TSTP Solution File: KLE097+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE097+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 02:28:30 EDT 2022
% Result : Theorem 63.94s 64.12s
% Output : Refutation 65.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 24
% Syntax : Number of clauses : 241 ( 230 unt; 0 nHn; 241 RR)
% Number of literals : 252 ( 0 equ; 16 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE097+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE097+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE097+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE097+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,zero),zero),
file('KLE097+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(zero,u),zero),
file('KLE097+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE097+1.p',unknown),
[] ).
cnf(8,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE097+1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE097+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE097+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE097+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE097+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE097+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE097+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE097+1.p',unknown),
[] ).
cnf(18,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE097+1.p',unknown),
[] ).
cnf(22,axiom,
~ equal(addition(forward_diamond(skc3,domain__dfg(skc4)),domain__dfg(skc5)),domain__dfg(skc5)),
file('KLE097+1.p',unknown),
[] ).
cnf(23,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE097+1.p',unknown),
[] ).
cnf(24,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE097+1.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE097+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE097+1.p',unknown),
[] ).
cnf(27,axiom,
equal(addition(multiplication(skc3,domain__dfg(skc4)),multiplication(domain__dfg(skc5),skc3)),multiplication(domain__dfg(skc5),skc3)),
file('KLE097+1.p',unknown),
[] ).
cnf(28,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE097+1.p',unknown),
[] ).
cnf(29,axiom,
equal(addition(coantidomain(multiplication(u,v)),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),
file('KLE097+1.p',unknown),
[] ).
cnf(31,plain,
equal(addition(coantidomain(u),coantidomain(coantidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[12,14]),
[iquote('0:Rew:12.0,14.0')] ).
cnf(32,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[12,13]),
[iquote('0:Rew:12.0,13.0')] ).
cnf(37,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[8,18]),
[iquote('0:Rew:8.0,18.0,8.0,18.0')] ).
cnf(38,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[8,17]),
[iquote('0:Rew:8.0,17.0')] ).
cnf(39,plain,
~ equal(addition(antidomain(antidomain(skc5)),forward_diamond(skc3,antidomain(antidomain(skc4)))),antidomain(antidomain(skc5))),
inference(rew,[status(thm),theory(equality)],[12,22,8]),
[iquote('0:Rew:12.0,22.0,8.0,22.0,8.0,22.0')] ).
cnf(40,plain,
equal(addition(multiplication(skc3,antidomain(antidomain(skc4))),multiplication(antidomain(antidomain(skc5)),skc3)),multiplication(antidomain(antidomain(skc5)),skc3)),
inference(rew,[status(thm),theory(equality)],[8,27]),
[iquote('0:Rew:8.0,27.0,8.0,27.0')] ).
cnf(55,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(59,plain,
equal(coantidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(66,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(75,plain,
equal(addition(zero,coantidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[59,31]),
[iquote('0:SpR:59.0,31.0')] ).
cnf(77,plain,
equal(coantidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[66,75]),
[iquote('0:Rew:66.0,75.0')] ).
cnf(89,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[55,32]),
[iquote('0:SpR:55.0,32.0')] ).
cnf(91,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[66,89]),
[iquote('0:Rew:66.0,89.0')] ).
cnf(99,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[15,12]),
[iquote('0:SpR:15.1,12.0')] ).
cnf(110,plain,
( ~ equal(u,u)
| leq(zero,u) ),
inference(spl,[status(thm),theory(equality)],[66,16]),
[iquote('0:SpL:66.0,16.0')] ).
cnf(114,plain,
leq(zero,u),
inference(obv,[status(thm),theory(equality)],[110]),
[iquote('0:Obv:110.0')] ).
cnf(161,plain,
equal(antidomain(antidomain(multiplication(u,forward_diamond(v,w)))),forward_diamond(u,multiplication(v,antidomain(antidomain(w))))),
inference(spr,[status(thm),theory(equality)],[37]),
[iquote('0:SpR:37.0,37.0')] ).
cnf(163,plain,
equal(multiplication(antidomain(antidomain(u)),forward_diamond(v,w)),domain_difference(u,antidomain(multiplication(v,antidomain(antidomain(w)))))),
inference(spr,[status(thm),theory(equality)],[37,38]),
[iquote('0:SpR:37.0,38.0')] ).
cnf(170,plain,
equal(antidomain(antidomain(domain_difference(u,antidomain(v)))),forward_diamond(antidomain(antidomain(u)),v)),
inference(spr,[status(thm),theory(equality)],[38,37]),
[iquote('0:SpR:38.0,37.0')] ).
cnf(195,plain,
equal(antidomain(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w)))))),forward_diamond(multiplication(u,v),w)),
inference(spr,[status(thm),theory(equality)],[24,37]),
[iquote('0:SpR:24.0,37.0')] ).
cnf(200,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),multiplication(zero,v)),
inference(spr,[status(thm),theory(equality)],[7,24]),
[iquote('0:SpR:7.0,24.0')] ).
cnf(204,plain,
equal(multiplication(domain_difference(u,v),w),multiplication(antidomain(antidomain(u)),multiplication(antidomain(v),w))),
inference(spr,[status(thm),theory(equality)],[38,24]),
[iquote('0:SpR:38.0,24.0')] ).
cnf(210,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),zero),
inference(rew,[status(thm),theory(equality)],[6,200]),
[iquote('0:Rew:6.0,200.0')] ).
cnf(270,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,23]),
[iquote('0:SpR:2.0,23.0')] ).
cnf(299,plain,
equal(addition(coantidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[31,270]),
[iquote('0:SpR:31.0,270.0')] ).
cnf(300,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[32,270]),
[iquote('0:SpR:32.0,270.0')] ).
cnf(302,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[270,16]),
[iquote('0:SpL:270.0,16.0')] ).
cnf(304,plain,
equal(addition(one,coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,299]),
[iquote('0:Rew:12.0,299.0')] ).
cnf(305,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,300]),
[iquote('0:Rew:12.0,300.0')] ).
cnf(308,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[302]),
[iquote('0:Obv:302.0')] ).
cnf(314,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[12,308]),
[iquote('0:SpR:12.0,308.0')] ).
cnf(371,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
inference(spr,[status(thm),theory(equality)],[26,9]),
[iquote('0:SpR:26.0,9.0')] ).
cnf(379,plain,
( ~ leq(u,v)
| equal(addition(multiplication(u,w),multiplication(v,w)),multiplication(v,w)) ),
inference(spr,[status(thm),theory(equality)],[15,26]),
[iquote('0:SpR:15.1,26.0')] ).
cnf(385,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[31,26]),
[iquote('0:SpR:31.0,26.0')] ).
cnf(386,plain,
equal(addition(multiplication(one,u),multiplication(coantidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[304,26]),
[iquote('0:SpR:304.0,26.0')] ).
cnf(387,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[32,26]),
[iquote('0:SpR:32.0,26.0')] ).
cnf(388,plain,
equal(addition(multiplication(one,u),multiplication(antidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[305,26]),
[iquote('0:SpR:305.0,26.0')] ).
cnf(394,plain,
equal(addition(u,multiplication(coantidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,386]),
[iquote('0:Rew:4.0,386.0')] ).
cnf(395,plain,
equal(addition(u,multiplication(antidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,388]),
[iquote('0:Rew:4.0,388.0')] ).
cnf(399,plain,
equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,385]),
[iquote('0:Rew:4.0,385.0')] ).
cnf(400,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[4,387]),
[iquote('0:Rew:4.0,387.0')] ).
cnf(466,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),multiplication(antidomain(addition(u,v)),v)),zero),
inference(spr,[status(thm),theory(equality)],[25,7]),
[iquote('0:SpR:25.0,7.0')] ).
cnf(481,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[31,25]),
[iquote('0:SpR:31.0,25.0')] ).
cnf(483,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[32,25]),
[iquote('0:SpR:32.0,25.0')] ).
cnf(484,plain,
equal(addition(multiplication(u,one),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[305,25]),
[iquote('0:SpR:305.0,25.0')] ).
cnf(493,plain,
equal(addition(u,multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,484]),
[iquote('0:Rew:3.0,484.0')] ).
cnf(498,plain,
equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,481]),
[iquote('0:Rew:3.0,481.0')] ).
cnf(499,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[3,483]),
[iquote('0:Rew:3.0,483.0')] ).
cnf(558,plain,
( ~ leq(forward_diamond(skc3,antidomain(antidomain(skc4))),antidomain(antidomain(skc5)))
| ~ equal(antidomain(antidomain(skc5)),antidomain(antidomain(skc5))) ),
inference(spl,[status(thm),theory(equality)],[99,39]),
[iquote('0:SpL:99.1,39.0')] ).
cnf(559,plain,
~ leq(forward_diamond(skc3,antidomain(antidomain(skc4))),antidomain(antidomain(skc5))),
inference(obv,[status(thm),theory(equality)],[558]),
[iquote('0:Obv:558.1')] ).
cnf(630,plain,
equal(addition(multiplication(u,multiplication(skc3,antidomain(antidomain(skc4)))),multiplication(u,multiplication(antidomain(antidomain(skc5)),skc3))),multiplication(u,multiplication(antidomain(antidomain(skc5)),skc3))),
inference(spr,[status(thm),theory(equality)],[40,25]),
[iquote('0:SpR:40.0,25.0')] ).
cnf(791,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)],[29,25]),
[iquote('0:SpR:29.0,25.0')] ).
cnf(802,plain,
equal(addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u))),coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u))),
inference(spr,[status(thm),theory(equality)],[7,29]),
[iquote('0:SpR:7.0,29.0')] ).
cnf(824,plain,
equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
inference(rew,[status(thm),theory(equality)],[304,802,77]),
[iquote('0:Rew:304.0,802.0,77.0,802.0')] ).
cnf(848,plain,
leq(multiplication(antidomain(u),v),v),
inference(spr,[status(thm),theory(equality)],[395,314]),
[iquote('0:SpR:395.0,314.0')] ).
cnf(868,plain,
equal(addition(antidomain(u),domain_difference(v,u)),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[38,395]),
[iquote('0:SpR:38.0,395.0')] ).
cnf(887,plain,
leq(domain_difference(u,v),antidomain(v)),
inference(spr,[status(thm),theory(equality)],[38,848]),
[iquote('0:SpR:38.0,848.0')] ).
cnf(917,plain,
equal(addition(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w))))),antidomain(multiplication(u,forward_diamond(v,w)))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(spr,[status(thm),theory(equality)],[37,28]),
[iquote('0:SpR:37.0,28.0')] ).
cnf(926,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[7,28]),
[iquote('0:SpR:7.0,28.0')] ).
cnf(929,plain,
equal(addition(antidomain(zero),antidomain(multiplication(u,antidomain(antidomain(coantidomain(u)))))),antidomain(multiplication(u,antidomain(antidomain(coantidomain(u)))))),
inference(spr,[status(thm),theory(equality)],[9,28]),
[iquote('0:SpR:9.0,28.0')] ).
cnf(948,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[305,926,91]),
[iquote('0:Rew:305.0,926.0,91.0,926.0')] ).
cnf(949,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(coantidomain(u))))),one),
inference(rew,[status(thm),theory(equality)],[305,929,91]),
[iquote('0:Rew:305.0,929.0,91.0,929.0')] ).
cnf(952,plain,
equal(addition(antidomain(multiplication(u,forward_diamond(v,w))),antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w)))))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[12,917]),
[iquote('0:Rew:12.0,917.0')] ).
cnf(1056,plain,
equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
inference(spr,[status(thm),theory(equality)],[824,9]),
[iquote('0:SpR:824.0,9.0')] ).
cnf(1088,plain,
equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
inference(rew,[status(thm),theory(equality)],[3,1056,24]),
[iquote('0:Rew:3.0,1056.0,24.0,1056.0')] ).
cnf(1274,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[948,7]),
[iquote('0:SpR:948.0,7.0')] ).
cnf(1321,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,1274]),
[iquote('0:Rew:4.0,1274.0')] ).
cnf(1465,plain,
equal(multiplication(one,multiplication(u,antidomain(antidomain(coantidomain(u))))),zero),
inference(spr,[status(thm),theory(equality)],[949,7]),
[iquote('0:SpR:949.0,7.0')] ).
cnf(1512,plain,
equal(multiplication(u,antidomain(antidomain(coantidomain(u)))),zero),
inference(rew,[status(thm),theory(equality)],[4,1465]),
[iquote('0:Rew:4.0,1465.0')] ).
cnf(4126,plain,
equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
inference(spr,[status(thm),theory(equality)],[1088,399]),
[iquote('0:SpR:1088.0,399.0')] ).
cnf(4129,plain,
equal(addition(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),zero),coantidomain(coantidomain(coantidomain(u)))),
inference(spr,[status(thm),theory(equality)],[9,399]),
[iquote('0:SpR:9.0,399.0')] ).
cnf(4153,plain,
equal(multiplication(coantidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[66,4126,12]),
[iquote('0:Rew:66.0,4126.0,12.0,4126.0')] ).
cnf(4166,plain,
equal(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(coantidomain(u)))),
inference(rew,[status(thm),theory(equality)],[66,4129,12]),
[iquote('0:Rew:66.0,4129.0,12.0,4129.0')] ).
cnf(4314,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1321,400]),
[iquote('0:SpR:1321.0,400.0')] ).
cnf(4319,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),u)),u),
inference(spr,[status(thm),theory(equality)],[7,400]),
[iquote('0:SpR:7.0,400.0')] ).
cnf(4327,plain,
equal(addition(domain_difference(u,v),multiplication(antidomain(antidomain(antidomain(u))),antidomain(v))),antidomain(v)),
inference(spr,[status(thm),theory(equality)],[38,400]),
[iquote('0:SpR:38.0,400.0')] ).
cnf(4337,plain,
equal(multiplication(antidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[66,4319]),
[iquote('0:Rew:66.0,4319.0')] ).
cnf(4353,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[66,4314,12]),
[iquote('0:Rew:66.0,4314.0,12.0,4314.0')] ).
cnf(4354,plain,
equal(addition(domain_difference(u,v),domain_difference(antidomain(u),v)),antidomain(v)),
inference(rew,[status(thm),theory(equality)],[38,4327]),
[iquote('0:Rew:38.0,4327.0')] ).
cnf(4377,plain,
equal(forward_diamond(antidomain(antidomain(antidomain(antidomain(u)))),u),antidomain(antidomain(antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[4337,37]),
[iquote('0:SpR:4337.0,37.0')] ).
cnf(4572,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)],[4337,498]),
[iquote('0:SpR:4337.0,498.0')] ).
cnf(4584,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[9,498]),
[iquote('0:SpR:9.0,498.0')] ).
cnf(4598,plain,
equal(multiplication(u,coantidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[66,4584]),
[iquote('0:Rew:66.0,4584.0')] ).
cnf(4599,plain,
equal(coantidomain(coantidomain(coantidomain(u))),coantidomain(u)),
inference(rew,[status(thm),theory(equality)],[4598,4166]),
[iquote('0:Rew:4598.0,4166.0')] ).
cnf(4648,plain,
equal(addition(coantidomain(coantidomain(u)),multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u))),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[12,4572]),
[iquote('0:Rew:12.0,4572.0')] ).
cnf(4827,plain,
equal(addition(multiplication(u,antidomain(coantidomain(u))),zero),u),
inference(spr,[status(thm),theory(equality)],[1512,499]),
[iquote('0:SpR:1512.0,499.0')] ).
cnf(4828,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[38,499]),
[iquote('0:SpR:38.0,499.0')] ).
cnf(4834,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)],[4153,499]),
[iquote('0:SpR:4153.0,499.0')] ).
cnf(4846,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1321,499]),
[iquote('0:SpR:1321.0,499.0')] ).
cnf(4858,plain,
equal(multiplication(u,antidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[66,4827,12]),
[iquote('0:Rew:66.0,4827.0,12.0,4827.0')] ).
cnf(4869,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[66,4846]),
[iquote('0:Rew:66.0,4846.0')] ).
cnf(4870,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4353,4869]),
[iquote('0:Rew:4353.0,4869.0')] ).
cnf(4896,plain,
equal(forward_diamond(antidomain(antidomain(u)),u),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4870,4377]),
[iquote('0:Rew:4870.0,4377.0')] ).
cnf(4921,plain,
equal(addition(domain_difference(u,v),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[38,4828]),
[iquote('0:Rew:38.0,4828.0')] ).
cnf(4942,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(antidomain(antidomain(u)))),antidomain(u))),coantidomain(antidomain(antidomain(antidomain(u))))),
inference(rew,[status(thm),theory(equality)],[12,4834]),
[iquote('0:Rew:12.0,4834.0')] ).
cnf(4943,plain,
equal(addition(antidomain(antidomain(u)),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[4870,4942]),
[iquote('0:Rew:4870.0,4942.0')] ).
cnf(4992,plain,
equal(multiplication(antidomain(u),antidomain(v)),domain_difference(antidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[4870,38]),
[iquote('0:SpR:4870.0,38.0')] ).
cnf(5005,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4870,37]),
[iquote('0:SpR:4870.0,37.0')] ).
cnf(5010,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,antidomain(antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[4870,38]),
[iquote('0:SpR:4870.0,38.0')] ).
cnf(5039,plain,
equal(antidomain(antidomain(forward_diamond(u,v))),forward_diamond(u,v)),
inference(spr,[status(thm),theory(equality)],[37,4870]),
[iquote('0:SpR:37.0,4870.0')] ).
cnf(5042,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(v)))),antidomain(forward_diamond(u,v))),
inference(spr,[status(thm),theory(equality)],[37,4870]),
[iquote('0:SpR:37.0,4870.0')] ).
cnf(5043,plain,
equal(antidomain(domain_difference(u,antidomain(v))),antidomain(forward_diamond(antidomain(antidomain(u)),v))),
inference(spr,[status(thm),theory(equality)],[170,4870]),
[iquote('0:SpR:170.0,4870.0')] ).
cnf(5066,plain,
equal(domain_difference(antidomain(antidomain(u)),v),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4992,38]),
[iquote('0:Rew:4992.0,38.0')] ).
cnf(5091,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[5005,37]),
[iquote('0:Rew:5005.0,37.0')] ).
cnf(5097,plain,
~ leq(forward_diamond(skc3,skc4),antidomain(antidomain(skc5))),
inference(rew,[status(thm),theory(equality)],[5091,559]),
[iquote('0:Rew:5091.0,559.0')] ).
cnf(5099,plain,
equal(addition(antidomain(multiplication(u,v)),antidomain(forward_diamond(u,v))),antidomain(forward_diamond(u,v))),
inference(rew,[status(thm),theory(equality)],[5042,28]),
[iquote('0:Rew:5042.0,28.0')] ).
cnf(5103,plain,
equal(multiplication(antidomain(antidomain(u)),forward_diamond(v,w)),domain_difference(u,antidomain(forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[5042,163]),
[iquote('0:Rew:5042.0,163.0')] ).
cnf(5153,plain,
equal(domain_difference(u,antidomain(antidomain(v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[5066,5010,4992]),
[iquote('0:Rew:5066.0,5010.0,4992.0,5010.0')] ).
cnf(5210,plain,
equal(addition(antidomain(forward_diamond(u,v)),antidomain(multiplication(u,v))),antidomain(forward_diamond(u,v))),
inference(rew,[status(thm),theory(equality)],[12,5099]),
[iquote('0:Rew:12.0,5099.0')] ).
cnf(5844,plain,
equal(addition(antidomain(forward_diamond(multiplication(u,v),w)),antidomain(multiplication(u,multiplication(v,w)))),antidomain(forward_diamond(multiplication(u,v),w))),
inference(spr,[status(thm),theory(equality)],[24,5210]),
[iquote('0:SpR:24.0,5210.0')] ).
cnf(7007,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)],[204,4858]),
[iquote('0:SpR:204.0,4858.0')] ).
cnf(7038,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)],[4992,7007]),
[iquote('0:Rew:4992.0,7007.0')] ).
cnf(7181,plain,
equal(multiplication(antidomain(u),forward_diamond(v,w)),domain_difference(antidomain(u),antidomain(forward_diamond(v,w)))),
inference(spr,[status(thm),theory(equality)],[4870,5103]),
[iquote('0:SpR:4870.0,5103.0')] ).
cnf(7714,plain,
equal(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w))))),antidomain(forward_diamond(multiplication(u,v),w))),
inference(spr,[status(thm),theory(equality)],[195,4870]),
[iquote('0:SpR:195.0,4870.0')] ).
cnf(7802,plain,
equal(addition(antidomain(multiplication(u,forward_diamond(v,w))),antidomain(forward_diamond(multiplication(u,v),w))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[7714,952]),
[iquote('0:Rew:7714.0,952.0')] ).
cnf(7863,plain,
equal(addition(antidomain(forward_diamond(multiplication(u,v),w)),antidomain(multiplication(u,forward_diamond(v,w)))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[12,7802]),
[iquote('0:Rew:12.0,7802.0')] ).
cnf(8083,plain,
equal(addition(multiplication(u,coantidomain(addition(u,v))),zero),zero),
inference(spr,[status(thm),theory(equality)],[371,270]),
[iquote('0:SpR:371.0,270.0')] ).
cnf(8122,plain,
equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
inference(spr,[status(thm),theory(equality)],[493,371]),
[iquote('0:SpR:493.0,371.0')] ).
cnf(8198,plain,
equal(multiplication(u,coantidomain(addition(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[66,8083,12]),
[iquote('0:Rew:66.0,8083.0,12.0,8083.0')] ).
cnf(8242,plain,
equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[66,8122,9,24]),
[iquote('0:Rew:66.0,8122.0,9.0,8122.0,24.0,8122.0')] ).
cnf(9074,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),zero),zero),
inference(spr,[status(thm),theory(equality)],[466,270]),
[iquote('0:SpR:466.0,270.0')] ).
cnf(9110,plain,
equal(addition(multiplication(antidomain(u),u),multiplication(antidomain(u),multiplication(coantidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[394,466]),
[iquote('0:SpR:394.0,466.0')] ).
cnf(9133,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(u)),multiplication(antidomain(antidomain(u)),domain_difference(v,u))),zero),
inference(spr,[status(thm),theory(equality)],[868,466]),
[iquote('0:SpR:868.0,466.0')] ).
cnf(9185,plain,
equal(multiplication(antidomain(addition(u,v)),u),zero),
inference(rew,[status(thm),theory(equality)],[66,9074,12]),
[iquote('0:Rew:66.0,9074.0,12.0,9074.0')] ).
cnf(9226,plain,
equal(multiplication(antidomain(u),multiplication(coantidomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[66,9110,7]),
[iquote('0:Rew:66.0,9110.0,7.0,9110.0')] ).
cnf(9249,plain,
equal(multiplication(antidomain(antidomain(u)),domain_difference(v,u)),zero),
inference(rew,[status(thm),theory(equality)],[66,9133,7]),
[iquote('0:Rew:66.0,9133.0,7.0,9133.0')] ).
cnf(9851,plain,
( ~ leq(u,zero)
| equal(addition(multiplication(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[6,379]),
[iquote('0:SpR:6.0,379.1')] ).
cnf(9904,plain,
( ~ leq(u,zero)
| equal(multiplication(u,v),zero) ),
inference(rew,[status(thm),theory(equality)],[66,9851,12]),
[iquote('0:Rew:66.0,9851.1,12.0,9851.1')] ).
cnf(10987,plain,
equal(addition(zero,multiplication(u,coantidomain(coantidomain(addition(u,v))))),u),
inference(spr,[status(thm),theory(equality)],[8198,498]),
[iquote('0:SpR:8198.0,498.0')] ).
cnf(11090,plain,
equal(multiplication(u,coantidomain(coantidomain(addition(u,v)))),u),
inference(rew,[status(thm),theory(equality)],[66,10987]),
[iquote('0:Rew:66.0,10987.0')] ).
cnf(11274,plain,
equal(addition(antidomain(forward_diamond(antidomain(addition(u,v)),u)),antidomain(zero)),antidomain(forward_diamond(antidomain(addition(u,v)),u))),
inference(spr,[status(thm),theory(equality)],[9185,5210]),
[iquote('0:SpR:9185.0,5210.0')] ).
cnf(11385,plain,
equal(antidomain(forward_diamond(antidomain(addition(u,v)),u)),one),
inference(rew,[status(thm),theory(equality)],[305,11274,12,91]),
[iquote('0:Rew:305.0,11274.0,12.0,11274.0,91.0,11274.0')] ).
cnf(15468,plain,
equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4598,8242]),
[iquote('0:SpR:4598.0,8242.0')] ).
cnf(15479,plain,
equal(addition(antidomain(antidomain(u)),zero),coantidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[15468,4943]),
[iquote('0:Rew:15468.0,4943.0')] ).
cnf(15481,plain,
equal(coantidomain(antidomain(u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,15479,12]),
[iquote('0:Rew:66.0,15479.0,12.0,15479.0')] ).
cnf(16194,plain,
equal(multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[4858,9226]),
[iquote('0:SpR:4858.0,9226.0')] ).
cnf(16218,plain,
equal(addition(coantidomain(coantidomain(u)),zero),antidomain(antidomain(coantidomain(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[16194,4648]),
[iquote('0:Rew:16194.0,4648.0')] ).
cnf(16220,plain,
equal(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,16218,12]),
[iquote('0:Rew:66.0,16218.0,12.0,16218.0')] ).
cnf(16355,plain,
equal(antidomain(antidomain(coantidomain(u))),coantidomain(u)),
inference(spr,[status(thm),theory(equality)],[4599,16220]),
[iquote('0:SpR:4599.0,16220.0')] ).
cnf(16497,plain,
equal(coantidomain(coantidomain(u)),antidomain(coantidomain(u))),
inference(spr,[status(thm),theory(equality)],[16355,15481]),
[iquote('0:SpR:16355.0,15481.0')] ).
cnf(16600,plain,
equal(multiplication(u,antidomain(coantidomain(addition(u,v)))),u),
inference(rew,[status(thm),theory(equality)],[16497,11090]),
[iquote('0:Rew:16497.0,11090.0')] ).
cnf(16607,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)],[16497,791]),
[iquote('0:Rew:16497.0,791.0')] ).
cnf(17435,plain,
equal(addition(multiplication(antidomain(u),domain_difference(v,u)),zero),domain_difference(v,u)),
inference(spr,[status(thm),theory(equality)],[9249,400]),
[iquote('0:SpR:9249.0,400.0')] ).
cnf(17487,plain,
equal(multiplication(antidomain(u),domain_difference(v,u)),domain_difference(v,u)),
inference(rew,[status(thm),theory(equality)],[66,17435,12]),
[iquote('0:Rew:66.0,17435.0,12.0,17435.0')] ).
cnf(18047,plain,
( ~ leq(antidomain(antidomain(u)),zero)
| equal(zero,u) ),
inference(spr,[status(thm),theory(equality)],[9904,4337]),
[iquote('0:SpR:9904.1,4337.0')] ).
cnf(19506,plain,
equal(multiplication(one,forward_diamond(antidomain(addition(u,v)),u)),zero),
inference(spr,[status(thm),theory(equality)],[11385,7]),
[iquote('0:SpR:11385.0,7.0')] ).
cnf(19703,plain,
equal(forward_diamond(antidomain(addition(u,v)),u),zero),
inference(rew,[status(thm),theory(equality)],[4,19506]),
[iquote('0:Rew:4.0,19506.0')] ).
cnf(19805,plain,
equal(forward_diamond(antidomain(addition(u,v)),v),zero),
inference(spr,[status(thm),theory(equality)],[12,19703]),
[iquote('0:SpR:12.0,19703.0')] ).
cnf(19917,plain,
equal(antidomain(antidomain(multiplication(u,zero))),forward_diamond(u,multiplication(antidomain(addition(v,w)),antidomain(antidomain(w))))),
inference(spr,[status(thm),theory(equality)],[19805,161]),
[iquote('0:SpR:19805.0,161.0')] ).
cnf(20003,plain,
equal(forward_diamond(u,multiplication(antidomain(addition(v,w)),antidomain(antidomain(w)))),zero),
inference(rew,[status(thm),theory(equality)],[55,19917,91,5]),
[iquote('0:Rew:55.0,19917.0,91.0,19917.0,5.0,19917.0')] ).
cnf(20004,plain,
equal(forward_diamond(u,domain_difference(antidomain(addition(v,w)),antidomain(w))),zero),
inference(rew,[status(thm),theory(equality)],[4992,20003]),
[iquote('0:Rew:4992.0,20003.0')] ).
cnf(21305,plain,
equal(addition(multiplication(antidomain(antidomain(antidomain(skc5))),multiplication(skc3,antidomain(antidomain(skc4)))),zero),zero),
inference(spr,[status(thm),theory(equality)],[210,630]),
[iquote('0:SpR:210.0,630.0')] ).
cnf(21333,plain,
equal(multiplication(antidomain(skc5),multiplication(skc3,antidomain(antidomain(skc4)))),zero),
inference(rew,[status(thm),theory(equality)],[66,21305,12,4870]),
[iquote('0:Rew:66.0,21305.0,12.0,21305.0,4870.0,21305.0')] ).
cnf(23152,plain,
equal(addition(multiplication(multiplication(antidomain(coantidomain(u)),v),coantidomain(multiplication(u,v))),zero),zero),
inference(spr,[status(thm),theory(equality)],[9,16607]),
[iquote('0:SpR:9.0,16607.0')] ).
cnf(23211,plain,
equal(multiplication(antidomain(coantidomain(u)),multiplication(v,coantidomain(multiplication(u,v)))),zero),
inference(rew,[status(thm),theory(equality)],[66,23152,12,24]),
[iquote('0:Rew:66.0,23152.0,12.0,23152.0,24.0,23152.0')] ).
cnf(26829,plain,
equal(addition(antidomain(forward_diamond(multiplication(antidomain(skc5),skc3),antidomain(antidomain(skc4)))),antidomain(zero)),antidomain(forward_diamond(multiplication(antidomain(skc5),skc3),antidomain(antidomain(skc4))))),
inference(spr,[status(thm),theory(equality)],[21333,5844]),
[iquote('0:SpR:21333.0,5844.0')] ).
cnf(26896,plain,
equal(antidomain(forward_diamond(multiplication(antidomain(skc5),skc3),skc4)),one),
inference(rew,[status(thm),theory(equality)],[305,26829,12,91,5091]),
[iquote('0:Rew:305.0,26829.0,12.0,26829.0,91.0,26829.0,5091.0,26829.0')] ).
cnf(27027,plain,
equal(addition(one,antidomain(multiplication(antidomain(skc5),forward_diamond(skc3,skc4)))),antidomain(multiplication(antidomain(skc5),forward_diamond(skc3,skc4)))),
inference(spr,[status(thm),theory(equality)],[26896,7863]),
[iquote('0:SpR:26896.0,7863.0')] ).
cnf(27154,plain,
equal(antidomain(multiplication(antidomain(skc5),forward_diamond(skc3,skc4))),one),
inference(rew,[status(thm),theory(equality)],[305,27027]),
[iquote('0:Rew:305.0,27027.0')] ).
cnf(27155,plain,
equal(antidomain(forward_diamond(antidomain(antidomain(antidomain(skc5))),forward_diamond(skc3,skc4))),one),
inference(rew,[status(thm),theory(equality)],[5043,27154,7181]),
[iquote('0:Rew:5043.0,27154.0,7181.0,27154.0')] ).
cnf(27156,plain,
equal(antidomain(forward_diamond(antidomain(skc5),forward_diamond(skc3,skc4))),one),
inference(rew,[status(thm),theory(equality)],[4870,27155]),
[iquote('0:Rew:4870.0,27155.0')] ).
cnf(27312,plain,
equal(forward_diamond(antidomain(skc5),forward_diamond(skc3,skc4)),antidomain(one)),
inference(spr,[status(thm),theory(equality)],[27156,5039]),
[iquote('0:SpR:27156.0,5039.0')] ).
cnf(27367,plain,
equal(forward_diamond(antidomain(skc5),forward_diamond(skc3,skc4)),zero),
inference(rew,[status(thm),theory(equality)],[55,27312]),
[iquote('0:Rew:55.0,27312.0')] ).
cnf(60977,plain,
equal(multiplication(antidomain(coantidomain(u)),multiplication(coantidomain(addition(u,v)),coantidomain(zero))),zero),
inference(spr,[status(thm),theory(equality)],[8198,23211]),
[iquote('0:SpR:8198.0,23211.0')] ).
cnf(61030,plain,
equal(multiplication(antidomain(coantidomain(u)),coantidomain(addition(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[3,60977,77]),
[iquote('0:Rew:3.0,60977.0,77.0,60977.0')] ).
cnf(65234,plain,
equal(multiplication(domain_difference(u,v),antidomain(coantidomain(antidomain(antidomain(u))))),domain_difference(u,v)),
inference(spr,[status(thm),theory(equality)],[4921,16600]),
[iquote('0:SpR:4921.0,16600.0')] ).
cnf(65433,plain,
equal(multiplication(antidomain(antidomain(u)),multiplication(antidomain(v),antidomain(antidomain(u)))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[204,65234,4870,15481]),
[iquote('0:Rew:204.0,65234.0,4870.0,65234.0,15481.0,65234.0')] ).
cnf(65434,plain,
equal(domain_difference(antidomain(u),antidomain(v)),domain_difference(v,u)),
inference(rew,[status(thm),theory(equality)],[17487,65433,4992]),
[iquote('0:Rew:17487.0,65433.0,4992.0,65433.0')] ).
cnf(65440,plain,
equal(forward_diamond(u,domain_difference(v,addition(w,v))),zero),
inference(rew,[status(thm),theory(equality)],[65434,20004]),
[iquote('0:Rew:65434.0,20004.0')] ).
cnf(65672,plain,
equal(domain_difference(antidomain(u),v),domain_difference(antidomain(v),u)),
inference(spr,[status(thm),theory(equality)],[65434,5153]),
[iquote('0:SpR:65434.0,5153.0')] ).
cnf(65695,plain,
equal(domain_difference(u,antidomain(v)),domain_difference(v,antidomain(u))),
inference(spr,[status(thm),theory(equality)],[65434,5066]),
[iquote('0:SpR:65434.0,5066.0')] ).
cnf(65946,plain,
equal(antidomain(antidomain(domain_difference(u,addition(v,u)))),zero),
inference(spr,[status(thm),theory(equality)],[65440,4896]),
[iquote('0:SpR:65440.0,4896.0')] ).
cnf(66493,plain,
( ~ leq(zero,zero)
| equal(domain_difference(u,addition(v,u)),zero) ),
inference(spl,[status(thm),theory(equality)],[65946,18047]),
[iquote('0:SpL:65946.0,18047.0')] ).
cnf(66653,plain,
equal(domain_difference(u,addition(v,u)),zero),
inference(mrr,[status(thm)],[66493,114]),
[iquote('0:MRR:66493.0,114.0')] ).
cnf(66965,plain,
equal(domain_difference(domain_difference(u,v),antidomain(v)),zero),
inference(spr,[status(thm),theory(equality)],[868,66653]),
[iquote('0:SpR:868.0,66653.0')] ).
cnf(67017,plain,
equal(domain_difference(u,antidomain(domain_difference(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[5066,66965,65434]),
[iquote('0:Rew:5066.0,66965.0,65434.0,66965.0')] ).
cnf(67581,plain,
equal(addition(domain_difference(u,domain_difference(v,u)),zero),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[67017,4921]),
[iquote('0:SpR:67017.0,4921.0')] ).
cnf(67700,plain,
equal(domain_difference(u,domain_difference(v,u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[66,67581,12]),
[iquote('0:Rew:66.0,67581.0,12.0,67581.0')] ).
cnf(70377,plain,
leq(antidomain(antidomain(u)),antidomain(domain_difference(v,u))),
inference(spr,[status(thm),theory(equality)],[67700,887]),
[iquote('0:SpR:67700.0,887.0')] ).
cnf(70826,plain,
leq(antidomain(antidomain(domain_difference(u,v))),antidomain(antidomain(antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[67700,70377]),
[iquote('0:SpR:67700.0,70377.0')] ).
cnf(70905,plain,
leq(antidomain(antidomain(domain_difference(u,v))),antidomain(v)),
inference(rew,[status(thm),theory(equality)],[4870,70826]),
[iquote('0:Rew:4870.0,70826.0')] ).
cnf(71119,plain,
leq(antidomain(antidomain(domain_difference(u,antidomain(coantidomain(v))))),coantidomain(v)),
inference(spr,[status(thm),theory(equality)],[16355,70905]),
[iquote('0:SpR:16355.0,70905.0')] ).
cnf(71200,plain,
leq(antidomain(antidomain(forward_diamond(antidomain(antidomain(u)),coantidomain(v)))),coantidomain(v)),
inference(rew,[status(thm),theory(equality)],[5043,71119]),
[iquote('0:Rew:5043.0,71119.0')] ).
cnf(71201,plain,
leq(forward_diamond(antidomain(antidomain(u)),coantidomain(v)),coantidomain(v)),
inference(rew,[status(thm),theory(equality)],[5039,71200]),
[iquote('0:Rew:5039.0,71200.0')] ).
cnf(72671,plain,
leq(forward_diamond(antidomain(u),coantidomain(v)),coantidomain(v)),
inference(spr,[status(thm),theory(equality)],[4870,71201]),
[iquote('0:SpR:4870.0,71201.0')] ).
cnf(72845,plain,
leq(forward_diamond(antidomain(u),antidomain(antidomain(v))),antidomain(antidomain(v))),
inference(spr,[status(thm),theory(equality)],[15481,72671]),
[iquote('0:SpR:15481.0,72671.0')] ).
cnf(72926,plain,
leq(forward_diamond(antidomain(u),v),antidomain(antidomain(v))),
inference(rew,[status(thm),theory(equality)],[5091,72845]),
[iquote('0:Rew:5091.0,72845.0')] ).
cnf(73062,plain,
leq(forward_diamond(forward_diamond(u,v),w),antidomain(antidomain(w))),
inference(spr,[status(thm),theory(equality)],[5039,72926]),
[iquote('0:SpR:5039.0,72926.0')] ).
cnf(112210,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),coantidomain(antidomain(v))),zero),
inference(spr,[status(thm),theory(equality)],[4354,61030]),
[iquote('0:SpR:4354.0,61030.0')] ).
cnf(112211,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),coantidomain(antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[4921,61030]),
[iquote('0:SpR:4921.0,61030.0')] ).
cnf(112277,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),antidomain(antidomain(v))),zero),
inference(rew,[status(thm),theory(equality)],[15481,112210]),
[iquote('0:Rew:15481.0,112210.0')] ).
cnf(112278,plain,
equal(domain_difference(antidomain(coantidomain(domain_difference(u,v))),antidomain(v)),zero),
inference(rew,[status(thm),theory(equality)],[4992,112277]),
[iquote('0:Rew:4992.0,112277.0')] ).
cnf(112279,plain,
equal(domain_difference(u,coantidomain(domain_difference(v,u))),zero),
inference(rew,[status(thm),theory(equality)],[16355,112278,65695]),
[iquote('0:Rew:16355.0,112278.0,65695.0,112278.0')] ).
cnf(112295,plain,
equal(multiplication(antidomain(coantidomain(domain_difference(u,v))),antidomain(u)),zero),
inference(rew,[status(thm),theory(equality)],[4870,112211,15481]),
[iquote('0:Rew:4870.0,112211.0,15481.0,112211.0')] ).
cnf(112296,plain,
equal(domain_difference(antidomain(coantidomain(domain_difference(u,v))),u),zero),
inference(rew,[status(thm),theory(equality)],[4992,112295]),
[iquote('0:Rew:4992.0,112295.0')] ).
cnf(112297,plain,
equal(domain_difference(antidomain(u),coantidomain(domain_difference(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[65672,112296]),
[iquote('0:Rew:65672.0,112296.0')] ).
cnf(112881,plain,
equal(addition(zero,domain_difference(antidomain(u),coantidomain(domain_difference(v,u)))),antidomain(coantidomain(domain_difference(v,u)))),
inference(spr,[status(thm),theory(equality)],[112279,4354]),
[iquote('0:SpR:112279.0,4354.0')] ).
cnf(113133,plain,
equal(domain_difference(antidomain(u),coantidomain(domain_difference(v,u))),antidomain(coantidomain(domain_difference(v,u)))),
inference(rew,[status(thm),theory(equality)],[66,112881]),
[iquote('0:Rew:66.0,112881.0')] ).
cnf(113134,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(coantidomain(domain_difference(u,v)))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[113133,7038]),
[iquote('0:Rew:113133.0,7038.0')] ).
cnf(113135,plain,
equal(domain_difference(antidomain(antidomain(u)),coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4992,113134]),
[iquote('0:Rew:4992.0,113134.0')] ).
cnf(113136,plain,
equal(domain_difference(u,coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[5066,113135]),
[iquote('0:Rew:5066.0,113135.0')] ).
cnf(113226,plain,
equal(addition(domain_difference(u,coantidomain(domain_difference(u,v))),zero),antidomain(coantidomain(domain_difference(u,v)))),
inference(spr,[status(thm),theory(equality)],[112297,4354]),
[iquote('0:SpR:112297.0,4354.0')] ).
cnf(113422,plain,
equal(domain_difference(u,coantidomain(domain_difference(u,v))),antidomain(coantidomain(domain_difference(u,v)))),
inference(rew,[status(thm),theory(equality)],[66,113226,12]),
[iquote('0:Rew:66.0,113226.0,12.0,113226.0')] ).
cnf(113423,plain,
equal(antidomain(coantidomain(domain_difference(u,v))),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[113136,113422]),
[iquote('0:Rew:113136.0,113422.0')] ).
cnf(113895,plain,
equal(coantidomain(domain_difference(u,v)),antidomain(domain_difference(u,v))),
inference(spr,[status(thm),theory(equality)],[113423,15481]),
[iquote('0:SpR:113423.0,15481.0')] ).
cnf(114087,plain,
equal(antidomain(coantidomain(domain_difference(u,antidomain(v)))),domain_difference(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[65695,113423]),
[iquote('0:SpR:65695.0,113423.0')] ).
cnf(114454,plain,
equal(domain_difference(u,antidomain(v)),antidomain(antidomain(forward_diamond(antidomain(antidomain(u)),v)))),
inference(rew,[status(thm),theory(equality)],[5043,114087,113895]),
[iquote('0:Rew:5043.0,114087.0,113895.0,114087.0')] ).
cnf(114455,plain,
equal(domain_difference(u,antidomain(v)),forward_diamond(antidomain(antidomain(u)),v)),
inference(rew,[status(thm),theory(equality)],[5039,114454]),
[iquote('0:Rew:5039.0,114454.0')] ).
cnf(114462,plain,
equal(domain_difference(u,v),forward_diamond(antidomain(antidomain(antidomain(v))),u)),
inference(rew,[status(thm),theory(equality)],[114455,65434]),
[iquote('0:Rew:114455.0,65434.0')] ).
cnf(114466,plain,
equal(addition(domain_difference(u,v),forward_diamond(antidomain(antidomain(u)),v)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[114455,4921]),
[iquote('0:Rew:114455.0,4921.0')] ).
cnf(114720,plain,
equal(domain_difference(u,v),forward_diamond(antidomain(v),u)),
inference(rew,[status(thm),theory(equality)],[4870,114462]),
[iquote('0:Rew:4870.0,114462.0')] ).
cnf(116261,plain,
equal(addition(forward_diamond(antidomain(antidomain(u)),v),domain_difference(u,v)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[12,114466]),
[iquote('0:Rew:12.0,114466.0')] ).
cnf(116262,plain,
equal(addition(forward_diamond(antidomain(antidomain(u)),v),forward_diamond(antidomain(v),u)),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[114720,116261]),
[iquote('0:Rew:114720.0,116261.0')] ).
cnf(120266,plain,
equal(addition(forward_diamond(antidomain(antidomain(forward_diamond(skc3,skc4))),skc5),zero),antidomain(antidomain(forward_diamond(skc3,skc4)))),
inference(spr,[status(thm),theory(equality)],[27367,116262]),
[iquote('0:SpR:27367.0,116262.0')] ).
cnf(120473,plain,
equal(forward_diamond(forward_diamond(skc3,skc4),skc5),forward_diamond(skc3,skc4)),
inference(rew,[status(thm),theory(equality)],[66,120266,12,5039]),
[iquote('0:Rew:66.0,120266.0,12.0,120266.0,5039.0,120266.0')] ).
cnf(120703,plain,
leq(forward_diamond(skc3,skc4),antidomain(antidomain(skc5))),
inference(spr,[status(thm),theory(equality)],[120473,73062]),
[iquote('0:SpR:120473.0,73062.0')] ).
cnf(120716,plain,
$false,
inference(mrr,[status(thm)],[120703,5097]),
[iquote('0:MRR:120703.0,5097.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE097+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 15:54:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 63.94/64.12
% 63.94/64.12 SPASS V 3.9
% 63.94/64.12 SPASS beiseite: Proof found.
% 63.94/64.12 % SZS status Theorem
% 63.94/64.12 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 63.94/64.12 SPASS derived 78537 clauses, backtracked 0 clauses, performed 0 splits and kept 10538 clauses.
% 63.94/64.12 SPASS allocated 171494 KBytes.
% 63.94/64.12 SPASS spent 0:01:03.64 on the problem.
% 63.94/64.12 0:00:00.03 for the input.
% 63.94/64.12 0:00:00.03 for the FLOTTER CNF translation.
% 63.94/64.12 0:00:00.50 for inferences.
% 63.94/64.12 0:00:00.00 for the backtracking.
% 63.94/64.12 0:01:02.88 for the reduction.
% 63.94/64.12
% 63.94/64.12
% 63.94/64.12 Here is a proof with depth 17, length 241 :
% 63.94/64.12 % SZS output start Refutation
% See solution above
% 65.86/66.06 Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity right_annihilation left_annihilation domain1 domain4 codomain1 additive_commutativity domain3 codomain3 order domain_difference forward_diamond goals additive_associativity multiplicative_associativity right_distributivity left_distributivity domain2 codomain2
% 65.86/66.06
%------------------------------------------------------------------------------