TSTP Solution File: GRP701-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP701-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 : Sat Jul 16 11:49:02 EDT 2022
% Result : Unsatisfiable 215.62s 215.81s
% Output : Refutation 216.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 11
% Syntax : Number of clauses : 414 ( 414 unt; 0 nHn; 414 RR)
% Number of literals : 414 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP701-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP701-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP701-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP701-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP701-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP701-1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(mult(u,v),u),mult(u,w)),mult(u,mult(mult(mult(v,u),u),w))),
file('GRP701-1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(mult(u,mult(v,mult(v,w))),v),mult(mult(u,v),mult(v,mult(w,v)))),
file('GRP701-1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(u,i(u)),unit),
file('GRP701-1.p',unknown),
[] ).
cnf(10,axiom,
equal(mult(i(u),u),unit),
file('GRP701-1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(mult(a,i(mult(b,a))),i(b)),
file('GRP701-1.p',unknown),
[] ).
cnf(23,plain,
equal(rd(u,u),unit),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(24,plain,
equal(rd(unit,u),i(u)),
inference(spr,[status(thm),theory(equality)],[10,4]),
[iquote('0:SpR:10.0,4.0')] ).
cnf(26,plain,
equal(rd(unit,i(u)),u),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(27,plain,
equal(i(i(u)),u),
inference(rew,[status(thm),theory(equality)],[24,26]),
[iquote('0:Rew:24.0,26.0')] ).
cnf(52,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(59,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(91,plain,
equal(ld(mult(mult(u,v),u),mult(u,mult(mult(mult(v,u),u),w))),mult(u,w)),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(96,plain,
equal(mult(i(u),mult(mult(mult(v,i(u)),i(u)),u)),mult(mult(mult(i(u),v),i(u)),unit)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(97,plain,
equal(mult(u,mult(mult(mult(v,u),u),unit)),mult(mult(mult(u,v),u),u)),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(98,plain,
equal(mult(u,mult(mult(mult(v,u),u),i(u))),mult(mult(mult(u,v),u),unit)),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(99,plain,
equal(mult(u,mult(mult(mult(v,u),u),ld(u,w))),mult(mult(mult(u,v),u),w)),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(103,plain,
equal(mult(u,mult(mult(mult(unit,u),u),v)),mult(mult(u,u),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(105,plain,
equal(mult(u,mult(mult(mult(ld(u,v),u),u),w)),mult(mult(v,u),mult(u,w))),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(109,plain,
equal(mult(mult(mult(u,v),u),u),mult(u,mult(mult(v,u),u))),
inference(rew,[status(thm),theory(equality)],[5,97]),
[iquote('0:Rew:5.0,97.0')] ).
cnf(111,plain,
equal(mult(mult(u,u),mult(u,v)),mult(u,mult(mult(u,u),v))),
inference(rew,[status(thm),theory(equality)],[6,103]),
[iquote('0:Rew:6.0,103.0')] ).
cnf(113,plain,
equal(mult(u,mult(mult(mult(v,u),u),i(u))),mult(mult(u,v),u)),
inference(rew,[status(thm),theory(equality)],[5,98]),
[iquote('0:Rew:5.0,98.0')] ).
cnf(116,plain,
equal(mult(i(u),mult(mult(mult(v,i(u)),i(u)),u)),mult(mult(i(u),v),i(u))),
inference(rew,[status(thm),theory(equality)],[5,96]),
[iquote('0:Rew:5.0,96.0')] ).
cnf(118,plain,
equal(rd(mult(u,mult(mult(v,u),u)),u),mult(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[109,4]),
[iquote('0:SpR:109.0,4.0')] ).
cnf(119,plain,
equal(ld(mult(mult(u,v),u),mult(u,mult(mult(v,u),u))),u),
inference(spr,[status(thm),theory(equality)],[109,2]),
[iquote('0:SpR:109.0,2.0')] ).
cnf(126,plain,
equal(mult(u,mult(mult(unit,u),u)),mult(mult(u,u),u)),
inference(spr,[status(thm),theory(equality)],[5,109]),
[iquote('0:SpR:5.0,109.0')] ).
cnf(128,plain,
equal(mult(u,mult(mult(ld(u,v),u),u)),mult(mult(v,u),u)),
inference(spr,[status(thm),theory(equality)],[1,109]),
[iquote('0:SpR:1.0,109.0')] ).
cnf(134,plain,
equal(mult(mult(u,u),u),mult(u,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[6,126]),
[iquote('0:Rew:6.0,126.0')] ).
cnf(172,plain,
equal(rd(mult(mult(u,v),mult(v,mult(w,v))),v),mult(u,mult(v,mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(173,plain,
equal(ld(mult(u,mult(v,mult(v,w))),mult(mult(u,v),mult(v,mult(w,v)))),v),
inference(spr,[status(thm),theory(equality)],[8,2]),
[iquote('0:SpR:8.0,2.0')] ).
cnf(183,plain,
equal(mult(mult(u,v),mult(v,mult(unit,v))),mult(mult(u,mult(v,v)),v)),
inference(spr,[status(thm),theory(equality)],[5,8]),
[iquote('0:SpR:5.0,8.0')] ).
cnf(185,plain,
equal(mult(mult(u,v),mult(v,mult(ld(v,w),v))),mult(mult(u,mult(v,w)),v)),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(186,plain,
equal(mult(mult(u,rd(v,w)),mult(rd(v,w),mult(w,rd(v,w)))),mult(mult(u,mult(rd(v,w),v)),rd(v,w))),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(190,plain,
equal(mult(mult(unit,u),mult(u,mult(v,u))),mult(mult(u,mult(u,v)),u)),
inference(spr,[status(thm),theory(equality)],[6,8]),
[iquote('0:SpR:6.0,8.0')] ).
cnf(191,plain,
equal(mult(mult(i(mult(u,mult(u,v))),u),mult(u,mult(v,u))),mult(unit,u)),
inference(spr,[status(thm),theory(equality)],[10,8]),
[iquote('0:SpR:10.0,8.0')] ).
cnf(198,plain,
equal(mult(mult(u,mult(v,v)),v),mult(mult(u,v),mult(v,v))),
inference(rew,[status(thm),theory(equality)],[6,183]),
[iquote('0:Rew:6.0,183.0')] ).
cnf(204,plain,
equal(mult(mult(u,mult(u,v)),u),mult(u,mult(u,mult(v,u)))),
inference(rew,[status(thm),theory(equality)],[6,190]),
[iquote('0:Rew:6.0,190.0')] ).
cnf(206,plain,
equal(mult(mult(i(mult(u,mult(u,v))),u),mult(u,mult(v,u))),u),
inference(rew,[status(thm),theory(equality)],[6,191]),
[iquote('0:Rew:6.0,191.0')] ).
cnf(237,plain,
equal(mult(u,mult(mult(u,u),i(u))),mult(mult(u,u),unit)),
inference(spr,[status(thm),theory(equality)],[9,111]),
[iquote('0:SpR:9.0,111.0')] ).
cnf(238,plain,
equal(mult(u,mult(mult(u,u),ld(u,v))),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[1,111]),
[iquote('0:SpR:1.0,111.0')] ).
cnf(246,plain,
equal(mult(u,mult(mult(u,u),i(u))),mult(u,u)),
inference(rew,[status(thm),theory(equality)],[5,237]),
[iquote('0:Rew:5.0,237.0')] ).
cnf(259,plain,
equal(mult(mult(u,u),i(u)),ld(u,mult(u,u))),
inference(spr,[status(thm),theory(equality)],[246,2]),
[iquote('0:SpR:246.0,2.0')] ).
cnf(275,plain,
equal(mult(mult(u,u),i(u)),u),
inference(rew,[status(thm),theory(equality)],[2,259]),
[iquote('0:Rew:2.0,259.0')] ).
cnf(291,plain,
equal(rd(u,i(u)),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[275,4]),
[iquote('0:SpR:275.0,4.0')] ).
cnf(319,plain,
equal(mult(i(u),i(u)),rd(i(u),u)),
inference(spr,[status(thm),theory(equality)],[27,291]),
[iquote('0:SpR:27.0,291.0')] ).
cnf(340,plain,
equal(mult(mult(i(mult(u,u)),u),mult(u,u)),mult(unit,u)),
inference(spr,[status(thm),theory(equality)],[10,198]),
[iquote('0:SpR:10.0,198.0')] ).
cnf(349,plain,
equal(mult(mult(i(mult(u,u)),u),mult(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,340]),
[iquote('0:Rew:6.0,340.0')] ).
cnf(456,plain,
equal(mult(u,mult(u,mult(ld(u,v),u))),mult(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[1,204]),
[iquote('0:SpR:1.0,204.0')] ).
cnf(500,plain,
equal(mult(i(mult(u,u)),u),rd(u,mult(u,u))),
inference(spr,[status(thm),theory(equality)],[349,4]),
[iquote('0:SpR:349.0,4.0')] ).
cnf(536,plain,
equal(rd(rd(u,mult(u,u)),u),i(mult(u,u))),
inference(spr,[status(thm),theory(equality)],[500,4]),
[iquote('0:SpR:500.0,4.0')] ).
cnf(614,plain,
equal(mult(i(u),mult(mult(u,i(u)),i(i(u)))),mult(mult(i(u),mult(u,u)),i(u))),
inference(spr,[status(thm),theory(equality)],[275,113]),
[iquote('0:SpR:275.0,113.0')] ).
cnf(631,plain,
equal(mult(mult(i(u),mult(u,u)),i(u)),unit),
inference(rew,[status(thm),theory(equality)],[10,614,6,9,27]),
[iquote('0:Rew:10.0,614.0,6.0,614.0,9.0,614.0,27.0,614.0')] ).
cnf(659,plain,
equal(mult(i(u),mult(u,u)),rd(unit,i(u))),
inference(spr,[status(thm),theory(equality)],[631,4]),
[iquote('0:SpR:631.0,4.0')] ).
cnf(680,plain,
equal(mult(i(u),mult(u,u)),u),
inference(rew,[status(thm),theory(equality)],[27,659,24]),
[iquote('0:Rew:27.0,659.0,24.0,659.0')] ).
cnf(715,plain,
equal(rd(u,mult(u,u)),i(u)),
inference(spr,[status(thm),theory(equality)],[680,4]),
[iquote('0:SpR:680.0,4.0')] ).
cnf(730,plain,
equal(mult(u,mult(i(u),i(u))),i(u)),
inference(spr,[status(thm),theory(equality)],[27,680]),
[iquote('0:SpR:27.0,680.0')] ).
cnf(732,plain,
equal(mult(i(mult(u,u)),u),i(u)),
inference(rew,[status(thm),theory(equality)],[715,500]),
[iquote('0:Rew:715.0,500.0')] ).
cnf(733,plain,
equal(rd(i(u),u),i(mult(u,u))),
inference(rew,[status(thm),theory(equality)],[715,536]),
[iquote('0:Rew:715.0,536.0')] ).
cnf(742,plain,
equal(mult(i(u),i(u)),i(mult(u,u))),
inference(rew,[status(thm),theory(equality)],[733,319]),
[iquote('0:Rew:733.0,319.0')] ).
cnf(759,plain,
equal(mult(u,i(mult(u,u))),i(u)),
inference(rew,[status(thm),theory(equality)],[742,730]),
[iquote('0:Rew:742.0,730.0')] ).
cnf(814,plain,
equal(mult(i(mult(u,mult(u,v))),u),rd(u,mult(u,mult(v,u)))),
inference(spr,[status(thm),theory(equality)],[206,4]),
[iquote('0:SpR:206.0,4.0')] ).
cnf(1208,plain,
equal(ld(mult(mult(u,v),u),mult(u,unit)),mult(u,i(mult(mult(v,u),u)))),
inference(spr,[status(thm),theory(equality)],[9,91]),
[iquote('0:SpR:9.0,91.0')] ).
cnf(1249,plain,
equal(mult(u,i(mult(mult(v,u),u))),ld(mult(mult(u,v),u),u)),
inference(rew,[status(thm),theory(equality)],[5,1208]),
[iquote('0:Rew:5.0,1208.0')] ).
cnf(1379,plain,
equal(mult(mult(mult(u,v),v),ld(v,w)),ld(v,mult(mult(mult(v,u),v),w))),
inference(spr,[status(thm),theory(equality)],[99,2]),
[iquote('0:SpR:99.0,2.0')] ).
cnf(1412,plain,
equal(mult(mult(mult(u,rd(v,u)),u),w),mult(u,mult(mult(v,u),ld(u,w)))),
inference(spr,[status(thm),theory(equality)],[3,99]),
[iquote('0:SpR:3.0,99.0')] ).
cnf(1478,plain,
equal(rd(mult(u,mult(v,u)),u),mult(mult(u,rd(v,u)),u)),
inference(spr,[status(thm),theory(equality)],[3,118]),
[iquote('0:SpR:3.0,118.0')] ).
cnf(1631,plain,
equal(mult(mult(ld(u,v),u),u),ld(u,mult(mult(v,u),u))),
inference(spr,[status(thm),theory(equality)],[128,2]),
[iquote('0:SpR:128.0,2.0')] ).
cnf(1666,plain,
equal(mult(u,mult(ld(u,mult(mult(v,u),u)),w)),mult(mult(v,u),mult(u,w))),
inference(rew,[status(thm),theory(equality)],[1631,105]),
[iquote('0:Rew:1631.0,105.0')] ).
cnf(1748,plain,
equal(rd(mult(mult(u,v),mult(v,w)),v),mult(u,mult(v,mult(v,rd(w,v))))),
inference(spr,[status(thm),theory(equality)],[3,172]),
[iquote('0:SpR:3.0,172.0')] ).
cnf(1762,plain,
equal(rd(mult(unit,mult(u,mult(v,u))),u),mult(i(u),mult(u,mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[10,172]),
[iquote('0:SpR:10.0,172.0')] ).
cnf(1789,plain,
equal(mult(i(u),mult(u,mult(u,v))),rd(mult(u,mult(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[6,1762]),
[iquote('0:Rew:6.0,1762.0')] ).
cnf(1790,plain,
equal(mult(i(u),mult(u,mult(u,v))),mult(mult(u,rd(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[1478,1789]),
[iquote('0:Rew:1478.0,1789.0')] ).
cnf(1863,plain,
equal(mult(mult(u,u),ld(u,v)),ld(u,mult(mult(u,u),v))),
inference(spr,[status(thm),theory(equality)],[238,2]),
[iquote('0:SpR:238.0,2.0')] ).
cnf(2190,plain,
equal(ld(mult(u,mult(i(u),mult(i(u),v))),mult(unit,mult(i(u),mult(v,i(u))))),i(u)),
inference(spr,[status(thm),theory(equality)],[9,173]),
[iquote('0:SpR:9.0,173.0')] ).
cnf(2261,plain,
equal(ld(mult(u,mult(i(u),mult(i(u),v))),mult(i(u),mult(v,i(u)))),i(u)),
inference(rew,[status(thm),theory(equality)],[6,2190]),
[iquote('0:Rew:6.0,2190.0')] ).
cnf(2300,plain,
equal(mult(u,mult(ld(u,v),u)),ld(u,mult(mult(u,v),u))),
inference(spr,[status(thm),theory(equality)],[456,2]),
[iquote('0:SpR:456.0,2.0')] ).
cnf(2349,plain,
equal(mult(mult(u,v),ld(v,mult(mult(v,w),v))),mult(mult(u,mult(v,w)),v)),
inference(rew,[status(thm),theory(equality)],[2300,185]),
[iquote('0:Rew:2300.0,185.0')] ).
cnf(2438,plain,
equal(mult(mult(u,rd(i(mult(u,u)),u)),u),rd(mult(u,i(u)),u)),
inference(spr,[status(thm),theory(equality)],[732,1478]),
[iquote('0:SpR:732.0,1478.0')] ).
cnf(2445,plain,
equal(mult(mult(u,rd(rd(v,u),u)),u),rd(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[3,1478]),
[iquote('0:SpR:3.0,1478.0')] ).
cnf(2465,plain,
equal(mult(mult(u,rd(i(mult(u,u)),u)),u),i(u)),
inference(rew,[status(thm),theory(equality)],[24,2438,9]),
[iquote('0:Rew:24.0,2438.0,9.0,2438.0')] ).
cnf(2495,plain,
equal(mult(u,mult(mult(mult(rd(i(mult(u,u)),u),u),u),v)),mult(i(u),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[2465,7]),
[iquote('0:SpR:2465.0,7.0')] ).
cnf(2497,plain,
equal(ld(i(u),mult(u,mult(mult(mult(rd(i(mult(u,u)),u),u),u),v))),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[2465,91]),
[iquote('0:SpR:2465.0,91.0')] ).
cnf(2501,plain,
equal(mult(u,rd(i(mult(u,u)),u)),rd(i(u),u)),
inference(spr,[status(thm),theory(equality)],[2465,4]),
[iquote('0:SpR:2465.0,4.0')] ).
cnf(2531,plain,
equal(mult(u,rd(i(mult(u,u)),u)),i(mult(u,u))),
inference(rew,[status(thm),theory(equality)],[733,2501]),
[iquote('0:Rew:733.0,2501.0')] ).
cnf(2542,plain,
equal(ld(i(u),mult(u,mult(i(u),v))),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[732,2497,3]),
[iquote('0:Rew:732.0,2497.0,3.0,2497.0')] ).
cnf(2543,plain,
equal(mult(i(u),mult(u,v)),mult(u,mult(i(u),v))),
inference(rew,[status(thm),theory(equality)],[732,2495,3]),
[iquote('0:Rew:732.0,2495.0,3.0,2495.0')] ).
cnf(2545,plain,
equal(mult(u,mult(i(u),mult(u,v))),mult(mult(u,rd(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[2543,1790]),
[iquote('0:Rew:2543.0,1790.0')] ).
cnf(2548,plain,
equal(mult(u,mult(u,mult(i(u),v))),mult(mult(u,rd(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[2543,2545]),
[iquote('0:Rew:2543.0,2545.0')] ).
cnf(2620,plain,
equal(mult(mult(u,v),mult(v,mult(rd(i(mult(v,v)),v),v))),mult(mult(u,mult(v,i(mult(v,v)))),v)),
inference(spr,[status(thm),theory(equality)],[2531,8]),
[iquote('0:SpR:2531.0,8.0')] ).
cnf(2621,plain,
equal(ld(mult(u,mult(v,i(mult(v,v)))),mult(mult(u,v),mult(v,mult(rd(i(mult(v,v)),v),v)))),v),
inference(spr,[status(thm),theory(equality)],[2531,173]),
[iquote('0:SpR:2531.0,173.0')] ).
cnf(2644,plain,
equal(ld(mult(u,i(v)),mult(mult(u,v),i(v))),v),
inference(rew,[status(thm),theory(equality)],[759,2621,3]),
[iquote('0:Rew:759.0,2621.0,3.0,2621.0')] ).
cnf(2645,plain,
equal(mult(mult(u,i(v)),v),mult(mult(u,v),i(v))),
inference(rew,[status(thm),theory(equality)],[759,2620,3]),
[iquote('0:Rew:759.0,2620.0,3.0,2620.0,759.0,2620.0')] ).
cnf(2647,plain,
equal(mult(i(u),mult(mult(mult(v,i(u)),u),i(u))),mult(mult(i(u),v),i(u))),
inference(rew,[status(thm),theory(equality)],[2645,116]),
[iquote('0:Rew:2645.0,116.0')] ).
cnf(2648,plain,
equal(mult(i(u),mult(mult(mult(v,u),i(u)),i(u))),mult(mult(i(u),v),i(u))),
inference(rew,[status(thm),theory(equality)],[2645,2647]),
[iquote('0:Rew:2645.0,2647.0')] ).
cnf(2801,plain,
equal(mult(u,ld(i(u),v)),ld(i(u),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[1,2542]),
[iquote('0:SpR:1.0,2542.0')] ).
cnf(3027,plain,
equal(mult(mult(u,rd(ld(u,mult(mult(v,u),u)),u)),u),rd(mult(mult(v,u),mult(u,u)),u)),
inference(spr,[status(thm),theory(equality)],[1666,1478]),
[iquote('0:SpR:1666.0,1478.0')] ).
cnf(3042,plain,
equal(mult(u,mult(ld(u,mult(v,u)),w)),mult(v,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[3,1666]),
[iquote('0:SpR:3.0,1666.0')] ).
cnf(3076,plain,
equal(mult(mult(u,rd(ld(u,mult(mult(v,u),u)),u)),u),mult(v,mult(u,mult(u,rd(u,u))))),
inference(rew,[status(thm),theory(equality)],[1748,3027]),
[iquote('0:Rew:1748.0,3027.0')] ).
cnf(3077,plain,
equal(mult(mult(u,rd(ld(u,mult(mult(v,u),u)),u)),u),mult(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[5,3076,23]),
[iquote('0:Rew:5.0,3076.0,23.0,3076.0')] ).
cnf(3305,plain,
equal(mult(mult(u,v),ld(v,mult(w,v))),mult(mult(u,w),v)),
inference(spr,[status(thm),theory(equality)],[1,2349]),
[iquote('0:SpR:1.0,2349.0')] ).
cnf(3326,plain,
equal(mult(unit,ld(u,mult(mult(u,v),u))),mult(mult(i(u),mult(u,v)),u)),
inference(spr,[status(thm),theory(equality)],[10,2349]),
[iquote('0:SpR:10.0,2349.0')] ).
cnf(3331,plain,
equal(mult(unit,ld(i(u),mult(mult(i(u),v),i(u)))),mult(mult(u,mult(i(u),v)),i(u))),
inference(spr,[status(thm),theory(equality)],[9,2349]),
[iquote('0:SpR:9.0,2349.0')] ).
cnf(3337,plain,
equal(mult(i(mult(u,u)),ld(i(u),mult(mult(i(u),v),i(u)))),mult(mult(i(u),mult(i(u),v)),i(u))),
inference(spr,[status(thm),theory(equality)],[742,2349]),
[iquote('0:SpR:742.0,2349.0')] ).
cnf(3353,plain,
equal(mult(mult(u,mult(i(u),v)),u),ld(u,mult(mult(u,v),u))),
inference(rew,[status(thm),theory(equality)],[6,3326,2543]),
[iquote('0:Rew:6.0,3326.0,2543.0,3326.0')] ).
cnf(3355,plain,
equal(ld(i(u),mult(mult(i(u),v),i(u))),mult(mult(u,mult(i(u),v)),i(u))),
inference(rew,[status(thm),theory(equality)],[6,3331]),
[iquote('0:Rew:6.0,3331.0')] ).
cnf(3361,plain,
equal(mult(i(mult(u,u)),ld(i(u),mult(mult(i(u),v),i(u)))),mult(i(u),mult(i(u),mult(v,i(u))))),
inference(rew,[status(thm),theory(equality)],[204,3337]),
[iquote('0:Rew:204.0,3337.0')] ).
cnf(3362,plain,
equal(mult(i(mult(u,u)),mult(mult(u,mult(i(u),v)),i(u))),mult(i(u),mult(i(u),mult(v,i(u))))),
inference(rew,[status(thm),theory(equality)],[3355,3361]),
[iquote('0:Rew:3355.0,3361.0')] ).
cnf(3493,plain,
equal(rd(mult(mult(u,v),i(v)),v),mult(u,i(v))),
inference(spr,[status(thm),theory(equality)],[2644,59]),
[iquote('0:SpR:2644.0,59.0')] ).
cnf(3615,plain,
equal(mult(mult(i(u),rd(mult(mult(v,u),i(u)),i(u))),i(u)),rd(mult(mult(i(u),v),i(u)),i(u))),
inference(spr,[status(thm),theory(equality)],[2648,1478]),
[iquote('0:SpR:2648.0,1478.0')] ).
cnf(3633,plain,
equal(mult(i(u),mult(mult(v,i(u)),i(u))),mult(mult(i(u),rd(v,u)),i(u))),
inference(spr,[status(thm),theory(equality)],[3,2648]),
[iquote('0:SpR:3.0,2648.0')] ).
cnf(3680,plain,
equal(mult(mult(i(u),mult(v,u)),i(u)),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[4,3615]),
[iquote('0:Rew:4.0,3615.0,4.0,3615.0')] ).
cnf(3905,plain,
equal(mult(mult(rd(u,i(v)),v),i(v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[3,2645]),
[iquote('0:SpR:3.0,2645.0')] ).
cnf(4259,plain,
equal(ld(u,ld(i(u),mult(u,v))),ld(i(u),v)),
inference(spr,[status(thm),theory(equality)],[2801,2]),
[iquote('0:SpR:2801.0,2.0')] ).
cnf(4285,plain,
equal(mult(i(u),ld(u,v)),ld(u,mult(i(u),v))),
inference(spr,[status(thm),theory(equality)],[27,2801]),
[iquote('0:SpR:27.0,2801.0')] ).
cnf(4335,plain,
equal(rd(mult(u,i(v)),v),mult(rd(u,v),i(v))),
inference(spr,[status(thm),theory(equality)],[3,3493]),
[iquote('0:SpR:3.0,3493.0')] ).
cnf(4468,plain,
equal(ld(mult(mult(i(u),mult(rd(v,i(u)),u)),i(u)),mult(i(u),mult(mult(v,u),i(u)))),i(u)),
inference(spr,[status(thm),theory(equality)],[3905,119]),
[iquote('0:SpR:3905.0,119.0')] ).
cnf(4471,plain,
equal(rd(mult(u,v),i(v)),mult(rd(u,i(v)),v)),
inference(spr,[status(thm),theory(equality)],[3905,4]),
[iquote('0:SpR:3905.0,4.0')] ).
cnf(4542,plain,
equal(ld(mult(i(u),rd(v,i(u))),mult(i(u),mult(mult(v,u),i(u)))),i(u)),
inference(rew,[status(thm),theory(equality)],[3680,4468]),
[iquote('0:Rew:3680.0,4468.0')] ).
cnf(4880,plain,
equal(mult(mult(i(rd(u,v)),mult(rd(u,v),u)),rd(u,v)),mult(unit,mult(rd(u,v),mult(v,rd(u,v))))),
inference(spr,[status(thm),theory(equality)],[10,186]),
[iquote('0:SpR:10.0,186.0')] ).
cnf(4909,plain,
equal(mult(mult(rd(u,v),mult(i(rd(u,v)),u)),rd(u,v)),mult(rd(u,v),mult(v,rd(u,v)))),
inference(rew,[status(thm),theory(equality)],[2543,4880,6]),
[iquote('0:Rew:2543.0,4880.0,6.0,4880.0')] ).
cnf(4910,plain,
equal(ld(rd(u,v),mult(mult(rd(u,v),u),rd(u,v))),mult(rd(u,v),mult(v,rd(u,v)))),
inference(rew,[status(thm),theory(equality)],[3353,4909]),
[iquote('0:Rew:3353.0,4909.0')] ).
cnf(5456,plain,
equal(ld(i(u),ld(u,v)),ld(u,ld(i(u),v))),
inference(spr,[status(thm),theory(equality)],[1,4259]),
[iquote('0:SpR:1.0,4259.0')] ).
cnf(5665,plain,
equal(mult(rd(rd(u,i(v)),v),i(v)),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[3,4335]),
[iquote('0:SpR:3.0,4335.0')] ).
cnf(6110,plain,
equal(mult(rd(rd(u,v),i(v)),v),rd(u,i(v))),
inference(spr,[status(thm),theory(equality)],[3,4471]),
[iquote('0:SpR:3.0,4471.0')] ).
cnf(7024,plain,
equal(rd(rd(u,i(v)),v),rd(rd(u,v),i(v))),
inference(spr,[status(thm),theory(equality)],[5665,4]),
[iquote('0:SpR:5665.0,4.0')] ).
cnf(8352,plain,
equal(rd(mult(i(u),v),i(u)),mult(i(u),mult(v,u))),
inference(spr,[status(thm),theory(equality)],[3680,4]),
[iquote('0:SpR:3680.0,4.0')] ).
cnf(8380,plain,
equal(mult(rd(mult(i(u),mult(v,u)),u),i(u)),rd(mult(i(u),v),u)),
inference(spr,[status(thm),theory(equality)],[3680,4335]),
[iquote('0:SpR:3680.0,4335.0')] ).
cnf(8389,plain,
equal(mult(mult(u,mult(v,i(u))),u),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[27,3680]),
[iquote('0:SpR:27.0,3680.0')] ).
cnf(8394,plain,
equal(mult(mult(i(u),mult(u,mult(u,mult(v,u)))),i(u)),mult(i(u),mult(u,mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[204,3680]),
[iquote('0:SpR:204.0,3680.0')] ).
cnf(8400,plain,
equal(mult(mult(i(u),v),i(u)),mult(i(u),rd(v,u))),
inference(spr,[status(thm),theory(equality)],[3,3680]),
[iquote('0:SpR:3.0,3680.0')] ).
cnf(8411,plain,
equal(mult(mult(i(u),mult(u,mult(mult(v,u),u))),i(u)),mult(i(u),mult(mult(u,v),u))),
inference(spr,[status(thm),theory(equality)],[109,3680]),
[iquote('0:SpR:109.0,3680.0')] ).
cnf(8480,plain,
equal(mult(i(u),mult(mult(v,i(u)),i(u))),mult(i(u),rd(rd(v,u),u))),
inference(rew,[status(thm),theory(equality)],[8400,3633]),
[iquote('0:Rew:8400.0,3633.0')] ).
cnf(8484,plain,
equal(mult(mult(u,mult(i(u),v)),i(u)),ld(i(u),mult(i(u),rd(v,u)))),
inference(rew,[status(thm),theory(equality)],[8400,3355]),
[iquote('0:Rew:8400.0,3355.0')] ).
cnf(8515,plain,
equal(mult(mult(u,mult(i(u),v)),i(u)),rd(v,u)),
inference(rew,[status(thm),theory(equality)],[2,8484]),
[iquote('0:Rew:2.0,8484.0')] ).
cnf(8524,plain,
equal(mult(i(u),mult(i(u),mult(v,i(u)))),mult(i(mult(u,u)),rd(v,u))),
inference(rew,[status(thm),theory(equality)],[8515,3362]),
[iquote('0:Rew:8515.0,3362.0')] ).
cnf(8543,plain,
equal(mult(mult(u,mult(i(u),mult(mult(v,u),u))),i(u)),mult(i(u),mult(mult(u,v),u))),
inference(rew,[status(thm),theory(equality)],[2543,8411]),
[iquote('0:Rew:2543.0,8411.0')] ).
cnf(8544,plain,
equal(mult(i(u),mult(mult(u,v),u)),rd(mult(mult(v,u),u),u)),
inference(rew,[status(thm),theory(equality)],[8515,8543]),
[iquote('0:Rew:8515.0,8543.0')] ).
cnf(8545,plain,
equal(mult(i(u),mult(mult(u,v),u)),mult(v,u)),
inference(rew,[status(thm),theory(equality)],[4,8544]),
[iquote('0:Rew:4.0,8544.0')] ).
cnf(8554,plain,
equal(mult(mult(u,mult(u,mult(i(u),mult(v,u)))),i(u)),mult(u,mult(u,mult(i(u),v)))),
inference(rew,[status(thm),theory(equality)],[2543,8394]),
[iquote('0:Rew:2543.0,8394.0,2543.0,8394.0,2543.0,8394.0,2543.0,8394.0')] ).
cnf(8555,plain,
equal(mult(u,ld(u,mult(mult(mult(u,v),u),i(u)))),mult(mult(u,rd(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[1379,8554,1412,2548]),
[iquote('0:Rew:1379.0,8554.0,1412.0,8554.0,2548.0,8554.0,2548.0,8554.0')] ).
cnf(8556,plain,
equal(mult(mult(mult(u,v),u),i(u)),mult(mult(u,rd(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[1,8555]),
[iquote('0:Rew:1.0,8555.0')] ).
cnf(8773,plain,
equal(mult(u,mult(v,i(u))),rd(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[8389,4]),
[iquote('0:SpR:8389.0,4.0')] ).
cnf(8824,plain,
equal(mult(mult(u,mult(i(u),mult(i(u),mult(v,i(u))))),u),mult(u,mult(i(u),mult(i(u),v)))),
inference(spr,[status(thm),theory(equality)],[204,8389]),
[iquote('0:SpR:204.0,8389.0')] ).
cnf(8827,plain,
equal(mult(u,rd(v,i(u))),mult(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[3,8389]),
[iquote('0:SpR:3.0,8389.0')] ).
cnf(8837,plain,
equal(mult(mult(u,mult(i(u),mult(mult(v,i(u)),i(u)))),u),mult(u,mult(mult(i(u),v),i(u)))),
inference(spr,[status(thm),theory(equality)],[109,8389]),
[iquote('0:SpR:109.0,8389.0')] ).
cnf(8956,plain,
equal(mult(u,mult(i(u),rd(v,u))),ld(u,rd(mult(u,v),u))),
inference(rew,[status(thm),theory(equality)],[2445,8837,3353,8480,8400]),
[iquote('0:Rew:2445.0,8837.0,3353.0,8837.0,8480.0,8837.0,8400.0,8837.0')] ).
cnf(8959,plain,
equal(mult(mult(u,mult(i(mult(u,u)),rd(v,u))),u),mult(u,mult(i(u),mult(i(u),v)))),
inference(rew,[status(thm),theory(equality)],[8524,8824]),
[iquote('0:Rew:8524.0,8824.0')] ).
cnf(9047,plain,
equal(rd(mult(u,v),mult(mult(v,u),v)),i(v)),
inference(spr,[status(thm),theory(equality)],[8545,4]),
[iquote('0:SpR:8545.0,4.0')] ).
cnf(9048,plain,
equal(ld(i(u),mult(v,u)),mult(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[8545,2]),
[iquote('0:SpR:8545.0,2.0')] ).
cnf(9059,plain,
equal(mult(i(u),mult(i(u),mult(mult(mult(u,v),u),i(u)))),mult(mult(i(u),mult(v,u)),i(u))),
inference(spr,[status(thm),theory(equality)],[8545,204]),
[iquote('0:SpR:8545.0,204.0')] ).
cnf(9089,plain,
equal(mult(i(u),mult(v,u)),mult(ld(u,v),u)),
inference(spr,[status(thm),theory(equality)],[1,8545]),
[iquote('0:SpR:1.0,8545.0')] ).
cnf(9106,plain,
equal(mult(i(i(u)),mult(mult(u,mult(i(u),v)),i(u))),mult(mult(u,v),i(u))),
inference(spr,[status(thm),theory(equality)],[2543,8545]),
[iquote('0:SpR:2543.0,8545.0')] ).
cnf(9129,plain,
equal(mult(u,mult(mult(i(u),v),i(u))),mult(v,i(u))),
inference(spr,[status(thm),theory(equality)],[27,8545]),
[iquote('0:SpR:27.0,8545.0')] ).
cnf(9157,plain,
equal(rd(mult(i(u),v),i(u)),mult(ld(u,v),u)),
inference(rew,[status(thm),theory(equality)],[9089,8352]),
[iquote('0:Rew:9089.0,8352.0')] ).
cnf(9160,plain,
equal(mult(rd(mult(ld(u,v),u),u),i(u)),rd(mult(i(u),v),u)),
inference(rew,[status(thm),theory(equality)],[9089,8380]),
[iquote('0:Rew:9089.0,8380.0')] ).
cnf(9178,plain,
equal(ld(u,rd(mult(u,v),u)),mult(v,i(u))),
inference(rew,[status(thm),theory(equality)],[8956,9129,8400]),
[iquote('0:Rew:8956.0,9129.0,8400.0,9129.0')] ).
cnf(9194,plain,
equal(rd(mult(i(u),v),u),mult(ld(u,v),i(u))),
inference(rew,[status(thm),theory(equality)],[4,9160]),
[iquote('0:Rew:4.0,9160.0')] ).
cnf(9215,plain,
equal(mult(u,mult(mult(u,mult(i(u),v)),i(u))),mult(mult(u,v),i(u))),
inference(rew,[status(thm),theory(equality)],[27,9106]),
[iquote('0:Rew:27.0,9106.0')] ).
cnf(9216,plain,
equal(mult(mult(u,v),i(u)),mult(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[8515,9215]),
[iquote('0:Rew:8515.0,9215.0')] ).
cnf(9283,plain,
equal(mult(ld(u,ld(u,mult(u,rd(v,u)))),u),mult(mult(ld(u,v),u),i(u))),
inference(rew,[status(thm),theory(equality)],[9089,9059,8556]),
[iquote('0:Rew:9089.0,9059.0,9089.0,9059.0,8556.0,9059.0,9089.0,9059.0')] ).
cnf(9284,plain,
equal(mult(mult(ld(u,v),u),i(u)),mult(ld(u,rd(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[2,9283]),
[iquote('0:Rew:2.0,9283.0')] ).
cnf(9400,plain,
equal(ld(u,ld(i(u),rd(mult(u,v),u))),ld(i(u),mult(v,i(u)))),
inference(spr,[status(thm),theory(equality)],[8773,4259]),
[iquote('0:SpR:8773.0,4259.0')] ).
cnf(9452,plain,
equal(mult(u,mult(i(u),mult(i(u),mult(v,i(u))))),rd(mult(u,mult(i(u),mult(i(u),v))),u)),
inference(spr,[status(thm),theory(equality)],[204,8773]),
[iquote('0:SpR:204.0,8773.0')] ).
cnf(9526,plain,
equal(rd(mult(u,mult(i(u),mult(i(u),v))),u),mult(u,mult(i(mult(u,u)),rd(v,u)))),
inference(rew,[status(thm),theory(equality)],[8524,9452]),
[iquote('0:Rew:8524.0,9452.0')] ).
cnf(10025,plain,
equal(ld(u,mult(mult(u,v),u)),rd(v,i(u))),
inference(spr,[status(thm),theory(equality)],[8827,2]),
[iquote('0:SpR:8827.0,2.0')] ).
cnf(10041,plain,
equal(ld(u,ld(i(u),mult(mult(u,v),u))),ld(i(u),rd(v,i(u)))),
inference(spr,[status(thm),theory(equality)],[8827,4259]),
[iquote('0:SpR:8827.0,4259.0')] ).
cnf(10050,plain,
equal(ld(i(u),mult(u,mult(mult(i(u),v),i(u)))),mult(u,rd(v,i(i(u))))),
inference(spr,[status(thm),theory(equality)],[8827,2542]),
[iquote('0:SpR:8827.0,2542.0')] ).
cnf(10099,plain,
equal(mult(u,mult(ld(u,v),u)),rd(v,i(u))),
inference(rew,[status(thm),theory(equality)],[10025,2300]),
[iquote('0:Rew:10025.0,2300.0')] ).
cnf(10102,plain,
equal(mult(mult(u,mult(i(u),v)),u),rd(v,i(u))),
inference(rew,[status(thm),theory(equality)],[10025,3353]),
[iquote('0:Rew:10025.0,3353.0')] ).
cnf(10116,plain,
equal(mult(rd(u,v),mult(v,rd(u,v))),rd(u,i(rd(u,v)))),
inference(rew,[status(thm),theory(equality)],[10025,4910]),
[iquote('0:Rew:10025.0,4910.0')] ).
cnf(10187,plain,
equal(ld(i(u),rd(v,i(u))),rd(mult(u,v),i(u))),
inference(rew,[status(thm),theory(equality)],[10025,10041,9048]),
[iquote('0:Rew:10025.0,10041.0,9048.0,10041.0')] ).
cnf(10197,plain,
equal(ld(i(u),rd(mult(u,mult(i(u),v)),u)),mult(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[8773,10050,27]),
[iquote('0:Rew:8773.0,10050.0,27.0,10050.0')] ).
cnf(10444,plain,
equal(mult(mult(ld(u,v),u),ld(u,v)),ld(i(ld(u,v)),v)),
inference(spr,[status(thm),theory(equality)],[1,9048]),
[iquote('0:SpR:1.0,9048.0')] ).
cnf(10446,plain,
equal(mult(mult(u,rd(v,u)),u),ld(i(u),v)),
inference(spr,[status(thm),theory(equality)],[3,9048]),
[iquote('0:SpR:3.0,9048.0')] ).
cnf(10447,plain,
equal(mult(mult(u,rd(rd(v,u),i(u))),u),ld(i(u),rd(v,i(u)))),
inference(spr,[status(thm),theory(equality)],[6110,9048]),
[iquote('0:SpR:6110.0,9048.0')] ).
cnf(10474,plain,
equal(mult(mult(i(u),v),i(u)),ld(u,mult(v,i(u)))),
inference(spr,[status(thm),theory(equality)],[27,9048]),
[iquote('0:SpR:27.0,9048.0')] ).
cnf(10484,plain,
equal(rd(mult(u,mult(v,u)),u),ld(i(u),v)),
inference(rew,[status(thm),theory(equality)],[10446,1478]),
[iquote('0:Rew:10446.0,1478.0')] ).
cnf(10522,plain,
equal(ld(i(u),ld(u,mult(mult(v,u),u))),mult(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[10446,3077]),
[iquote('0:Rew:10446.0,3077.0')] ).
cnf(10524,plain,
equal(ld(i(u),rd(v,u)),rd(mult(u,v),u)),
inference(rew,[status(thm),theory(equality)],[10446,2445]),
[iquote('0:Rew:10446.0,2445.0')] ).
cnf(10529,plain,
equal(mult(u,mult(u,mult(i(u),v))),ld(i(u),v)),
inference(rew,[status(thm),theory(equality)],[10446,2548]),
[iquote('0:Rew:10446.0,2548.0')] ).
cnf(10546,plain,
equal(rd(mult(u,mult(u,mult(i(u),v))),u),mult(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[10524,10197]),
[iquote('0:Rew:10524.0,10197.0')] ).
cnf(10548,plain,
equal(ld(u,rd(mult(u,mult(u,v)),u)),ld(i(u),mult(v,i(u)))),
inference(rew,[status(thm),theory(equality)],[10524,9400]),
[iquote('0:Rew:10524.0,9400.0')] ).
cnf(10551,plain,
equal(mult(i(u),rd(v,u)),ld(u,mult(v,i(u)))),
inference(rew,[status(thm),theory(equality)],[8400,10474]),
[iquote('0:Rew:8400.0,10474.0')] ).
cnf(10613,plain,
equal(ld(u,mult(mult(u,mult(v,u)),u)),mult(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[9048,10522,5456]),
[iquote('0:Rew:9048.0,10522.0,5456.0,10522.0')] ).
cnf(10614,plain,
equal(rd(mult(u,v),i(v)),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[10025,10613]),
[iquote('0:Rew:10025.0,10613.0')] ).
cnf(10615,plain,
equal(mult(rd(u,i(v)),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[4471,10614]),
[iquote('0:Rew:4471.0,10614.0')] ).
cnf(10616,plain,
equal(mult(rd(u,v),mult(v,v)),rd(u,i(v))),
inference(rew,[status(thm),theory(equality)],[10615,6110]),
[iquote('0:Rew:10615.0,6110.0')] ).
cnf(10617,plain,
equal(mult(mult(u,mult(v,v)),i(v)),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[10615,3905]),
[iquote('0:Rew:10615.0,3905.0')] ).
cnf(10619,plain,
equal(rd(mult(u,v),i(v)),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[10615,4471]),
[iquote('0:Rew:10615.0,4471.0')] ).
cnf(10723,plain,
equal(rd(ld(i(u),v),u),mult(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[10529,10546]),
[iquote('0:Rew:10529.0,10546.0')] ).
cnf(10729,plain,
equal(ld(i(u),mult(v,i(u))),mult(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[9216,10548,9178]),
[iquote('0:Rew:9216.0,10548.0,9178.0,10548.0')] ).
cnf(10733,plain,
equal(ld(i(u),rd(v,i(u))),mult(u,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[3,10447,109,8827]),
[iquote('0:Rew:3.0,10447.0,109.0,10447.0,8827.0,10447.0')] ).
cnf(10734,plain,
equal(rd(mult(u,v),i(u)),mult(u,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[10187,10733]),
[iquote('0:Rew:10187.0,10733.0')] ).
cnf(10962,plain,
equal(mult(ld(u,rd(v,u)),u),mult(i(u),v)),
inference(spr,[status(thm),theory(equality)],[3,9089]),
[iquote('0:SpR:3.0,9089.0')] ).
cnf(10965,plain,
equal(mult(i(u),mult(mult(v,u),i(u))),mult(ld(u,mult(v,i(u))),u)),
inference(spr,[status(thm),theory(equality)],[2645,9089]),
[iquote('0:SpR:2645.0,9089.0')] ).
cnf(10996,plain,
equal(mult(mult(ld(u,v),u),i(u)),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[10962,9284]),
[iquote('0:Rew:10962.0,9284.0')] ).
cnf(11011,plain,
equal(ld(mult(i(u),rd(v,i(u))),mult(ld(u,mult(v,i(u))),u)),i(u)),
inference(rew,[status(thm),theory(equality)],[10965,4542]),
[iquote('0:Rew:10965.0,4542.0')] ).
cnf(11300,plain,
equal(ld(u,mult(i(u),rd(mult(u,v),u))),mult(i(u),mult(v,i(u)))),
inference(spr,[status(thm),theory(equality)],[9178,4285]),
[iquote('0:SpR:9178.0,4285.0')] ).
cnf(11318,plain,
equal(mult(ld(u,v),i(u)),ld(u,rd(v,u))),
inference(spr,[status(thm),theory(equality)],[1,9178]),
[iquote('0:SpR:1.0,9178.0')] ).
cnf(11386,plain,
equal(rd(mult(i(u),v),u),ld(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[11318,9194]),
[iquote('0:Rew:11318.0,9194.0')] ).
cnf(11395,plain,
equal(ld(u,ld(u,mult(u,rd(v,u)))),mult(i(u),mult(v,i(u)))),
inference(rew,[status(thm),theory(equality)],[9216,11300,10551]),
[iquote('0:Rew:9216.0,11300.0,10551.0,11300.0')] ).
cnf(11396,plain,
equal(mult(i(u),mult(v,i(u))),ld(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[2,11395]),
[iquote('0:Rew:2.0,11395.0')] ).
cnf(11398,plain,
equal(mult(ld(u,mult(v,i(u))),u),ld(u,rd(mult(v,u),u))),
inference(rew,[status(thm),theory(equality)],[11396,10965]),
[iquote('0:Rew:11396.0,10965.0')] ).
cnf(11420,plain,
equal(ld(mult(u,mult(i(u),mult(i(u),v))),ld(u,rd(v,u))),i(u)),
inference(rew,[status(thm),theory(equality)],[11396,2261]),
[iquote('0:Rew:11396.0,2261.0')] ).
cnf(11422,plain,
equal(mult(i(mult(u,u)),rd(v,u)),mult(i(u),ld(u,rd(v,u)))),
inference(rew,[status(thm),theory(equality)],[11396,8524]),
[iquote('0:Rew:11396.0,8524.0')] ).
cnf(11430,plain,
equal(mult(ld(u,mult(v,i(u))),u),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[4,11398]),
[iquote('0:Rew:4.0,11398.0')] ).
cnf(11437,plain,
equal(ld(mult(i(u),rd(v,i(u))),ld(u,v)),i(u)),
inference(rew,[status(thm),theory(equality)],[11430,11011]),
[iquote('0:Rew:11430.0,11011.0')] ).
cnf(11440,plain,
equal(mult(i(mult(u,u)),rd(v,u)),ld(u,mult(i(u),rd(v,u)))),
inference(rew,[status(thm),theory(equality)],[4285,11422]),
[iquote('0:Rew:4285.0,11422.0')] ).
cnf(11441,plain,
equal(mult(i(mult(u,u)),rd(v,u)),ld(u,ld(u,mult(v,i(u))))),
inference(rew,[status(thm),theory(equality)],[10551,11440]),
[iquote('0:Rew:10551.0,11440.0')] ).
cnf(11445,plain,
equal(mult(mult(u,ld(u,ld(u,mult(v,i(u))))),u),mult(u,mult(i(u),mult(i(u),v)))),
inference(rew,[status(thm),theory(equality)],[11441,8959]),
[iquote('0:Rew:11441.0,8959.0')] ).
cnf(11446,plain,
equal(rd(mult(u,mult(i(u),mult(i(u),v))),u),mult(u,ld(u,ld(u,mult(v,i(u)))))),
inference(rew,[status(thm),theory(equality)],[11441,9526]),
[iquote('0:Rew:11441.0,9526.0')] ).
cnf(11484,plain,
equal(mult(u,mult(i(u),mult(i(u),v))),mult(ld(u,mult(v,i(u))),u)),
inference(rew,[status(thm),theory(equality)],[1,11445]),
[iquote('0:Rew:1.0,11445.0')] ).
cnf(11485,plain,
equal(mult(u,mult(i(u),mult(i(u),v))),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[11430,11484]),
[iquote('0:Rew:11430.0,11484.0')] ).
cnf(11493,plain,
equal(ld(ld(u,v),ld(u,rd(v,u))),i(u)),
inference(rew,[status(thm),theory(equality)],[11485,11420]),
[iquote('0:Rew:11485.0,11420.0')] ).
cnf(11511,plain,
equal(rd(mult(u,mult(i(u),mult(i(u),v))),u),ld(u,mult(v,i(u)))),
inference(rew,[status(thm),theory(equality)],[1,11446]),
[iquote('0:Rew:1.0,11446.0')] ).
cnf(11512,plain,
equal(ld(u,mult(v,i(u))),rd(ld(u,v),u)),
inference(rew,[status(thm),theory(equality)],[11485,11511]),
[iquote('0:Rew:11485.0,11511.0')] ).
cnf(11529,plain,
equal(mult(i(u),rd(v,u)),rd(ld(u,v),u)),
inference(rew,[status(thm),theory(equality)],[11512,10551]),
[iquote('0:Rew:11512.0,10551.0')] ).
cnf(11674,plain,
equal(mult(i(u),rd(v,i(u))),mult(mult(i(u),v),u)),
inference(spr,[status(thm),theory(equality)],[27,9216]),
[iquote('0:SpR:27.0,9216.0')] ).
cnf(11683,plain,
equal(mult(u,rd(ld(u,v),u)),mult(v,i(u))),
inference(spr,[status(thm),theory(equality)],[1,9216]),
[iquote('0:SpR:1.0,9216.0')] ).
cnf(11726,plain,
equal(ld(mult(mult(i(u),v),u),ld(u,v)),i(u)),
inference(rew,[status(thm),theory(equality)],[11674,11437]),
[iquote('0:Rew:11674.0,11437.0')] ).
cnf(12896,plain,
equal(ld(u,mult(i(u),mult(mult(u,v),u))),mult(i(u),rd(v,i(u)))),
inference(spr,[status(thm),theory(equality)],[10025,4285]),
[iquote('0:SpR:10025.0,4285.0')] ).
cnf(12913,plain,
equal(rd(ld(u,v),i(u)),ld(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[1,10025]),
[iquote('0:SpR:1.0,10025.0')] ).
cnf(12978,plain,
equal(mult(i(u),rd(v,i(u))),ld(u,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[2,12896,9089]),
[iquote('0:Rew:2.0,12896.0,9089.0,12896.0')] ).
cnf(12979,plain,
equal(mult(mult(i(u),v),u),ld(u,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[11674,12978]),
[iquote('0:Rew:11674.0,12978.0')] ).
cnf(12986,plain,
equal(mult(i(u),rd(v,i(u))),ld(u,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[12979,11674]),
[iquote('0:Rew:12979.0,11674.0')] ).
cnf(12988,plain,
equal(ld(ld(u,mult(v,u)),ld(u,v)),i(u)),
inference(rew,[status(thm),theory(equality)],[12979,11726]),
[iquote('0:Rew:12979.0,11726.0')] ).
cnf(14238,plain,
equal(rd(rd(u,v),i(v)),ld(v,ld(i(v),u))),
inference(spr,[status(thm),theory(equality)],[10446,10025]),
[iquote('0:SpR:10446.0,10025.0')] ).
cnf(14336,plain,
equal(rd(rd(u,i(v)),v),ld(v,ld(i(v),u))),
inference(rew,[status(thm),theory(equality)],[14238,7024]),
[iquote('0:Rew:14238.0,7024.0')] ).
cnf(14558,plain,
equal(mult(mult(u,v),i(v)),ld(v,ld(i(v),u))),
inference(spr,[status(thm),theory(equality)],[10484,9178]),
[iquote('0:SpR:10484.0,9178.0')] ).
cnf(14620,plain,
equal(mult(mult(u,i(v)),v),ld(v,ld(i(v),u))),
inference(rew,[status(thm),theory(equality)],[14558,2645]),
[iquote('0:Rew:14558.0,2645.0')] ).
cnf(14674,plain,
equal(ld(u,ld(i(u),ld(u,v))),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[14558,10996]),
[iquote('0:Rew:14558.0,10996.0')] ).
cnf(14688,plain,
equal(ld(u,ld(u,ld(i(u),v))),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[5456,14674]),
[iquote('0:Rew:5456.0,14674.0')] ).
cnf(15646,plain,
equal(rd(mult(u,mult(v,v)),v),rd(u,i(v))),
inference(spr,[status(thm),theory(equality)],[10615,4]),
[iquote('0:SpR:10615.0,4.0')] ).
cnf(15706,plain,
equal(mult(u,mult(i(v),i(v))),mult(rd(u,v),i(v))),
inference(spr,[status(thm),theory(equality)],[27,10615]),
[iquote('0:SpR:27.0,10615.0')] ).
cnf(15707,plain,
equal(mult(mult(u,i(v)),mult(v,v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[4,10615]),
[iquote('0:SpR:4.0,10615.0')] ).
cnf(15726,plain,
equal(mult(rd(u,v),i(v)),mult(u,i(mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[742,15706]),
[iquote('0:Rew:742.0,15706.0')] ).
cnf(15728,plain,
equal(rd(mult(u,i(v)),v),mult(u,i(mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[15726,4335]),
[iquote('0:Rew:15726.0,4335.0')] ).
cnf(15873,plain,
equal(rd(rd(u,i(v)),mult(v,v)),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[10616,4]),
[iquote('0:SpR:10616.0,4.0')] ).
cnf(16104,plain,
equal(mult(mult(u,mult(v,mult(mult(v,v),v))),i(mult(v,v))),mult(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[111,10617]),
[iquote('0:SpR:111.0,10617.0')] ).
cnf(16219,plain,
equal(mult(mult(u,mult(v,mult(v,mult(v,v)))),i(mult(v,v))),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[134,16104]),
[iquote('0:Rew:134.0,16104.0')] ).
cnf(16652,plain,
equal(mult(mult(u,mult(v,v)),mult(i(v),i(v))),rd(mult(u,v),i(i(v)))),
inference(spr,[status(thm),theory(equality)],[10619,10616]),
[iquote('0:SpR:10619.0,10616.0')] ).
cnf(16726,plain,
equal(mult(mult(u,mult(v,v)),i(mult(v,v))),u),
inference(rew,[status(thm),theory(equality)],[742,16652,4,27]),
[iquote('0:Rew:742.0,16652.0,4.0,16652.0,27.0,16652.0')] ).
cnf(16727,plain,
equal(ld(mult(u,u),ld(i(mult(u,u)),v)),v),
inference(rew,[status(thm),theory(equality)],[14558,16726]),
[iquote('0:Rew:14558.0,16726.0')] ).
cnf(16975,plain,
equal(ld(mult(u,mult(v,u)),mult(u,v)),i(u)),
inference(spr,[status(thm),theory(equality)],[10734,52]),
[iquote('0:SpR:10734.0,52.0')] ).
cnf(17126,plain,
equal(rd(rd(u,i(v)),v),mult(v,mult(i(v),u))),
inference(spr,[status(thm),theory(equality)],[10102,4]),
[iquote('0:SpR:10102.0,4.0')] ).
cnf(17223,plain,
equal(mult(u,mult(i(u),v)),ld(u,ld(i(u),v))),
inference(rew,[status(thm),theory(equality)],[14336,17126]),
[iquote('0:Rew:14336.0,17126.0')] ).
cnf(17225,plain,
equal(mult(i(u),mult(u,v)),ld(u,ld(i(u),v))),
inference(rew,[status(thm),theory(equality)],[17223,2543]),
[iquote('0:Rew:17223.0,2543.0')] ).
cnf(17227,plain,
equal(mult(ld(u,ld(i(u),v)),u),rd(v,i(u))),
inference(rew,[status(thm),theory(equality)],[17223,10102]),
[iquote('0:Rew:17223.0,10102.0')] ).
cnf(18223,plain,
equal(rd(ld(i(i(u)),mult(i(u),v)),i(u)),mult(ld(u,ld(i(i(u)),v)),u)),
inference(spr,[status(thm),theory(equality)],[4259,17227]),
[iquote('0:SpR:4259.0,17227.0')] ).
cnf(18279,plain,
equal(rd(ld(u,mult(i(u),v)),i(u)),mult(ld(u,ld(u,v)),u)),
inference(rew,[status(thm),theory(equality)],[27,18223]),
[iquote('0:Rew:27.0,18223.0')] ).
cnf(18280,plain,
equal(mult(ld(u,ld(u,v)),u),ld(u,ld(u,mult(v,u)))),
inference(rew,[status(thm),theory(equality)],[12979,18279,12913]),
[iquote('0:Rew:12979.0,18279.0,12913.0,18279.0')] ).
cnf(19307,plain,
equal(mult(rd(u,v),mult(v,w)),mult(v,mult(ld(v,u),w))),
inference(spr,[status(thm),theory(equality)],[3,3042]),
[iquote('0:SpR:3.0,3042.0')] ).
cnf(19348,plain,
equal(mult(u,mult(v,i(ld(v,mult(u,v))))),mult(v,unit)),
inference(spr,[status(thm),theory(equality)],[9,3042]),
[iquote('0:SpR:9.0,3042.0')] ).
cnf(19365,plain,
equal(mult(u,mult(v,i(ld(v,mult(u,v))))),v),
inference(rew,[status(thm),theory(equality)],[5,19348]),
[iquote('0:Rew:5.0,19348.0')] ).
cnf(19388,plain,
equal(mult(u,mult(ld(u,v),rd(v,u))),rd(v,i(rd(v,u)))),
inference(rew,[status(thm),theory(equality)],[19307,10116]),
[iquote('0:Rew:19307.0,10116.0')] ).
cnf(21713,plain,
equal(rd(mult(u,mult(v,mult(mult(v,v),v))),mult(v,v)),rd(u,i(mult(v,v)))),
inference(spr,[status(thm),theory(equality)],[111,15646]),
[iquote('0:SpR:111.0,15646.0')] ).
cnf(21783,plain,
equal(rd(mult(u,mult(v,mult(v,mult(v,v)))),mult(v,v)),rd(u,i(mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[134,21713]),
[iquote('0:Rew:134.0,21713.0')] ).
cnf(21910,plain,
equal(mult(mult(u,rd(v,w)),w),mult(mult(u,w),ld(w,v))),
inference(spr,[status(thm),theory(equality)],[3,3305]),
[iquote('0:SpR:3.0,3305.0')] ).
cnf(22020,plain,
equal(mult(mult(u,u),ld(u,v)),ld(i(u),v)),
inference(rew,[status(thm),theory(equality)],[21910,10446]),
[iquote('0:Rew:21910.0,10446.0')] ).
cnf(22067,plain,
equal(ld(u,mult(mult(u,u),v)),ld(i(u),v)),
inference(rew,[status(thm),theory(equality)],[1863,22020]),
[iquote('0:Rew:1863.0,22020.0')] ).
cnf(22068,plain,
equal(mult(mult(u,u),ld(u,v)),ld(i(u),v)),
inference(rew,[status(thm),theory(equality)],[22067,1863]),
[iquote('0:Rew:22067.0,1863.0')] ).
cnf(22695,plain,
equal(rd(mult(u,i(v)),v),rd(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[4,15873]),
[iquote('0:SpR:4.0,15873.0')] ).
cnf(22720,plain,
equal(mult(u,i(mult(v,v))),rd(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[15728,22695]),
[iquote('0:Rew:15728.0,22695.0')] ).
cnf(22735,plain,
equal(rd(mult(u,mult(v,mult(v,mult(v,v)))),mult(v,v)),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[22720,16219]),
[iquote('0:Rew:22720.0,16219.0')] ).
cnf(22849,plain,
equal(rd(u,i(mult(v,v))),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[21783,22735]),
[iquote('0:Rew:21783.0,22735.0')] ).
cnf(24125,plain,
equal(ld(u,ld(mult(v,v),rd(ld(i(mult(v,v)),u),mult(v,v)))),i(mult(v,v))),
inference(spr,[status(thm),theory(equality)],[16727,11493]),
[iquote('0:SpR:16727.0,11493.0')] ).
cnf(24142,plain,
equal(mult(i(mult(u,u)),v),ld(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[2,16727]),
[iquote('0:SpR:2.0,16727.0')] ).
cnf(24330,plain,
equal(ld(u,rd(u,mult(v,v))),i(mult(v,v))),
inference(rew,[status(thm),theory(equality)],[2,24125,10723]),
[iquote('0:Rew:2.0,24125.0,10723.0,24125.0')] ).
cnf(24770,plain,
equal(rd(u,mult(u,mult(ld(u,v),u))),mult(i(mult(u,v)),u)),
inference(spr,[status(thm),theory(equality)],[1,814]),
[iquote('0:SpR:1.0,814.0')] ).
cnf(24798,plain,
equal(rd(i(u),mult(i(u),mult(mult(v,u),i(u)))),mult(i(mult(i(u),mult(ld(u,v),u))),i(u))),
inference(spr,[status(thm),theory(equality)],[9089,814]),
[iquote('0:SpR:9089.0,814.0')] ).
cnf(24805,plain,
equal(rd(u,mult(u,mult(rd(ld(u,v),u),u))),mult(i(mult(u,mult(v,i(u)))),u)),
inference(spr,[status(thm),theory(equality)],[11683,814]),
[iquote('0:SpR:11683.0,814.0')] ).
cnf(24816,plain,
equal(rd(u,rd(v,i(u))),mult(i(mult(u,v)),u)),
inference(rew,[status(thm),theory(equality)],[10099,24770]),
[iquote('0:Rew:10099.0,24770.0')] ).
cnf(24825,plain,
equal(mult(i(rd(mult(u,v),u)),u),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[1,24805,3,8773]),
[iquote('0:Rew:1.0,24805.0,3.0,24805.0,8773.0,24805.0')] ).
cnf(24845,plain,
equal(rd(i(u),mult(i(u),mult(mult(v,u),i(u)))),mult(i(mult(ld(u,ld(u,v)),u)),i(u))),
inference(rew,[status(thm),theory(equality)],[9089,24798]),
[iquote('0:Rew:9089.0,24798.0')] ).
cnf(24846,plain,
equal(rd(i(u),mult(i(u),ld(u,ld(i(u),v)))),mult(i(ld(u,ld(u,mult(v,u)))),i(u))),
inference(rew,[status(thm),theory(equality)],[14558,24845,18280]),
[iquote('0:Rew:14558.0,24845.0,18280.0,24845.0')] ).
cnf(24847,plain,
equal(mult(i(ld(u,ld(u,mult(v,u)))),i(u)),rd(i(u),ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1,24846,4285]),
[iquote('0:Rew:1.0,24846.0,4285.0,24846.0')] ).
cnf(25457,plain,
equal(mult(u,i(ld(u,mult(v,u)))),ld(v,u)),
inference(spr,[status(thm),theory(equality)],[19365,2]),
[iquote('0:SpR:19365.0,2.0')] ).
cnf(25469,plain,
equal(mult(u,mult(mult(u,u),mult(v,i(ld(v,mult(u,v)))))),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[19365,111]),
[iquote('0:SpR:19365.0,111.0')] ).
cnf(25671,plain,
equal(mult(u,ld(i(u),v)),mult(mult(u,u),v)),
inference(rew,[status(thm),theory(equality)],[22068,25469,25457]),
[iquote('0:Rew:22068.0,25469.0,25457.0,25469.0')] ).
cnf(25672,plain,
equal(ld(i(u),mult(u,v)),mult(mult(u,u),v)),
inference(rew,[status(thm),theory(equality)],[2801,25671]),
[iquote('0:Rew:2801.0,25671.0')] ).
cnf(25971,plain,
equal(ld(mult(mult(u,rd(v,u)),u),u),mult(u,i(mult(v,u)))),
inference(spr,[status(thm),theory(equality)],[3,1249]),
[iquote('0:SpR:3.0,1249.0')] ).
cnf(26017,plain,
equal(mult(u,i(mult(v,u))),ld(ld(i(u),v),u)),
inference(rew,[status(thm),theory(equality)],[22068,25971,21910]),
[iquote('0:Rew:22068.0,25971.0,21910.0,25971.0')] ).
cnf(26020,plain,
~ equal(ld(ld(i(a),b),a),i(b)),
inference(rew,[status(thm),theory(equality)],[26017,11]),
[iquote('0:Rew:26017.0,11.0')] ).
cnf(27203,plain,
equal(mult(mult(rd(u,v),rd(u,v)),v),ld(i(rd(u,v)),u)),
inference(spr,[status(thm),theory(equality)],[52,22068]),
[iquote('0:SpR:52.0,22068.0')] ).
cnf(27248,plain,
equal(mult(mult(rd(u,v),v),ld(v,u)),ld(i(rd(u,v)),u)),
inference(rew,[status(thm),theory(equality)],[21910,27203]),
[iquote('0:Rew:21910.0,27203.0')] ).
cnf(27249,plain,
equal(ld(i(rd(u,v)),u),mult(u,ld(v,u))),
inference(rew,[status(thm),theory(equality)],[3,27248]),
[iquote('0:Rew:3.0,27248.0')] ).
cnf(30677,plain,
equal(i(rd(mult(u,v),u)),rd(rd(u,v),u)),
inference(spr,[status(thm),theory(equality)],[24825,4]),
[iquote('0:SpR:24825.0,4.0')] ).
cnf(30706,plain,
equal(ld(mult(i(rd(mult(u,v),u)),mult(u,i(rd(mult(u,v),u)))),rd(u,v)),i(i(rd(mult(u,v),u)))),
inference(spr,[status(thm),theory(equality)],[24825,16975]),
[iquote('0:SpR:24825.0,16975.0')] ).
cnf(30720,plain,
equal(rd(mult(u,i(rd(mult(i(u),v),i(u)))),u),mult(u,rd(i(u),v))),
inference(spr,[status(thm),theory(equality)],[24825,8773]),
[iquote('0:SpR:24825.0,8773.0')] ).
cnf(30764,plain,
equal(mult(i(rd(u,v)),v),rd(v,ld(v,u))),
inference(spr,[status(thm),theory(equality)],[1,24825]),
[iquote('0:SpR:1.0,24825.0')] ).
cnf(30800,plain,
equal(mult(i(rd(rd(ld(u,v),u),i(u))),i(u)),rd(i(u),rd(v,u))),
inference(spr,[status(thm),theory(equality)],[11529,24825]),
[iquote('0:SpR:11529.0,24825.0')] ).
cnf(30874,plain,
equal(rd(ld(ld(i(u),ld(u,v)),u),u),mult(u,rd(i(u),v))),
inference(rew,[status(thm),theory(equality)],[26017,30720,9157]),
[iquote('0:Rew:26017.0,30720.0,9157.0,30720.0')] ).
cnf(30875,plain,
equal(rd(ld(ld(u,ld(i(u),v)),u),u),mult(u,rd(i(u),v))),
inference(rew,[status(thm),theory(equality)],[5456,30874]),
[iquote('0:Rew:5456.0,30874.0')] ).
cnf(30890,plain,
equal(mult(i(ld(u,ld(i(u),ld(u,v)))),i(u)),rd(i(u),rd(v,u))),
inference(rew,[status(thm),theory(equality)],[14238,30800]),
[iquote('0:Rew:14238.0,30800.0')] ).
cnf(30891,plain,
equal(mult(i(ld(u,ld(u,ld(i(u),v)))),i(u)),rd(i(u),rd(v,u))),
inference(rew,[status(thm),theory(equality)],[5456,30890]),
[iquote('0:Rew:5456.0,30890.0')] ).
cnf(30892,plain,
equal(mult(i(mult(i(u),v)),i(u)),rd(i(u),rd(v,u))),
inference(rew,[status(thm),theory(equality)],[14688,30891]),
[iquote('0:Rew:14688.0,30891.0')] ).
cnf(30950,plain,
equal(ld(mult(i(rd(mult(u,v),u)),mult(u,i(rd(mult(u,v),u)))),rd(u,v)),rd(mult(u,v),u)),
inference(rew,[status(thm),theory(equality)],[27,30706]),
[iquote('0:Rew:27.0,30706.0')] ).
cnf(30951,plain,
equal(ld(rd(rd(u,v),i(rd(rd(u,v),u))),rd(u,v)),rd(mult(u,v),u)),
inference(rew,[status(thm),theory(equality)],[19388,30950,19307,30677]),
[iquote('0:Rew:19388.0,30950.0,19307.0,30950.0,30677.0,30950.0')] ).
cnf(30952,plain,
equal(i(rd(rd(u,v),u)),rd(mult(u,v),u)),
inference(rew,[status(thm),theory(equality)],[52,30951]),
[iquote('0:Rew:52.0,30951.0')] ).
cnf(31074,plain,
equal(i(ld(u,mult(v,u))),ld(u,ld(v,u))),
inference(spr,[status(thm),theory(equality)],[25457,2]),
[iquote('0:SpR:25457.0,2.0')] ).
cnf(31091,plain,
equal(rd(ld(u,v),mult(mult(i(ld(v,mult(u,v))),v),i(ld(v,mult(u,v))))),i(i(ld(v,mult(u,v))))),
inference(spr,[status(thm),theory(equality)],[25457,9047]),
[iquote('0:SpR:25457.0,9047.0')] ).
cnf(31114,plain,
equal(ld(u,mult(i(ld(i(u),mult(v,i(u)))),u)),mult(ld(v,i(u)),u)),
inference(spr,[status(thm),theory(equality)],[25457,12979]),
[iquote('0:SpR:25457.0,12979.0')] ).
cnf(31159,plain,
equal(mult(u,i(ld(u,v))),ld(rd(v,u),u)),
inference(spr,[status(thm),theory(equality)],[3,25457]),
[iquote('0:SpR:3.0,25457.0')] ).
cnf(31367,plain,
equal(ld(u,mult(i(mult(u,rd(v,u))),u)),mult(ld(v,i(u)),u)),
inference(rew,[status(thm),theory(equality)],[10729,31114]),
[iquote('0:Rew:10729.0,31114.0')] ).
cnf(31487,plain,
equal(rd(ld(u,v),mult(mult(i(ld(v,mult(u,v))),v),i(ld(v,mult(u,v))))),ld(v,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[27,31091]),
[iquote('0:Rew:27.0,31091.0')] ).
cnf(31488,plain,
equal(rd(ld(u,v),ld(i(ld(v,ld(u,v))),ld(u,v))),ld(v,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[10444,31487,31074]),
[iquote('0:Rew:10444.0,31487.0,31074.0,31487.0')] ).
cnf(31489,plain,
equal(i(ld(u,ld(v,u))),ld(u,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[59,31488]),
[iquote('0:Rew:59.0,31488.0')] ).
cnf(31696,plain,
equal(mult(mult(i(u),i(u)),v),ld(u,mult(i(u),v))),
inference(spr,[status(thm),theory(equality)],[27,25672]),
[iquote('0:SpR:27.0,25672.0')] ).
cnf(31708,plain,
equal(ld(u,mult(i(u),v)),ld(mult(u,u),v)),
inference(rew,[status(thm),theory(equality)],[24142,31696,742]),
[iquote('0:Rew:24142.0,31696.0,742.0,31696.0')] ).
cnf(33648,plain,
equal(mult(u,ld(ld(v,u),u)),ld(i(v),u)),
inference(spr,[status(thm),theory(equality)],[59,27249]),
[iquote('0:SpR:59.0,27249.0')] ).
cnf(33883,plain,
equal(rd(rd(i(u),rd(v,u)),i(u)),i(rd(rd(ld(u,v),u),i(u)))),
inference(spr,[status(thm),theory(equality)],[11529,30677]),
[iquote('0:SpR:11529.0,30677.0')] ).
cnf(33916,plain,
equal(rd(rd(i(u),rd(v,u)),i(u)),i(ld(u,ld(i(u),ld(u,v))))),
inference(rew,[status(thm),theory(equality)],[14238,33883]),
[iquote('0:Rew:14238.0,33883.0')] ).
cnf(33917,plain,
equal(rd(rd(i(u),rd(v,u)),i(u)),i(ld(u,ld(u,ld(i(u),v))))),
inference(rew,[status(thm),theory(equality)],[5456,33916]),
[iquote('0:Rew:5456.0,33916.0')] ).
cnf(33918,plain,
equal(rd(rd(i(u),rd(v,u)),i(u)),i(mult(i(u),v))),
inference(rew,[status(thm),theory(equality)],[14688,33917]),
[iquote('0:Rew:14688.0,33917.0')] ).
cnf(34043,plain,
equal(mult(ld(u,i(rd(v,u))),u),mult(i(u),rd(u,ld(u,v)))),
inference(spr,[status(thm),theory(equality)],[30764,9089]),
[iquote('0:SpR:30764.0,9089.0')] ).
cnf(34046,plain,
equal(ld(ld(u,rd(u,ld(u,v))),ld(u,i(rd(v,u)))),i(u)),
inference(spr,[status(thm),theory(equality)],[30764,12988]),
[iquote('0:SpR:30764.0,12988.0')] ).
cnf(34129,plain,
equal(rd(u,ld(u,mult(v,u))),mult(i(v),u)),
inference(spr,[status(thm),theory(equality)],[4,30764]),
[iquote('0:SpR:4.0,30764.0')] ).
cnf(34149,plain,
equal(rd(u,ld(u,ld(i(u),v))),mult(i(mult(u,rd(v,u))),u)),
inference(spr,[status(thm),theory(equality)],[10723,30764]),
[iquote('0:SpR:10723.0,30764.0')] ).
cnf(34752,plain,
equal(rd(u,ld(u,rd(u,v))),mult(rd(mult(u,v),u),u)),
inference(spr,[status(thm),theory(equality)],[30952,30764]),
[iquote('0:SpR:30952.0,30764.0')] ).
cnf(34764,plain,
equal(rd(mult(u,ld(v,u)),u),i(rd(v,u))),
inference(spr,[status(thm),theory(equality)],[59,30952]),
[iquote('0:SpR:59.0,30952.0')] ).
cnf(34816,plain,
equal(rd(u,ld(u,rd(u,v))),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[3,34752]),
[iquote('0:Rew:3.0,34752.0')] ).
cnf(34934,plain,
equal(ld(mult(u,v),u),ld(u,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[34816,52]),
[iquote('0:SpR:34816.0,52.0')] ).
cnf(34965,plain,
equal(rd(u,ld(u,v)),mult(u,ld(v,u))),
inference(spr,[status(thm),theory(equality)],[59,34816]),
[iquote('0:SpR:59.0,34816.0')] ).
cnf(35090,plain,
equal(mult(i(mult(u,rd(v,u))),u),mult(u,ld(ld(i(u),v),u))),
inference(rew,[status(thm),theory(equality)],[34965,34149]),
[iquote('0:Rew:34965.0,34149.0')] ).
cnf(35108,plain,
equal(mult(u,ld(mult(v,u),u)),mult(i(v),u)),
inference(rew,[status(thm),theory(equality)],[34965,34129]),
[iquote('0:Rew:34965.0,34129.0')] ).
cnf(35121,plain,
equal(mult(ld(u,i(rd(v,u))),u),mult(i(u),mult(u,ld(v,u)))),
inference(rew,[status(thm),theory(equality)],[34965,34043]),
[iquote('0:Rew:34965.0,34043.0')] ).
cnf(35122,plain,
equal(ld(ld(u,mult(u,ld(v,u))),ld(u,i(rd(v,u)))),i(u)),
inference(rew,[status(thm),theory(equality)],[34965,34046]),
[iquote('0:Rew:34965.0,34046.0')] ).
cnf(35176,plain,
equal(ld(u,mult(u,ld(ld(i(u),v),u))),mult(ld(v,i(u)),u)),
inference(rew,[status(thm),theory(equality)],[35090,31367]),
[iquote('0:Rew:35090.0,31367.0')] ).
cnf(35182,plain,
equal(mult(ld(u,i(rd(v,u))),u),ld(u,ld(i(u),ld(v,u)))),
inference(rew,[status(thm),theory(equality)],[17225,35121]),
[iquote('0:Rew:17225.0,35121.0')] ).
cnf(35183,plain,
equal(ld(ld(u,v),ld(v,i(rd(u,v)))),i(v)),
inference(rew,[status(thm),theory(equality)],[2,35122]),
[iquote('0:Rew:2.0,35122.0')] ).
cnf(35198,plain,
equal(mult(ld(u,i(v)),v),ld(ld(i(v),u),v)),
inference(rew,[status(thm),theory(equality)],[2,35176]),
[iquote('0:Rew:2.0,35176.0')] ).
cnf(36787,plain,
equal(ld(u,ld(ld(u,rd(v,u)),u)),i(ld(u,mult(i(u),v)))),
inference(spr,[status(thm),theory(equality)],[10962,31074]),
[iquote('0:SpR:10962.0,31074.0')] ).
cnf(36794,plain,
equal(ld(u,ld(rd(v,u),u)),i(ld(u,v))),
inference(spr,[status(thm),theory(equality)],[3,31074]),
[iquote('0:SpR:3.0,31074.0')] ).
cnf(36867,plain,
equal(ld(u,ld(ld(u,rd(v,u)),u)),i(ld(mult(u,u),v))),
inference(rew,[status(thm),theory(equality)],[31708,36787]),
[iquote('0:Rew:31708.0,36787.0')] ).
cnf(37089,plain,
equal(ld(u,rd(ld(rd(v,u),u),u)),mult(i(ld(u,v)),i(u))),
inference(spr,[status(thm),theory(equality)],[31159,9178]),
[iquote('0:SpR:31159.0,9178.0')] ).
cnf(37784,plain,
equal(mult(u,ld(u,mult(v,u))),ld(rd(ld(v,u),u),u)),
inference(spr,[status(thm),theory(equality)],[31489,31159]),
[iquote('0:SpR:31489.0,31159.0')] ).
cnf(37818,plain,
equal(ld(u,mult(i(rd(u,v)),u)),i(ld(u,mult(u,ld(v,u))))),
inference(spr,[status(thm),theory(equality)],[27249,31489]),
[iquote('0:SpR:27249.0,31489.0')] ).
cnf(37852,plain,
equal(ld(rd(ld(u,v),v),v),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[1,37784]),
[iquote('0:Rew:1.0,37784.0')] ).
cnf(37872,plain,
equal(ld(u,mult(i(rd(u,v)),u)),i(ld(v,u))),
inference(rew,[status(thm),theory(equality)],[2,37818]),
[iquote('0:Rew:2.0,37818.0')] ).
cnf(37997,plain,
equal(rd(ld(u,v),v),rd(v,mult(u,v))),
inference(spr,[status(thm),theory(equality)],[37852,59]),
[iquote('0:SpR:37852.0,59.0')] ).
cnf(38015,plain,
equal(mult(rd(u,v),u),ld(rd(v,u),u)),
inference(spr,[status(thm),theory(equality)],[52,37852]),
[iquote('0:SpR:52.0,37852.0')] ).
cnf(38035,plain,
equal(ld(rd(mult(u,ld(v,u)),u),u),mult(i(rd(u,v)),u)),
inference(spr,[status(thm),theory(equality)],[27249,37852]),
[iquote('0:SpR:27249.0,37852.0')] ).
cnf(38066,plain,
equal(ld(u,rd(u,mult(rd(v,u),u))),mult(i(ld(u,v)),i(u))),
inference(rew,[status(thm),theory(equality)],[37997,37089]),
[iquote('0:Rew:37997.0,37089.0')] ).
cnf(38069,plain,
equal(rd(u,mult(ld(u,ld(i(u),v)),u)),mult(u,rd(i(u),v))),
inference(rew,[status(thm),theory(equality)],[37997,30875]),
[iquote('0:Rew:37997.0,30875.0')] ).
cnf(38156,plain,
equal(mult(i(rd(u,v)),u),ld(i(rd(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[34764,38035]),
[iquote('0:Rew:34764.0,38035.0')] ).
cnf(38158,plain,
equal(ld(u,ld(i(rd(v,u)),u)),i(ld(v,u))),
inference(rew,[status(thm),theory(equality)],[38156,37872]),
[iquote('0:Rew:38156.0,37872.0')] ).
cnf(38160,plain,
equal(mult(i(ld(u,v)),i(u)),ld(u,rd(u,v))),
inference(rew,[status(thm),theory(equality)],[3,38066]),
[iquote('0:Rew:3.0,38066.0')] ).
cnf(38166,plain,
equal(ld(u,rd(u,ld(u,mult(v,u)))),rd(i(u),ld(u,v))),
inference(rew,[status(thm),theory(equality)],[38160,24847]),
[iquote('0:Rew:38160.0,24847.0')] ).
cnf(38169,plain,
equal(rd(i(u),ld(u,v)),ld(mult(v,u),u)),
inference(rew,[status(thm),theory(equality)],[2,38166,34965]),
[iquote('0:Rew:2.0,38166.0,34965.0,38166.0')] ).
cnf(38188,plain,
equal(rd(u,rd(v,i(u))),mult(u,rd(i(u),v))),
inference(rew,[status(thm),theory(equality)],[17227,38069]),
[iquote('0:Rew:17227.0,38069.0')] ).
cnf(38189,plain,
equal(mult(i(mult(u,v)),u),mult(u,rd(i(u),v))),
inference(rew,[status(thm),theory(equality)],[24816,38188]),
[iquote('0:Rew:24816.0,38188.0')] ).
cnf(38190,plain,
equal(mult(u,rd(i(u),mult(u,v))),rd(u,mult(u,mult(v,u)))),
inference(rew,[status(thm),theory(equality)],[38189,814]),
[iquote('0:Rew:38189.0,814.0')] ).
cnf(38193,plain,
equal(mult(i(u),rd(i(i(u)),v)),rd(i(u),rd(v,u))),
inference(rew,[status(thm),theory(equality)],[38189,30892]),
[iquote('0:Rew:38189.0,30892.0')] ).
cnf(38225,plain,
equal(rd(i(u),rd(v,u)),mult(i(u),rd(u,v))),
inference(rew,[status(thm),theory(equality)],[27,38193]),
[iquote('0:Rew:27.0,38193.0')] ).
cnf(38231,plain,
equal(rd(mult(i(u),rd(u,v)),i(u)),i(mult(i(u),v))),
inference(rew,[status(thm),theory(equality)],[38225,33918]),
[iquote('0:Rew:38225.0,33918.0')] ).
cnf(38236,plain,
equal(mult(ld(u,rd(u,v)),u),i(mult(i(u),v))),
inference(rew,[status(thm),theory(equality)],[9157,38231]),
[iquote('0:Rew:9157.0,38231.0')] ).
cnf(38468,plain,
equal(mult(rd(i(u),mult(v,i(u))),u),mult(ld(v,i(u)),mult(u,u))),
inference(spr,[status(thm),theory(equality)],[37997,10615]),
[iquote('0:SpR:37997.0,10615.0')] ).
cnf(38676,plain,
equal(mult(ld(rd(u,i(v)),i(v)),mult(v,v)),mult(rd(i(v),u),v)),
inference(spr,[status(thm),theory(equality)],[38015,15707]),
[iquote('0:SpR:38015.0,15707.0')] ).
cnf(38868,plain,
equal(mult(u,mult(mult(rd(i(u),mult(u,v)),u),u)),mult(mult(rd(u,mult(u,mult(v,u))),u),u)),
inference(spr,[status(thm),theory(equality)],[38190,109]),
[iquote('0:SpR:38190.0,109.0')] ).
cnf(38911,plain,
equal(mult(rd(i(u),mult(i(u),mult(v,i(u)))),u),ld(u,mult(rd(i(i(u)),mult(i(u),v)),u))),
inference(spr,[status(thm),theory(equality)],[38190,12979]),
[iquote('0:SpR:38190.0,12979.0')] ).
cnf(39076,plain,
equal(mult(u,mult(mult(rd(i(u),mult(u,v)),u),u)),mult(ld(ld(i(u),v),u),u)),
inference(rew,[status(thm),theory(equality)],[10484,38868,38015]),
[iquote('0:Rew:10484.0,38868.0,38015.0,38868.0')] ).
cnf(39094,plain,
equal(mult(rd(i(u),mult(i(u),mult(v,i(u)))),u),ld(u,ld(ld(u,rd(v,u)),u))),
inference(rew,[status(thm),theory(equality)],[11386,38911,38015,27]),
[iquote('0:Rew:11386.0,38911.0,38015.0,38911.0,27.0,38911.0')] ).
cnf(39095,plain,
equal(mult(ld(mult(rd(u,v),v),v),v),i(ld(mult(v,v),u))),
inference(rew,[status(thm),theory(equality)],[38169,39094,11396,36867]),
[iquote('0:Rew:38169.0,39094.0,11396.0,39094.0,36867.0,39094.0')] ).
cnf(39096,plain,
equal(i(ld(mult(u,u),v)),mult(ld(v,u),u)),
inference(rew,[status(thm),theory(equality)],[3,39095]),
[iquote('0:Rew:3.0,39095.0')] ).
cnf(40697,plain,
equal(mult(u,i(ld(mult(u,u),v))),ld(rd(mult(i(u),v),u),u)),
inference(spr,[status(thm),theory(equality)],[31708,31159]),
[iquote('0:SpR:31708.0,31159.0')] ).
cnf(40781,plain,
equal(mult(u,i(ld(mult(u,u),v))),ld(ld(u,rd(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[11386,40697]),
[iquote('0:Rew:11386.0,40697.0')] ).
cnf(40782,plain,
equal(mult(u,mult(ld(v,u),u)),ld(ld(u,rd(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[39096,40781]),
[iquote('0:Rew:39096.0,40781.0')] ).
cnf(42862,plain,
equal(ld(u,ld(i(v),u)),ld(ld(v,u),u)),
inference(spr,[status(thm),theory(equality)],[33648,2]),
[iquote('0:SpR:33648.0,2.0')] ).
cnf(42880,plain,
equal(mult(u,rd(ld(ld(v,u),u),u)),mult(ld(i(v),u),i(u))),
inference(spr,[status(thm),theory(equality)],[33648,9216]),
[iquote('0:SpR:33648.0,9216.0')] ).
cnf(42995,plain,
equal(ld(ld(rd(u,v),v),v),i(ld(u,v))),
inference(rew,[status(thm),theory(equality)],[42862,38158]),
[iquote('0:Rew:42862.0,38158.0')] ).
cnf(43013,plain,
equal(mult(u,rd(u,mult(ld(v,u),u))),mult(ld(i(v),u),i(u))),
inference(rew,[status(thm),theory(equality)],[37997,42880]),
[iquote('0:Rew:37997.0,42880.0')] ).
cnf(43193,plain,
equal(mult(ld(u,v),i(v)),ld(v,i(rd(u,v)))),
inference(spr,[status(thm),theory(equality)],[34764,9178]),
[iquote('0:SpR:34764.0,9178.0')] ).
cnf(43279,plain,
equal(mult(u,rd(u,mult(ld(v,u),u))),ld(u,i(rd(i(v),u)))),
inference(rew,[status(thm),theory(equality)],[43193,43013]),
[iquote('0:Rew:43193.0,43013.0')] ).
cnf(44694,plain,
equal(mult(u,mult(ld(mult(v,u),u),u)),rd(mult(i(v),u),i(u))),
inference(spr,[status(thm),theory(equality)],[35108,10734]),
[iquote('0:SpR:35108.0,10734.0')] ).
cnf(44858,plain,
equal(mult(u,mult(ld(mult(v,u),u),u)),mult(i(v),mult(u,u))),
inference(rew,[status(thm),theory(equality)],[10619,44694]),
[iquote('0:Rew:10619.0,44694.0')] ).
cnf(44859,plain,
equal(ld(ld(u,rd(mult(v,u),u)),u),mult(i(v),mult(u,u))),
inference(rew,[status(thm),theory(equality)],[40782,44858]),
[iquote('0:Rew:40782.0,44858.0')] ).
cnf(44860,plain,
equal(mult(i(u),mult(v,v)),ld(ld(v,u),v)),
inference(rew,[status(thm),theory(equality)],[4,44859]),
[iquote('0:Rew:4.0,44859.0')] ).
cnf(46490,plain,
equal(ld(rd(ld(u,v),i(u)),i(u)),mult(ld(mult(v,u),u),i(u))),
inference(spr,[status(thm),theory(equality)],[38169,38015]),
[iquote('0:SpR:38169.0,38015.0')] ).
cnf(46509,plain,
equal(rd(i(u),rd(ld(u,v),u)),ld(mult(mult(v,i(u)),u),u)),
inference(spr,[status(thm),theory(equality)],[11512,38169]),
[iquote('0:SpR:11512.0,38169.0')] ).
cnf(46514,plain,
equal(ld(mult(rd(mult(u,v),u),u),u),rd(i(u),mult(v,i(u)))),
inference(spr,[status(thm),theory(equality)],[9178,38169]),
[iquote('0:SpR:9178.0,38169.0')] ).
cnf(46516,plain,
equal(ld(mult(rd(u,mult(v,v)),u),u),rd(i(u),i(mult(v,v)))),
inference(spr,[status(thm),theory(equality)],[24330,38169]),
[iquote('0:SpR:24330.0,38169.0')] ).
cnf(46576,plain,
equal(mult(i(u),rd(u,ld(u,v))),ld(ld(u,ld(i(u),v)),u)),
inference(rew,[status(thm),theory(equality)],[38225,46509,14620]),
[iquote('0:Rew:38225.0,46509.0,14620.0,46509.0')] ).
cnf(46577,plain,
equal(mult(i(u),mult(u,ld(v,u))),ld(ld(u,ld(i(u),v)),u)),
inference(rew,[status(thm),theory(equality)],[34965,46576]),
[iquote('0:Rew:34965.0,46576.0')] ).
cnf(46578,plain,
equal(ld(ld(u,ld(i(u),v)),u),ld(u,ld(i(u),ld(v,u)))),
inference(rew,[status(thm),theory(equality)],[17225,46577]),
[iquote('0:Rew:17225.0,46577.0')] ).
cnf(46585,plain,
equal(rd(i(u),mult(v,i(u))),ld(u,rd(u,v))),
inference(rew,[status(thm),theory(equality)],[34934,46514,3]),
[iquote('0:Rew:34934.0,46514.0,3.0,46514.0')] ).
cnf(46588,plain,
equal(mult(ld(u,i(v)),mult(v,v)),mult(ld(v,rd(v,u)),v)),
inference(rew,[status(thm),theory(equality)],[46585,38468]),
[iquote('0:Rew:46585.0,38468.0')] ).
cnf(46592,plain,
equal(mult(ld(u,i(v)),mult(v,v)),i(mult(i(v),u))),
inference(rew,[status(thm),theory(equality)],[38236,46588]),
[iquote('0:Rew:38236.0,46588.0')] ).
cnf(46593,plain,
equal(i(mult(i(u),rd(v,i(u)))),mult(rd(i(u),v),u)),
inference(rew,[status(thm),theory(equality)],[46592,38676]),
[iquote('0:Rew:46592.0,38676.0')] ).
cnf(46607,plain,
equal(mult(rd(i(u),v),u),i(ld(u,mult(v,u)))),
inference(rew,[status(thm),theory(equality)],[12986,46593]),
[iquote('0:Rew:12986.0,46593.0')] ).
cnf(46608,plain,
equal(mult(rd(i(u),v),u),ld(u,ld(v,u))),
inference(rew,[status(thm),theory(equality)],[31074,46607]),
[iquote('0:Rew:31074.0,46607.0')] ).
cnf(46611,plain,
equal(mult(u,mult(ld(u,ld(mult(u,v),u)),u)),mult(ld(ld(i(u),v),u),u)),
inference(rew,[status(thm),theory(equality)],[46608,39076]),
[iquote('0:Rew:46608.0,39076.0')] ).
cnf(46633,plain,
equal(ld(ld(rd(mult(u,u),v),v),v),mult(i(v),mult(u,u))),
inference(rew,[status(thm),theory(equality)],[38015,46516,22849]),
[iquote('0:Rew:38015.0,46516.0,22849.0,46516.0')] ).
cnf(46634,plain,
equal(mult(ld(u,v),v),ld(ld(v,u),v)),
inference(rew,[status(thm),theory(equality)],[39096,46633,42995,44860]),
[iquote('0:Rew:39096.0,46633.0,42995.0,46633.0,44860.0,46633.0')] ).
cnf(46690,plain,
equal(mult(u,rd(u,ld(ld(u,v),u))),ld(u,i(rd(i(v),u)))),
inference(rew,[status(thm),theory(equality)],[46634,43279]),
[iquote('0:Rew:46634.0,43279.0')] ).
cnf(46770,plain,
equal(ld(u,i(rd(i(v),u))),v),
inference(rew,[status(thm),theory(equality)],[1,46690,59]),
[iquote('0:Rew:1.0,46690.0,59.0,46690.0')] ).
cnf(46773,plain,
equal(mult(ld(mult(u,v),v),i(v)),ld(ld(v,mult(u,v)),i(v))),
inference(rew,[status(thm),theory(equality)],[12913,46490]),
[iquote('0:Rew:12913.0,46490.0')] ).
cnf(46774,plain,
equal(ld(ld(u,mult(v,u)),i(u)),ld(u,i(rd(mult(v,u),u)))),
inference(rew,[status(thm),theory(equality)],[43193,46773]),
[iquote('0:Rew:43193.0,46773.0')] ).
cnf(46775,plain,
equal(ld(ld(u,mult(v,u)),i(u)),ld(u,i(v))),
inference(rew,[status(thm),theory(equality)],[4,46774]),
[iquote('0:Rew:4.0,46774.0')] ).
cnf(46807,plain,
equal(mult(ld(ld(i(u),v),u),u),i(ld(u,v))),
inference(rew,[status(thm),theory(equality)],[36794,46611,38015,12913,10099,34934]),
[iquote('0:Rew:36794.0,46611.0,38015.0,46611.0,12913.0,46611.0,10099.0,46611.0,34934.0,46611.0')] ).
cnf(46808,plain,
equal(ld(u,ld(i(u),ld(v,u))),i(ld(u,v))),
inference(rew,[status(thm),theory(equality)],[46578,46807,46634]),
[iquote('0:Rew:46578.0,46807.0,46634.0,46807.0')] ).
cnf(46809,plain,
equal(mult(ld(u,i(rd(v,u))),u),i(ld(u,v))),
inference(rew,[status(thm),theory(equality)],[46808,35182]),
[iquote('0:Rew:46808.0,35182.0')] ).
cnf(46961,plain,
equal(ld(u,i(rd(v,u))),i(v)),
inference(spr,[status(thm),theory(equality)],[27,46770]),
[iquote('0:SpR:27.0,46770.0')] ).
cnf(47019,plain,
equal(ld(ld(u,v),i(u)),i(v)),
inference(rew,[status(thm),theory(equality)],[46961,35183]),
[iquote('0:Rew:46961.0,35183.0')] ).
cnf(47022,plain,
equal(mult(i(u),v),i(ld(v,u))),
inference(rew,[status(thm),theory(equality)],[46961,46809]),
[iquote('0:Rew:46961.0,46809.0')] ).
cnf(47038,plain,
equal(ld(u,i(v)),i(mult(v,u))),
inference(rew,[status(thm),theory(equality)],[47019,46775]),
[iquote('0:Rew:47019.0,46775.0')] ).
cnf(48190,plain,
equal(mult(i(mult(u,v)),u),ld(ld(i(u),v),u)),
inference(rew,[status(thm),theory(equality)],[47038,35198]),
[iquote('0:Rew:47038.0,35198.0')] ).
cnf(49012,plain,
equal(ld(ld(i(u),v),u),i(ld(u,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[47022,48190]),
[iquote('0:Rew:47022.0,48190.0')] ).
cnf(49013,plain,
equal(ld(ld(i(u),v),u),i(v)),
inference(rew,[status(thm),theory(equality)],[2,49012]),
[iquote('0:Rew:2.0,49012.0')] ).
cnf(49014,plain,
$false,
inference(unc,[status(thm)],[49013,26020]),
[iquote('0:UnC:49013.0,26020.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP701-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.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 : Mon Jun 13 19:24:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 215.62/215.81
% 215.62/215.81 SPASS V 3.9
% 215.62/215.81 SPASS beiseite: Proof found.
% 215.62/215.81 % SZS status Theorem
% 215.62/215.81 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 215.62/215.81 SPASS derived 28740 clauses, backtracked 0 clauses, performed 0 splits and kept 14861 clauses.
% 215.62/215.81 SPASS allocated 238751 KBytes.
% 215.62/215.81 SPASS spent 0:3:35.39 on the problem.
% 215.62/215.81 0:00:00.03 for the input.
% 215.62/215.81 0:00:00.00 for the FLOTTER CNF translation.
% 215.62/215.81 0:00:00.26 for inferences.
% 215.62/215.81 0:00:00.00 for the backtracking.
% 215.62/215.81 0:3:35.03 for the reduction.
% 215.62/215.81
% 215.62/215.81
% 215.62/215.81 Here is a proof with depth 14, length 414 :
% 215.62/215.81 % SZS output start Refutation
% See solution above
% 216.86/217.05 Formulae used in the proof : c01 c02 c03 c04 c05 c06 c07 c08 c09 c10 goals
% 216.86/217.05
%------------------------------------------------------------------------------