TSTP Solution File: KLE104+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE104+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 02:28:32 EDT 2022
% Result : Theorem 282.45s 282.71s
% Output : Refutation 290.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 29
% Syntax : Number of clauses : 350 ( 342 unt; 0 nHn; 350 RR)
% Number of literals : 358 ( 0 equ; 14 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE104+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE104+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE104+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE104+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,zero),zero),
file('KLE104+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(zero,u),zero),
file('KLE104+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE104+1.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE104+1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE104+1.p',unknown),
[] ).
cnf(10,axiom,
equal(codomain(u),coantidomain(coantidomain(u))),
file('KLE104+1.p',unknown),
[] ).
cnf(11,axiom,
equal(antidomain(domain__dfg(u)),c(u)),
file('KLE104+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE104+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE104+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE104+1.p',unknown),
[] ).
cnf(15,axiom,
equal(addition(domain__dfg(skc4),backward_box(skc3,domain__dfg(skc5))),one),
file('KLE104+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE104+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE104+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE104+1.p',unknown),
[] ).
cnf(19,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE104+1.p',unknown),
[] ).
cnf(20,axiom,
equal(codomain(multiplication(codomain(u),v)),backward_diamond(v,u)),
file('KLE104+1.p',unknown),
[] ).
cnf(21,axiom,
equal(c(forward_diamond(u,c(v))),forward_box(u,v)),
file('KLE104+1.p',unknown),
[] ).
cnf(22,axiom,
equal(c(backward_diamond(u,c(v))),backward_box(u,v)),
file('KLE104+1.p',unknown),
[] ).
cnf(23,axiom,
~ equal(addition(forward_box(skc3,domain__dfg(skc4)),domain__dfg(skc5)),one),
file('KLE104+1.p',unknown),
[] ).
cnf(24,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE104+1.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE104+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE104+1.p',unknown),
[] ).
cnf(27,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE104+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('KLE104+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('KLE104+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)],[30,22]),
[iquote('0:Rew:30.0,22.0,30.0,22.0')] ).
cnf(34,plain,
equal(antidomain(antidomain(antidomain(forward_diamond(u,antidomain(antidomain(antidomain(v))))))),forward_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)],[10,20]),
[iquote('0:Rew:10.0,20.0,10.0,20.0')] ).
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(forward_diamond(u,v),antidomain(antidomain(multiplication(u,antidomain(antidomain(v)))))),
inference(rew,[status(thm),theory(equality)],[8,19]),
[iquote('0:Rew:8.0,19.0,8.0,19.0')] ).
cnf(38,plain,
equal(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v))))))))))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[37,34]),
[iquote('0:Rew:37.0,34.0')] ).
cnf(39,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[8,18]),
[iquote('0:Rew:8.0,18.0')] ).
cnf(40,plain,
equal(addition(antidomain(antidomain(skc4)),backward_box(skc3,antidomain(antidomain(skc5)))),one),
inference(rew,[status(thm),theory(equality)],[8,15]),
[iquote('0:Rew:8.0,15.0,8.0,15.0')] ).
cnf(41,plain,
~ equal(addition(antidomain(antidomain(skc5)),forward_box(skc3,antidomain(antidomain(skc4)))),one),
inference(rew,[status(thm),theory(equality)],[12,23,8]),
[iquote('0:Rew:12.0,23.0,8.0,23.0,8.0,23.0')] ).
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)],[16,12]),
[iquote('0:SpR:16.1,12.0')] ).
cnf(117,plain,
equal(domain_difference(u,u),zero),
inference(spr,[status(thm),theory(equality)],[39,7]),
[iquote('0:SpR:39.0,7.0')] ).
cnf(210,plain,
equal(multiplication(u,multiplication(v,coantidomain(multiplication(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[25,9]),
[iquote('0:SpR:25.0,9.0')] ).
cnf(218,plain,
equal(multiplication(u,multiplication(coantidomain(u),v)),multiplication(zero,v)),
inference(spr,[status(thm),theory(equality)],[9,25]),
[iquote('0:SpR:9.0,25.0')] ).
cnf(219,plain,
equal(multiplication(domain_difference(u,v),w),multiplication(antidomain(antidomain(u)),multiplication(antidomain(v),w))),
inference(spr,[status(thm),theory(equality)],[39,25]),
[iquote('0:SpR:39.0,25.0')] ).
cnf(226,plain,
equal(multiplication(u,multiplication(coantidomain(u),v)),zero),
inference(rew,[status(thm),theory(equality)],[6,218]),
[iquote('0:Rew:6.0,218.0')] ).
cnf(253,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,24]),
[iquote('0:SpR:2.0,24.0')] ).
cnf(260,plain,
equal(addition(antidomain(u),addition(antidomain(antidomain(u)),v)),addition(one,v)),
inference(spr,[status(thm),theory(equality)],[32,24]),
[iquote('0:SpR:32.0,24.0')] ).
cnf(298,plain,
equal(addition(coantidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[31,253]),
[iquote('0:SpR:31.0,253.0')] ).
cnf(299,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[32,253]),
[iquote('0:SpR:32.0,253.0')] ).
cnf(302,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[253,17]),
[iquote('0:SpL:253.0,17.0')] ).
cnf(304,plain,
equal(addition(one,coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,298]),
[iquote('0:Rew:12.0,298.0')] ).
cnf(305,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,299]),
[iquote('0:Rew:12.0,299.0')] ).
cnf(309,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[302]),
[iquote('0:Obv:302.0')] ).
cnf(315,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,309]),
[iquote('0:SpR:12.0,309.0')] ).
cnf(368,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[27,9]),
[iquote('0:SpR:27.0,9.0')] ).
cnf(381,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(382,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(383,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(384,plain,
equal(addition(multiplication(antidomain(antidomain(skc4)),u),multiplication(backward_box(skc3,antidomain(antidomain(skc5))),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[40,27]),
[iquote('0:SpR:40.0,27.0')] ).
cnf(386,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(391,plain,
equal(addition(u,multiplication(coantidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,382]),
[iquote('0:Rew:4.0,382.0')] ).
cnf(392,plain,
equal(addition(u,multiplication(antidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,386]),
[iquote('0:Rew:4.0,386.0')] ).
cnf(396,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,381]),
[iquote('0:Rew:4.0,381.0')] ).
cnf(397,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,383]),
[iquote('0:Rew:4.0,383.0')] ).
cnf(400,plain,
equal(addition(multiplication(antidomain(antidomain(skc4)),u),multiplication(backward_box(skc3,antidomain(antidomain(skc5))),u)),u),
inference(rew,[status(thm),theory(equality)],[4,384]),
[iquote('0:Rew:4.0,384.0')] ).
cnf(446,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(461,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(462,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(463,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(466,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(472,plain,
equal(addition(u,multiplication(u,coantidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,462]),
[iquote('0:Rew:3.0,462.0')] ).
cnf(473,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,466]),
[iquote('0:Rew:3.0,466.0')] ).
cnf(477,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,461]),
[iquote('0:Rew:3.0,461.0')] ).
cnf(478,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,463]),
[iquote('0:Rew:3.0,463.0')] ).
cnf(542,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(547,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)],[36,39]),
[iquote('0:SpR:36.0,39.0')] ).
cnf(553,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(563,plain,
equal(backward_box(u,zero),antidomain(antidomain(antidomain(coantidomain(coantidomain(u)))))),
inference(rew,[status(thm),theory(equality)],[4,553,77,59,91,55]),
[iquote('0:Rew:4.0,553.0,77.0,553.0,59.0,553.0,91.0,553.0,55.0,553.0')] ).
cnf(602,plain,
equal(addition(one,forward_box(u,v)),one),
inference(spr,[status(thm),theory(equality)],[38,305]),
[iquote('0:SpR:38.0,305.0')] ).
cnf(607,plain,
equal(multiplication(forward_box(u,v),antidomain(w)),domain_difference(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v))))))))),w)),
inference(spr,[status(thm),theory(equality)],[38,39]),
[iquote('0:SpR:38.0,39.0')] ).
cnf(609,plain,
equal(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(forward_box(u,v))),w)))))),backward_box(w,antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v)))))))))),
inference(spr,[status(thm),theory(equality)],[38,36]),
[iquote('0:SpR:38.0,36.0')] ).
cnf(615,plain,
equal(multiplication(antidomain(antidomain(u)),forward_box(v,w)),domain_difference(u,antidomain(antidomain(antidomain(antidomain(multiplication(v,antidomain(antidomain(antidomain(antidomain(antidomain(w)))))))))))),
inference(spr,[status(thm),theory(equality)],[38,39]),
[iquote('0:SpR:38.0,39.0')] ).
cnf(618,plain,
equal(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(backward_box(v,w))))))))))),forward_box(u,antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(w))))),v))))))),
inference(spr,[status(thm),theory(equality)],[36,38]),
[iquote('0:SpR:36.0,38.0')] ).
cnf(619,plain,
equal(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(one)))))))))),forward_box(u,zero)),
inference(spr,[status(thm),theory(equality)],[91,38]),
[iquote('0:SpR:91.0,38.0')] ).
cnf(622,plain,
equal(forward_box(zero,u),antidomain(antidomain(antidomain(antidomain(antidomain(zero)))))),
inference(spr,[status(thm),theory(equality)],[6,38]),
[iquote('0:SpR:6.0,38.0')] ).
cnf(623,plain,
equal(forward_box(one,u),antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(u))))))))))),
inference(spr,[status(thm),theory(equality)],[4,38]),
[iquote('0:SpR:4.0,38.0')] ).
cnf(625,plain,
equal(antidomain(antidomain(antidomain(antidomain(antidomain(domain_difference(u,antidomain(antidomain(antidomain(antidomain(v)))))))))),forward_box(antidomain(antidomain(u)),v)),
inference(spr,[status(thm),theory(equality)],[39,38]),
[iquote('0:SpR:39.0,38.0')] ).
cnf(626,plain,
equal(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(antidomain(antidomain(antidomain(w)))))))))))),forward_box(multiplication(u,v),w)),
inference(spr,[status(thm),theory(equality)],[25,38]),
[iquote('0:SpR:25.0,38.0')] ).
cnf(630,plain,
equal(forward_box(zero,u),one),
inference(rew,[status(thm),theory(equality)],[91,622,55]),
[iquote('0:Rew:91.0,622.0,55.0,622.0,91.0,622.0,55.0,622.0,91.0,622.0')] ).
cnf(632,plain,
equal(forward_box(u,zero),antidomain(antidomain(antidomain(antidomain(antidomain(u)))))),
inference(rew,[status(thm),theory(equality)],[3,619,91,55]),
[iquote('0:Rew:3.0,619.0,91.0,619.0,55.0,619.0,91.0,619.0,55.0,619.0')] ).
cnf(683,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(691,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)],[25,29]),
[iquote('0:SpR:25.0,29.0')] ).
cnf(705,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
inference(rew,[status(thm),theory(equality)],[304,683,77]),
[iquote('0:Rew:304.0,683.0,77.0,683.0')] ).
cnf(781,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(784,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(785,plain,
equal(addition(antidomain(zero),antidomain(multiplication(u,antidomain(antidomain(multiplication(coantidomain(u),v)))))),antidomain(multiplication(u,antidomain(antidomain(multiplication(coantidomain(u),v)))))),
inference(spr,[status(thm),theory(equality)],[226,28]),
[iquote('0:SpR:226.0,28.0')] ).
cnf(803,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[305,781,91]),
[iquote('0:Rew:305.0,781.0,91.0,781.0')] ).
cnf(804,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(coantidomain(u))))),one),
inference(rew,[status(thm),theory(equality)],[305,784,91]),
[iquote('0:Rew:305.0,784.0,91.0,784.0')] ).
cnf(806,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(multiplication(coantidomain(u),v))))),one),
inference(rew,[status(thm),theory(equality)],[305,785,91]),
[iquote('0:Rew:305.0,785.0,91.0,785.0')] ).
cnf(959,plain,
equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
inference(spr,[status(thm),theory(equality)],[705,9]),
[iquote('0:SpR:705.0,9.0')] ).
cnf(986,plain,
equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
inference(rew,[status(thm),theory(equality)],[3,959,25]),
[iquote('0:Rew:3.0,959.0,25.0,959.0')] ).
cnf(1162,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[803,7]),
[iquote('0:SpR:803.0,7.0')] ).
cnf(1203,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,1162]),
[iquote('0:Rew:4.0,1162.0')] ).
cnf(1361,plain,
equal(multiplication(one,multiplication(u,antidomain(antidomain(coantidomain(u))))),zero),
inference(spr,[status(thm),theory(equality)],[804,7]),
[iquote('0:SpR:804.0,7.0')] ).
cnf(1397,plain,
equal(multiplication(u,antidomain(antidomain(coantidomain(u)))),zero),
inference(rew,[status(thm),theory(equality)],[4,1361]),
[iquote('0:Rew:4.0,1361.0')] ).
cnf(1465,plain,
leq(multiplication(antidomain(u),v),v),
inference(spr,[status(thm),theory(equality)],[392,315]),
[iquote('0:SpR:392.0,315.0')] ).
cnf(1488,plain,
equal(addition(antidomain(u),domain_difference(v,u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[39,392]),
[iquote('0:SpR:39.0,392.0')] ).
cnf(1621,plain,
leq(multiplication(u,coantidomain(v)),u),
inference(spr,[status(thm),theory(equality)],[472,315]),
[iquote('0:SpR:472.0,315.0')] ).
cnf(3452,plain,
( ~ leq(antidomain(antidomain(u)),v)
| equal(addition(antidomain(u),v),addition(one,v)) ),
inference(spr,[status(thm),theory(equality)],[16,260]),
[iquote('0:SpR:16.1,260.0')] ).
cnf(3640,plain,
equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
inference(spr,[status(thm),theory(equality)],[986,396]),
[iquote('0:SpR:986.0,396.0')] ).
cnf(3643,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(3666,plain,
equal(multiplication(coantidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[66,3640,12]),
[iquote('0:Rew:66.0,3640.0,12.0,3640.0')] ).
cnf(3679,plain,
equal(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[66,3643,12]),
[iquote('0:Rew:66.0,3643.0,12.0,3643.0')] ).
cnf(3807,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1203,397]),
[iquote('0:SpR:1203.0,397.0')] ).
cnf(3812,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(3817,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),multiplication(v,coantidomain(multiplication(antidomain(u),v))))),multiplication(v,coantidomain(multiplication(antidomain(u),v)))),
inference(spr,[status(thm),theory(equality)],[210,397]),
[iquote('0:SpR:210.0,397.0')] ).
cnf(3820,plain,
equal(addition(domain_difference(u,v),multiplication(antidomain(antidomain(antidomain(u))),antidomain(v))),antidomain(v)),
inference(spr,[status(thm),theory(equality)],[39,397]),
[iquote('0:SpR:39.0,397.0')] ).
cnf(3822,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),antidomain(antidomain(u)))),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[1203,397]),
[iquote('0:SpR:1203.0,397.0')] ).
cnf(3829,plain,
equal(multiplication(antidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[66,3812]),
[iquote('0:Rew:66.0,3812.0')] ).
cnf(3842,plain,
equal(domain_difference(u,antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,3822,39]),
[iquote('0:Rew:66.0,3822.0,39.0,3822.0')] ).
cnf(3845,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[66,3807,12]),
[iquote('0:Rew:66.0,3807.0,12.0,3807.0')] ).
cnf(3846,plain,
equal(addition(domain_difference(u,v),domain_difference(antidomain(u),v)),antidomain(v)),
inference(rew,[status(thm),theory(equality)],[39,3820]),
[iquote('0:Rew:39.0,3820.0')] ).
cnf(3857,plain,
equal(multiplication(antidomain(antidomain(u)),multiplication(v,coantidomain(multiplication(antidomain(u),v)))),multiplication(v,coantidomain(multiplication(antidomain(u),v)))),
inference(rew,[status(thm),theory(equality)],[66,3817]),
[iquote('0:Rew:66.0,3817.0')] ).
cnf(3883,plain,
equal(domain_difference(antidomain(u),u),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[3829,39]),
[iquote('0:SpR:3829.0,39.0')] ).
cnf(3933,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)],[36,3883]),
[iquote('0:SpR:36.0,3883.0')] ).
cnf(3934,plain,
equal(domain_difference(forward_box(u,v),antidomain(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v))))))))))),forward_box(u,v)),
inference(spr,[status(thm),theory(equality)],[38,3883]),
[iquote('0:SpR:38.0,3883.0')] ).
cnf(4011,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)],[3829,477]),
[iquote('0:SpR:3829.0,477.0')] ).
cnf(4023,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[9,477]),
[iquote('0:SpR:9.0,477.0')] ).
cnf(4036,plain,
equal(multiplication(u,coantidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[66,4023]),
[iquote('0:Rew:66.0,4023.0')] ).
cnf(4037,plain,
equal(coantidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4036,3679]),
[iquote('0:Rew:4036.0,3679.0')] ).
cnf(4096,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)],[12,4011]),
[iquote('0:Rew:12.0,4011.0')] ).
cnf(4268,plain,
equal(addition(multiplication(u,antidomain(coantidomain(u))),zero),u),
inference(spr,[status(thm),theory(equality)],[1397,478]),
[iquote('0:SpR:1397.0,478.0')] ).
cnf(4269,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[39,478]),
[iquote('0:SpR:39.0,478.0')] ).
cnf(4275,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)],[3666,478]),
[iquote('0:SpR:3666.0,478.0')] ).
cnf(4287,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1203,478]),
[iquote('0:SpR:1203.0,478.0')] ).
cnf(4298,plain,
equal(multiplication(u,antidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[66,4268,12]),
[iquote('0:Rew:66.0,4268.0,12.0,4268.0')] ).
cnf(4309,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[66,4287]),
[iquote('0:Rew:66.0,4287.0')] ).
cnf(4310,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[3845,4309]),
[iquote('0:Rew:3845.0,4309.0')] ).
cnf(4311,plain,
equal(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v))))))))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4310,38]),
[iquote('0:Rew:4310.0,38.0')] ).
cnf(4316,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(u))))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4310,36]),
[iquote('0:Rew:4310.0,36.0')] ).
cnf(4339,plain,
equal(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(backward_box(v,w))))))))),forward_box(u,antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(w))))),v))))))),
inference(rew,[status(thm),theory(equality)],[4310,618]),
[iquote('0:Rew:4310.0,618.0')] ).
cnf(4340,plain,
equal(antidomain(antidomain(antidomain(domain_difference(u,antidomain(antidomain(antidomain(antidomain(v)))))))),forward_box(antidomain(antidomain(u)),v)),
inference(rew,[status(thm),theory(equality)],[4310,625]),
[iquote('0:Rew:4310.0,625.0')] ).
cnf(4341,plain,
equal(multiplication(antidomain(antidomain(u)),forward_box(v,w)),domain_difference(u,antidomain(antidomain(multiplication(v,antidomain(antidomain(antidomain(antidomain(antidomain(w)))))))))),
inference(rew,[status(thm),theory(equality)],[4310,615]),
[iquote('0:Rew:4310.0,615.0')] ).
cnf(4350,plain,
equal(antidomain(antidomain(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(antidomain(antidomain(antidomain(w)))))))))),forward_box(multiplication(u,v),w)),
inference(rew,[status(thm),theory(equality)],[4310,626]),
[iquote('0:Rew:4310.0,626.0')] ).
cnf(4376,plain,
equal(domain_difference(forward_box(u,v),antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v))))))))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4310,3934]),
[iquote('0:Rew:4310.0,3934.0')] ).
cnf(4378,plain,
equal(multiplication(forward_box(u,v),antidomain(w)),domain_difference(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v))))))),w)),
inference(rew,[status(thm),theory(equality)],[4310,607]),
[iquote('0:Rew:4310.0,607.0')] ).
cnf(4393,plain,
equal(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(forward_box(u,v))),w)))))),backward_box(w,antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(v)))))))),
inference(rew,[status(thm),theory(equality)],[4310,609]),
[iquote('0:Rew:4310.0,609.0')] ).
cnf(4401,plain,
equal(forward_box(one,u),antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(u))))))))),
inference(rew,[status(thm),theory(equality)],[4310,623]),
[iquote('0:Rew:4310.0,623.0')] ).
cnf(4406,plain,
equal(forward_box(u,zero),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[4310,632]),
[iquote('0:Rew:4310.0,632.0')] ).
cnf(4419,plain,
equal(backward_box(u,zero),antidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[4310,563]),
[iquote('0:Rew:4310.0,563.0')] ).
cnf(4432,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)],[4310,3933]),
[iquote('0:Rew:4310.0,3933.0')] ).
cnf(4434,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)],[4310,547]),
[iquote('0:Rew:4310.0,547.0')] ).
cnf(4483,plain,
equal(forward_box(u,zero),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4310,4406]),
[iquote('0:Rew:4310.0,4406.0')] ).
cnf(4497,plain,
equal(forward_box(one,u),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4310,4401]),
[iquote('0:Rew:4310.0,4401.0,4310.0,4401.0,4310.0,4401.0')] ).
cnf(4500,plain,
equal(addition(domain_difference(u,v),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[39,4269]),
[iquote('0:Rew:39.0,4269.0')] ).
cnf(4502,plain,
equal(antidomain(multiplication(u,antidomain(v))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4310,4311]),
[iquote('0:Rew:4310.0,4311.0,4310.0,4311.0,4310.0,4311.0')] ).
cnf(4504,plain,
equal(addition(antidomain(multiplication(u,v)),forward_box(u,antidomain(v))),forward_box(u,antidomain(v))),
inference(rew,[status(thm),theory(equality)],[4502,28]),
[iquote('0:Rew:4502.0,28.0')] ).
cnf(4519,plain,
equal(forward_box(u,antidomain(multiplication(coantidomain(u),v))),one),
inference(rew,[status(thm),theory(equality)],[4502,806]),
[iquote('0:Rew:4502.0,806.0')] ).
cnf(4529,plain,
equal(addition(forward_box(u,antidomain(v)),antidomain(multiplication(u,v))),forward_box(u,antidomain(v))),
inference(rew,[status(thm),theory(equality)],[12,4504]),
[iquote('0:Rew:12.0,4504.0')] ).
cnf(4530,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4310,4316]),
[iquote('0:Rew:4310.0,4316.0')] ).
cnf(4555,plain,
equal(antidomain(domain_difference(u,antidomain(antidomain(v)))),forward_box(antidomain(antidomain(u)),v)),
inference(rew,[status(thm),theory(equality)],[4310,4340]),
[iquote('0:Rew:4310.0,4340.0,4310.0,4340.0')] ).
cnf(4598,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)],[12,4275]),
[iquote('0:Rew:12.0,4275.0')] ).
cnf(4599,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4310,4598]),
[iquote('0:Rew:4310.0,4598.0')] ).
cnf(4606,plain,
equal(antidomain(antidomain(forward_box(u,v))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[3842,4376,4502,4310]),
[iquote('0:Rew:3842.0,4376.0,4502.0,4376.0,4310.0,4376.0,4310.0,4376.0')] ).
cnf(4612,plain,
equal(multiplication(forward_box(u,v),antidomain(w)),domain_difference(forward_box(u,v),w)),
inference(rew,[status(thm),theory(equality)],[4502,4378,4310]),
[iquote('0:Rew:4502.0,4378.0,4310.0,4378.0,4310.0,4378.0')] ).
cnf(4615,plain,
equal(antidomain(antidomain(backward_box(u,v))),backward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[3842,4432,4530]),
[iquote('0:Rew:3842.0,4432.0,4530.0,4432.0')] ).
cnf(4621,plain,
equal(multiplication(backward_box(u,v),antidomain(w)),domain_difference(backward_box(u,v),w)),
inference(rew,[status(thm),theory(equality)],[4530,4434]),
[iquote('0:Rew:4530.0,4434.0')] ).
cnf(4633,plain,
equal(antidomain(multiplication(u,multiplication(v,antidomain(w)))),forward_box(multiplication(u,v),w)),
inference(rew,[status(thm),theory(equality)],[4310,4350]),
[iquote('0:Rew:4310.0,4350.0,4310.0,4350.0,4310.0,4350.0')] ).
cnf(4639,plain,
equal(multiplication(antidomain(antidomain(u)),forward_box(v,w)),domain_difference(u,antidomain(forward_box(v,w)))),
inference(rew,[status(thm),theory(equality)],[4502,4341,4310]),
[iquote('0:Rew:4502.0,4341.0,4310.0,4341.0,4310.0,4341.0')] ).
cnf(4676,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(forward_box(u,v))),w)))),backward_box(w,antidomain(forward_box(u,v)))),
inference(rew,[status(thm),theory(equality)],[4310,4393,4502]),
[iquote('0:Rew:4310.0,4393.0,4502.0,4393.0,4310.0,4393.0')] ).
cnf(4691,plain,
equal(antidomain(multiplication(u,backward_box(v,w))),forward_box(u,antidomain(backward_box(v,w)))),
inference(rew,[status(thm),theory(equality)],[4310,4339,4615,4530]),
[iquote('0:Rew:4310.0,4339.0,4310.0,4339.0,4615.0,4339.0,4530.0,4339.0,4310.0,4339.0')] ).
cnf(4756,plain,
equal(multiplication(antidomain(u),antidomain(v)),domain_difference(antidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[4310,39]),
[iquote('0:SpR:4310.0,39.0')] ).
cnf(4771,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,antidomain(antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[4310,39]),
[iquote('0:SpR:4310.0,39.0')] ).
cnf(4799,plain,
equal(domain_difference(antidomain(antidomain(u)),v),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4756,39]),
[iquote('0:Rew:4756.0,39.0')] ).
cnf(4821,plain,
equal(domain_difference(u,antidomain(antidomain(v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4799,4771,4756]),
[iquote('0:Rew:4799.0,4771.0,4756.0,4771.0')] ).
cnf(4823,plain,
equal(antidomain(domain_difference(u,v)),forward_box(antidomain(antidomain(u)),v)),
inference(rew,[status(thm),theory(equality)],[4821,4555]),
[iquote('0:Rew:4821.0,4555.0')] ).
cnf(4859,plain,
equal(multiplication(forward_box(u,v),multiplication(u,antidomain(v))),zero),
inference(spr,[status(thm),theory(equality)],[4502,7]),
[iquote('0:SpR:4502.0,7.0')] ).
cnf(4906,plain,
equal(antidomain(multiplication(u,antidomain(v))),forward_box(u,antidomain(antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[4310,4502]),
[iquote('0:SpR:4310.0,4502.0')] ).
cnf(4930,plain,
equal(forward_box(u,antidomain(antidomain(v))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4502,4906]),
[iquote('0:Rew:4502.0,4906.0')] ).
cnf(4931,plain,
~ equal(addition(antidomain(antidomain(skc5)),forward_box(skc3,skc4)),one),
inference(rew,[status(thm),theory(equality)],[4930,41]),
[iquote('0:Rew:4930.0,41.0')] ).
cnf(5195,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)],[4298,396]),
[iquote('0:SpR:4298.0,396.0')] ).
cnf(5211,plain,
equal(addition(coantidomain(coantidomain(u)),multiplication(coantidomain(u),antidomain(coantidomain(u)))),antidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[12,5195,4037]),
[iquote('0:Rew:12.0,5195.0,4037.0,5195.0')] ).
cnf(5393,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),v)))),backward_box(v,antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[4310,4530]),
[iquote('0:SpR:4310.0,4530.0')] ).
cnf(5395,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(forward_box(u,v))),w)))),backward_box(w,multiplication(u,antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[4502,4530]),
[iquote('0:SpR:4502.0,4530.0')] ).
cnf(5396,plain,
equal(backward_box(u,u),antidomain(coantidomain(coantidomain(zero)))),
inference(spr,[status(thm),theory(equality)],[986,4530]),
[iquote('0:SpR:986.0,4530.0')] ).
cnf(5410,plain,
equal(backward_box(u,u),one),
inference(rew,[status(thm),theory(equality)],[91,5396,59,77]),
[iquote('0:Rew:91.0,5396.0,59.0,5396.0,77.0,5396.0')] ).
cnf(5423,plain,
equal(backward_box(u,antidomain(antidomain(v))),backward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4530,5393]),
[iquote('0:Rew:4530.0,5393.0')] ).
cnf(5433,plain,
equal(addition(multiplication(antidomain(antidomain(skc4)),u),multiplication(backward_box(skc3,skc5),u)),u),
inference(rew,[status(thm),theory(equality)],[5423,400]),
[iquote('0:Rew:5423.0,400.0')] ).
cnf(5445,plain,
equal(backward_box(u,multiplication(v,antidomain(w))),backward_box(u,antidomain(forward_box(v,w)))),
inference(rew,[status(thm),theory(equality)],[4676,5395]),
[iquote('0:Rew:4676.0,5395.0')] ).
cnf(5756,plain,
equal(addition(forward_box(u,forward_box(v,w)),antidomain(multiplication(u,multiplication(v,antidomain(w))))),forward_box(u,forward_box(v,w))),
inference(spr,[status(thm),theory(equality)],[4502,4529]),
[iquote('0:SpR:4502.0,4529.0')] ).
cnf(5796,plain,
equal(addition(forward_box(u,forward_box(v,w)),forward_box(multiplication(u,v),w)),forward_box(u,forward_box(v,w))),
inference(rew,[status(thm),theory(equality)],[4633,5756]),
[iquote('0:Rew:4633.0,5756.0')] ).
cnf(6078,plain,
equal(multiplication(forward_box(antidomain(antidomain(u)),v),domain_difference(u,v)),zero),
inference(spr,[status(thm),theory(equality)],[4823,7]),
[iquote('0:SpR:4823.0,7.0')] ).
cnf(7425,plain,
equal(addition(zero,multiplication(backward_box(skc3,skc5),antidomain(skc4))),antidomain(skc4)),
inference(spr,[status(thm),theory(equality)],[7,5433]),
[iquote('0:SpR:7.0,5433.0')] ).
cnf(7447,plain,
equal(domain_difference(backward_box(skc3,skc5),skc4),antidomain(skc4)),
inference(rew,[status(thm),theory(equality)],[66,7425,4621]),
[iquote('0:Rew:66.0,7425.0,4621.0,7425.0')] ).
cnf(7486,plain,
equal(forward_box(antidomain(antidomain(backward_box(skc3,skc5))),skc4),antidomain(antidomain(skc4))),
inference(spr,[status(thm),theory(equality)],[7447,4823]),
[iquote('0:SpR:7447.0,4823.0')] ).
cnf(7498,plain,
equal(forward_box(backward_box(skc3,skc5),skc4),antidomain(antidomain(skc4))),
inference(rew,[status(thm),theory(equality)],[4615,7486]),
[iquote('0:Rew:4615.0,7486.0')] ).
cnf(7805,plain,
equal(antidomain(multiplication(u,domain_difference(backward_box(v,w),x))),forward_box(multiplication(u,backward_box(v,w)),x)),
inference(spr,[status(thm),theory(equality)],[4621,4633]),
[iquote('0:SpR:4621.0,4633.0')] ).
cnf(8863,plain,
equal(multiplication(one,multiplication(u,antidomain(antidomain(multiplication(coantidomain(u),v))))),zero),
inference(spr,[status(thm),theory(equality)],[4519,4859]),
[iquote('0:SpR:4519.0,4859.0')] ).
cnf(8896,plain,
equal(forward_box(u,forward_box(coantidomain(u),v)),one),
inference(spr,[status(thm),theory(equality)],[4502,4519]),
[iquote('0:SpR:4502.0,4519.0')] ).
cnf(8917,plain,
equal(multiplication(u,antidomain(antidomain(multiplication(coantidomain(u),v)))),zero),
inference(rew,[status(thm),theory(equality)],[4,8863]),
[iquote('0:Rew:4.0,8863.0')] ).
cnf(8928,plain,
equal(multiplication(one,multiplication(u,antidomain(forward_box(coantidomain(u),v)))),zero),
inference(spr,[status(thm),theory(equality)],[8896,4859]),
[iquote('0:SpR:8896.0,4859.0')] ).
cnf(8967,plain,
equal(multiplication(u,antidomain(forward_box(coantidomain(u),v))),zero),
inference(rew,[status(thm),theory(equality)],[4,8928]),
[iquote('0:Rew:4.0,8928.0')] ).
cnf(10018,plain,
equal(addition(zero,multiplication(u,antidomain(antidomain(forward_box(coantidomain(u),v))))),u),
inference(spr,[status(thm),theory(equality)],[8967,478]),
[iquote('0:SpR:8967.0,478.0')] ).
cnf(10089,plain,
equal(multiplication(u,antidomain(antidomain(forward_box(coantidomain(u),v)))),u),
inference(rew,[status(thm),theory(equality)],[66,10018]),
[iquote('0:Rew:66.0,10018.0')] ).
cnf(10090,plain,
equal(multiplication(u,forward_box(coantidomain(u),v)),u),
inference(rew,[status(thm),theory(equality)],[4606,10089]),
[iquote('0:Rew:4606.0,10089.0')] ).
cnf(10199,plain,
equal(addition(antidomain(u),multiplication(antidomain(antidomain(u)),forward_box(coantidomain(antidomain(u)),v))),forward_box(coantidomain(antidomain(u)),v)),
inference(spr,[status(thm),theory(equality)],[10090,397]),
[iquote('0:SpR:10090.0,397.0')] ).
cnf(10241,plain,
equal(addition(antidomain(u),domain_difference(u,antidomain(forward_box(coantidomain(antidomain(u)),v)))),forward_box(coantidomain(antidomain(u)),v)),
inference(rew,[status(thm),theory(equality)],[4639,10199]),
[iquote('0:Rew:4639.0,10199.0')] ).
cnf(10818,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)],[219,4298]),
[iquote('0:SpR:219.0,4298.0')] ).
cnf(10884,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)],[4756,10818]),
[iquote('0:Rew:4756.0,10818.0')] ).
cnf(11537,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),zero),zero),
inference(spr,[status(thm),theory(equality)],[368,253]),
[iquote('0:SpR:368.0,253.0')] ).
cnf(11575,plain,
equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[473,368]),
[iquote('0:SpR:473.0,368.0')] ).
cnf(11660,plain,
equal(multiplication(u,coantidomain(addition(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[66,11537,12]),
[iquote('0:Rew:66.0,11537.0,12.0,11537.0')] ).
cnf(11661,plain,
equal(addition(zero,multiplication(u,coantidomain(addition(v,u)))),zero),
inference(rew,[status(thm),theory(equality)],[11660,368]),
[iquote('0:Rew:11660.0,368.0')] ).
cnf(11669,plain,
equal(multiplication(u,coantidomain(addition(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[66,11661]),
[iquote('0:Rew:66.0,11661.0')] ).
cnf(11705,plain,
equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[66,11575,9,25]),
[iquote('0:Rew:66.0,11575.0,9.0,11575.0,25.0,11575.0')] ).
cnf(12741,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(addition(v,u))))),u),
inference(spr,[status(thm),theory(equality)],[11669,477]),
[iquote('0:SpR:11669.0,477.0')] ).
cnf(12867,plain,
equal(multiplication(u,coantidomain(coantidomain(addition(v,u)))),u),
inference(rew,[status(thm),theory(equality)],[66,12741]),
[iquote('0:Rew:66.0,12741.0')] ).
cnf(13186,plain,
equal(addition(multiplication(antidomain(u),u),multiplication(antidomain(u),multiplication(coantidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[391,446]),
[iquote('0:SpR:391.0,446.0')] ).
cnf(13187,plain,
equal(addition(multiplication(antidomain(u),u),multiplication(antidomain(u),multiplication(antidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[392,446]),
[iquote('0:SpR:392.0,446.0')] ).
cnf(13200,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(u)),multiplication(antidomain(antidomain(u)),domain_difference(v,u))),zero),
inference(spr,[status(thm),theory(equality)],[1488,446]),
[iquote('0:SpR:1488.0,446.0')] ).
cnf(13313,plain,
equal(multiplication(antidomain(u),multiplication(coantidomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[66,13186,7]),
[iquote('0:Rew:66.0,13186.0,7.0,13186.0')] ).
cnf(13314,plain,
equal(multiplication(antidomain(u),multiplication(antidomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[66,13187,7]),
[iquote('0:Rew:66.0,13187.0,7.0,13187.0')] ).
cnf(13337,plain,
equal(multiplication(antidomain(antidomain(u)),domain_difference(v,u)),zero),
inference(rew,[status(thm),theory(equality)],[66,13200,7]),
[iquote('0:Rew:66.0,13200.0,7.0,13200.0')] ).
cnf(15625,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(addition(u,v))))),u),
inference(spr,[status(thm),theory(equality)],[11660,477]),
[iquote('0:SpR:11660.0,477.0')] ).
cnf(15749,plain,
equal(multiplication(u,coantidomain(coantidomain(addition(u,v)))),u),
inference(rew,[status(thm),theory(equality)],[66,15625]),
[iquote('0:Rew:66.0,15625.0')] ).
cnf(16835,plain,
equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4036,11705]),
[iquote('0:SpR:4036.0,11705.0')] ).
cnf(16851,plain,
equal(addition(antidomain(antidomain(u)),zero),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[16835,4599]),
[iquote('0:Rew:16835.0,4599.0')] ).
cnf(16908,plain,
equal(coantidomain(antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,16851,12]),
[iquote('0:Rew:66.0,16851.0,12.0,16851.0')] ).
cnf(16919,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(antidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[16908,4530]),
[iquote('0:Rew:16908.0,4530.0')] ).
cnf(17095,plain,
equal(addition(antidomain(u),domain_difference(u,antidomain(forward_box(antidomain(antidomain(u)),v)))),forward_box(antidomain(antidomain(u)),v)),
inference(rew,[status(thm),theory(equality)],[16908,10241]),
[iquote('0:Rew:16908.0,10241.0')] ).
cnf(17239,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(u))),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[16908,16919]),
[iquote('0:Rew:16908.0,16919.0')] ).
cnf(17240,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(antidomain(u),v)))),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[4310,17239]),
[iquote('0:Rew:4310.0,17239.0')] ).
cnf(17982,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(forward_box(u,v),w)))),backward_box(w,multiplication(u,antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[4502,17240]),
[iquote('0:SpR:4502.0,17240.0')] ).
cnf(18147,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(forward_box(u,v),w)))),backward_box(w,antidomain(forward_box(u,v)))),
inference(rew,[status(thm),theory(equality)],[5445,17982]),
[iquote('0:Rew:5445.0,17982.0')] ).
cnf(19905,plain,
equal(multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4298,13313]),
[iquote('0:SpR:4298.0,13313.0')] ).
cnf(19946,plain,
equal(addition(coantidomain(coantidomain(u)),zero),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[19905,4096]),
[iquote('0:Rew:19905.0,4096.0')] ).
cnf(19952,plain,
equal(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,19946,12]),
[iquote('0:Rew:66.0,19946.0,12.0,19946.0')] ).
cnf(19989,plain,
equal(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(u)),v)))),backward_box(v,antidomain(coantidomain(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[19952,17240]),
[iquote('0:SpR:19952.0,17240.0')] ).
cnf(20023,plain,
equal(coantidomain(coantidomain(coantidomain(u))),antidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[19952,16908]),
[iquote('0:SpR:19952.0,16908.0')] ).
cnf(20096,plain,
equal(antidomain(antidomain(coantidomain(u))),coantidomain(u)),
inference(spr,[status(thm),theory(equality)],[4037,19952]),
[iquote('0:SpR:4037.0,19952.0')] ).
cnf(20135,plain,
equal(antidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4037,20023]),
[iquote('0:Rew:4037.0,20023.0')] ).
cnf(20136,plain,
equal(coantidomain(multiplication(antidomain(u),v)),backward_box(v,u)),
inference(rew,[status(thm),theory(equality)],[20135,17240]),
[iquote('0:Rew:20135.0,17240.0')] ).
cnf(20138,plain,
equal(backward_box(u,zero),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[20135,4419]),
[iquote('0:Rew:20135.0,4419.0')] ).
cnf(20143,plain,
equal(coantidomain(multiplication(forward_box(u,v),w)),backward_box(w,antidomain(forward_box(u,v)))),
inference(rew,[status(thm),theory(equality)],[20135,18147]),
[iquote('0:Rew:20135.0,18147.0')] ).
cnf(20196,plain,
equal(multiplication(antidomain(antidomain(u)),multiplication(v,backward_box(v,u))),multiplication(v,backward_box(v,u))),
inference(rew,[status(thm),theory(equality)],[20136,3857]),
[iquote('0:Rew:20136.0,3857.0')] ).
cnf(20298,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(u)),v)),backward_box(v,coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[20135,19989]),
[iquote('0:Rew:20135.0,19989.0,20135.0,19989.0')] ).
cnf(20299,plain,
equal(addition(coantidomain(multiplication(u,v)),backward_box(v,coantidomain(u))),backward_box(v,coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[20298,29]),
[iquote('0:Rew:20298.0,29.0')] ).
cnf(20323,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)],[20298,691]),
[iquote('0:Rew:20298.0,691.0')] ).
cnf(20326,plain,
equal(addition(backward_box(u,coantidomain(v)),coantidomain(multiplication(v,u))),backward_box(u,coantidomain(v))),
inference(rew,[status(thm),theory(equality)],[12,20299]),
[iquote('0:Rew:12.0,20299.0')] ).
cnf(20368,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)],[12,20323]),
[iquote('0:Rew:12.0,20323.0')] ).
cnf(20390,plain,
equal(multiplication(coantidomain(u),antidomain(v)),domain_difference(coantidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[20138,4621]),
[iquote('0:SpR:20138.0,4621.0')] ).
cnf(20423,plain,
equal(addition(coantidomain(coantidomain(u)),domain_difference(coantidomain(u),coantidomain(u))),antidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[20390,5211]),
[iquote('0:Rew:20390.0,5211.0')] ).
cnf(20440,plain,
equal(coantidomain(coantidomain(u)),antidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,20423,12,117]),
[iquote('0:Rew:66.0,20423.0,12.0,20423.0,117.0,20423.0')] ).
cnf(20446,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(antidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[20440,396]),
[iquote('0:Rew:20440.0,396.0')] ).
cnf(20469,plain,
equal(multiplication(u,antidomain(coantidomain(addition(v,u)))),u),
inference(rew,[status(thm),theory(equality)],[20440,12867]),
[iquote('0:Rew:20440.0,12867.0')] ).
cnf(20473,plain,
equal(multiplication(u,antidomain(coantidomain(addition(u,v)))),u),
inference(rew,[status(thm),theory(equality)],[20440,15749]),
[iquote('0:Rew:20440.0,15749.0')] ).
cnf(20961,plain,
equal(multiplication(multiplication(antidomain(u),v),backward_box(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[20136,9]),
[iquote('0:SpR:20136.0,9.0')] ).
cnf(21087,plain,
equal(multiplication(antidomain(u),multiplication(v,backward_box(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[25,20961]),
[iquote('0:Rew:25.0,20961.0')] ).
cnf(21402,plain,
equal(forward_box(multiplication(antidomain(antidomain(u)),antidomain(v)),u),antidomain(zero)),
inference(spr,[status(thm),theory(equality)],[13314,4633]),
[iquote('0:SpR:13314.0,4633.0')] ).
cnf(21496,plain,
equal(forward_box(multiplication(antidomain(antidomain(u)),antidomain(v)),u),one),
inference(rew,[status(thm),theory(equality)],[91,21402]),
[iquote('0:Rew:91.0,21402.0')] ).
cnf(21497,plain,
equal(forward_box(domain_difference(antidomain(antidomain(u)),v),u),one),
inference(rew,[status(thm),theory(equality)],[4756,21496]),
[iquote('0:Rew:4756.0,21496.0')] ).
cnf(21498,plain,
equal(forward_box(domain_difference(u,v),u),one),
inference(rew,[status(thm),theory(equality)],[4799,21497]),
[iquote('0:Rew:4799.0,21497.0')] ).
cnf(21587,plain,
equal(addition(multiplication(antidomain(u),domain_difference(v,u)),zero),domain_difference(v,u)),
inference(spr,[status(thm),theory(equality)],[13337,397]),
[iquote('0:SpR:13337.0,397.0')] ).
cnf(21656,plain,
equal(multiplication(antidomain(u),domain_difference(v,u)),domain_difference(v,u)),
inference(rew,[status(thm),theory(equality)],[66,21587,12]),
[iquote('0:Rew:66.0,21587.0,12.0,21587.0')] ).
cnf(21736,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)],[20136,20326]),
[iquote('0:SpR:20136.0,20326.0')] ).
cnf(21797,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)],[20136,21736,25]),
[iquote('0:Rew:20136.0,21736.0,25.0,21736.0')] ).
cnf(25128,plain,
equal(coantidomain(domain_difference(forward_box(u,v),w)),backward_box(antidomain(w),antidomain(forward_box(u,v)))),
inference(spr,[status(thm),theory(equality)],[4612,20143]),
[iquote('0:SpR:4612.0,20143.0')] ).
cnf(26369,plain,
equal(addition(forward_box(antidomain(u),forward_box(multiplication(v,backward_box(v,u)),w)),forward_box(zero,w)),forward_box(antidomain(u),forward_box(multiplication(v,backward_box(v,u)),w))),
inference(spr,[status(thm),theory(equality)],[21087,5796]),
[iquote('0:SpR:21087.0,5796.0')] ).
cnf(26554,plain,
equal(forward_box(antidomain(u),forward_box(multiplication(v,backward_box(v,u)),w)),one),
inference(rew,[status(thm),theory(equality)],[602,26369,12,630]),
[iquote('0:Rew:602.0,26369.0,12.0,26369.0,630.0,26369.0')] ).
cnf(26988,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)],[5410,21797]),
[iquote('0:SpR:5410.0,21797.0')] ).
cnf(27090,plain,
equal(backward_box(u,backward_box(v,multiplication(v,u))),one),
inference(rew,[status(thm),theory(equality)],[542,26988,12]),
[iquote('0:Rew:542.0,26988.0,12.0,26988.0')] ).
cnf(31852,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)],[7,20368]),
[iquote('0:SpR:7.0,20368.0')] ).
cnf(31912,plain,
equal(addition(backward_box(antidomain(u),coantidomain(multiplication(forward_box(v,u),v))),coantidomain(zero)),backward_box(antidomain(u),coantidomain(multiplication(forward_box(v,u),v)))),
inference(spr,[status(thm),theory(equality)],[4859,20368]),
[iquote('0:SpR:4859.0,20368.0')] ).
cnf(32047,plain,
equal(backward_box(u,coantidomain(multiplication(v,antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[542,31852,12,77,5]),
[iquote('0:Rew:542.0,31852.0,12.0,31852.0,77.0,31852.0,5.0,31852.0')] ).
cnf(32053,plain,
equal(backward_box(antidomain(u),backward_box(v,antidomain(forward_box(v,u)))),one),
inference(rew,[status(thm),theory(equality)],[542,31912,12,77,20143]),
[iquote('0:Rew:542.0,31912.0,12.0,31912.0,77.0,31912.0,20143.0,31912.0')] ).
cnf(33909,plain,
equal(multiplication(antidomain(coantidomain(multiplication(u,antidomain(v)))),multiplication(v,one)),zero),
inference(spr,[status(thm),theory(equality)],[32047,21087]),
[iquote('0:SpR:32047.0,21087.0')] ).
cnf(34035,plain,
equal(multiplication(antidomain(coantidomain(multiplication(u,antidomain(v)))),v),zero),
inference(rew,[status(thm),theory(equality)],[3,33909]),
[iquote('0:Rew:3.0,33909.0')] ).
cnf(38185,plain,
equal(domain_difference(u,domain_difference(v,w)),domain_difference(u,antidomain(forward_box(antidomain(antidomain(v)),w)))),
inference(spr,[status(thm),theory(equality)],[4823,4821]),
[iquote('0:SpR:4823.0,4821.0')] ).
cnf(80812,plain,
equal(backward_box(antidomain(u),backward_box(domain_difference(u,v),antidomain(one))),one),
inference(spr,[status(thm),theory(equality)],[21498,32053]),
[iquote('0:SpR:21498.0,32053.0')] ).
cnf(80926,plain,
equal(backward_box(antidomain(u),coantidomain(domain_difference(u,v))),one),
inference(rew,[status(thm),theory(equality)],[20138,80812,55]),
[iquote('0:Rew:20138.0,80812.0,55.0,80812.0')] ).
cnf(81247,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),multiplication(antidomain(u),one)),zero),
inference(spr,[status(thm),theory(equality)],[80926,21087]),
[iquote('0:SpR:80926.0,21087.0')] ).
cnf(81482,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),antidomain(u)),zero),
inference(rew,[status(thm),theory(equality)],[3,81247]),
[iquote('0:Rew:3.0,81247.0')] ).
cnf(81483,plain,
equal(domain_difference(antidomain(coantidomain(domain_difference(u,v))),u),zero),
inference(rew,[status(thm),theory(equality)],[4756,81482]),
[iquote('0:Rew:4756.0,81482.0')] ).
cnf(86517,plain,
equal(addition(domain_difference(coantidomain(domain_difference(u,v)),u),zero),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[81483,3846]),
[iquote('0:SpR:81483.0,3846.0')] ).
cnf(86636,plain,
equal(domain_difference(coantidomain(domain_difference(u,v)),u),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[66,86517,12]),
[iquote('0:Rew:66.0,86517.0,12.0,86517.0')] ).
cnf(86949,plain,
equal(forward_box(antidomain(u),coantidomain(domain_difference(u,v))),one),
inference(spr,[status(thm),theory(equality)],[86636,21498]),
[iquote('0:SpR:86636.0,21498.0')] ).
cnf(86965,plain,
equal(domain_difference(coantidomain(antidomain(u)),coantidomain(domain_difference(u,v))),antidomain(coantidomain(domain_difference(u,v)))),
inference(spr,[status(thm),theory(equality)],[86636]),
[iquote('0:SpR:86636.0,86636.0')] ).
cnf(87127,plain,
equal(domain_difference(u,coantidomain(domain_difference(u,v))),antidomain(coantidomain(domain_difference(u,v)))),
inference(rew,[status(thm),theory(equality)],[4799,86965,16908]),
[iquote('0:Rew:4799.0,86965.0,16908.0,86965.0')] ).
cnf(87344,plain,
equal(multiplication(one,domain_difference(u,coantidomain(domain_difference(antidomain(u),v)))),zero),
inference(spr,[status(thm),theory(equality)],[86949,6078]),
[iquote('0:SpR:86949.0,6078.0')] ).
cnf(87501,plain,
equal(domain_difference(u,coantidomain(domain_difference(antidomain(u),v))),zero),
inference(rew,[status(thm),theory(equality)],[4,87344]),
[iquote('0:Rew:4.0,87344.0')] ).
cnf(93499,plain,
equal(addition(multiplication(u,antidomain(multiplication(coantidomain(u),v))),zero),u),
inference(spr,[status(thm),theory(equality)],[8917,478]),
[iquote('0:SpR:8917.0,478.0')] ).
cnf(93731,plain,
equal(multiplication(u,antidomain(multiplication(coantidomain(u),v))),u),
inference(rew,[status(thm),theory(equality)],[66,93499,12]),
[iquote('0:Rew:66.0,93499.0,12.0,93499.0')] ).
cnf(94037,plain,
leq(antidomain(u),antidomain(multiplication(coantidomain(antidomain(u)),v))),
inference(spr,[status(thm),theory(equality)],[93731,1465]),
[iquote('0:SpR:93731.0,1465.0')] ).
cnf(94197,plain,
leq(antidomain(u),antidomain(multiplication(antidomain(antidomain(u)),v))),
inference(rew,[status(thm),theory(equality)],[16908,94037]),
[iquote('0:Rew:16908.0,94037.0')] ).
cnf(122192,plain,
equal(multiplication(domain_difference(u,v),antidomain(coantidomain(antidomain(antidomain(u))))),domain_difference(u,v)),
inference(spr,[status(thm),theory(equality)],[4500,20473]),
[iquote('0:SpR:4500.0,20473.0')] ).
cnf(122428,plain,
equal(addition(antidomain(u),domain_difference(coantidomain(domain_difference(u,v)),antidomain(u))),antidomain(antidomain(coantidomain(domain_difference(u,v))))),
inference(spr,[status(thm),theory(equality)],[86636,4500]),
[iquote('0:SpR:86636.0,4500.0')] ).
cnf(122535,plain,
equal(multiplication(antidomain(antidomain(u)),multiplication(antidomain(v),antidomain(antidomain(u)))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[219,122192,4310,16908]),
[iquote('0:Rew:219.0,122192.0,4310.0,122192.0,16908.0,122192.0')] ).
cnf(122536,plain,
equal(domain_difference(antidomain(u),antidomain(v)),domain_difference(v,u)),
inference(rew,[status(thm),theory(equality)],[21656,122535,4756]),
[iquote('0:Rew:21656.0,122535.0,4756.0,122535.0')] ).
cnf(123002,plain,
equal(addition(antidomain(u),domain_difference(coantidomain(domain_difference(u,v)),antidomain(u))),coantidomain(domain_difference(u,v))),
inference(rew,[status(thm),theory(equality)],[20096,122428]),
[iquote('0:Rew:20096.0,122428.0')] ).
cnf(123003,plain,
equal(addition(antidomain(u),domain_difference(antidomain(antidomain(u)),antidomain(coantidomain(domain_difference(u,v))))),coantidomain(domain_difference(u,v))),
inference(rew,[status(thm),theory(equality)],[122536,123002]),
[iquote('0:Rew:122536.0,123002.0')] ).
cnf(123004,plain,
equal(addition(antidomain(u),domain_difference(u,antidomain(coantidomain(domain_difference(u,v))))),coantidomain(domain_difference(u,v))),
inference(rew,[status(thm),theory(equality)],[4799,123003]),
[iquote('0:Rew:4799.0,123003.0')] ).
cnf(127962,plain,
equal(domain_difference(u,coantidomain(domain_difference(v,u))),zero),
inference(spr,[status(thm),theory(equality)],[122536,87501]),
[iquote('0:SpR:122536.0,87501.0')] ).
cnf(128541,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)],[127962,3846]),
[iquote('0:SpR:127962.0,3846.0')] ).
cnf(128754,plain,
equal(domain_difference(antidomain(u),coantidomain(domain_difference(v,u))),antidomain(coantidomain(domain_difference(v,u)))),
inference(rew,[status(thm),theory(equality)],[66,128541]),
[iquote('0:Rew:66.0,128541.0')] ).
cnf(128755,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(coantidomain(domain_difference(u,v)))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[128754,10884]),
[iquote('0:Rew:128754.0,10884.0')] ).
cnf(128756,plain,
equal(domain_difference(antidomain(antidomain(u)),coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4756,128755]),
[iquote('0:Rew:4756.0,128755.0')] ).
cnf(128757,plain,
equal(domain_difference(u,coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4799,128756]),
[iquote('0:Rew:4799.0,128756.0')] ).
cnf(128758,plain,
equal(antidomain(coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[87127,128757]),
[iquote('0:Rew:87127.0,128757.0')] ).
cnf(128790,plain,
equal(addition(antidomain(u),domain_difference(u,domain_difference(u,v))),coantidomain(domain_difference(u,v))),
inference(rew,[status(thm),theory(equality)],[128758,123004]),
[iquote('0:Rew:128758.0,123004.0')] ).
cnf(128801,plain,
equal(coantidomain(domain_difference(u,v)),forward_box(antidomain(antidomain(u)),v)),
inference(rew,[status(thm),theory(equality)],[17095,128790,38185]),
[iquote('0:Rew:17095.0,128790.0,38185.0,128790.0')] ).
cnf(128860,plain,
equal(backward_box(antidomain(u),antidomain(forward_box(v,w))),forward_box(antidomain(antidomain(forward_box(v,w))),u)),
inference(rew,[status(thm),theory(equality)],[128801,25128]),
[iquote('0:Rew:128801.0,25128.0')] ).
cnf(128897,plain,
equal(domain_difference(u,v),antidomain(forward_box(antidomain(antidomain(u)),v))),
inference(rew,[status(thm),theory(equality)],[128801,128758]),
[iquote('0:Rew:128801.0,128758.0')] ).
cnf(129389,plain,
equal(antidomain(multiplication(u,antidomain(forward_box(antidomain(antidomain(backward_box(v,w))),x)))),forward_box(multiplication(u,backward_box(v,w)),x)),
inference(rew,[status(thm),theory(equality)],[128897,7805]),
[iquote('0:Rew:128897.0,7805.0')] ).
cnf(130652,plain,
equal(backward_box(antidomain(u),antidomain(forward_box(v,w))),forward_box(forward_box(v,w),u)),
inference(rew,[status(thm),theory(equality)],[4606,128860]),
[iquote('0:Rew:4606.0,128860.0')] ).
cnf(131159,plain,
equal(forward_box(multiplication(u,backward_box(v,w)),x),forward_box(u,forward_box(backward_box(v,w),x))),
inference(rew,[status(thm),theory(equality)],[4502,129389,4615]),
[iquote('0:Rew:4502.0,129389.0,4615.0,129389.0')] ).
cnf(131162,plain,
equal(forward_box(antidomain(u),forward_box(v,forward_box(backward_box(v,u),w))),one),
inference(rew,[status(thm),theory(equality)],[131159,26554]),
[iquote('0:Rew:131159.0,26554.0')] ).
cnf(155040,plain,
equal(forward_box(antidomain(skc5),forward_box(skc3,antidomain(antidomain(skc4)))),one),
inference(spr,[status(thm),theory(equality)],[7498,131162]),
[iquote('0:SpR:7498.0,131162.0')] ).
cnf(155150,plain,
equal(forward_box(antidomain(skc5),forward_box(skc3,skc4)),one),
inference(rew,[status(thm),theory(equality)],[4930,155040]),
[iquote('0:Rew:4930.0,155040.0')] ).
cnf(180357,plain,
equal(backward_box(antidomain(u),antidomain(antidomain(v))),forward_box(antidomain(v),u)),
inference(spr,[status(thm),theory(equality)],[4483,130652]),
[iquote('0:SpR:4483.0,130652.0')] ).
cnf(180568,plain,
equal(backward_box(antidomain(u),v),forward_box(antidomain(v),u)),
inference(rew,[status(thm),theory(equality)],[5423,180357]),
[iquote('0:Rew:5423.0,180357.0')] ).
cnf(200452,plain,
( ~ leq(antidomain(antidomain(antidomain(skc5))),forward_box(skc3,skc4))
| ~ equal(addition(one,forward_box(skc3,skc4)),one) ),
inference(spl,[status(thm),theory(equality)],[3452,4931]),
[iquote('0:SpL:3452.1,4931.0')] ).
cnf(200569,plain,
( ~ leq(antidomain(skc5),forward_box(skc3,skc4))
| ~ equal(one,one) ),
inference(rew,[status(thm),theory(equality)],[602,200452,4310]),
[iquote('0:Rew:602.0,200452.1,4310.0,200452.0')] ).
cnf(200570,plain,
~ leq(antidomain(skc5),forward_box(skc3,skc4)),
inference(obv,[status(thm),theory(equality)],[200569]),
[iquote('0:Obv:200569.1')] ).
cnf(214280,plain,
equal(addition(multiplication(coantidomain(multiplication(u,antidomain(v))),v),zero),v),
inference(spr,[status(thm),theory(equality)],[34035,20446]),
[iquote('0:SpR:34035.0,20446.0')] ).
cnf(214465,plain,
equal(multiplication(coantidomain(multiplication(u,antidomain(v))),v),v),
inference(rew,[status(thm),theory(equality)],[66,214280,12]),
[iquote('0:Rew:66.0,214280.0,12.0,214280.0')] ).
cnf(214668,plain,
leq(coantidomain(u),coantidomain(multiplication(v,antidomain(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[214465,1621]),
[iquote('0:SpR:214465.0,1621.0')] ).
cnf(215156,plain,
leq(coantidomain(addition(u,v)),coantidomain(v)),
inference(spr,[status(thm),theory(equality)],[20469,214668]),
[iquote('0:SpR:20469.0,214668.0')] ).
cnf(215325,plain,
( ~ leq(u,v)
| leq(coantidomain(v),coantidomain(u)) ),
inference(spr,[status(thm),theory(equality)],[99,215156]),
[iquote('0:SpR:99.1,215156.0')] ).
cnf(261288,plain,
leq(antidomain(u),antidomain(multiplication(v,backward_box(v,u)))),
inference(spr,[status(thm),theory(equality)],[20196,94197]),
[iquote('0:SpR:20196.0,94197.0')] ).
cnf(261489,plain,
leq(antidomain(u),forward_box(v,antidomain(backward_box(v,u)))),
inference(rew,[status(thm),theory(equality)],[4691,261288]),
[iquote('0:Rew:4691.0,261288.0')] ).
cnf(264533,plain,
leq(antidomain(backward_box(u,multiplication(u,v))),forward_box(v,antidomain(one))),
inference(spr,[status(thm),theory(equality)],[27090,261489]),
[iquote('0:SpR:27090.0,261489.0')] ).
cnf(264652,plain,
leq(antidomain(backward_box(u,multiplication(u,v))),antidomain(v)),
inference(rew,[status(thm),theory(equality)],[4483,264533,55]),
[iquote('0:Rew:4483.0,264533.0,55.0,264533.0')] ).
cnf(265094,plain,
leq(coantidomain(antidomain(u)),coantidomain(antidomain(backward_box(v,multiplication(v,u))))),
inference(res,[status(thm),theory(equality)],[264652,215325]),
[iquote('0:Res:264652.0,215325.0')] ).
cnf(265152,plain,
leq(antidomain(antidomain(u)),backward_box(v,multiplication(v,u))),
inference(rew,[status(thm),theory(equality)],[16908,265094,4615]),
[iquote('0:Rew:16908.0,265094.0,4615.0,265094.0,16908.0,265094.0')] ).
cnf(266820,plain,
leq(antidomain(u),backward_box(v,multiplication(v,antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[4310,265152]),
[iquote('0:SpR:4310.0,265152.0')] ).
cnf(266844,plain,
leq(antidomain(u),backward_box(v,antidomain(forward_box(v,u)))),
inference(rew,[status(thm),theory(equality)],[5445,266820]),
[iquote('0:Rew:5445.0,266820.0')] ).
cnf(267043,plain,
leq(antidomain(forward_box(skc3,skc4)),backward_box(antidomain(skc5),antidomain(one))),
inference(spr,[status(thm),theory(equality)],[155150,266844]),
[iquote('0:SpR:155150.0,266844.0')] ).
cnf(267169,plain,
leq(antidomain(forward_box(skc3,skc4)),antidomain(antidomain(skc5))),
inference(rew,[status(thm),theory(equality)],[4497,267043,91,180568,55]),
[iquote('0:Rew:4497.0,267043.0,91.0,267043.0,180568.0,267043.0,55.0,267043.0')] ).
cnf(268173,plain,
leq(coantidomain(antidomain(antidomain(skc5))),coantidomain(antidomain(forward_box(skc3,skc4)))),
inference(res,[status(thm),theory(equality)],[267169,215325]),
[iquote('0:Res:267169.0,215325.0')] ).
cnf(268183,plain,
leq(antidomain(skc5),forward_box(skc3,skc4)),
inference(rew,[status(thm),theory(equality)],[4310,268173,16908,4606]),
[iquote('0:Rew:4310.0,268173.0,16908.0,268173.0,4606.0,268173.0,16908.0,268173.0')] ).
cnf(268184,plain,
$false,
inference(mrr,[status(thm)],[268183,200570]),
[iquote('0:MRR:268183.0,200570.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE104+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.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 07:58:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 282.45/282.71
% 282.45/282.71 SPASS V 3.9
% 282.45/282.71 SPASS beiseite: Proof found.
% 282.45/282.71 % SZS status Theorem
% 282.45/282.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 282.45/282.71 SPASS derived 177165 clauses, backtracked 0 clauses, performed 0 splits and kept 23103 clauses.
% 282.45/282.71 SPASS allocated 277138 KBytes.
% 282.45/282.71 SPASS spent 0:4:42.02 on the problem.
% 282.45/282.71 0:00:00.04 for the input.
% 282.45/282.71 0:00:00.03 for the FLOTTER CNF translation.
% 282.45/282.71 0:00:01.15 for inferences.
% 282.45/282.71 0:00:00.00 for the backtracking.
% 282.45/282.71 0:4:40.16 for the reduction.
% 282.45/282.71
% 282.45/282.71
% 282.45/282.71 Here is a proof with depth 12, length 350 :
% 282.45/282.71 % SZS output start Refutation
% See solution above
% 290.16/290.43 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 goals order domain_difference forward_diamond backward_diamond forward_box backward_box additive_associativity multiplicative_associativity right_distributivity left_distributivity domain2 codomain2
% 290.16/290.43
%------------------------------------------------------------------------------