(multiplication(one,u),multiplication(antidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[305,27]),
[iquote('0:SpR:305.0,27.0')] ).
cnf(403,plain,
equal(addition(u,multiplication(antidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,393]),
[iquote('0:Rew:4.0,393.0')] ).
cnf(456,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),multiplication(antidomain(addition(u,v)),v)),zero),
inference(spr,[status(thm),theory(equality)],[26,7]),
[iquote('0:SpR:26.0,7.0')] ).
cnf(471,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[31,26]),
[iquote('0:SpR:31.0,26.0')] ).
cnf(472,plain,
equal(addition(multiplication(u,one),multiplication(u,coantidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[304,26]),
[iquote('0:SpR:304.0,26.0')] ).
cnf(473,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[32,26]),
[iquote('0:SpR:32.0,26.0')] ).
cnf(474,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[305,26]),
[iquote('0:SpR:305.0,26.0')] ).
cnf(482,plain,
equal(addition(u,multiplication(u,coantidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,472]),
[iquote('0:Rew:3.0,472.0')] ).
cnf(483,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,474]),
[iquote('0:Rew:3.0,474.0')] ).
cnf(488,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,471]),
[iquote('0:Rew:3.0,471.0')] ).
cnf(489,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,473]),
[iquote('0:Rew:3.0,473.0')] ).
cnf(543,plain,
( ~ leq(forward_diamond(skc3,antidomain(antidomain(skc4))),antidomain(antidomain(skc5)))
| ~ equal(antidomain(antidomain(skc5)),antidomain(antidomain(skc5))) ),
inference(spl,[status(thm),theory(equality)],[99,39]),
[iquote('0:SpL:99.1,39.0')] ).
cnf(544,plain,
~ leq(forward_diamond(skc3,antidomain(antidomain(skc4))),antidomain(antidomain(skc5))),
inference(obv,[status(thm),theory(equality)],[543]),
[iquote('0:Obv:543.1')] ).
cnf(606,plain,
equal(addition(multiplication(antidomain(antidomain(skc4)),u),multiplication(backward_box(skc3,antidomain(antidomain(skc5))),u)),multiplication(backward_box(skc3,antidomain(antidomain(skc5))),u)),
inference(spr,[status(thm),theory(equality)],[40,27]),
[iquote('0:SpR:40.0,27.0')] ).
cnf(696,plain,
equal(addition(one,backward_box(u,v)),one),
inference(spr,[status(thm),theory(equality)],[36,305]),
[iquote('0:SpR:36.0,305.0')] ).
cnf(702,plain,
equal(multiplication(backward_box(u,v),antidomain(w)),domain_difference(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(v))))),u)))),w)),
inference(spr,[status(thm),theory(equality)],[36,38]),
[iquote('0:SpR:36.0,38.0')] ).
cnf(712,plain,
equal(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(one)))),u)))))),backward_box(u,zero)),
inference(spr,[status(thm),theory(equality)],[91,36]),
[iquote('0:SpR:91.0,36.0')] ).
cnf(721,plain,
equal(backward_box(u,zero),antidomain(antidomain(antidomain(coantidomain(coantidomain(u)))))),
inference(rew,[status(thm),theory(equality)],[4,712,77,59,91,55]),
[iquote('0:Rew:4.0,712.0,77.0,712.0,59.0,712.0,91.0,712.0,55.0,712.0')] ).
cnf(751,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)],[7,29]),
[iquote('0:SpR:7.0,29.0')] ).
cnf(759,plain,
equal(addition(coantidomain(multiplication(u,multiplication(v,w))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(u,v))),w))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(u,v))),w))),
inference(spr,[status(thm),theory(equality)],[24,29]),
[iquote('0:SpR:24.0,29.0')] ).
cnf(773,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
inference(rew,[status(thm),theory(equality)],[304,751,77]),
[iquote('0:Rew:304.0,751.0,77.0,751.0')] ).
cnf(784,plain,
equal(addition(multiplication(one,u),multiplication(backward_box(v,w),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[696,27]),
[iquote('0:SpR:696.0,27.0')] ).
cnf(799,plain,
equal(addition(u,multiplication(backward_box(v,w),u)),u),
inference(rew,[status(thm),theory(equality)],[4,784]),
[iquote('0:Rew:4.0,784.0')] ).
cnf(860,plain,
equal(addition(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w))))),antidomain(multiplication(u,forward_diamond(v,w)))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(spr,[status(thm),theory(equality)],[37,28]),
[iquote('0:SpR:37.0,28.0')] ).
cnf(869,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)],[7,28]),
[iquote('0:SpR:7.0,28.0')] ).
cnf(872,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)],[9,28]),
[iquote('0:SpR:9.0,28.0')] ).
cnf(891,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[305,869,91]),
[iquote('0:Rew:305.0,869.0,91.0,869.0')] ).
cnf(892,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(coantidomain(u))))),one),
inference(rew,[status(thm),theory(equality)],[305,872,91]),
[iquote('0:Rew:305.0,872.0,91.0,872.0')] ).
cnf(895,plain,
equal(addition(antidomain(multiplication(u,forward_diamond(v,w))),antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w)))))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[12,860]),
[iquote('0:Rew:12.0,860.0')] ).
cnf(997,plain,
equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
inference(spr,[status(thm),theory(equality)],[773,9]),
[iquote('0:SpR:773.0,9.0')] ).
cnf(1027,plain,
equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
inference(rew,[status(thm),theory(equality)],[3,997,24]),
[iquote('0:Rew:3.0,997.0,24.0,997.0')] ).
cnf(1107,plain,
equal(addition(antidomain(u),domain_difference(v,u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[38,403]),
[iquote('0:SpR:38.0,403.0')] ).
cnf(1228,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[891,7]),
[iquote('0:SpR:891.0,7.0')] ).
cnf(1274,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,1228]),
[iquote('0:Rew:4.0,1228.0')] ).
cnf(1425,plain,
equal(multiplication(one,multiplication(u,antidomain(antidomain(coantidomain(u))))),zero),
inference(spr,[status(thm),theory(equality)],[892,7]),
[iquote('0:SpR:892.0,7.0')] ).
cnf(1468,plain,
equal(multiplication(u,antidomain(antidomain(coantidomain(u)))),zero),
inference(rew,[status(thm),theory(equality)],[4,1425]),
[iquote('0:Rew:4.0,1425.0')] ).
cnf(1547,plain,
leq(multiplication(u,coantidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[482,314]),
[iquote('0:SpR:482.0,314.0')] ).
cnf(4117,plain,
equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
inference(spr,[status(thm),theory(equality)],[1027,384]),
[iquote('0:SpR:1027.0,384.0')] ).
cnf(4120,plain,
equal(addition(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),zero),coantidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[9,384]),
[iquote('0:SpR:9.0,384.0')] ).
cnf(4143,plain,
equal(multiplication(coantidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[66,4117,12]),
[iquote('0:Rew:66.0,4117.0,12.0,4117.0')] ).
cnf(4156,plain,
equal(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[66,4120,12]),
[iquote('0:Rew:66.0,4120.0,12.0,4120.0')] ).
cnf(4345,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1274,385]),
[iquote('0:SpR:1274.0,385.0')] ).
cnf(4351,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),u)),u),
inference(spr,[status(thm),theory(equality)],[7,385]),
[iquote('0:SpR:7.0,385.0')] ).
cnf(4359,plain,
equal(addition(domain_difference(u,v),multiplication(antidomain(antidomain(antidomain(u))),antidomain(v))),antidomain(v)),
inference(spr,[status(thm),theory(equality)],[38,385]),
[iquote('0:SpR:38.0,385.0')] ).
cnf(4369,plain,
equal(multiplication(antidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[66,4351]),
[iquote('0:Rew:66.0,4351.0')] ).
cnf(4386,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[66,4345,12]),
[iquote('0:Rew:66.0,4345.0,12.0,4345.0')] ).
cnf(4387,plain,
equal(addition(domain_difference(u,v),domain_difference(antidomain(u),v)),antidomain(v)),
inference(rew,[status(thm),theory(equality)],[38,4359]),
[iquote('0:Rew:38.0,4359.0')] ).
cnf(4600,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)],[4369,488]),
[iquote('0:SpR:4369.0,488.0')] ).
cnf(4612,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[9,488]),
[iquote('0:SpR:9.0,488.0')] ).
cnf(4626,plain,
equal(multiplication(u,coantidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[66,4612]),
[iquote('0:Rew:66.0,4612.0')] ).
cnf(4627,plain,
equal(coantidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4626,4156]),
[iquote('0:Rew:4626.0,4156.0')] ).
cnf(4689,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)],[12,4600]),
[iquote('0:Rew:12.0,4600.0')] ).
cnf(4877,plain,
equal(addition(multiplication(u,antidomain(coantidomain(u))),zero),u),
inference(spr,[status(thm),theory(equality)],[1468,489]),
[iquote('0:SpR:1468.0,489.0')] ).
cnf(4878,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[38,489]),
[iquote('0:SpR:38.0,489.0')] ).
cnf(4885,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)],[4143,489]),
[iquote('0:SpR:4143.0,489.0')] ).
cnf(4897,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1274,489]),
[iquote('0:SpR:1274.0,489.0')] ).
cnf(4910,plain,
equal(multiplication(u,antidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[66,4877,12]),
[iquote('0:Rew:66.0,4877.0,12.0,4877.0')] ).
cnf(4921,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[66,4897]),
[iquote('0:Rew:66.0,4897.0')] ).
cnf(4922,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4386,4921]),
[iquote('0:Rew:4386.0,4921.0')] ).
cnf(4923,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(u))))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4922,36]),
[iquote('0:Rew:4922.0,36.0')] ).
cnf(4974,plain,
equal(multiplication(backward_box(u,v),antidomain(w)),domain_difference(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(v))),u)))),w)),
inference(rew,[status(thm),theory(equality)],[4922,702]),
[iquote('0:Rew:4922.0,702.0')] ).
cnf(5001,plain,
equal(backward_box(u,zero),antidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[4922,721]),
[iquote('0:Rew:4922.0,721.0')] ).
cnf(5047,plain,
equal(addition(domain_difference(u,v),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[38,4878]),
[iquote('0:Rew:38.0,4878.0')] ).
cnf(5049,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4922,4923]),
[iquote('0:Rew:4922.0,4923.0')] ).
cnf(5093,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)],[12,4885]),
[iquote('0:Rew:12.0,4885.0')] ).
cnf(5094,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4922,5093]),
[iquote('0:Rew:4922.0,5093.0')] ).
cnf(5104,plain,
equal(multiplication(backward_box(u,v),antidomain(w)),domain_difference(backward_box(u,v),w)),
inference(rew,[status(thm),theory(equality)],[5049,4974]),
[iquote('0:Rew:5049.0,4974.0')] ).
cnf(5201,plain,
equal(multiplication(antidomain(u),antidomain(v)),domain_difference(antidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[4922,38]),
[iquote('0:SpR:4922.0,38.0')] ).
cnf(5214,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4922,37]),
[iquote('0:SpR:4922.0,37.0')] ).
cnf(5241,plain,
equal(antidomain(antidomain(forward_diamond(u,v))),forward_diamond(u,v)),
inference(spr,[status(thm),theory(equality)],[37,4922]),
[iquote('0:SpR:37.0,4922.0')] ).
cnf(5244,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(v)))),antidomain(forward_diamond(u,v))),
inference(spr,[status(thm),theory(equality)],[37,4922]),
[iquote('0:SpR:37.0,4922.0')] ).
cnf(5245,plain,
equal(antidomain(domain_difference(u,antidomain(v))),antidomain(forward_diamond(antidomain(antidomain(u)),v))),
inference(spr,[status(thm),theory(equality)],[160,4922]),
[iquote('0:SpR:160.0,4922.0')] ).
cnf(5266,plain,
equal(domain_difference(antidomain(antidomain(u)),v),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[5201,38]),
[iquote('0:Rew:5201.0,38.0')] ).
cnf(5289,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[5214,37]),
[iquote('0:Rew:5214.0,37.0')] ).
cnf(5294,plain,
~ leq(forward_diamond(skc3,skc4),antidomain(antidomain(skc5))),
inference(rew,[status(thm),theory(equality)],[5289,544]),
[iquote('0:Rew:5289.0,544.0')] ).
cnf(5296,plain,
equal(addition(antidomain(multiplication(u,v)),antidomain(forward_diamond(u,v))),antidomain(forward_diamond(u,v))),
inference(rew,[status(thm),theory(equality)],[5244,28]),
[iquote('0:Rew:5244.0,28.0')] ).
cnf(5298,plain,
equal(multiplication(antidomain(antidomain(u)),forward_diamond(v,w)),domain_difference(u,antidomain(forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[5244,153]),
[iquote('0:Rew:5244.0,153.0')] ).
cnf(5402,plain,
equal(addition(antidomain(forward_diamond(u,v)),antidomain(multiplication(u,v))),antidomain(forward_diamond(u,v))),
inference(rew,[status(thm),theory(equality)],[12,5296]),
[iquote('0:Rew:12.0,5296.0')] ).
cnf(5620,plain,
equal(addition(multiplication(coantidomain(u),antidomain(coantidomain(coantidomain(coantidomain(u))))),coantidomain(coantidomain(u))),antidomain(coantidomain(coantidomain(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[4910,384]),
[iquote('0:SpR:4910.0,384.0')] ).
cnf(5639,plain,
equal(addition(coantidomain(coantidomain(u)),multiplication(coantidomain(u),antidomain(coantidomain(u)))),antidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[12,5620,4627]),
[iquote('0:Rew:12.0,5620.0,4627.0,5620.0')] ).
cnf(5854,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),v)))),backward_box(v,antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[4922,5049]),
[iquote('0:SpR:4922.0,5049.0')] ).
cnf(5881,plain,
equal(backward_box(u,antidomain(antidomain(v))),backward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[5049,5854]),
[iquote('0:Rew:5049.0,5854.0')] ).
cnf(5892,plain,
equal(addition(multiplication(antidomain(antidomain(skc4)),u),multiplication(backward_box(skc3,skc5),u)),multiplication(backward_box(skc3,skc5),u)),
inference(rew,[status(thm),theory(equality)],[5881,606]),
[iquote('0:Rew:5881.0,606.0')] ).
cnf(6131,plain,
equal(addition(antidomain(forward_diamond(multiplication(u,v),w)),antidomain(multiplication(u,multiplication(v,w)))),antidomain(forward_diamond(multiplication(u,v),w))),
inference(spr,[status(thm),theory(equality)],[24,5402]),
[iquote('0:SpR:24.0,5402.0')] ).
cnf(7996,plain,
equal(multiplication(antidomain(antidomain(u)),multiplication(antidomain(v),antidomain(coantidomain(domain_difference(u,v))))),domain_difference(u,v)),
inference(spr,[status(thm),theory(equality)],[194,4910]),
[iquote('0:SpR:194.0,4910.0')] ).
cnf(8038,plain,
equal(multiplication(antidomain(antidomain(u)),domain_difference(antidomain(v),coantidomain(domain_difference(u,v)))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[5201,7996]),
[iquote('0:Rew:5201.0,7996.0')] ).
cnf(8343,plain,
equal(multiplication(antidomain(u),forward_diamond(v,w)),domain_difference(antidomain(u),antidomain(forward_diamond(v,w)))),
inference(spr,[status(thm),theory(equality)],[4922,5298]),
[iquote('0:SpR:4922.0,5298.0')] ).
cnf(9535,plain,
equal(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w))))),antidomain(forward_diamond(multiplication(u,v),w))),
inference(spr,[status(thm),theory(equality)],[185,4922]),
[iquote('0:SpR:185.0,4922.0')] ).
cnf(9625,plain,
equal(addition(antidomain(multiplication(u,forward_diamond(v,w))),antidomain(forward_diamond(multiplication(u,v),w))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[9535,895]),
[iquote('0:Rew:9535.0,895.0')] ).
cnf(9686,plain,
equal(addition(antidomain(forward_diamond(multiplication(u,v),w)),antidomain(multiplication(u,forward_diamond(v,w)))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[12,9625]),
[iquote('0:Rew:12.0,9625.0')] ).
cnf(9967,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),zero),zero),
inference(spr,[status(thm),theory(equality)],[358,259]),
[iquote('0:SpR:358.0,259.0')] ).
cnf(10004,plain,
equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[483,358]),
[iquote('0:SpR:483.0,358.0')] ).
cnf(10087,plain,
equal(multiplication(u,coantidomain(addition(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[66,9967,12]),
[iquote('0:Rew:66.0,9967.0,12.0,9967.0')] ).
cnf(10088,plain,
equal(addition(zero,multiplication(u,coantidomain(addition(v,u)))),zero),
inference(rew,[status(thm),theory(equality)],[10087,358]),
[iquote('0:Rew:10087.0,358.0')] ).
cnf(10095,plain,
equal(multiplication(u,coantidomain(addition(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[66,10088]),
[iquote('0:Rew:66.0,10088.0')] ).
cnf(10131,plain,
equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[66,10004,9,24]),
[iquote('0:Rew:66.0,10004.0,9.0,10004.0,24.0,10004.0')] ).
cnf(10983,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(addition(v,u))))),u),
inference(spr,[status(thm),theory(equality)],[10095,488]),
[iquote('0:SpR:10095.0,488.0')] ).
cnf(10988,plain,
equal(addition(antidomain(forward_diamond(u,coantidomain(addition(v,u)))),antidomain(zero)),antidomain(forward_diamond(u,coantidomain(addition(v,u))))),
inference(spr,[status(thm),theory(equality)],[10095,5402]),
[iquote('0:SpR:10095.0,5402.0')] ).
cnf(11095,plain,
equal(multiplication(u,coantidomain(coantidomain(addition(v,u)))),u),
inference(rew,[status(thm),theory(equality)],[66,10983]),
[iquote('0:Rew:66.0,10983.0')] ).
cnf(11123,plain,
equal(antidomain(forward_diamond(u,coantidomain(addition(v,u)))),one),
inference(rew,[status(thm),theory(equality)],[305,10988,12,91]),
[iquote('0:Rew:305.0,10988.0,12.0,10988.0,91.0,10988.0')] ).
cnf(11380,plain,
equal(addition(multiplication(antidomain(u),u),multiplication(antidomain(u),multiplication(coantidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[380,456]),
[iquote('0:SpR:380.0,456.0')] ).
cnf(11406,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(u)),multiplication(antidomain(antidomain(u)),domain_difference(v,u))),zero),
inference(spr,[status(thm),theory(equality)],[1107,456]),
[iquote('0:SpR:1107.0,456.0')] ).
cnf(11504,plain,
equal(multiplication(antidomain(u),multiplication(coantidomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[66,11380,7]),
[iquote('0:Rew:66.0,11380.0,7.0,11380.0')] ).
cnf(11530,plain,
equal(multiplication(antidomain(antidomain(u)),domain_difference(v,u)),zero),
inference(rew,[status(thm),theory(equality)],[66,11406,7]),
[iquote('0:Rew:66.0,11406.0,7.0,11406.0')] ).
cnf(13191,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(addition(u,v))))),u),
inference(spr,[status(thm),theory(equality)],[10087,488]),
[iquote('0:SpR:10087.0,488.0')] ).
cnf(13194,plain,
equal(addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(u)),coantidomain(addition(u,v))))),coantidomain(multiplication(coantidomain(coantidomain(u)),coantidomain(addition(u,v))))),
inference(spr,[status(thm),theory(equality)],[10087,29]),
[iquote('0:SpR:10087.0,29.0')] ).
cnf(13298,plain,
equal(multiplication(u,coantidomain(coantidomain(addition(u,v)))),u),
inference(rew,[status(thm),theory(equality)],[66,13191]),
[iquote('0:Rew:66.0,13191.0')] ).
cnf(13312,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(u)),coantidomain(addition(u,v)))),one),
inference(rew,[status(thm),theory(equality)],[304,13194,77]),
[iquote('0:Rew:304.0,13194.0,77.0,13194.0')] ).
cnf(14198,plain,
equal(addition(skc4,multiplication(backward_box(skc3,skc5),skc4)),multiplication(backward_box(skc3,skc5),skc4)),
inference(spr,[status(thm),theory(equality)],[4369,5892]),
[iquote('0:SpR:4369.0,5892.0')] ).
cnf(14208,plain,
equal(multiplication(backward_box(skc3,skc5),skc4),skc4),
inference(rew,[status(thm),theory(equality)],[799,14198]),
[iquote('0:Rew:799.0,14198.0')] ).
cnf(16209,plain,
equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4626,10131]),
[iquote('0:SpR:4626.0,10131.0')] ).
cnf(16220,plain,
equal(addition(antidomain(antidomain(u)),zero),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[16209,5094]),
[iquote('0:Rew:16209.0,5094.0')] ).
cnf(16222,plain,
equal(coantidomain(antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,16220,12]),
[iquote('0:Rew:66.0,16220.0,12.0,16220.0')] ).
cnf(16234,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(antidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[16222,5049]),
[iquote('0:Rew:16222.0,5049.0')] ).
cnf(16600,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[16222,16234]),
[iquote('0:Rew:16222.0,16234.0')] ).
cnf(16601,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(antidomain(u),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4922,16600]),
[iquote('0:Rew:4922.0,16600.0')] ).
cnf(18478,plain,
equal(multiplication(one,forward_diamond(u,coantidomain(addition(v,u)))),zero),
inference(spr,[status(thm),theory(equality)],[11123,7]),
[iquote('0:SpR:11123.0,7.0')] ).
cnf(18662,plain,
equal(forward_diamond(u,coantidomain(addition(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[4,18478]),
[iquote('0:Rew:4.0,18478.0')] ).
cnf(18778,plain,
equal(forward_diamond(multiplication(u,antidomain(v)),coantidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[483,18662]),
[iquote('0:SpR:483.0,18662.0')] ).
cnf(19249,plain,
equal(multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4910,11504]),
[iquote('0:SpR:4910.0,11504.0')] ).
cnf(19282,plain,
equal(addition(coantidomain(coantidomain(u)),zero),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[19249,4689]),
[iquote('0:Rew:19249.0,4689.0')] ).
cnf(19285,plain,
equal(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,19282,12]),
[iquote('0:Rew:66.0,19282.0,12.0,19282.0')] ).
cnf(19318,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(u)),v)))),backward_box(v,antidomain(coantidomain(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[19285,16601]),
[iquote('0:SpR:19285.0,16601.0')] ).
cnf(19348,plain,
equal(coantidomain(coantidomain(coantidomain(u))),antidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[19285,16222]),
[iquote('0:SpR:19285.0,16222.0')] ).
cnf(19410,plain,
equal(antidomain(antidomain(coantidomain(u))),coantidomain(u)),
inference(spr,[status(thm),theory(equality)],[4627,19285]),
[iquote('0:SpR:4627.0,19285.0')] ).
cnf(19450,plain,
equal(antidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4627,19348]),
[iquote('0:Rew:4627.0,19348.0')] ).
cnf(19452,plain,
equal(coantidomain(multiplication(antidomain(u),v)),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[19450,16601]),
[iquote('0:Rew:19450.0,16601.0')] ).
cnf(19454,plain,
equal(backward_box(u,zero),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[19450,5001]),
[iquote('0:Rew:19450.0,5001.0')] ).
cnf(19622,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(u)),v)),backward_box(v,coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[19450,19318]),
[iquote('0:Rew:19450.0,19318.0,19450.0,19318.0')] ).
cnf(19627,plain,
equal(backward_box(coantidomain(addition(u,v)),coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[19622,13312]),
[iquote('0:Rew:19622.0,13312.0')] ).
cnf(19649,plain,
equal(addition(coantidomain(multiplication(u,multiplication(v,w))),backward_box(w,coantidomain(multiplication(u,v)))),backward_box(w,coantidomain(multiplication(u,v)))),
inference(rew,[status(thm),theory(equality)],[19622,759]),
[iquote('0:Rew:19622.0,759.0')] ).
cnf(19695,plain,
equal(addition(backward_box(u,coantidomain(multiplication(v,w))),coantidomain(multiplication(v,multiplication(w,u)))),backward_box(u,coantidomain(multiplication(v,w)))),
inference(rew,[status(thm),theory(equality)],[12,19649]),
[iquote('0:Rew:12.0,19649.0')] ).
cnf(19728,plain,
equal(multiplication(coantidomain(u),antidomain(v)),domain_difference(coantidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[19454,5104]),
[iquote('0:SpR:19454.0,5104.0')] ).
cnf(19758,plain,
equal(addition(coantidomain(coantidomain(u)),domain_difference(coantidomain(u),coantidomain(u))),antidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[19728,5639]),
[iquote('0:Rew:19728.0,5639.0')] ).
cnf(19772,plain,
equal(coantidomain(coantidomain(u)),antidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,19758,12,116]),
[iquote('0:Rew:66.0,19758.0,12.0,19758.0,116.0,19758.0')] ).
cnf(19777,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(antidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[19772,384]),
[iquote('0:Rew:19772.0,384.0')] ).
cnf(19798,plain,
equal(multiplication(u,antidomain(coantidomain(addition(v,u)))),u),
inference(rew,[status(thm),theory(equality)],[19772,11095]),
[iquote('0:Rew:19772.0,11095.0')] ).
cnf(19802,plain,
equal(multiplication(u,antidomain(coantidomain(addition(u,v)))),u),
inference(rew,[status(thm),theory(equality)],[19772,13298]),
[iquote('0:Rew:19772.0,13298.0')] ).
cnf(20223,plain,
equal(multiplication(multiplication(antidomain(u),v),backward_box(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[19452,9]),
[iquote('0:SpR:19452.0,9.0')] ).
cnf(20224,plain,
equal(multiplication(multiplication(antidomain(u),v),multiplication(backward_box(v,u),w)),zero),
inference(spr,[status(thm),theory(equality)],[19452,201]),
[iquote('0:SpR:19452.0,201.0')] ).
cnf(20340,plain,
equal(multiplication(antidomain(u),multiplication(v,backward_box(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[24,20223]),
[iquote('0:Rew:24.0,20223.0')] ).
cnf(20361,plain,
equal(multiplication(antidomain(u),multiplication(v,multiplication(backward_box(v,u),w))),zero),
inference(rew,[status(thm),theory(equality)],[24,20224]),
[iquote('0:Rew:24.0,20224.0')] ).
cnf(20744,plain,
equal(addition(multiplication(antidomain(u),domain_difference(v,u)),zero),domain_difference(v,u)),
inference(spr,[status(thm),theory(equality)],[11530,385]),
[iquote('0:SpR:11530.0,385.0')] ).
cnf(20799,plain,
equal(multiplication(antidomain(u),domain_difference(v,u)),domain_difference(v,u)),
inference(rew,[status(thm),theory(equality)],[66,20744,12]),
[iquote('0:Rew:66.0,20744.0,12.0,20744.0')] ).
cnf(25523,plain,
equal(multiplication(antidomain(coantidomain(u)),multiplication(coantidomain(addition(u,v)),one)),zero),
inference(spr,[status(thm),theory(equality)],[19627,20340]),
[iquote('0:SpR:19627.0,20340.0')] ).
cnf(25636,plain,
equal(multiplication(antidomain(coantidomain(u)),coantidomain(addition(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[3,25523]),
[iquote('0:Rew:3.0,25523.0')] ).
cnf(29048,plain,
equal(addition(antidomain(zero),antidomain(multiplication(u,forward_diamond(antidomain(v),coantidomain(u))))),antidomain(multiplication(u,forward_diamond(antidomain(v),coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[18778,9686]),
[iquote('0:SpR:18778.0,9686.0')] ).
cnf(29104,plain,
equal(antidomain(multiplication(u,forward_diamond(antidomain(v),coantidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[305,29048,91]),
[iquote('0:Rew:305.0,29048.0,91.0,29048.0')] ).
cnf(31288,plain,
equal(addition(backward_box(u,coantidomain(multiplication(v,antidomain(u)))),coantidomain(multiplication(v,zero))),backward_box(u,coantidomain(multiplication(v,antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[7,19695]),
[iquote('0:SpR:7.0,19695.0')] ).
cnf(31486,plain,
equal(backward_box(u,coantidomain(multiplication(v,antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[696,31288,12,77,5]),
[iquote('0:Rew:696.0,31288.0,12.0,31288.0,77.0,31288.0,5.0,31288.0')] ).
cnf(37031,plain,
equal(multiplication(antidomain(coantidomain(multiplication(u,antidomain(v)))),multiplication(v,one)),zero),
inference(spr,[status(thm),theory(equality)],[31486,20340]),
[iquote('0:SpR:31486.0,20340.0')] ).
cnf(37153,plain,
equal(multiplication(antidomain(coantidomain(multiplication(u,antidomain(v)))),v),zero),
inference(rew,[status(thm),theory(equality)],[3,37031]),
[iquote('0:Rew:3.0,37031.0')] ).
cnf(101523,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),coantidomain(antidomain(v))),zero),
inference(spr,[status(thm),theory(equality)],[4387,25636]),
[iquote('0:SpR:4387.0,25636.0')] ).
cnf(101582,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),antidomain(antidomain(v))),zero),
inference(rew,[status(thm),theory(equality)],[16222,101523]),
[iquote('0:Rew:16222.0,101523.0')] ).
cnf(101583,plain,
equal(domain_difference(antidomain(coantidomain(domain_difference(u,v))),antidomain(v)),zero),
inference(rew,[status(thm),theory(equality)],[5201,101582]),
[iquote('0:Rew:5201.0,101582.0')] ).
cnf(104920,plain,
equal(multiplication(one,multiplication(u,forward_diamond(antidomain(v),coantidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[29104,7]),
[iquote('0:SpR:29104.0,7.0')] ).
cnf(105298,plain,
equal(multiplication(u,forward_diamond(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,104920]),
[iquote('0:Rew:4.0,104920.0')] ).
cnf(105842,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),forward_diamond(antidomain(v),coantidomain(antidomain(u))))),forward_diamond(antidomain(v),coantidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[105298,385]),
[iquote('0:SpR:105298.0,385.0')] ).
cnf(106059,plain,
equal(multiplication(antidomain(antidomain(u)),forward_diamond(antidomain(v),u)),forward_diamond(antidomain(v),u)),
inference(rew,[status(thm),theory(equality)],[66,105842,5289,16222]),
[iquote('0:Rew:66.0,105842.0,5289.0,105842.0,16222.0,105842.0')] ).
cnf(106060,plain,
equal(domain_difference(antidomain(antidomain(u)),antidomain(forward_diamond(antidomain(v),u))),forward_diamond(antidomain(v),u)),
inference(rew,[status(thm),theory(equality)],[8343,106059]),
[iquote('0:Rew:8343.0,106059.0')] ).
cnf(106061,plain,
equal(domain_difference(u,antidomain(forward_diamond(antidomain(v),u))),forward_diamond(antidomain(v),u)),
inference(rew,[status(thm),theory(equality)],[5266,106060]),
[iquote('0:Rew:5266.0,106060.0')] ).
cnf(110617,plain,
equal(addition(multiplication(coantidomain(multiplication(u,antidomain(v))),v),zero),v),
inference(spr,[status(thm),theory(equality)],[37153,19777]),
[iquote('0:SpR:37153.0,19777.0')] ).
cnf(110757,plain,
equal(multiplication(coantidomain(multiplication(u,antidomain(v))),v),v),
inference(rew,[status(thm),theory(equality)],[66,110617,12]),
[iquote('0:Rew:66.0,110617.0,12.0,110617.0')] ).
cnf(111304,plain,
leq(coantidomain(u),coantidomain(multiplication(v,antidomain(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[110757,1547]),
[iquote('0:SpR:110757.0,1547.0')] ).
cnf(111677,plain,
leq(coantidomain(addition(u,v)),coantidomain(v)),
inference(spr,[status(thm),theory(equality)],[19798,111304]),
[iquote('0:SpR:19798.0,111304.0')] ).
cnf(111797,plain,
leq(coantidomain(u),coantidomain(multiplication(u,antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[483,111677]),
[iquote('0:SpR:483.0,111677.0')] ).
cnf(113107,plain,
leq(antidomain(coantidomain(u)),coantidomain(multiplication(coantidomain(u),antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[19772,111797]),
[iquote('0:SpR:19772.0,111797.0')] ).
cnf(113140,plain,
leq(antidomain(coantidomain(u)),coantidomain(domain_difference(coantidomain(u),v))),
inference(rew,[status(thm),theory(equality)],[19728,113107]),
[iquote('0:Rew:19728.0,113107.0')] ).
cnf(116685,plain,
leq(antidomain(antidomain(antidomain(u))),coantidomain(domain_difference(antidomain(antidomain(u)),v))),
inference(spr,[status(thm),theory(equality)],[16222,113140]),
[iquote('0:SpR:16222.0,113140.0')] ).
cnf(116786,plain,
leq(antidomain(u),coantidomain(domain_difference(u,v))),
inference(rew,[status(thm),theory(equality)],[4922,116685,5266]),
[iquote('0:Rew:4922.0,116685.0,5266.0,116685.0')] ).
cnf(116815,plain,
equal(multiplication(domain_difference(u,v),antidomain(coantidomain(antidomain(antidomain(u))))),domain_difference(u,v)),
inference(spr,[status(thm),theory(equality)],[5047,19802]),
[iquote('0:SpR:5047.0,19802.0')] ).
cnf(116819,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),coantidomain(antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[5047,25636]),
[iquote('0:SpR:5047.0,25636.0')] ).
cnf(117066,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),antidomain(u)),zero),
inference(rew,[status(thm),theory(equality)],[4922,116819,16222]),
[iquote('0:Rew:4922.0,116819.0,16222.0,116819.0')] ).
cnf(117067,plain,
equal(domain_difference(antidomain(coantidomain(domain_difference(u,v))),u),zero),
inference(rew,[status(thm),theory(equality)],[5201,117066]),
[iquote('0:Rew:5201.0,117066.0')] ).
cnf(117092,plain,
equal(multiplication(antidomain(antidomain(u)),multiplication(antidomain(v),antidomain(antidomain(u)))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[194,116815,4922,16222]),
[iquote('0:Rew:194.0,116815.0,4922.0,116815.0,16222.0,116815.0')] ).
cnf(117093,plain,
equal(domain_difference(antidomain(u),antidomain(v)),domain_difference(v,u)),
inference(rew,[status(thm),theory(equality)],[20799,117092,5201]),
[iquote('0:Rew:20799.0,117092.0,5201.0,117092.0')] ).
cnf(117113,plain,
equal(domain_difference(u,coantidomain(domain_difference(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[117093,101583]),
[iquote('0:Rew:117093.0,101583.0')] ).
cnf(117273,plain,
equal(domain_difference(antidomain(u),antidomain(antidomain(coantidomain(domain_difference(u,v))))),zero),
inference(rew,[status(thm),theory(equality)],[117093,117067]),
[iquote('0:Rew:117093.0,117067.0')] ).
cnf(117296,plain,
equal(domain_difference(antidomain(u),coantidomain(domain_difference(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[19410,117273]),
[iquote('0:Rew:19410.0,117273.0')] ).
cnf(118835,plain,
equal(addition(zero,domain_difference(antidomain(u),coantidomain(domain_difference(v,u)))),antidomain(coantidomain(domain_difference(v,u)))),
inference(spr,[status(thm),theory(equality)],[117113,4387]),
[iquote('0:SpR:117113.0,4387.0')] ).
cnf(118857,plain,
equal(addition(domain_difference(u,coantidomain(domain_difference(v,antidomain(u)))),zero),antidomain(coantidomain(domain_difference(v,antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[117113,4387]),
[iquote('0:SpR:117113.0,4387.0')] ).
cnf(119000,plain,
equal(domain_difference(antidomain(u),coantidomain(domain_difference(v,u))),antidomain(coantidomain(domain_difference(v,u)))),
inference(rew,[status(thm),theory(equality)],[66,118835]),
[iquote('0:Rew:66.0,118835.0')] ).
cnf(119001,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(coantidomain(domain_difference(u,v)))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[119000,8038]),
[iquote('0:Rew:119000.0,8038.0')] ).
cnf(119002,plain,
equal(domain_difference(antidomain(antidomain(u)),coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[5201,119001]),
[iquote('0:Rew:5201.0,119001.0')] ).
cnf(119003,plain,
equal(domain_difference(u,coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[5266,119002]),
[iquote('0:Rew:5266.0,119002.0')] ).
cnf(119004,plain,
equal(domain_difference(u,coantidomain(domain_difference(v,antidomain(u)))),antidomain(coantidomain(domain_difference(v,antidomain(u))))),
inference(rew,[status(thm),theory(equality)],[66,118857,12]),
[iquote('0:Rew:66.0,118857.0,12.0,118857.0')] ).
cnf(121210,plain,
equal(addition(domain_difference(u,coantidomain(domain_difference(u,v))),zero),antidomain(coantidomain(domain_difference(u,v)))),
inference(spr,[status(thm),theory(equality)],[117296,4387]),
[iquote('0:SpR:117296.0,4387.0')] ).
cnf(121369,plain,
equal(domain_difference(u,coantidomain(domain_difference(u,v))),antidomain(coantidomain(domain_difference(u,v)))),
inference(rew,[status(thm),theory(equality)],[66,121210,12]),
[iquote('0:Rew:66.0,121210.0,12.0,121210.0')] ).
cnf(121370,plain,
equal(antidomain(coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[119003,121369]),
[iquote('0:Rew:119003.0,121369.0')] ).
cnf(121371,plain,
equal(domain_difference(u,coantidomain(domain_difference(v,antidomain(u)))),domain_difference(v,antidomain(u))),
inference(rew,[status(thm),theory(equality)],[121370,119004]),
[iquote('0:Rew:121370.0,119004.0')] ).
cnf(135264,plain,
equal(multiplication(antidomain(skc5),multiplication(skc3,skc4)),zero),
inference(spr,[status(thm),theory(equality)],[14208,20361]),
[iquote('0:SpR:14208.0,20361.0')] ).
cnf(136066,plain,
equal(addition(antidomain(forward_diamond(multiplication(antidomain(skc5),skc3),skc4)),antidomain(zero)),antidomain(forward_diamond(multiplication(antidomain(skc5),skc3),skc4))),
inference(spr,[status(thm),theory(equality)],[135264,6131]),
[iquote('0:SpR:135264.0,6131.0')] ).
cnf(136193,plain,
equal(antidomain(forward_diamond(multiplication(antidomain(skc5),skc3),skc4)),one),
inference(rew,[status(thm),theory(equality)],[305,136066,12,91]),
[iquote('0:Rew:305.0,136066.0,12.0,136066.0,91.0,136066.0')] ).
cnf(138049,plain,
equal(addition(one,antidomain(multiplication(antidomain(skc5),forward_diamond(skc3,skc4)))),antidomain(multiplication(antidomain(skc5),forward_diamond(skc3,skc4)))),
inference(spr,[status(thm),theory(equality)],[136193,9686]),
[iquote('0:SpR:136193.0,9686.0')] ).
cnf(138353,plain,
equal(antidomain(multiplication(antidomain(skc5),forward_diamond(skc3,skc4))),one),
inference(rew,[status(thm),theory(equality)],[305,138049]),
[iquote('0:Rew:305.0,138049.0')] ).
cnf(138354,plain,
equal(antidomain(forward_diamond(antidomain(antidomain(antidomain(skc5))),forward_diamond(skc3,skc4))),one),
inference(rew,[status(thm),theory(equality)],[5245,138353,8343]),
[iquote('0:Rew:5245.0,138353.0,8343.0,138353.0')] ).
cnf(138355,plain,
equal(antidomain(forward_diamond(antidomain(skc5),forward_diamond(skc3,skc4))),one),
inference(rew,[status(thm),theory(equality)],[4922,138354]),
[iquote('0:Rew:4922.0,138354.0')] ).
cnf(139186,plain,
equal(forward_diamond(antidomain(skc5),forward_diamond(skc3,skc4)),antidomain(one)),
inference(spr,[status(thm),theory(equality)],[138355,5241]),
[iquote('0:SpR:138355.0,5241.0')] ).
cnf(139312,plain,
equal(forward_diamond(antidomain(skc5),forward_diamond(skc3,skc4)),zero),
inference(rew,[status(thm),theory(equality)],[55,139186]),
[iquote('0:Rew:55.0,139186.0')] ).
cnf(141493,plain,
equal(coantidomain(domain_difference(u,v)),antidomain(domain_difference(u,v))),
inference(spr,[status(thm),theory(equality)],[121370,16222]),
[iquote('0:SpR:121370.0,16222.0')] ).
cnf(141801,plain,
leq(antidomain(u),antidomain(domain_difference(u,v))),
inference(rew,[status(thm),theory(equality)],[141493,116786]),
[iquote('0:Rew:141493.0,116786.0')] ).
cnf(141822,plain,
equal(domain_difference(u,antidomain(domain_difference(v,antidomain(u)))),domain_difference(v,antidomain(u))),
inference(rew,[status(thm),theory(equality)],[141493,121371]),
[iquote('0:Rew:141493.0,121371.0')] ).
cnf(142007,plain,
equal(domain_difference(u,antidomain(v)),forward_diamond(antidomain(antidomain(u)),v)),
inference(rew,[status(thm),theory(equality)],[106061,141822,5245]),
[iquote('0:Rew:106061.0,141822.0,5245.0,141822.0')] ).
cnf(142012,plain,
equal(domain_difference(u,v),forward_diamond(antidomain(antidomain(antidomain(v))),u)),
inference(rew,[status(thm),theory(equality)],[142007,117093]),
[iquote('0:Rew:142007.0,117093.0')] ).
cnf(142397,plain,
equal(domain_difference(u,v),forward_diamond(antidomain(v),u)),
inference(rew,[status(thm),theory(equality)],[4922,142012]),
[iquote('0:Rew:4922.0,142012.0')] ).
cnf(142442,plain,
equal(addition(domain_difference(u,v),forward_diamond(antidomain(v),antidomain(u))),antidomain(v)),
inference(rew,[status(thm),theory(equality)],[142397,4387]),
[iquote('0:Rew:142397.0,4387.0')] ).
cnf(143353,plain,
leq(antidomain(u),antidomain(forward_diamond(antidomain(v),u))),
inference(rew,[status(thm),theory(equality)],[142397,141801]),
[iquote('0:Rew:142397.0,141801.0')] ).
cnf(143650,plain,
equal(addition(forward_diamond(antidomain(u),antidomain(v)),domain_difference(v,u)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[12,142442]),
[iquote('0:Rew:12.0,142442.0')] ).
cnf(143651,plain,
equal(addition(forward_diamond(antidomain(u),antidomain(v)),forward_diamond(antidomain(u),v)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[142397,143650]),
[iquote('0:Rew:142397.0,143650.0')] ).
cnf(143652,plain,
equal(addition(forward_diamond(antidomain(u),v),forward_diamond(antidomain(u),antidomain(v))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[12,143651]),
[iquote('0:Rew:12.0,143651.0')] ).
cnf(164499,plain,
equal(addition(zero,forward_diamond(antidomain(skc5),antidomain(forward_diamond(skc3,skc4)))),antidomain(skc5)),
inference(spr,[status(thm),theory(equality)],[139312,143652]),
[iquote('0:SpR:139312.0,143652.0')] ).
cnf(164605,plain,
equal(forward_diamond(antidomain(skc5),antidomain(forward_diamond(skc3,skc4))),antidomain(skc5)),
inference(rew,[status(thm),theory(equality)],[66,164499]),
[iquote('0:Rew:66.0,164499.0')] ).
cnf(165236,plain,
leq(antidomain(antidomain(forward_diamond(skc3,skc4))),antidomain(antidomain(skc5))),
inference(spr,[status(thm),theory(equality)],[164605,143353]),
[iquote('0:SpR:164605.0,143353.0')] ).
cnf(165267,plain,
leq(forward_diamond(skc3,skc4),antidomain(antidomain(skc5))),
inference(rew,[status(thm),theory(equality)],[5241,165236]),
[iquote('0:Rew:5241.0,165236.0')] ).
cnf(165268,plain,
$false,
inference(mrr,[status(thm)],[165267,5294]),
[iquote('0:MRR:165267.0,5294.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : KLE106+1 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.15 % Command : run_spass %d %s
% 0.14/0.37 % Computer : n026.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Thu Jun 16 08:14:53 EDT 2022
% 0.14/0.37 % CPUTime :
% 116.48/116.67
% 116.48/116.67 SPASS V 3.9
% 116.48/116.67 SPASS beiseite: Proof found.
% 116.48/116.67 % SZS status Theorem
% 116.48/116.67 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 116.48/116.67 SPASS derived 107820 clauses, backtracked 0 clauses, performed 0 splits and kept 13717 clauses.
% 116.48/116.67 SPASS allocated 204114 KBytes.
% 116.48/116.67 SPASS spent 0:1:56.02 on the problem.
% 116.48/116.67 0:00:00.03 for the input.
% 116.48/116.67 0:00:00.03 for the FLOTTER CNF translation.
% 116.48/116.67 0:00:00.72 for inferences.
% 116.48/116.67 0:00:00.00 for the backtracking.
% 116.48/116.67 0:1:54.89 for the reduction.
% 116.48/116.67
% 116.48/116.67
% 116.48/116.67 Here is a proof with depth 10, length 283 :
% 116.48/116.67 % SZS output start Refutation
% See solution above
% 120.48/120.69 Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity right_annihilation left_annihilation domain1 domain4 codomain1 codomain4 complement additive_commutativity domain3 codomain3 order domain_difference forward_diamond backward_diamond backward_box goals additive_associativity multiplicative_associativity right_distributivity left_distributivity domain2 codomain2
% 120.48/120.69
%------------------------------------------------------------------------------