TSTP Solution File: KLE104-10 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE104-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 02:28:32 EDT 2022
% Result : Timeout 291.53s 291.70s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 31
% Syntax : Number of clauses : 435 ( 435 unt; 0 nHn; 435 RR)
% Number of literals : 435 ( 0 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq2(u,u,v,w),v),
file('KLE104-10.p',unknown),
[] ).
cnf(2,axiom,
equal(ifeq(u,u,v,w),v),
file('KLE104-10.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE104-10.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE104-10.p',unknown),
[] ).
cnf(5,axiom,
equal(addition(u,zero),u),
file('KLE104-10.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,u),u),
file('KLE104-10.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE104-10.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(u,one),u),
file('KLE104-10.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(one,u),u),
file('KLE104-10.p',unknown),
[] ).
cnf(10,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE104-10.p',unknown),
[] ).
cnf(11,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE104-10.p',unknown),
[] ).
cnf(12,axiom,
equal(multiplication(u,zero),zero),
file('KLE104-10.p',unknown),
[] ).
cnf(13,axiom,
equal(multiplication(zero,u),zero),
file('KLE104-10.p',unknown),
[] ).
cnf(14,axiom,
equal(ifeq(leq(u,v),true__dfg,addition(u,v),v),v),
file('KLE104-10.p',unknown),
[] ).
cnf(15,axiom,
equal(ifeq2(addition(u,v),v,leq(u,v),true__dfg),true__dfg),
file('KLE104-10.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE104-10.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE104-10.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE104-10.p',unknown),
[] ).
cnf(19,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE104-10.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE104-10.p',unknown),
[] ).
cnf(21,axiom,
equal(addition(coantidomain(multiplication(u,v)),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),
file('KLE104-10.p',unknown),
[] ).
cnf(22,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE104-10.p',unknown),
[] ).
cnf(23,axiom,
equal(codomain(u),coantidomain(coantidomain(u))),
file('KLE104-10.p',unknown),
[] ).
cnf(24,axiom,
equal(c(u),antidomain(domain__dfg(u))),
file('KLE104-10.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE104-10.p',unknown),
[] ).
cnf(26,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE104-10.p',unknown),
[] ).
cnf(27,axiom,
equal(codomain(multiplication(codomain(u),v)),backward_diamond(v,u)),
file('KLE104-10.p',unknown),
[] ).
cnf(28,axiom,
equal(c(forward_diamond(u,c(v))),forward_box(u,v)),
file('KLE104-10.p',unknown),
[] ).
cnf(29,axiom,
equal(c(backward_diamond(u,c(v))),backward_box(u,v)),
file('KLE104-10.p',unknown),
[] ).
cnf(30,axiom,
equal(addition(domain__dfg(sK2_goals_X1),backward_box(sK3_goals_X0,domain__dfg(sK1_goals_X2))),one),
file('KLE104-10.p',unknown),
[] ).
cnf(31,axiom,
~ equal(addition(forward_box(sK3_goals_X0,domain__dfg(sK2_goals_X1)),domain__dfg(sK1_goals_X2)),one),
file('KLE104-10.p',unknown),
[] ).
cnf(32,plain,
equal(c(u),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[19,24]),
[iquote('0:Rew:19.0,24.0')] ).
cnf(33,plain,
equal(addition(coantidomain(u),coantidomain(coantidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[3,22]),
[iquote('0:Rew:3.0,22.0')] ).
cnf(34,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[3,18]),
[iquote('0:Rew:3.0,18.0')] ).
cnf(35,plain,
equal(addition(antidomain(antidomain(sK2_goals_X1)),backward_box(sK3_goals_X0,antidomain(antidomain(sK1_goals_X2)))),one),
inference(rew,[status(thm),theory(equality)],[19,30]),
[iquote('0:Rew:19.0,30.0,19.0,30.0')] ).
cnf(36,plain,
equal(backward_box(u,v),antidomain(antidomain(antidomain(backward_diamond(u,antidomain(antidomain(antidomain(v)))))))),
inference(rew,[status(thm),theory(equality)],[32,29]),
[iquote('0:Rew:32.0,29.0,32.0,29.0')] ).
cnf(37,plain,
equal(addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(backward_diamond(sK3_goals_X0,antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2)))))))))),one),
inference(rew,[status(thm),theory(equality)],[36,35]),
[iquote('0:Rew:36.0,35.0')] ).
cnf(38,plain,
equal(forward_box(u,v),antidomain(antidomain(antidomain(forward_diamond(u,antidomain(antidomain(antidomain(v)))))))),
inference(rew,[status(thm),theory(equality)],[32,28]),
[iquote('0:Rew:32.0,28.0,32.0,28.0')] ).
cnf(39,plain,
equal(backward_diamond(u,v),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(v)),u)))),
inference(rew,[status(thm),theory(equality)],[23,27]),
[iquote('0:Rew:23.0,27.0,23.0,27.0')] ).
cnf(41,plain,
equal(forward_diamond(u,v),antidomain(antidomain(multiplication(u,antidomain(antidomain(v)))))),
inference(rew,[status(thm),theory(equality)],[19,26]),
[iquote('0:Rew:19.0,26.0,19.0,26.0')] ).
cnf(42,plain,
equal(forward_box(u,v),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v)))))))))))),
inference(rew,[status(thm),theory(equality)],[41,38]),
[iquote('0:Rew:41.0,38.0')] ).
cnf(43,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[19,25]),
[iquote('0:Rew:19.0,25.0')] ).
cnf(44,plain,
~ equal(addition(antidomain(antidomain(sK1_goals_X2)),forward_box(sK3_goals_X0,antidomain(antidomain(sK2_goals_X1)))),one),
inference(rew,[status(thm),theory(equality)],[3,31,19]),
[iquote('0:Rew:3.0,31.0,19.0,31.0,19.0,31.0')] ).
cnf(45,plain,
equal(addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0))))))),one),
inference(rew,[status(thm),theory(equality)],[39,37]),
[iquote('0:Rew:39.0,37.0')] ).
cnf(46,plain,
~ equal(addition(antidomain(antidomain(sK1_goals_X2)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2_goals_X1)))))))))))))),one),
inference(rew,[status(thm),theory(equality)],[42,44]),
[iquote('0:Rew:42.0,44.0')] ).
cnf(60,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[16,8]),
[iquote('0:SpR:16.0,8.0')] ).
cnf(64,plain,
equal(coantidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[20,9]),
[iquote('0:SpR:20.0,9.0')] ).
cnf(71,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(87,plain,
equal(addition(zero,coantidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[64,33]),
[iquote('0:SpR:64.0,33.0')] ).
cnf(89,plain,
equal(coantidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[71,87]),
[iquote('0:Rew:71.0,87.0')] ).
cnf(96,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[60,34]),
[iquote('0:SpR:60.0,34.0')] ).
cnf(98,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[71,96]),
[iquote('0:Rew:71.0,96.0')] ).
cnf(171,plain,
equal(ifeq(leq(u,v),true__dfg,addition(v,u),v),v),
inference(spr,[status(thm),theory(equality)],[3,14]),
[iquote('0:SpR:3.0,14.0')] ).
cnf(187,plain,
equal(multiplication(u,multiplication(v,coantidomain(multiplication(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[7,20]),
[iquote('0:SpR:7.0,20.0')] ).
cnf(192,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),multiplication(zero,v)),
inference(spr,[status(thm),theory(equality)],[16,7]),
[iquote('0:SpR:16.0,7.0')] ).
cnf(196,plain,
equal(multiplication(domain_difference(u,v),w),multiplication(antidomain(antidomain(u)),multiplication(antidomain(v),w))),
inference(spr,[status(thm),theory(equality)],[43,7]),
[iquote('0:SpR:43.0,7.0')] ).
cnf(202,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),zero),
inference(rew,[status(thm),theory(equality)],[13,192]),
[iquote('0:Rew:13.0,192.0')] ).
cnf(238,plain,
equal(addition(u,addition(v,w)),addition(w,addition(u,v))),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(246,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(247,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(254,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[4,247]),
[iquote('0:Rew:4.0,247.0')] ).
cnf(257,plain,
equal(ifeq2(addition(u,v),addition(u,v),leq(u,addition(u,v)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[246,15]),
[iquote('0:SpR:246.0,15.0')] ).
cnf(267,plain,
equal(addition(u,addition(v,u)),addition(v,u)),
inference(spr,[status(thm),theory(equality)],[3,246]),
[iquote('0:SpR:3.0,246.0')] ).
cnf(270,plain,
equal(addition(coantidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[33,246]),
[iquote('0:SpR:33.0,246.0')] ).
cnf(271,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[34,246]),
[iquote('0:SpR:34.0,246.0')] ).
cnf(273,plain,
equal(addition(one,coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[3,270]),
[iquote('0:Rew:3.0,270.0')] ).
cnf(274,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[3,271]),
[iquote('0:Rew:3.0,271.0')] ).
cnf(277,plain,
equal(leq(u,addition(u,v)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,257]),
[iquote('0:Rew:1.0,257.0')] ).
cnf(310,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[11,20]),
[iquote('0:SpR:11.0,20.0')] ).
cnf(321,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[33,11]),
[iquote('0:SpR:33.0,11.0')] ).
cnf(322,plain,
equal(addition(multiplication(one,u),multiplication(coantidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[273,11]),
[iquote('0:SpR:273.0,11.0')] ).
cnf(323,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[34,11]),
[iquote('0:SpR:34.0,11.0')] ).
cnf(324,plain,
equal(addition(multiplication(one,u),multiplication(antidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[274,11]),
[iquote('0:SpR:274.0,11.0')] ).
cnf(330,plain,
equal(addition(u,multiplication(coantidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[9,322]),
[iquote('0:Rew:9.0,322.0')] ).
cnf(331,plain,
equal(addition(u,multiplication(antidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[9,324]),
[iquote('0:Rew:9.0,324.0')] ).
cnf(335,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[9,321]),
[iquote('0:Rew:9.0,321.0')] ).
cnf(336,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[9,323]),
[iquote('0:Rew:9.0,323.0')] ).
cnf(356,plain,
equal(leq(u,addition(v,u)),true__dfg),
inference(spr,[status(thm),theory(equality)],[3,277]),
[iquote('0:SpR:3.0,277.0')] ).
cnf(385,plain,
equal(leq(u,addition(v,addition(w,u))),true__dfg),
inference(spr,[status(thm),theory(equality)],[4,356]),
[iquote('0:SpR:4.0,356.0')] ).
cnf(413,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),multiplication(antidomain(addition(u,v)),v)),zero),
inference(spr,[status(thm),theory(equality)],[10,16]),
[iquote('0:SpR:10.0,16.0')] ).
cnf(428,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[33,10]),
[iquote('0:SpR:33.0,10.0')] ).
cnf(429,plain,
equal(addition(multiplication(u,one),multiplication(u,coantidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[273,10]),
[iquote('0:SpR:273.0,10.0')] ).
cnf(430,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[34,10]),
[iquote('0:SpR:34.0,10.0')] ).
cnf(431,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[274,10]),
[iquote('0:SpR:274.0,10.0')] ).
cnf(438,plain,
equal(addition(u,multiplication(u,coantidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[8,429]),
[iquote('0:Rew:8.0,429.0')] ).
cnf(439,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[8,431]),
[iquote('0:Rew:8.0,431.0')] ).
cnf(443,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[8,428]),
[iquote('0:Rew:8.0,428.0')] ).
cnf(444,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[8,430]),
[iquote('0:Rew:8.0,430.0')] ).
cnf(479,plain,
equal(leq(multiplication(antidomain(u),v),v),true__dfg),
inference(spr,[status(thm),theory(equality)],[331,356]),
[iquote('0:SpR:331.0,356.0')] ).
cnf(491,plain,
equal(addition(antidomain(u),domain_difference(v,u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[43,331]),
[iquote('0:SpR:43.0,331.0')] ).
cnf(513,plain,
equal(leq(domain_difference(u,v),antidomain(v)),true__dfg),
inference(spr,[status(thm),theory(equality)],[43,479]),
[iquote('0:SpR:43.0,479.0')] ).
cnf(599,plain,
equal(leq(multiplication(u,antidomain(v)),u),true__dfg),
inference(spr,[status(thm),theory(equality)],[439,356]),
[iquote('0:SpR:439.0,356.0')] ).
cnf(629,plain,
equal(leq(domain_difference(u,v),antidomain(antidomain(u))),true__dfg),
inference(spr,[status(thm),theory(equality)],[43,599]),
[iquote('0:SpR:43.0,599.0')] ).
cnf(667,plain,
equal(leq(u,addition(v,addition(u,w))),true__dfg),
inference(spr,[status(thm),theory(equality)],[3,385]),
[iquote('0:SpR:3.0,385.0')] ).
cnf(733,plain,
equal(addition(multiplication(u,coantidomain(multiplication(v,w))),multiplication(u,coantidomain(multiplication(coantidomain(coantidomain(v)),w)))),multiplication(u,coantidomain(multiplication(coantidomain(coantidomain(v)),w)))),
inference(spr,[status(thm),theory(equality)],[21,10]),
[iquote('0:SpR:21.0,10.0')] ).
cnf(743,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)],[16,21]),
[iquote('0:SpR:16.0,21.0')] ).
cnf(751,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)],[7,21]),
[iquote('0:SpR:7.0,21.0')] ).
cnf(763,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
inference(rew,[status(thm),theory(equality)],[273,743,89]),
[iquote('0:Rew:273.0,743.0,89.0,743.0')] ).
cnf(819,plain,
equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
inference(spr,[status(thm),theory(equality)],[763,20]),
[iquote('0:SpR:763.0,20.0')] ).
cnf(847,plain,
equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
inference(rew,[status(thm),theory(equality)],[8,819,7]),
[iquote('0:Rew:8.0,819.0,7.0,819.0')] ).
cnf(881,plain,
equal(addition(multiplication(antidomain(multiplication(u,v)),w),multiplication(antidomain(multiplication(u,antidomain(antidomain(v)))),w)),multiplication(antidomain(multiplication(u,antidomain(antidomain(v)))),w)),
inference(spr,[status(thm),theory(equality)],[17,11]),
[iquote('0:SpR:17.0,11.0')] ).
cnf(893,plain,
equal(addition(antidomain(multiplication(antidomain(antidomain(u)),v)),antidomain(domain_difference(u,antidomain(v)))),antidomain(domain_difference(u,antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[43,17]),
[iquote('0:SpR:43.0,17.0')] ).
cnf(898,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)],[16,17]),
[iquote('0:SpR:16.0,17.0')] ).
cnf(902,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)],[20,17]),
[iquote('0:SpR:20.0,17.0')] ).
cnf(904,plain,
equal(addition(antidomain(addition(multiplication(u,v),multiplication(u,w))),antidomain(multiplication(u,antidomain(antidomain(addition(v,w)))))),antidomain(multiplication(u,antidomain(antidomain(addition(v,w)))))),
inference(spr,[status(thm),theory(equality)],[10,17]),
[iquote('0:SpR:10.0,17.0')] ).
cnf(906,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v)))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v)))))),
inference(spr,[status(thm),theory(equality)],[202,17]),
[iquote('0:SpR:202.0,17.0')] ).
cnf(919,plain,
equal(addition(antidomain(domain_difference(u,antidomain(v))),antidomain(multiplication(antidomain(antidomain(u)),v))),antidomain(domain_difference(u,antidomain(v)))),
inference(rew,[status(thm),theory(equality)],[3,893]),
[iquote('0:Rew:3.0,893.0')] ).
cnf(920,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[274,898,98]),
[iquote('0:Rew:274.0,898.0,98.0,898.0')] ).
cnf(921,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(coantidomain(u))))),one),
inference(rew,[status(thm),theory(equality)],[274,902,98]),
[iquote('0:Rew:274.0,902.0,98.0,902.0')] ).
cnf(922,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v))))),one),
inference(rew,[status(thm),theory(equality)],[274,906,98]),
[iquote('0:Rew:274.0,906.0,98.0,906.0')] ).
cnf(989,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[920,16]),
[iquote('0:SpR:920.0,16.0')] ).
cnf(1025,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[9,989]),
[iquote('0:Rew:9.0,989.0')] ).
cnf(1093,plain,
equal(addition(multiplication(antidomain(antidomain(sK2_goals_X1)),u),multiplication(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0)))))),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[45,11]),
[iquote('0:SpR:45.0,11.0')] ).
cnf(1101,plain,
equal(addition(multiplication(antidomain(antidomain(sK2_goals_X1)),u),multiplication(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0)))))),u)),u),
inference(rew,[status(thm),theory(equality)],[9,1093]),
[iquote('0:Rew:9.0,1093.0')] ).
cnf(1132,plain,
equal(multiplication(one,multiplication(u,antidomain(antidomain(coantidomain(u))))),zero),
inference(spr,[status(thm),theory(equality)],[921,16]),
[iquote('0:SpR:921.0,16.0')] ).
cnf(1137,plain,
equal(multiplication(one,multiplication(multiplication(u,antidomain(antidomain(coantidomain(u)))),v)),zero),
inference(spr,[status(thm),theory(equality)],[921,202]),
[iquote('0:SpR:921.0,202.0')] ).
cnf(1170,plain,
equal(multiplication(u,antidomain(antidomain(coantidomain(u)))),zero),
inference(rew,[status(thm),theory(equality)],[9,1132]),
[iquote('0:Rew:9.0,1132.0')] ).
cnf(1175,plain,
equal(multiplication(u,multiplication(antidomain(antidomain(coantidomain(u))),v)),zero),
inference(rew,[status(thm),theory(equality)],[9,1137,7]),
[iquote('0:Rew:9.0,1137.0,7.0,1137.0')] ).
cnf(1545,plain,
equal(ifeq(leq(coantidomain(multiplication(coantidomain(coantidomain(u)),v)),coantidomain(multiplication(u,v))),true__dfg,coantidomain(multiplication(coantidomain(coantidomain(u)),v)),coantidomain(multiplication(u,v))),coantidomain(multiplication(u,v))),
inference(spr,[status(thm),theory(equality)],[21,171]),
[iquote('0:SpR:21.0,171.0')] ).
cnf(1571,plain,
equal(ifeq(true__dfg,true__dfg,addition(addition(u,addition(v,w)),v),addition(u,addition(v,w))),addition(u,addition(v,w))),
inference(spr,[status(thm),theory(equality)],[667,171]),
[iquote('0:SpR:667.0,171.0')] ).
cnf(1602,plain,
equal(addition(u,addition(v,w)),addition(u,addition(w,v))),
inference(rew,[status(thm),theory(equality)],[2,1571,267,4]),
[iquote('0:Rew:2.0,1571.0,267.0,1571.0,4.0,1571.0,4.0,1571.0')] ).
cnf(1690,plain,
equal(addition(addition(u,addition(v,w)),x),addition(v,addition(addition(w,u),x))),
inference(spr,[status(thm),theory(equality)],[238,4]),
[iquote('0:SpR:238.0,4.0')] ).
cnf(1770,plain,
equal(addition(u,addition(v,w)),addition(w,addition(v,u))),
inference(spr,[status(thm),theory(equality)],[3,238]),
[iquote('0:SpR:3.0,238.0')] ).
cnf(1850,plain,
equal(addition(u,addition(v,addition(w,x))),addition(v,addition(w,addition(u,x)))),
inference(rew,[status(thm),theory(equality)],[4,1690]),
[iquote('0:Rew:4.0,1690.0,4.0,1690.0,4.0,1690.0')] ).
cnf(2818,plain,
equal(multiplication(u,domain_difference(coantidomain(u),v)),zero),
inference(spr,[status(thm),theory(equality)],[43,1175]),
[iquote('0:SpR:43.0,1175.0')] ).
cnf(3181,plain,
equal(addition(multiplication(coantidomain(u),v),addition(multiplication(coantidomain(coantidomain(u)),v),w)),addition(v,w)),
inference(spr,[status(thm),theory(equality)],[335,4]),
[iquote('0:SpR:335.0,4.0')] ).
cnf(3191,plain,
equal(addition(multiplication(coantidomain(u),v),addition(w,multiplication(coantidomain(coantidomain(u)),v))),addition(w,v)),
inference(spr,[status(thm),theory(equality)],[335,254]),
[iquote('0:SpR:335.0,254.0')] ).
cnf(3198,plain,
equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
inference(spr,[status(thm),theory(equality)],[847,335]),
[iquote('0:SpR:847.0,335.0')] ).
cnf(3201,plain,
equal(addition(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),zero),coantidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[20,335]),
[iquote('0:SpR:20.0,335.0')] ).
cnf(3218,plain,
equal(addition(zero,multiplication(coantidomain(coantidomain(u)),multiplication(v,coantidomain(multiplication(coantidomain(u),v))))),multiplication(v,coantidomain(multiplication(coantidomain(u),v)))),
inference(spr,[status(thm),theory(equality)],[187,335]),
[iquote('0:SpR:187.0,335.0')] ).
cnf(3229,plain,
equal(multiplication(coantidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[71,3198,3]),
[iquote('0:Rew:71.0,3198.0,3.0,3198.0')] ).
cnf(3241,plain,
equal(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[71,3201,3]),
[iquote('0:Rew:71.0,3201.0,3.0,3201.0')] ).
cnf(3258,plain,
equal(multiplication(coantidomain(coantidomain(u)),multiplication(v,coantidomain(multiplication(coantidomain(u),v)))),multiplication(v,coantidomain(multiplication(coantidomain(u),v)))),
inference(rew,[status(thm),theory(equality)],[71,3218]),
[iquote('0:Rew:71.0,3218.0')] ).
cnf(3385,plain,
equal(addition(multiplication(antidomain(u),v),addition(multiplication(antidomain(antidomain(u)),v),w)),addition(v,w)),
inference(spr,[status(thm),theory(equality)],[336,4]),
[iquote('0:SpR:336.0,4.0')] ).
cnf(3395,plain,
equal(addition(multiplication(antidomain(u),v),addition(w,multiplication(antidomain(antidomain(u)),v))),addition(w,v)),
inference(spr,[status(thm),theory(equality)],[336,254]),
[iquote('0:SpR:336.0,254.0')] ).
cnf(3396,plain,
equal(addition(multiplication(u,multiplication(antidomain(v),w)),multiplication(u,multiplication(antidomain(antidomain(v)),w))),multiplication(u,w)),
inference(spr,[status(thm),theory(equality)],[336,10]),
[iquote('0:SpR:336.0,10.0')] ).
cnf(3416,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1025,336]),
[iquote('0:SpR:1025.0,336.0')] ).
cnf(3420,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),u)),u),
inference(spr,[status(thm),theory(equality)],[16,336]),
[iquote('0:SpR:16.0,336.0')] ).
cnf(3430,plain,
equal(addition(domain_difference(u,v),multiplication(antidomain(antidomain(antidomain(u))),antidomain(v))),antidomain(v)),
inference(spr,[status(thm),theory(equality)],[43,336]),
[iquote('0:SpR:43.0,336.0')] ).
cnf(3440,plain,
equal(multiplication(antidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[71,3420]),
[iquote('0:Rew:71.0,3420.0')] ).
cnf(3457,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[71,3416,3]),
[iquote('0:Rew:71.0,3416.0,3.0,3416.0')] ).
cnf(3459,plain,
equal(addition(domain_difference(u,v),domain_difference(antidomain(u),v)),antidomain(v)),
inference(rew,[status(thm),theory(equality)],[43,3430]),
[iquote('0:Rew:43.0,3430.0')] ).
cnf(3616,plain,
equal(addition(multiplication(u,coantidomain(v)),addition(w,multiplication(u,coantidomain(coantidomain(v))))),addition(w,u)),
inference(spr,[status(thm),theory(equality)],[443,254]),
[iquote('0:SpR:443.0,254.0')] ).
cnf(3629,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)],[3440,443]),
[iquote('0:SpR:3440.0,443.0')] ).
cnf(3642,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[20,443]),
[iquote('0:SpR:20.0,443.0')] ).
cnf(3654,plain,
equal(multiplication(u,coantidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[71,3642]),
[iquote('0:Rew:71.0,3642.0')] ).
cnf(3655,plain,
equal(coantidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[3654,3241]),
[iquote('0:Rew:3654.0,3241.0')] ).
cnf(3718,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)],[3,3629]),
[iquote('0:Rew:3.0,3629.0')] ).
cnf(3881,plain,
equal(addition(multiplication(u,antidomain(v)),addition(multiplication(u,antidomain(antidomain(v))),w)),addition(u,w)),
inference(spr,[status(thm),theory(equality)],[444,4]),
[iquote('0:SpR:444.0,4.0')] ).
cnf(3891,plain,
equal(addition(multiplication(u,antidomain(v)),addition(w,multiplication(u,antidomain(antidomain(v))))),addition(w,u)),
inference(spr,[status(thm),theory(equality)],[444,254]),
[iquote('0:SpR:444.0,254.0')] ).
cnf(3902,plain,
equal(addition(multiplication(u,antidomain(coantidomain(u))),zero),u),
inference(spr,[status(thm),theory(equality)],[1170,444]),
[iquote('0:SpR:1170.0,444.0')] ).
cnf(3903,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[43,444]),
[iquote('0:SpR:43.0,444.0')] ).
cnf(3911,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)],[3229,444]),
[iquote('0:SpR:3229.0,444.0')] ).
cnf(3920,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1025,444]),
[iquote('0:SpR:1025.0,444.0')] ).
cnf(3931,plain,
equal(multiplication(u,antidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[71,3902,3]),
[iquote('0:Rew:71.0,3902.0,3.0,3902.0')] ).
cnf(3940,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[71,3920]),
[iquote('0:Rew:71.0,3920.0')] ).
cnf(3941,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[3457,3940]),
[iquote('0:Rew:3457.0,3940.0')] ).
cnf(3942,plain,
~ equal(addition(antidomain(antidomain(sK1_goals_X2)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(antidomain(antidomain(antidomain(antidomain(sK2_goals_X1)))))))))))),one),
inference(rew,[status(thm),theory(equality)],[3941,46]),
[iquote('0:Rew:3941.0,46.0')] ).
cnf(3961,plain,
equal(addition(multiplication(antidomain(antidomain(sK2_goals_X1)),u),multiplication(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))),sK3_goals_X0)))),u)),u),
inference(rew,[status(thm),theory(equality)],[3941,1101]),
[iquote('0:Rew:3941.0,1101.0')] ).
cnf(3998,plain,
equal(addition(domain_difference(u,v),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[43,3903]),
[iquote('0:Rew:43.0,3903.0')] ).
cnf(4020,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)],[3,3911]),
[iquote('0:Rew:3.0,3911.0')] ).
cnf(4021,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[3941,4020]),
[iquote('0:Rew:3941.0,4020.0')] ).
cnf(4024,plain,
~ equal(addition(antidomain(antidomain(sK1_goals_X2)),antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))),one),
inference(rew,[status(thm),theory(equality)],[3941,3942]),
[iquote('0:Rew:3941.0,3942.0,3941.0,3942.0,3941.0,3942.0,3941.0,3942.0')] ).
cnf(4031,plain,
equal(addition(multiplication(antidomain(antidomain(sK2_goals_X1)),u),multiplication(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(sK1_goals_X2))),sK3_goals_X0)))),u)),u),
inference(rew,[status(thm),theory(equality)],[3941,3961]),
[iquote('0:Rew:3941.0,3961.0,3941.0,3961.0')] ).
cnf(4074,plain,
equal(multiplication(antidomain(u),antidomain(v)),domain_difference(antidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[3941,43]),
[iquote('0:SpR:3941.0,43.0')] ).
cnf(4075,plain,
equal(leq(domain_difference(antidomain(u),v),antidomain(u)),true__dfg),
inference(spr,[status(thm),theory(equality)],[3941,629]),
[iquote('0:SpR:3941.0,629.0')] ).
cnf(4088,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,antidomain(antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[3941,43]),
[iquote('0:SpR:3941.0,43.0')] ).
cnf(4112,plain,
equal(domain_difference(antidomain(antidomain(u)),v),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4074,43]),
[iquote('0:Rew:4074.0,43.0')] ).
cnf(4126,plain,
equal(antidomain(domain_difference(antidomain(u),antidomain(multiplication(u,v)))),one),
inference(rew,[status(thm),theory(equality)],[4074,922]),
[iquote('0:Rew:4074.0,922.0')] ).
cnf(4137,plain,
equal(domain_difference(u,antidomain(antidomain(v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4112,4088,4074]),
[iquote('0:Rew:4112.0,4088.0,4074.0,4088.0')] ).
cnf(4150,plain,
equal(multiplication(u,multiplication(antidomain(coantidomain(u)),v)),multiplication(u,v)),
inference(spr,[status(thm),theory(equality)],[3931,7]),
[iquote('0:SpR:3931.0,7.0')] ).
cnf(4563,plain,
equal(ifeq(true__dfg,true__dfg,addition(domain_difference(antidomain(u),v),antidomain(u)),antidomain(u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[4075,14]),
[iquote('0:SpR:4075.0,14.0')] ).
cnf(4589,plain,
equal(addition(antidomain(u),domain_difference(antidomain(u),v)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[2,4563,3]),
[iquote('0:Rew:2.0,4563.0,3.0,4563.0')] ).
cnf(5346,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)],[196,3931]),
[iquote('0:SpR:196.0,3931.0')] ).
cnf(5387,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)],[4074,5346]),
[iquote('0:Rew:4074.0,5346.0')] ).
cnf(5648,plain,
equal(addition(multiplication(u,coantidomain(addition(v,u))),zero),zero),
inference(spr,[status(thm),theory(equality)],[310,267]),
[iquote('0:SpR:310.0,267.0')] ).
cnf(5669,plain,
equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[439,310]),
[iquote('0:SpR:439.0,310.0')] ).
cnf(5757,plain,
equal(multiplication(u,coantidomain(addition(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[71,5648,3]),
[iquote('0:Rew:71.0,5648.0,3.0,5648.0')] ).
cnf(5786,plain,
equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[71,5669,20,7]),
[iquote('0:Rew:71.0,5669.0,20.0,5669.0,7.0,5669.0')] ).
cnf(6407,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),zero),zero),
inference(spr,[status(thm),theory(equality)],[413,246]),
[iquote('0:SpR:413.0,246.0')] ).
cnf(6414,plain,
equal(addition(multiplication(antidomain(addition(u,v)),v),zero),zero),
inference(spr,[status(thm),theory(equality)],[413,267]),
[iquote('0:SpR:413.0,267.0')] ).
cnf(6432,plain,
equal(addition(multiplication(antidomain(u),u),multiplication(antidomain(u),multiplication(coantidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[330,413]),
[iquote('0:SpR:330.0,413.0')] ).
cnf(6452,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(u)),multiplication(antidomain(antidomain(u)),domain_difference(v,u))),zero),
inference(spr,[status(thm),theory(equality)],[491,413]),
[iquote('0:SpR:491.0,413.0')] ).
cnf(6516,plain,
equal(multiplication(antidomain(addition(u,v)),u),zero),
inference(rew,[status(thm),theory(equality)],[71,6407,3]),
[iquote('0:Rew:71.0,6407.0,3.0,6407.0')] ).
cnf(6519,plain,
equal(multiplication(antidomain(addition(u,v)),v),zero),
inference(rew,[status(thm),theory(equality)],[71,6414,3]),
[iquote('0:Rew:71.0,6414.0,3.0,6414.0')] ).
cnf(6545,plain,
equal(multiplication(antidomain(u),multiplication(coantidomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[71,6432,16]),
[iquote('0:Rew:71.0,6432.0,16.0,6432.0')] ).
cnf(6571,plain,
equal(multiplication(antidomain(antidomain(u)),domain_difference(v,u)),zero),
inference(rew,[status(thm),theory(equality)],[71,6452,16]),
[iquote('0:Rew:71.0,6452.0,16.0,6452.0')] ).
cnf(7611,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(addition(v,u))))),u),
inference(spr,[status(thm),theory(equality)],[5757,443]),
[iquote('0:SpR:5757.0,443.0')] ).
cnf(7702,plain,
equal(multiplication(u,coantidomain(coantidomain(addition(v,u)))),u),
inference(rew,[status(thm),theory(equality)],[71,7611]),
[iquote('0:Rew:71.0,7611.0')] ).
cnf(7933,plain,
equal(addition(zero,multiplication(antidomain(antidomain(addition(u,v))),u)),u),
inference(spr,[status(thm),theory(equality)],[6516,336]),
[iquote('0:SpR:6516.0,336.0')] ).
cnf(7992,plain,
equal(multiplication(antidomain(antidomain(addition(u,v))),u),u),
inference(rew,[status(thm),theory(equality)],[71,7933]),
[iquote('0:Rew:71.0,7933.0')] ).
cnf(8034,plain,
equal(addition(zero,multiplication(antidomain(antidomain(addition(u,v))),v)),v),
inference(spr,[status(thm),theory(equality)],[6519,336]),
[iquote('0:SpR:6519.0,336.0')] ).
cnf(8094,plain,
equal(multiplication(antidomain(antidomain(addition(u,v))),v),v),
inference(rew,[status(thm),theory(equality)],[71,8034]),
[iquote('0:Rew:71.0,8034.0')] ).
cnf(8381,plain,
equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[3654,5786]),
[iquote('0:SpR:3654.0,5786.0')] ).
cnf(8399,plain,
equal(addition(antidomain(antidomain(u)),zero),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[8381,4021]),
[iquote('0:Rew:8381.0,4021.0')] ).
cnf(8423,plain,
equal(coantidomain(antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[71,8399,3]),
[iquote('0:Rew:71.0,8399.0,3.0,8399.0')] ).
cnf(8444,plain,
equal(addition(multiplication(antidomain(antidomain(sK2_goals_X1)),u),multiplication(antidomain(coantidomain(coantidomain(multiplication(coantidomain(antidomain(antidomain(sK1_goals_X2))),sK3_goals_X0)))),u)),u),
inference(rew,[status(thm),theory(equality)],[8423,4031]),
[iquote('0:Rew:8423.0,4031.0')] ).
cnf(8646,plain,
equal(addition(multiplication(antidomain(antidomain(sK2_goals_X1)),u),multiplication(antidomain(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(sK1_goals_X2))),sK3_goals_X0)))),u)),u),
inference(rew,[status(thm),theory(equality)],[8423,8444]),
[iquote('0:Rew:8423.0,8444.0')] ).
cnf(8647,plain,
equal(addition(multiplication(antidomain(antidomain(sK2_goals_X1)),u),multiplication(antidomain(coantidomain(coantidomain(multiplication(antidomain(sK1_goals_X2),sK3_goals_X0)))),u)),u),
inference(rew,[status(thm),theory(equality)],[3941,8646]),
[iquote('0:Rew:3941.0,8646.0')] ).
cnf(8837,plain,
equal(multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[3931,6545]),
[iquote('0:SpR:3931.0,6545.0')] ).
cnf(8865,plain,
equal(addition(coantidomain(coantidomain(u)),zero),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[8837,3718]),
[iquote('0:Rew:8837.0,3718.0')] ).
cnf(8866,plain,
equal(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[71,8865,3]),
[iquote('0:Rew:71.0,8865.0,3.0,8865.0')] ).
cnf(8911,plain,
equal(coantidomain(coantidomain(coantidomain(u))),antidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[8866,8423]),
[iquote('0:SpR:8866.0,8423.0')] ).
cnf(8951,plain,
equal(antidomain(antidomain(coantidomain(u))),coantidomain(u)),
inference(spr,[status(thm),theory(equality)],[3655,8866]),
[iquote('0:SpR:3655.0,8866.0')] ).
cnf(8975,plain,
equal(antidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[3655,8911]),
[iquote('0:Rew:3655.0,8911.0')] ).
cnf(8981,plain,
equal(addition(multiplication(antidomain(antidomain(sK2_goals_X1)),u),multiplication(coantidomain(multiplication(antidomain(sK1_goals_X2),sK3_goals_X0)),u)),u),
inference(rew,[status(thm),theory(equality)],[8975,8647]),
[iquote('0:Rew:8975.0,8647.0')] ).
cnf(9054,plain,
equal(leq(domain_difference(coantidomain(u),v),coantidomain(u)),true__dfg),
inference(spr,[status(thm),theory(equality)],[8951,4075]),
[iquote('0:SpR:8951.0,4075.0')] ).
cnf(9059,plain,
equal(coantidomain(coantidomain(u)),antidomain(coantidomain(u))),
inference(spr,[status(thm),theory(equality)],[8951,8423]),
[iquote('0:SpR:8951.0,8423.0')] ).
cnf(9077,plain,
equal(leq(domain_difference(u,antidomain(coantidomain(v))),coantidomain(v)),true__dfg),
inference(spr,[status(thm),theory(equality)],[8951,513]),
[iquote('0:SpR:8951.0,513.0')] ).
cnf(9122,plain,
equal(multiplication(u,antidomain(coantidomain(addition(v,u)))),u),
inference(rew,[status(thm),theory(equality)],[9059,7702]),
[iquote('0:Rew:9059.0,7702.0')] ).
cnf(9125,plain,
equal(addition(multiplication(u,coantidomain(multiplication(v,w))),multiplication(u,coantidomain(multiplication(antidomain(coantidomain(v)),w)))),multiplication(u,coantidomain(multiplication(antidomain(coantidomain(v)),w)))),
inference(rew,[status(thm),theory(equality)],[9059,733]),
[iquote('0:Rew:9059.0,733.0')] ).
cnf(9135,plain,
equal(addition(multiplication(u,coantidomain(v)),addition(w,multiplication(u,antidomain(coantidomain(v))))),addition(w,u)),
inference(rew,[status(thm),theory(equality)],[9059,3616]),
[iquote('0:Rew:9059.0,3616.0')] ).
cnf(9147,plain,
equal(addition(coantidomain(multiplication(u,multiplication(v,w))),coantidomain(multiplication(antidomain(coantidomain(multiplication(u,v))),w))),coantidomain(multiplication(antidomain(coantidomain(multiplication(u,v))),w))),
inference(rew,[status(thm),theory(equality)],[9059,751]),
[iquote('0:Rew:9059.0,751.0')] ).
cnf(9155,plain,
equal(ifeq(leq(coantidomain(multiplication(antidomain(coantidomain(u)),v)),coantidomain(multiplication(u,v))),true__dfg,coantidomain(multiplication(antidomain(coantidomain(u)),v)),coantidomain(multiplication(u,v))),coantidomain(multiplication(u,v))),
inference(rew,[status(thm),theory(equality)],[9059,1545]),
[iquote('0:Rew:9059.0,1545.0')] ).
cnf(9158,plain,
equal(addition(multiplication(coantidomain(u),v),addition(multiplication(antidomain(coantidomain(u)),v),w)),addition(v,w)),
inference(rew,[status(thm),theory(equality)],[9059,3181]),
[iquote('0:Rew:9059.0,3181.0')] ).
cnf(9159,plain,
equal(addition(multiplication(coantidomain(u),v),addition(w,multiplication(antidomain(coantidomain(u)),v))),addition(w,v)),
inference(rew,[status(thm),theory(equality)],[9059,3191]),
[iquote('0:Rew:9059.0,3191.0')] ).
cnf(9176,plain,
equal(multiplication(antidomain(coantidomain(u)),multiplication(v,coantidomain(multiplication(coantidomain(u),v)))),multiplication(v,coantidomain(multiplication(coantidomain(u),v)))),
inference(rew,[status(thm),theory(equality)],[9059,3258]),
[iquote('0:Rew:9059.0,3258.0')] ).
cnf(9459,plain,
equal(addition(multiplication(antidomain(u),domain_difference(v,u)),zero),domain_difference(v,u)),
inference(spr,[status(thm),theory(equality)],[6571,336]),
[iquote('0:SpR:6571.0,336.0')] ).
cnf(9499,plain,
equal(multiplication(antidomain(u),domain_difference(v,u)),domain_difference(v,u)),
inference(rew,[status(thm),theory(equality)],[71,9459,3]),
[iquote('0:Rew:71.0,9459.0,3.0,9459.0')] ).
cnf(9691,plain,
equal(ifeq(true__dfg,true__dfg,addition(domain_difference(coantidomain(u),v),coantidomain(u)),coantidomain(u)),coantidomain(u)),
inference(spr,[status(thm),theory(equality)],[9054,14]),
[iquote('0:SpR:9054.0,14.0')] ).
cnf(9734,plain,
equal(addition(coantidomain(u),domain_difference(coantidomain(u),v)),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[2,9691,3]),
[iquote('0:Rew:2.0,9691.0,3.0,9691.0')] ).
cnf(10920,plain,
equal(multiplication(one,domain_difference(antidomain(u),antidomain(multiplication(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[4126,16]),
[iquote('0:SpR:4126.0,16.0')] ).
cnf(11066,plain,
equal(domain_difference(antidomain(u),antidomain(multiplication(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[9,10920]),
[iquote('0:Rew:9.0,10920.0')] ).
cnf(11150,plain,
equal(domain_difference(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[7992,11066]),
[iquote('0:SpR:7992.0,11066.0')] ).
cnf(11153,plain,
equal(domain_difference(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(v)),zero),
inference(spr,[status(thm),theory(equality)],[8094,11066]),
[iquote('0:SpR:8094.0,11066.0')] ).
cnf(11201,plain,
equal(domain_difference(antidomain(addition(u,v)),antidomain(u)),zero),
inference(rew,[status(thm),theory(equality)],[3941,11150]),
[iquote('0:Rew:3941.0,11150.0')] ).
cnf(11203,plain,
equal(domain_difference(antidomain(addition(u,v)),antidomain(v)),zero),
inference(rew,[status(thm),theory(equality)],[3941,11153]),
[iquote('0:Rew:3941.0,11153.0')] ).
cnf(11464,plain,
equal(domain_difference(antidomain(addition(u,addition(v,w))),antidomain(addition(u,v))),zero),
inference(spr,[status(thm),theory(equality)],[4,11201]),
[iquote('0:SpR:4.0,11201.0')] ).
cnf(11821,plain,
equal(addition(zero,multiplication(coantidomain(multiplication(antidomain(sK1_goals_X2),sK3_goals_X0)),antidomain(sK2_goals_X1))),antidomain(sK2_goals_X1)),
inference(spr,[status(thm),theory(equality)],[16,8981]),
[iquote('0:SpR:16.0,8981.0')] ).
cnf(11850,plain,
equal(multiplication(coantidomain(multiplication(antidomain(sK1_goals_X2),sK3_goals_X0)),antidomain(sK2_goals_X1)),antidomain(sK2_goals_X1)),
inference(rew,[status(thm),theory(equality)],[71,11821]),
[iquote('0:Rew:71.0,11821.0')] ).
cnf(13175,plain,
equal(multiplication(antidomain(antidomain(antidomain(domain_difference(u,antidomain(v))))),antidomain(multiplication(antidomain(antidomain(u)),v))),antidomain(multiplication(antidomain(antidomain(u)),v))),
inference(spr,[status(thm),theory(equality)],[919,8094]),
[iquote('0:SpR:919.0,8094.0')] ).
cnf(13319,plain,
equal(multiplication(antidomain(domain_difference(u,antidomain(v))),antidomain(multiplication(antidomain(antidomain(u)),v))),antidomain(multiplication(antidomain(antidomain(u)),v))),
inference(rew,[status(thm),theory(equality)],[3941,13175]),
[iquote('0:Rew:3941.0,13175.0')] ).
cnf(13320,plain,
equal(domain_difference(antidomain(domain_difference(u,antidomain(v))),multiplication(antidomain(antidomain(u)),v)),antidomain(multiplication(antidomain(antidomain(u)),v))),
inference(rew,[status(thm),theory(equality)],[4074,13319]),
[iquote('0:Rew:4074.0,13319.0')] ).
cnf(15543,plain,
equal(multiplication(antidomain(u),coantidomain(v)),domain_difference(antidomain(u),antidomain(coantidomain(v)))),
inference(spr,[status(thm),theory(equality)],[8951,4074]),
[iquote('0:SpR:8951.0,4074.0')] ).
cnf(15553,plain,
equal(multiplication(coantidomain(u),antidomain(v)),domain_difference(coantidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[8951,4074]),
[iquote('0:SpR:8951.0,4074.0')] ).
cnf(15599,plain,
equal(domain_difference(coantidomain(multiplication(antidomain(sK1_goals_X2),sK3_goals_X0)),sK2_goals_X1),antidomain(sK2_goals_X1)),
inference(rew,[status(thm),theory(equality)],[15553,11850]),
[iquote('0:Rew:15553.0,11850.0')] ).
cnf(16164,plain,
equal(multiplication(multiplication(antidomain(sK1_goals_X2),sK3_goals_X0),antidomain(sK2_goals_X1)),zero),
inference(spr,[status(thm),theory(equality)],[15599,2818]),
[iquote('0:SpR:15599.0,2818.0')] ).
cnf(16172,plain,
equal(multiplication(antidomain(sK1_goals_X2),multiplication(sK3_goals_X0,antidomain(sK2_goals_X1))),zero),
inference(rew,[status(thm),theory(equality)],[7,16164]),
[iquote('0:Rew:7.0,16164.0')] ).
cnf(16731,plain,
equal(multiplication(domain_difference(antidomain(u),v),antidomain(coantidomain(antidomain(u)))),domain_difference(antidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[4589,9122]),
[iquote('0:SpR:4589.0,9122.0')] ).
cnf(16823,plain,
equal(multiplication(antidomain(u),domain_difference(antidomain(v),u)),domain_difference(antidomain(u),v)),
inference(rew,[status(thm),theory(equality)],[3941,16731,4074,196,8423]),
[iquote('0:Rew:3941.0,16731.0,4074.0,16731.0,196.0,16731.0,3941.0,16731.0,8423.0,16731.0')] ).
cnf(16824,plain,
equal(domain_difference(antidomain(u),v),domain_difference(antidomain(v),u)),
inference(rew,[status(thm),theory(equality)],[9499,16823]),
[iquote('0:Rew:9499.0,16823.0')] ).
cnf(16828,plain,
equal(domain_difference(antidomain(antidomain(u)),addition(v,u)),zero),
inference(rew,[status(thm),theory(equality)],[16824,11203]),
[iquote('0:Rew:16824.0,11203.0')] ).
cnf(16838,plain,
equal(domain_difference(antidomain(antidomain(addition(u,v))),addition(u,addition(v,w))),zero),
inference(rew,[status(thm),theory(equality)],[16824,11464]),
[iquote('0:Rew:16824.0,11464.0')] ).
cnf(16854,plain,
equal(domain_difference(u,addition(v,u)),zero),
inference(rew,[status(thm),theory(equality)],[4112,16828]),
[iquote('0:Rew:4112.0,16828.0')] ).
cnf(16859,plain,
equal(domain_difference(addition(u,v),addition(u,addition(v,w))),zero),
inference(rew,[status(thm),theory(equality)],[4112,16838]),
[iquote('0:Rew:4112.0,16838.0')] ).
cnf(16935,plain,
equal(addition(multiplication(antidomain(multiplication(u,v)),multiplication(u,antidomain(antidomain(v)))),zero),zero),
inference(spr,[status(thm),theory(equality)],[16,881]),
[iquote('0:SpR:16.0,881.0')] ).
cnf(17020,plain,
equal(multiplication(antidomain(multiplication(u,v)),multiplication(u,antidomain(antidomain(v)))),zero),
inference(rew,[status(thm),theory(equality)],[71,16935,3]),
[iquote('0:Rew:71.0,16935.0,3.0,16935.0')] ).
cnf(17609,plain,
equal(addition(multiplication(multiplication(antidomain(coantidomain(u)),v),coantidomain(multiplication(u,v))),zero),zero),
inference(spr,[status(thm),theory(equality)],[20,9125]),
[iquote('0:SpR:20.0,9125.0')] ).
cnf(17677,plain,
equal(multiplication(antidomain(coantidomain(u)),multiplication(v,coantidomain(multiplication(u,v)))),zero),
inference(rew,[status(thm),theory(equality)],[71,17609,3,7]),
[iquote('0:Rew:71.0,17609.0,3.0,17609.0,7.0,17609.0')] ).
cnf(18282,plain,
equal(addition(coantidomain(multiplication(u,zero)),coantidomain(multiplication(antidomain(coantidomain(multiplication(u,antidomain(v)))),v))),coantidomain(multiplication(antidomain(coantidomain(multiplication(u,antidomain(v)))),v))),
inference(spr,[status(thm),theory(equality)],[16,9147]),
[iquote('0:SpR:16.0,9147.0')] ).
cnf(18285,plain,
equal(addition(coantidomain(multiplication(u,zero)),coantidomain(multiplication(antidomain(coantidomain(multiplication(u,v))),coantidomain(v)))),coantidomain(multiplication(antidomain(coantidomain(multiplication(u,v))),coantidomain(v)))),
inference(spr,[status(thm),theory(equality)],[20,9147]),
[iquote('0:SpR:20.0,9147.0')] ).
cnf(18400,plain,
equal(coantidomain(multiplication(antidomain(coantidomain(multiplication(u,v))),coantidomain(v))),one),
inference(rew,[status(thm),theory(equality)],[273,18285,89,12]),
[iquote('0:Rew:273.0,18285.0,89.0,18285.0,12.0,18285.0')] ).
cnf(18401,plain,
equal(coantidomain(domain_difference(antidomain(antidomain(coantidomain(u))),coantidomain(multiplication(v,u)))),one),
inference(rew,[status(thm),theory(equality)],[16824,18400,15543]),
[iquote('0:Rew:16824.0,18400.0,15543.0,18400.0')] ).
cnf(18402,plain,
equal(coantidomain(domain_difference(coantidomain(u),coantidomain(multiplication(v,u)))),one),
inference(rew,[status(thm),theory(equality)],[8951,18401]),
[iquote('0:Rew:8951.0,18401.0')] ).
cnf(18403,plain,
equal(coantidomain(multiplication(antidomain(coantidomain(multiplication(u,antidomain(v)))),v)),one),
inference(rew,[status(thm),theory(equality)],[273,18282,89,12]),
[iquote('0:Rew:273.0,18282.0,89.0,18282.0,12.0,18282.0')] ).
cnf(18832,plain,
equal(domain_difference(antidomain(u),antidomain(v)),domain_difference(v,u)),
inference(spr,[status(thm),theory(equality)],[16824,4112]),
[iquote('0:SpR:16824.0,4112.0')] ).
cnf(18856,plain,
equal(addition(antidomain(domain_difference(antidomain(antidomain(u)),v)),antidomain(multiplication(antidomain(antidomain(antidomain(v))),u))),antidomain(domain_difference(antidomain(antidomain(u)),v))),
inference(spr,[status(thm),theory(equality)],[16824,919]),
[iquote('0:SpR:16824.0,919.0')] ).
cnf(19036,plain,
equal(addition(antidomain(domain_difference(u,v)),antidomain(multiplication(antidomain(v),u))),antidomain(domain_difference(u,v))),
inference(rew,[status(thm),theory(equality)],[3941,18856,4112]),
[iquote('0:Rew:3941.0,18856.0,4112.0,18856.0')] ).
cnf(19596,plain,
equal(domain_difference(u,antidomain(v)),domain_difference(v,antidomain(u))),
inference(spr,[status(thm),theory(equality)],[18832,4112]),
[iquote('0:SpR:18832.0,4112.0')] ).
cnf(19992,plain,
equal(addition(antidomain(addition(multiplication(antidomain(u),v),zero)),antidomain(multiplication(antidomain(u),antidomain(antidomain(addition(v,u)))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(addition(v,u)))))),
inference(spr,[status(thm),theory(equality)],[16,904]),
[iquote('0:SpR:16.0,904.0')] ).
cnf(20017,plain,
equal(addition(antidomain(addition(multiplication(antidomain(addition(u,v)),w),zero)),antidomain(multiplication(antidomain(addition(u,v)),antidomain(antidomain(addition(w,u)))))),antidomain(multiplication(antidomain(addition(u,v)),antidomain(antidomain(addition(w,u)))))),
inference(spr,[status(thm),theory(equality)],[6516,904]),
[iquote('0:SpR:6516.0,904.0')] ).
cnf(20032,plain,
equal(addition(antidomain(addition(zero,multiplication(antidomain(u),v))),antidomain(multiplication(antidomain(u),antidomain(antidomain(addition(u,v)))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(addition(u,v)))))),
inference(spr,[status(thm),theory(equality)],[16,904]),
[iquote('0:SpR:16.0,904.0')] ).
cnf(20128,plain,
equal(addition(antidomain(domain_difference(antidomain(u),antidomain(addition(u,v)))),antidomain(multiplication(antidomain(u),v))),antidomain(domain_difference(antidomain(u),antidomain(addition(u,v))))),
inference(rew,[status(thm),theory(equality)],[3,20032,71,4074]),
[iquote('0:Rew:3.0,20032.0,71.0,20032.0,4074.0,20032.0')] ).
cnf(20129,plain,
equal(addition(antidomain(domain_difference(antidomain(u),antidomain(addition(v,u)))),antidomain(multiplication(antidomain(u),v))),antidomain(domain_difference(antidomain(u),antidomain(addition(v,u))))),
inference(rew,[status(thm),theory(equality)],[3,19992,71,4074]),
[iquote('0:Rew:3.0,19992.0,71.0,19992.0,3.0,19992.0,4074.0,19992.0')] ).
cnf(20212,plain,
equal(addition(antidomain(domain_difference(antidomain(addition(u,v)),antidomain(addition(w,u)))),antidomain(multiplication(antidomain(addition(u,v)),w))),antidomain(domain_difference(antidomain(addition(u,v)),antidomain(addition(w,u))))),
inference(rew,[status(thm),theory(equality)],[3,20017,71,4074]),
[iquote('0:Rew:3.0,20017.0,71.0,20017.0,3.0,20017.0,4074.0,20017.0')] ).
cnf(20327,plain,
equal(multiplication(domain_difference(coantidomain(u),coantidomain(multiplication(v,u))),one),zero),
inference(spr,[status(thm),theory(equality)],[18402,20]),
[iquote('0:SpR:18402.0,20.0')] ).
cnf(20477,plain,
equal(multiplication(coantidomain(u),antidomain(coantidomain(multiplication(v,u)))),zero),
inference(rew,[status(thm),theory(equality)],[8951,20327,8,196]),
[iquote('0:Rew:8951.0,20327.0,8.0,20327.0,196.0,20327.0')] ).
cnf(20478,plain,
equal(domain_difference(coantidomain(u),coantidomain(multiplication(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[15553,20477]),
[iquote('0:Rew:15553.0,20477.0')] ).
cnf(20568,plain,
equal(domain_difference(coantidomain(antidomain(u)),coantidomain(domain_difference(antidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[4074,20478]),
[iquote('0:SpR:4074.0,20478.0')] ).
cnf(20635,plain,
equal(domain_difference(u,coantidomain(domain_difference(antidomain(v),u))),zero),
inference(rew,[status(thm),theory(equality)],[4112,20568,8423]),
[iquote('0:Rew:4112.0,20568.0,8423.0,20568.0')] ).
cnf(20720,plain,
equal(domain_difference(antidomain(u),coantidomain(domain_difference(u,v))),zero),
inference(spr,[status(thm),theory(equality)],[18832,20635]),
[iquote('0:SpR:18832.0,20635.0')] ).
cnf(26916,plain,
equal(multiplication(multiplication(antidomain(coantidomain(multiplication(u,antidomain(v)))),v),one),zero),
inference(spr,[status(thm),theory(equality)],[18403,20]),
[iquote('0:SpR:18403.0,20.0')] ).
cnf(27074,plain,
equal(multiplication(antidomain(coantidomain(multiplication(u,antidomain(v)))),v),zero),
inference(rew,[status(thm),theory(equality)],[8,26916,7]),
[iquote('0:Rew:8.0,26916.0,7.0,26916.0')] ).
cnf(27165,plain,
equal(addition(zero,multiplication(antidomain(antidomain(coantidomain(multiplication(u,antidomain(v))))),v)),v),
inference(spr,[status(thm),theory(equality)],[27074,336]),
[iquote('0:SpR:27074.0,336.0')] ).
cnf(27263,plain,
equal(multiplication(coantidomain(multiplication(u,antidomain(v))),v),v),
inference(rew,[status(thm),theory(equality)],[71,27165,8951]),
[iquote('0:Rew:71.0,27165.0,8951.0,27165.0')] ).
cnf(27402,plain,
equal(multiplication(coantidomain(multiplication(u,antidomain(v))),antidomain(antidomain(v))),antidomain(antidomain(v))),
inference(spr,[status(thm),theory(equality)],[3941,27263]),
[iquote('0:SpR:3941.0,27263.0')] ).
cnf(27417,plain,
equal(multiplication(coantidomain(domain_difference(antidomain(u),v)),v),v),
inference(spr,[status(thm),theory(equality)],[4074,27263]),
[iquote('0:SpR:4074.0,27263.0')] ).
cnf(27459,plain,
equal(domain_difference(coantidomain(multiplication(u,antidomain(v))),antidomain(v)),antidomain(antidomain(v))),
inference(rew,[status(thm),theory(equality)],[15553,27402]),
[iquote('0:Rew:15553.0,27402.0')] ).
cnf(27460,plain,
equal(domain_difference(u,antidomain(coantidomain(multiplication(v,antidomain(u))))),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[19596,27459]),
[iquote('0:Rew:19596.0,27459.0')] ).
cnf(27661,plain,
equal(multiplication(coantidomain(domain_difference(u,v)),v),v),
inference(spr,[status(thm),theory(equality)],[4112,27417]),
[iquote('0:SpR:4112.0,27417.0')] ).
cnf(27662,plain,
equal(multiplication(coantidomain(domain_difference(antidomain(u),v)),u),u),
inference(spr,[status(thm),theory(equality)],[16824,27417]),
[iquote('0:SpR:16824.0,27417.0')] ).
cnf(27815,plain,
equal(addition(coantidomain(domain_difference(u,coantidomain(v))),coantidomain(v)),coantidomain(domain_difference(u,coantidomain(v)))),
inference(spr,[status(thm),theory(equality)],[27661,438]),
[iquote('0:SpR:27661.0,438.0')] ).
cnf(27837,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),v),zero),
inference(spr,[status(thm),theory(equality)],[27661,202]),
[iquote('0:SpR:27661.0,202.0')] ).
cnf(27966,plain,
equal(addition(coantidomain(u),coantidomain(domain_difference(v,coantidomain(u)))),coantidomain(domain_difference(v,coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[3,27815]),
[iquote('0:Rew:3.0,27815.0')] ).
cnf(28235,plain,
equal(addition(multiplication(antidomain(coantidomain(domain_difference(u,antidomain(antidomain(v))))),antidomain(v)),zero),antidomain(coantidomain(domain_difference(u,antidomain(antidomain(v)))))),
inference(spr,[status(thm),theory(equality)],[27837,444]),
[iquote('0:SpR:27837.0,444.0')] ).
cnf(28408,plain,
equal(domain_difference(antidomain(u),coantidomain(domain_difference(v,u))),antidomain(coantidomain(domain_difference(v,u)))),
inference(rew,[status(thm),theory(equality)],[71,28235,3,16824,4074,4137]),
[iquote('0:Rew:71.0,28235.0,3.0,28235.0,16824.0,28235.0,4074.0,28235.0,4137.0,28235.0')] ).
cnf(28409,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(coantidomain(domain_difference(u,v)))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[28408,5387]),
[iquote('0:Rew:28408.0,5387.0')] ).
cnf(28410,plain,
equal(domain_difference(u,coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4112,28409,4074]),
[iquote('0:Rew:4112.0,28409.0,4074.0,28409.0')] ).
cnf(28454,plain,
equal(addition(coantidomain(domain_difference(antidomain(coantidomain(u)),v)),coantidomain(u)),coantidomain(domain_difference(antidomain(coantidomain(u)),v))),
inference(spr,[status(thm),theory(equality)],[27662,438]),
[iquote('0:SpR:27662.0,438.0')] ).
cnf(28625,plain,
equal(addition(coantidomain(u),coantidomain(domain_difference(antidomain(coantidomain(u)),v))),coantidomain(domain_difference(antidomain(coantidomain(u)),v))),
inference(rew,[status(thm),theory(equality)],[3,28454]),
[iquote('0:Rew:3.0,28454.0')] ).
cnf(28961,plain,
equal(addition(domain_difference(u,coantidomain(domain_difference(u,v))),zero),antidomain(coantidomain(domain_difference(u,v)))),
inference(spr,[status(thm),theory(equality)],[20720,3459]),
[iquote('0:SpR:20720.0,3459.0')] ).
cnf(28976,plain,
equal(addition(zero,domain_difference(antidomain(u),addition(v,u))),antidomain(addition(v,u))),
inference(spr,[status(thm),theory(equality)],[16854,3459]),
[iquote('0:SpR:16854.0,3459.0')] ).
cnf(29039,plain,
equal(domain_difference(antidomain(u),addition(v,u)),antidomain(addition(v,u))),
inference(rew,[status(thm),theory(equality)],[71,28976]),
[iquote('0:Rew:71.0,28976.0')] ).
cnf(29061,plain,
equal(domain_difference(u,coantidomain(domain_difference(u,v))),antidomain(coantidomain(domain_difference(u,v)))),
inference(rew,[status(thm),theory(equality)],[71,28961,3]),
[iquote('0:Rew:71.0,28961.0,3.0,28961.0')] ).
cnf(29062,plain,
equal(antidomain(coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[28410,29061]),
[iquote('0:Rew:28410.0,29061.0')] ).
cnf(29210,plain,
equal(antidomain(antidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(spr,[status(thm),theory(equality)],[29062,3941]),
[iquote('0:SpR:29062.0,3941.0')] ).
cnf(29224,plain,
equal(coantidomain(domain_difference(u,v)),antidomain(domain_difference(u,v))),
inference(spr,[status(thm),theory(equality)],[29062,8423]),
[iquote('0:SpR:29062.0,8423.0')] ).
cnf(29263,plain,
equal(multiplication(antidomain(u),domain_difference(v,w)),domain_difference(antidomain(u),coantidomain(domain_difference(v,w)))),
inference(spr,[status(thm),theory(equality)],[29062,4074]),
[iquote('0:SpR:29062.0,4074.0')] ).
cnf(29377,plain,
equal(multiplication(antidomain(domain_difference(antidomain(u),v)),u),u),
inference(rew,[status(thm),theory(equality)],[29224,27662]),
[iquote('0:Rew:29224.0,27662.0')] ).
cnf(29379,plain,
equal(multiplication(antidomain(domain_difference(u,v)),v),v),
inference(rew,[status(thm),theory(equality)],[29224,27661]),
[iquote('0:Rew:29224.0,27661.0')] ).
cnf(29425,plain,
equal(addition(coantidomain(u),antidomain(domain_difference(v,coantidomain(u)))),antidomain(domain_difference(v,coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[29224,27966]),
[iquote('0:Rew:29224.0,27966.0')] ).
cnf(29483,plain,
equal(addition(coantidomain(u),antidomain(domain_difference(antidomain(coantidomain(u)),v))),antidomain(domain_difference(antidomain(coantidomain(u)),v))),
inference(rew,[status(thm),theory(equality)],[29224,28625]),
[iquote('0:Rew:29224.0,28625.0')] ).
cnf(29607,plain,
equal(multiplication(antidomain(u),domain_difference(v,w)),domain_difference(antidomain(u),antidomain(domain_difference(v,w)))),
inference(rew,[status(thm),theory(equality)],[29224,29263]),
[iquote('0:Rew:29224.0,29263.0')] ).
cnf(30213,plain,
equal(addition(u,addition(addition(v,w),x)),addition(x,addition(w,addition(v,u)))),
inference(spr,[status(thm),theory(equality)],[1770,238]),
[iquote('0:SpR:1770.0,238.0')] ).
cnf(30255,plain,
equal(addition(u,addition(v,addition(w,x))),addition(x,addition(u,addition(w,v)))),
inference(spr,[status(thm),theory(equality)],[1770,254]),
[iquote('0:SpR:1770.0,254.0')] ).
cnf(30737,plain,
equal(addition(u,addition(v,addition(w,x))),addition(x,addition(w,addition(v,u)))),
inference(rew,[status(thm),theory(equality)],[4,30213]),
[iquote('0:Rew:4.0,30213.0')] ).
cnf(34203,plain,
equal(multiplication(antidomain(zero),multiplication(antidomain(sK1_goals_X2),antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))))),zero),
inference(spr,[status(thm),theory(equality)],[16172,17020]),
[iquote('0:SpR:16172.0,17020.0')] ).
cnf(34256,plain,
equal(domain_difference(antidomain(sK1_goals_X2),antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))),zero),
inference(rew,[status(thm),theory(equality)],[9,34203,98,4074]),
[iquote('0:Rew:9.0,34203.0,98.0,34203.0,4074.0,34203.0')] ).
cnf(38948,plain,
equal(addition(domain_difference(antidomain(u),multiplication(u,v)),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[11066,3998]),
[iquote('0:SpR:11066.0,3998.0')] ).
cnf(38956,plain,
equal(addition(domain_difference(antidomain(sK1_goals_X2),multiplication(sK3_goals_X0,antidomain(sK2_goals_X1))),zero),antidomain(antidomain(antidomain(sK1_goals_X2)))),
inference(spr,[status(thm),theory(equality)],[34256,3998]),
[iquote('0:SpR:34256.0,3998.0')] ).
cnf(39003,plain,
equal(addition(zero,domain_difference(coantidomain(u),antidomain(coantidomain(multiplication(v,u))))),antidomain(antidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[20478,3998]),
[iquote('0:SpR:20478.0,3998.0')] ).
cnf(39115,plain,
equal(domain_difference(antidomain(u),multiplication(u,v)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[71,38948,3,3941]),
[iquote('0:Rew:71.0,38948.0,3.0,38948.0,3941.0,38948.0')] ).
cnf(39129,plain,
equal(domain_difference(antidomain(sK1_goals_X2),multiplication(sK3_goals_X0,antidomain(sK2_goals_X1))),antidomain(sK1_goals_X2)),
inference(rew,[status(thm),theory(equality)],[71,38956,3,3941]),
[iquote('0:Rew:71.0,38956.0,3.0,38956.0,3941.0,38956.0')] ).
cnf(39166,plain,
equal(domain_difference(coantidomain(u),antidomain(coantidomain(multiplication(v,u)))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[71,39003,8951]),
[iquote('0:Rew:71.0,39003.0,8951.0,39003.0')] ).
cnf(39219,plain,
equal(leq(antidomain(u),antidomain(multiplication(u,v))),true__dfg),
inference(spr,[status(thm),theory(equality)],[39115,513]),
[iquote('0:SpR:39115.0,513.0')] ).
cnf(39240,plain,
equal(addition(antidomain(multiplication(u,v)),antidomain(u)),antidomain(multiplication(u,v))),
inference(spr,[status(thm),theory(equality)],[39115,491]),
[iquote('0:SpR:39115.0,491.0')] ).
cnf(39365,plain,
equal(addition(antidomain(u),antidomain(multiplication(u,v))),antidomain(multiplication(u,v))),
inference(rew,[status(thm),theory(equality)],[3,39240]),
[iquote('0:Rew:3.0,39240.0')] ).
cnf(39424,plain,
equal(leq(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(u)),true__dfg),
inference(spr,[status(thm),theory(equality)],[7992,39219]),
[iquote('0:SpR:7992.0,39219.0')] ).
cnf(39432,plain,
equal(leq(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(v)),true__dfg),
inference(spr,[status(thm),theory(equality)],[8094,39219]),
[iquote('0:SpR:8094.0,39219.0')] ).
cnf(39504,plain,
equal(leq(antidomain(addition(u,v)),antidomain(u)),true__dfg),
inference(rew,[status(thm),theory(equality)],[3941,39424]),
[iquote('0:Rew:3941.0,39424.0')] ).
cnf(39506,plain,
equal(leq(antidomain(addition(u,v)),antidomain(v)),true__dfg),
inference(rew,[status(thm),theory(equality)],[3941,39432]),
[iquote('0:Rew:3941.0,39432.0')] ).
cnf(39518,plain,
equal(ifeq(true__dfg,true__dfg,addition(antidomain(addition(u,v)),antidomain(u)),antidomain(u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[39504,14]),
[iquote('0:SpR:39504.0,14.0')] ).
cnf(39568,plain,
equal(leq(antidomain(u),antidomain(multiplication(antidomain(v),u))),true__dfg),
inference(spr,[status(thm),theory(equality)],[336,39504]),
[iquote('0:SpR:336.0,39504.0')] ).
cnf(39618,plain,
equal(addition(antidomain(u),antidomain(addition(u,v))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[2,39518,3]),
[iquote('0:Rew:2.0,39518.0,3.0,39518.0')] ).
cnf(39622,plain,
equal(ifeq(true__dfg,true__dfg,addition(antidomain(addition(u,v)),antidomain(v)),antidomain(v)),antidomain(v)),
inference(spr,[status(thm),theory(equality)],[39506,14]),
[iquote('0:SpR:39506.0,14.0')] ).
cnf(39728,plain,
equal(addition(antidomain(u),antidomain(addition(v,u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[2,39622,3]),
[iquote('0:Rew:2.0,39622.0,3.0,39622.0')] ).
cnf(40151,plain,
equal(ifeq(true__dfg,true__dfg,addition(antidomain(multiplication(antidomain(u),v)),antidomain(v)),antidomain(multiplication(antidomain(u),v))),antidomain(multiplication(antidomain(u),v))),
inference(spr,[status(thm),theory(equality)],[39568,171]),
[iquote('0:SpR:39568.0,171.0')] ).
cnf(40289,plain,
equal(addition(antidomain(u),antidomain(multiplication(antidomain(v),u))),antidomain(multiplication(antidomain(v),u))),
inference(rew,[status(thm),theory(equality)],[2,40151,3]),
[iquote('0:Rew:2.0,40151.0,3.0,40151.0')] ).
cnf(41688,plain,
equal(addition(antidomain(u),addition(antidomain(addition(u,v)),w)),addition(antidomain(u),w)),
inference(spr,[status(thm),theory(equality)],[39618,4]),
[iquote('0:SpR:39618.0,4.0')] ).
cnf(62092,plain,
equal(addition(antidomain(u),addition(v,addition(w,antidomain(addition(u,x))))),addition(v,addition(w,antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[39618,1850]),
[iquote('0:SpR:39618.0,1850.0')] ).
cnf(62093,plain,
equal(addition(antidomain(u),addition(v,addition(w,antidomain(addition(x,u))))),addition(v,addition(w,antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[39728,1850]),
[iquote('0:SpR:39728.0,1850.0')] ).
cnf(77595,plain,
equal(leq(coantidomain(u),coantidomain(multiplication(v,u))),true__dfg),
inference(spr,[status(thm),theory(equality)],[39166,9077]),
[iquote('0:SpR:39166.0,9077.0')] ).
cnf(92357,plain,
equal(addition(antidomain(u),multiplication(antidomain(antidomain(v)),antidomain(antidomain(u)))),addition(multiplication(antidomain(v),antidomain(u)),antidomain(antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[444,3385]),
[iquote('0:SpR:444.0,3385.0')] ).
cnf(92591,plain,
equal(addition(antidomain(antidomain(u)),domain_difference(antidomain(u),v)),addition(antidomain(v),domain_difference(u,antidomain(v)))),
inference(rew,[status(thm),theory(equality)],[4112,92357,4074,3]),
[iquote('0:Rew:4112.0,92357.0,4074.0,92357.0,3.0,92357.0,4074.0,92357.0')] ).
cnf(95602,plain,
equal(addition(multiplication(antidomain(u),coantidomain(v)),antidomain(antidomain(u))),addition(antidomain(antidomain(u)),coantidomain(v))),
inference(spr,[status(thm),theory(equality)],[438,3395]),
[iquote('0:SpR:438.0,3395.0')] ).
cnf(95603,plain,
equal(addition(multiplication(antidomain(u),antidomain(v)),antidomain(antidomain(u))),addition(antidomain(antidomain(u)),antidomain(v))),
inference(spr,[status(thm),theory(equality)],[439,3395]),
[iquote('0:SpR:439.0,3395.0')] ).
cnf(95792,plain,
equal(addition(antidomain(antidomain(u)),multiplication(antidomain(u),coantidomain(v))),addition(antidomain(antidomain(u)),coantidomain(v))),
inference(rew,[status(thm),theory(equality)],[3,95602]),
[iquote('0:Rew:3.0,95602.0')] ).
cnf(95793,plain,
equal(addition(antidomain(antidomain(coantidomain(u))),domain_difference(v,antidomain(antidomain(coantidomain(u))))),addition(antidomain(antidomain(v)),coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[92591,95792,15543]),
[iquote('0:Rew:92591.0,95792.0,15543.0,95792.0')] ).
cnf(95794,plain,
equal(addition(coantidomain(u),domain_difference(v,coantidomain(u))),addition(antidomain(antidomain(v)),coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[8951,95793]),
[iquote('0:Rew:8951.0,95793.0')] ).
cnf(95795,plain,
equal(addition(antidomain(antidomain(u)),domain_difference(antidomain(u),v)),addition(antidomain(antidomain(u)),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[3,95603,4074]),
[iquote('0:Rew:3.0,95603.0,4074.0,95603.0')] ).
cnf(95796,plain,
equal(addition(antidomain(u),domain_difference(v,antidomain(u))),addition(antidomain(antidomain(v)),antidomain(u))),
inference(rew,[status(thm),theory(equality)],[92591,95795]),
[iquote('0:Rew:92591.0,95795.0')] ).
cnf(108021,plain,
equal(addition(coantidomain(u),addition(v,multiplication(antidomain(domain_difference(antidomain(coantidomain(u)),w)),antidomain(coantidomain(u))))),addition(v,antidomain(domain_difference(antidomain(coantidomain(u)),w)))),
inference(spr,[status(thm),theory(equality)],[29377,9135]),
[iquote('0:SpR:29377.0,9135.0')] ).
cnf(108029,plain,
equal(addition(coantidomain(u),addition(v,multiplication(antidomain(domain_difference(w,coantidomain(u))),antidomain(coantidomain(u))))),addition(v,antidomain(domain_difference(w,coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[29379,9135]),
[iquote('0:SpR:29379.0,9135.0')] ).
cnf(108204,plain,
equal(addition(coantidomain(u),addition(v,domain_difference(antidomain(coantidomain(u)),domain_difference(w,coantidomain(u))))),addition(v,antidomain(domain_difference(w,coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[16824,108029,4074]),
[iquote('0:Rew:16824.0,108029.0,4074.0,108029.0')] ).
cnf(108222,plain,
equal(addition(coantidomain(u),addition(v,domain_difference(antidomain(coantidomain(u)),domain_difference(antidomain(coantidomain(u)),w)))),addition(v,antidomain(domain_difference(antidomain(coantidomain(u)),w)))),
inference(rew,[status(thm),theory(equality)],[16824,108021,4074]),
[iquote('0:Rew:16824.0,108021.0,4074.0,108021.0')] ).
cnf(109681,plain,
equal(addition(multiplication(antidomain(coantidomain(u)),antidomain(v)),coantidomain(u)),addition(antidomain(v),multiplication(coantidomain(u),antidomain(antidomain(v))))),
inference(spr,[status(thm),theory(equality)],[9158,3891]),
[iquote('0:SpR:9158.0,3891.0')] ).
cnf(109907,plain,
equal(addition(coantidomain(u),domain_difference(antidomain(coantidomain(u)),v)),addition(antidomain(v),domain_difference(coantidomain(u),antidomain(v)))),
inference(rew,[status(thm),theory(equality)],[3,109681,4074,15553]),
[iquote('0:Rew:3.0,109681.0,4074.0,109681.0,15553.0,109681.0')] ).
cnf(109908,plain,
equal(addition(coantidomain(u),domain_difference(antidomain(coantidomain(u)),v)),addition(antidomain(antidomain(coantidomain(u))),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[95796,109907]),
[iquote('0:Rew:95796.0,109907.0')] ).
cnf(109909,plain,
equal(addition(coantidomain(u),domain_difference(antidomain(coantidomain(u)),v)),addition(coantidomain(u),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[8951,109908]),
[iquote('0:Rew:8951.0,109908.0')] ).
cnf(111621,plain,
equal(addition(multiplication(coantidomain(u),antidomain(v)),addition(w,antidomain(antidomain(v)))),addition(coantidomain(u),addition(w,multiplication(antidomain(coantidomain(u)),antidomain(antidomain(v)))))),
inference(spr,[status(thm),theory(equality)],[9159,3881]),
[iquote('0:SpR:9159.0,3881.0')] ).
cnf(111998,plain,
equal(addition(antidomain(antidomain(u)),addition(domain_difference(coantidomain(v),u),w)),addition(coantidomain(v),addition(w,domain_difference(antidomain(coantidomain(v)),antidomain(u))))),
inference(rew,[status(thm),theory(equality)],[238,111621,15553,4074]),
[iquote('0:Rew:238.0,111621.0,15553.0,111621.0,4074.0,111621.0')] ).
cnf(137009,plain,
equal(addition(zero,multiplication(antidomain(coantidomain(u)),multiplication(antidomain(antidomain(v)),coantidomain(multiplication(u,antidomain(v)))))),multiplication(antidomain(coantidomain(u)),coantidomain(multiplication(u,antidomain(v))))),
inference(spr,[status(thm),theory(equality)],[17677,3396]),
[iquote('0:SpR:17677.0,3396.0')] ).
cnf(137285,plain,
equal(multiplication(antidomain(coantidomain(u)),multiplication(antidomain(antidomain(v)),coantidomain(multiplication(u,antidomain(v))))),multiplication(antidomain(coantidomain(u)),coantidomain(multiplication(u,antidomain(v))))),
inference(rew,[status(thm),theory(equality)],[71,137009]),
[iquote('0:Rew:71.0,137009.0')] ).
cnf(137286,plain,
equal(domain_difference(antidomain(coantidomain(u)),antidomain(domain_difference(antidomain(antidomain(v)),antidomain(coantidomain(multiplication(u,antidomain(v))))))),domain_difference(antidomain(coantidomain(u)),antidomain(coantidomain(multiplication(u,antidomain(v)))))),
inference(rew,[status(thm),theory(equality)],[29607,137285,15543]),
[iquote('0:Rew:29607.0,137285.0,15543.0,137285.0,15543.0,137285.0')] ).
cnf(137287,plain,
equal(domain_difference(antidomain(coantidomain(u)),antidomain(domain_difference(v,antidomain(coantidomain(multiplication(u,antidomain(v))))))),domain_difference(antidomain(coantidomain(u)),antidomain(coantidomain(multiplication(u,antidomain(v)))))),
inference(rew,[status(thm),theory(equality)],[4112,137286]),
[iquote('0:Rew:4112.0,137286.0')] ).
cnf(137288,plain,
equal(domain_difference(antidomain(coantidomain(u)),antidomain(coantidomain(multiplication(u,antidomain(v))))),domain_difference(antidomain(coantidomain(u)),antidomain(antidomain(antidomain(v))))),
inference(rew,[status(thm),theory(equality)],[27460,137287]),
[iquote('0:Rew:27460.0,137287.0')] ).
cnf(137289,plain,
equal(domain_difference(antidomain(coantidomain(u)),antidomain(coantidomain(multiplication(u,antidomain(v))))),domain_difference(antidomain(coantidomain(u)),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[3941,137288]),
[iquote('0:Rew:3941.0,137288.0')] ).
cnf(164201,plain,
equal(leq(coantidomain(multiplication(antidomain(coantidomain(u)),v)),coantidomain(multiplication(u,v))),true__dfg),
inference(spr,[status(thm),theory(equality)],[4150,77595]),
[iquote('0:SpR:4150.0,77595.0')] ).
cnf(164507,plain,
equal(ifeq(true__dfg,true__dfg,coantidomain(multiplication(antidomain(coantidomain(u)),v)),coantidomain(multiplication(u,v))),coantidomain(multiplication(u,v))),
inference(rew,[status(thm),theory(equality)],[164201,9155]),
[iquote('0:Rew:164201.0,9155.0')] ).
cnf(164833,plain,
equal(coantidomain(multiplication(antidomain(coantidomain(u)),v)),coantidomain(multiplication(u,v))),
inference(rew,[status(thm),theory(equality)],[2,164507]),
[iquote('0:Rew:2.0,164507.0')] ).
cnf(166544,plain,
equal(coantidomain(multiplication(u,antidomain(v))),coantidomain(domain_difference(antidomain(coantidomain(u)),v))),
inference(spr,[status(thm),theory(equality)],[4074,164833]),
[iquote('0:SpR:4074.0,164833.0')] ).
cnf(166583,plain,
equal(coantidomain(multiplication(u,antidomain(v))),antidomain(domain_difference(antidomain(coantidomain(u)),v))),
inference(rew,[status(thm),theory(equality)],[29224,166544]),
[iquote('0:Rew:29224.0,166544.0')] ).
cnf(166886,plain,
equal(domain_difference(antidomain(coantidomain(u)),antidomain(antidomain(domain_difference(antidomain(coantidomain(u)),v)))),domain_difference(antidomain(coantidomain(u)),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[166583,137289]),
[iquote('0:Rew:166583.0,137289.0')] ).
cnf(167047,plain,
equal(domain_difference(antidomain(coantidomain(u)),domain_difference(antidomain(coantidomain(u)),v)),domain_difference(antidomain(coantidomain(u)),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[29210,166886]),
[iquote('0:Rew:29210.0,166886.0')] ).
cnf(167049,plain,
equal(addition(coantidomain(u),addition(v,domain_difference(antidomain(coantidomain(u)),antidomain(w)))),addition(v,antidomain(domain_difference(antidomain(coantidomain(u)),w)))),
inference(rew,[status(thm),theory(equality)],[167047,108222]),
[iquote('0:Rew:167047.0,108222.0')] ).
cnf(167140,plain,
equal(addition(antidomain(antidomain(u)),addition(domain_difference(coantidomain(v),u),w)),addition(w,antidomain(domain_difference(antidomain(coantidomain(v)),u)))),
inference(rew,[status(thm),theory(equality)],[167049,111998]),
[iquote('0:Rew:167049.0,111998.0')] ).
cnf(167144,plain,
equal(antidomain(domain_difference(antidomain(coantidomain(u)),v)),addition(antidomain(antidomain(v)),addition(domain_difference(coantidomain(u),v),coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[167140,29483]),
[iquote('0:Rew:167140.0,29483.0')] ).
cnf(167145,plain,
equal(antidomain(domain_difference(antidomain(coantidomain(u)),v)),addition(antidomain(antidomain(v)),coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[9734,167144,3]),
[iquote('0:Rew:9734.0,167144.0,3.0,167144.0')] ).
cnf(175026,plain,
equal(domain_difference(addition(u,v),addition(v,u)),zero),
inference(spr,[status(thm),theory(equality)],[267,16859]),
[iquote('0:SpR:267.0,16859.0')] ).
cnf(175344,plain,
equal(addition(zero,domain_difference(antidomain(addition(u,v)),addition(v,u))),antidomain(addition(v,u))),
inference(spr,[status(thm),theory(equality)],[175026,3459]),
[iquote('0:SpR:175026.0,3459.0')] ).
cnf(175351,plain,
equal(addition(zero,domain_difference(addition(u,v),antidomain(addition(v,u)))),antidomain(antidomain(addition(u,v)))),
inference(spr,[status(thm),theory(equality)],[175026,3998]),
[iquote('0:SpR:175026.0,3998.0')] ).
cnf(175397,plain,
equal(domain_difference(antidomain(addition(u,v)),antidomain(addition(v,u))),zero),
inference(spr,[status(thm),theory(equality)],[175026,18832]),
[iquote('0:SpR:175026.0,18832.0')] ).
cnf(175756,plain,
equal(domain_difference(antidomain(addition(u,v)),addition(v,u)),antidomain(addition(v,u))),
inference(rew,[status(thm),theory(equality)],[71,175344]),
[iquote('0:Rew:71.0,175344.0')] ).
cnf(175758,plain,
equal(domain_difference(addition(u,v),antidomain(addition(v,u))),antidomain(antidomain(addition(u,v)))),
inference(rew,[status(thm),theory(equality)],[71,175351]),
[iquote('0:Rew:71.0,175351.0')] ).
cnf(175896,plain,
equal(addition(domain_difference(antidomain(addition(u,v)),addition(v,u)),zero),antidomain(antidomain(antidomain(addition(u,v))))),
inference(spr,[status(thm),theory(equality)],[175397,3998]),
[iquote('0:SpR:175397.0,3998.0')] ).
cnf(175944,plain,
equal(addition(domain_difference(addition(u,v),antidomain(addition(v,u))),zero),antidomain(antidomain(addition(v,u)))),
inference(spr,[status(thm),theory(equality)],[175397,3459]),
[iquote('0:SpR:175397.0,3459.0')] ).
cnf(176438,plain,
equal(domain_difference(addition(u,v),antidomain(addition(v,u))),antidomain(antidomain(addition(v,u)))),
inference(rew,[status(thm),theory(equality)],[71,175944,3]),
[iquote('0:Rew:71.0,175944.0,3.0,175944.0')] ).
cnf(176439,plain,
equal(antidomain(antidomain(addition(u,v))),antidomain(antidomain(addition(v,u)))),
inference(rew,[status(thm),theory(equality)],[175758,176438]),
[iquote('0:Rew:175758.0,176438.0')] ).
cnf(176452,plain,
equal(domain_difference(antidomain(addition(u,v)),addition(v,u)),antidomain(addition(u,v))),
inference(rew,[status(thm),theory(equality)],[71,175896,3,3941]),
[iquote('0:Rew:71.0,175896.0,3.0,175896.0,3941.0,175896.0')] ).
cnf(176453,plain,
equal(antidomain(addition(u,v)),antidomain(addition(v,u))),
inference(rew,[status(thm),theory(equality)],[175756,176452]),
[iquote('0:Rew:175756.0,176452.0')] ).
cnf(176640,plain,
equal(domain_difference(addition(u,v),antidomain(w)),domain_difference(w,antidomain(addition(v,u)))),
inference(spr,[status(thm),theory(equality)],[176453,19596]),
[iquote('0:SpR:176453.0,19596.0')] ).
cnf(178001,plain,
equal(addition(antidomain(addition(u,v)),antidomain(antidomain(addition(v,u)))),one),
inference(spr,[status(thm),theory(equality)],[176439,34]),
[iquote('0:SpR:176439.0,34.0')] ).
cnf(180658,plain,
equal(multiplication(antidomain(coantidomain(u)),multiplication(domain_difference(coantidomain(coantidomain(u)),v),coantidomain(zero))),multiplication(domain_difference(coantidomain(coantidomain(u)),v),coantidomain(zero))),
inference(spr,[status(thm),theory(equality)],[2818,9176]),
[iquote('0:SpR:2818.0,9176.0')] ).
cnf(180750,plain,
equal(multiplication(antidomain(coantidomain(u)),domain_difference(antidomain(coantidomain(u)),v)),domain_difference(antidomain(coantidomain(u)),v)),
inference(rew,[status(thm),theory(equality)],[4074,180658,8951,8,196,9059,89]),
[iquote('0:Rew:4074.0,180658.0,8951.0,180658.0,8.0,180658.0,196.0,180658.0,9059.0,180658.0,89.0,180658.0')] ).
cnf(180751,plain,
equal(domain_difference(antidomain(coantidomain(u)),v),antidomain(addition(antidomain(antidomain(v)),coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[29039,180750,167145,29607]),
[iquote('0:Rew:29039.0,180750.0,167145.0,180750.0,29607.0,180750.0')] ).
cnf(180905,plain,
equal(addition(coantidomain(u),addition(v,antidomain(addition(antidomain(antidomain(domain_difference(w,coantidomain(u)))),coantidomain(u))))),addition(v,antidomain(domain_difference(w,coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[180751,108204]),
[iquote('0:Rew:180751.0,108204.0')] ).
cnf(180938,plain,
equal(addition(coantidomain(u),antidomain(addition(antidomain(antidomain(v)),coantidomain(u)))),addition(coantidomain(u),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[180751,109909]),
[iquote('0:Rew:180751.0,109909.0')] ).
cnf(181113,plain,
equal(addition(coantidomain(u),addition(v,antidomain(addition(coantidomain(u),domain_difference(w,coantidomain(u)))))),addition(v,antidomain(domain_difference(w,coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[3,180905,29210]),
[iquote('0:Rew:3.0,180905.0,29210.0,180905.0')] ).
cnf(181114,plain,
equal(addition(coantidomain(u),addition(v,antidomain(addition(antidomain(antidomain(w)),coantidomain(u))))),addition(v,antidomain(domain_difference(w,coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[95794,181113]),
[iquote('0:Rew:95794.0,181113.0')] ).
cnf(181115,plain,
equal(antidomain(domain_difference(u,coantidomain(v))),addition(coantidomain(v),addition(coantidomain(v),antidomain(addition(antidomain(antidomain(u)),coantidomain(v)))))),
inference(rew,[status(thm),theory(equality)],[181114,29425]),
[iquote('0:Rew:181114.0,29425.0')] ).
cnf(181116,plain,
equal(antidomain(domain_difference(u,coantidomain(v))),addition(coantidomain(v),antidomain(addition(antidomain(antidomain(u)),coantidomain(v))))),
inference(rew,[status(thm),theory(equality)],[246,181115]),
[iquote('0:Rew:246.0,181115.0')] ).
cnf(181117,plain,
equal(antidomain(domain_difference(u,coantidomain(v))),addition(coantidomain(v),antidomain(u))),
inference(rew,[status(thm),theory(equality)],[180938,181116]),
[iquote('0:Rew:180938.0,181116.0')] ).
cnf(181786,plain,
equal(antidomain(domain_difference(u,antidomain(antidomain(v)))),addition(antidomain(antidomain(v)),antidomain(u))),
inference(spr,[status(thm),theory(equality)],[8423,181117]),
[iquote('0:SpR:8423.0,181117.0')] ).
cnf(182152,plain,
equal(antidomain(domain_difference(u,v)),addition(antidomain(antidomain(v)),antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4137,181786]),
[iquote('0:Rew:4137.0,181786.0')] ).
cnf(182205,plain,
equal(domain_difference(u,v),antidomain(addition(antidomain(antidomain(v)),antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[182152,29210]),
[iquote('0:Rew:182152.0,29210.0')] ).
cnf(183255,plain,
equal(addition(addition(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(antidomain(addition(v,w)))),antidomain(multiplication(antidomain(addition(v,w)),u))),addition(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(antidomain(addition(v,w))))),
inference(rew,[status(thm),theory(equality)],[182152,20212]),
[iquote('0:Rew:182152.0,20212.0')] ).
cnf(183270,plain,
equal(addition(addition(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(antidomain(v))),antidomain(multiplication(antidomain(v),u))),addition(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(antidomain(v)))),
inference(rew,[status(thm),theory(equality)],[182152,20129]),
[iquote('0:Rew:182152.0,20129.0')] ).
cnf(183278,plain,
equal(addition(addition(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(antidomain(u))),antidomain(multiplication(antidomain(u),v))),addition(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[182152,20128]),
[iquote('0:Rew:182152.0,20128.0')] ).
cnf(183316,plain,
equal(domain_difference(addition(antidomain(antidomain(antidomain(u))),antidomain(v)),multiplication(antidomain(antidomain(v)),u)),antidomain(multiplication(antidomain(antidomain(v)),u))),
inference(rew,[status(thm),theory(equality)],[182152,13320]),
[iquote('0:Rew:182152.0,13320.0')] ).
cnf(183386,plain,
equal(addition(addition(antidomain(antidomain(u)),antidomain(v)),antidomain(multiplication(antidomain(u),v))),addition(antidomain(antidomain(u)),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[182152,19036]),
[iquote('0:Rew:182152.0,19036.0')] ).
cnf(183513,plain,
equal(antidomain(addition(antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))),antidomain(antidomain(sK1_goals_X2)))),antidomain(sK1_goals_X2)),
inference(rew,[status(thm),theory(equality)],[182205,39129]),
[iquote('0:Rew:182205.0,39129.0')] ).
cnf(183520,plain,
equal(multiplication(antidomain(u),antidomain(v)),antidomain(addition(antidomain(antidomain(v)),antidomain(antidomain(u))))),
inference(rew,[status(thm),theory(equality)],[182205,4074]),
[iquote('0:Rew:182205.0,4074.0')] ).
cnf(183686,plain,
equal(domain_difference(u,antidomain(addition(v,w))),antidomain(addition(antidomain(antidomain(antidomain(u))),antidomain(addition(w,v))))),
inference(rew,[status(thm),theory(equality)],[182205,176640]),
[iquote('0:Rew:182205.0,176640.0')] ).
cnf(185838,plain,
equal(addition(antidomain(u),antidomain(addition(antidomain(antidomain(antidomain(u))),antidomain(v)))),addition(antidomain(antidomain(v)),antidomain(u))),
inference(rew,[status(thm),theory(equality)],[182205,95796]),
[iquote('0:Rew:182205.0,95796.0')] ).
cnf(186683,plain,
equal(antidomain(addition(antidomain(antidomain(sK1_goals_X2)),antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))))),antidomain(sK1_goals_X2)),
inference(rew,[status(thm),theory(equality)],[3,183513]),
[iquote('0:Rew:3.0,183513.0')] ).
cnf(187904,plain,
equal(domain_difference(u,antidomain(addition(v,w))),antidomain(addition(antidomain(u),antidomain(addition(w,v))))),
inference(rew,[status(thm),theory(equality)],[3941,183686]),
[iquote('0:Rew:3941.0,183686.0')] ).
cnf(187905,plain,
equal(antidomain(addition(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(w))),antidomain(addition(antidomain(w),antidomain(addition(v,u))))),
inference(rew,[status(thm),theory(equality)],[182205,187904]),
[iquote('0:Rew:182205.0,187904.0')] ).
cnf(187906,plain,
equal(antidomain(addition(antidomain(addition(u,v)),antidomain(w))),antidomain(addition(antidomain(w),antidomain(addition(v,u))))),
inference(rew,[status(thm),theory(equality)],[3941,187905]),
[iquote('0:Rew:3941.0,187905.0')] ).
cnf(188402,plain,
equal(addition(antidomain(u),antidomain(addition(antidomain(u),antidomain(v)))),addition(antidomain(antidomain(v)),antidomain(u))),
inference(rew,[status(thm),theory(equality)],[3941,185838]),
[iquote('0:Rew:3941.0,185838.0')] ).
cnf(188743,plain,
equal(addition(antidomain(antidomain(u)),addition(antidomain(v),antidomain(multiplication(antidomain(u),v)))),addition(antidomain(antidomain(u)),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[4,183386]),
[iquote('0:Rew:4.0,183386.0')] ).
cnf(188744,plain,
equal(antidomain(multiplication(antidomain(u),v)),addition(antidomain(antidomain(u)),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[39365,188743,40289]),
[iquote('0:Rew:39365.0,188743.0,40289.0,188743.0')] ).
cnf(189663,plain,
equal(domain_difference(addition(antidomain(u),antidomain(v)),multiplication(antidomain(antidomain(v)),u)),antidomain(multiplication(antidomain(antidomain(v)),u))),
inference(rew,[status(thm),theory(equality)],[3941,183316]),
[iquote('0:Rew:3941.0,183316.0')] ).
cnf(189664,plain,
equal(antidomain(addition(antidomain(addition(antidomain(u),antidomain(v))),antidomain(addition(antidomain(antidomain(antidomain(u))),antidomain(v))))),addition(antidomain(antidomain(antidomain(u))),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[187906,189663,188744,182205]),
[iquote('0:Rew:187906.0,189663.0,188744.0,189663.0,182205.0,189663.0,188744.0,189663.0')] ).
cnf(189665,plain,
equal(antidomain(antidomain(addition(antidomain(u),antidomain(v)))),addition(antidomain(u),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[6,189664,3941]),
[iquote('0:Rew:6.0,189664.0,3941.0,189664.0')] ).
cnf(191820,plain,
equal(addition(antidomain(antidomain(u)),addition(antidomain(addition(v,u)),antidomain(multiplication(antidomain(u),v)))),addition(antidomain(antidomain(u)),antidomain(addition(v,u)))),
inference(rew,[status(thm),theory(equality)],[4,183270,3,3941]),
[iquote('0:Rew:4.0,183270.0,3.0,183270.0,3941.0,183270.0')] ).
cnf(191821,plain,
equal(addition(antidomain(antidomain(u)),addition(antidomain(antidomain(u)),antidomain(v))),addition(antidomain(antidomain(u)),antidomain(addition(v,u)))),
inference(rew,[status(thm),theory(equality)],[62092,191820,1602,30737,188744]),
[iquote('0:Rew:62092.0,191820.0,1602.0,191820.0,30737.0,191820.0,188744.0,191820.0')] ).
cnf(191822,plain,
equal(addition(antidomain(antidomain(u)),antidomain(addition(v,u))),addition(antidomain(antidomain(u)),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[246,191821]),
[iquote('0:Rew:246.0,191821.0')] ).
cnf(191823,plain,
equal(addition(antidomain(antidomain(u)),addition(antidomain(addition(u,v)),antidomain(multiplication(antidomain(u),v)))),addition(antidomain(antidomain(u)),antidomain(addition(u,v)))),
inference(rew,[status(thm),theory(equality)],[4,183278,3,3941]),
[iquote('0:Rew:4.0,183278.0,3.0,183278.0,3941.0,183278.0')] ).
cnf(191824,plain,
equal(addition(antidomain(antidomain(u)),addition(antidomain(antidomain(u)),antidomain(v))),addition(antidomain(antidomain(u)),antidomain(addition(u,v)))),
inference(rew,[status(thm),theory(equality)],[62093,191823,1602,30737,188744]),
[iquote('0:Rew:62093.0,191823.0,1602.0,191823.0,30737.0,191823.0,188744.0,191823.0')] ).
cnf(191825,plain,
equal(addition(antidomain(antidomain(u)),antidomain(addition(u,v))),addition(antidomain(antidomain(u)),antidomain(v))),
inference(rew,[status(thm),theory(equality)],[246,191824]),
[iquote('0:Rew:246.0,191824.0')] ).
cnf(192279,plain,
equal(addition(antidomain(addition(u,v)),addition(antidomain(antidomain(addition(v,w))),antidomain(multiplication(antidomain(addition(v,w)),u)))),addition(antidomain(addition(u,v)),antidomain(antidomain(addition(v,w))))),
inference(rew,[status(thm),theory(equality)],[4,183255,3941]),
[iquote('0:Rew:4.0,183255.0,3941.0,183255.0')] ).
cnf(192280,plain,
equal(addition(antidomain(u),addition(antidomain(antidomain(addition(v,w))),antidomain(antidomain(addition(v,w))))),addition(antidomain(addition(u,v)),antidomain(antidomain(addition(v,w))))),
inference(rew,[status(thm),theory(equality)],[41688,192279,30255,188744]),
[iquote('0:Rew:41688.0,192279.0,30255.0,192279.0,188744.0,192279.0')] ).
cnf(192281,plain,
equal(addition(antidomain(addition(u,v)),antidomain(antidomain(addition(v,w)))),addition(antidomain(u),antidomain(antidomain(addition(v,w))))),
inference(rew,[status(thm),theory(equality)],[6,192280]),
[iquote('0:Rew:6.0,192280.0')] ).
cnf(192284,plain,
equal(addition(antidomain(u),antidomain(antidomain(addition(v,u)))),one),
inference(rew,[status(thm),theory(equality)],[192281,178001]),
[iquote('0:Rew:192281.0,178001.0')] ).
cnf(197084,plain,
equal(multiplication(antidomain(antidomain(addition(antidomain(antidomain(u)),antidomain(v)))),antidomain(addition(v,u))),antidomain(addition(v,u))),
inference(spr,[status(thm),theory(equality)],[191822,8094]),
[iquote('0:SpR:191822.0,8094.0')] ).
cnf(197443,plain,
equal(multiplication(addition(antidomain(antidomain(u)),antidomain(v)),antidomain(addition(v,u))),antidomain(addition(v,u))),
inference(rew,[status(thm),theory(equality)],[189665,197084]),
[iquote('0:Rew:189665.0,197084.0')] ).
cnf(197444,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(addition(v,u))),multiplication(antidomain(v),antidomain(addition(v,u)))),antidomain(addition(v,u))),
inference(rew,[status(thm),theory(equality)],[11,197443]),
[iquote('0:Rew:11.0,197443.0')] ).
cnf(197445,plain,
equal(addition(antidomain(addition(antidomain(antidomain(antidomain(u))),antidomain(addition(antidomain(antidomain(antidomain(u))),antidomain(addition(v,u)))))),antidomain(addition(antidomain(antidomain(v)),antidomain(addition(antidomain(antidomain(v)),antidomain(u)))))),antidomain(addition(v,u))),
inference(rew,[status(thm),theory(equality)],[188402,197444,183520,191825]),
[iquote('0:Rew:188402.0,197444.0,183520.0,197444.0,191825.0,197444.0,188402.0,197444.0,183520.0,197444.0')] ).
cnf(197446,plain,
equal(antidomain(addition(antidomain(antidomain(u)),antidomain(addition(antidomain(antidomain(u)),antidomain(v))))),antidomain(addition(u,v))),
inference(rew,[status(thm),theory(equality)],[71,197445,60,34,39728,3941]),
[iquote('0:Rew:71.0,197445.0,60.0,197445.0,34.0,197445.0,39728.0,197445.0,3941.0,197445.0')] ).
cnf(199302,plain,
equal(addition(antidomain(u),antidomain(addition(antidomain(u),v))),addition(antidomain(u),antidomain(v))),
inference(spr,[status(thm),theory(equality)],[3941,191825]),
[iquote('0:SpR:3941.0,191825.0')] ).
cnf(199355,plain,
equal(antidomain(addition(antidomain(antidomain(u)),antidomain(antidomain(v)))),antidomain(addition(u,v))),
inference(rew,[status(thm),theory(equality)],[199302,197446]),
[iquote('0:Rew:199302.0,197446.0')] ).
cnf(199769,plain,
equal(antidomain(addition(sK1_goals_X2,multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))),antidomain(sK1_goals_X2)),
inference(rew,[status(thm),theory(equality)],[199355,186683]),
[iquote('0:Rew:199355.0,186683.0')] ).
cnf(204154,plain,
equal(addition(antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1))),antidomain(antidomain(sK1_goals_X2))),one),
inference(spr,[status(thm),theory(equality)],[199769,192284]),
[iquote('0:SpR:199769.0,192284.0')] ).
cnf(204171,plain,
equal(addition(antidomain(antidomain(sK1_goals_X2)),antidomain(multiplication(sK3_goals_X0,antidomain(sK2_goals_X1)))),one),
inference(rew,[status(thm),theory(equality)],[3,204154]),
[iquote('0:Rew:3.0,204154.0')] ).
cnf(204172,plain,
$false,
inference(mrr,[status(thm)],[204171,4024]),
[iquote('0:MRR:204171.0,4024.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE104-10 : TPTP v8.1.0. Released v7.3.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 15:37:34 EDT 2022
% 0.14/0.37 % CPUTime :
% 291.53/291.70
% 291.53/291.70 SPASS V 3.9
% 291.53/291.70 SPASS beiseite: Proof found.
% 291.53/291.70 % SZS status Theorem
% 291.53/291.70 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 291.53/291.70 SPASS derived 123461 clauses, backtracked 0 clauses, performed 0 splits and kept 19502 clauses.
% 291.53/291.70 SPASS allocated 262887 KBytes.
% 291.53/291.70 SPASS spent 0:4:51.06 on the problem.
% 291.53/291.70 0:00:00.04 for the input.
% 291.53/291.70 0:00:00.00 for the FLOTTER CNF translation.
% 291.53/291.70 0:00:00.76 for inferences.
% 291.53/291.70 0:00:00.00 for the backtracking.
% 291.53/291.70 0:4:50.02 for the reduction.
% 291.53/291.70
% 291.53/291.70
% 291.53/291.70 Here is a proof with depth 13, length 435 :
% 291.53/291.70 % SZS output start Refutation
% See solution above
% 299.20/299.36 Formulae used in the proof : ifeq_axiom ifeq_axiom_001 additive_commutativity additive_associativity additive_identity additive_idempotence multiplicative_associativity multiplicative_right_identity multiplicative_left_identity right_distributivity left_distributivity right_annihilation left_annihilation order_1 order domain1 domain2 domain3 domain4 codomain1 codomain2 codomain3 codomain4 complement domain_difference forward_diamond backward_diamond forward_box backward_box goals goals_1
% 299.20/299.36
%------------------------------------------------------------------------------