TSTP Solution File: BOO007-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO007-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : Thu Jul 14 23:49:23 EDT 2022
% Result : Unsatisfiable 47.49s 47.70s
% Output : Refutation 47.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of clauses : 148 ( 148 unt; 0 nHn; 148 RR)
% Number of literals : 148 ( 0 equ; 4 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 : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(multiply(multiply(a,b),c),multiply(a,multiply(b,c))),
file('BOO007-2.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO007-2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO007-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(add(u,v),add(w,v)),add(multiply(u,w),v)),
file('BOO007-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO007-2.p',unknown),
[] ).
cnf(6,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(add(u,w),v)),
file('BOO007-2.p',unknown),
[] ).
cnf(7,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO007-2.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO007-2.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO007-2.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO007-2.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(multiplicative_identity,u),u),
file('BOO007-2.p',unknown),
[] ).
cnf(14,axiom,
equal(add(u,additive_identity),u),
file('BOO007-2.p',unknown),
[] ).
cnf(15,axiom,
equal(add(additive_identity,u),u),
file('BOO007-2.p',unknown),
[] ).
cnf(18,plain,
~ equal(multiply(c,multiply(a,b)),multiply(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(51,plain,
equal(add(multiply(u,v),multiply(w,v)),multiply(add(w,u),v)),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(54,plain,
equal(add(multiply(u,v),v),multiply(add(u,multiplicative_identity),v)),
inference(spr,[status(thm),theory(equality)],[13,6]),
[iquote('0:SpR:13.0,6.0')] ).
cnf(57,plain,
equal(add(multiply(u,inverse(v)),additive_identity),multiply(add(u,v),inverse(v))),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.0')] ).
cnf(64,plain,
equal(add(u,multiply(v,u)),multiply(add(v,multiplicative_identity),u)),
inference(rew,[status(thm),theory(equality)],[2,54]),
[iquote('0:Rew:2.0,54.0')] ).
cnf(68,plain,
equal(multiply(add(u,v),w),multiply(add(v,u),w)),
inference(rew,[status(thm),theory(equality)],[6,51]),
[iquote('0:Rew:6.0,51.0')] ).
cnf(70,plain,
equal(multiply(inverse(u),add(v,u)),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[15,57,2,3]),
[iquote('0:Rew:15.0,57.0,2.0,57.0,3.0,57.0')] ).
cnf(75,plain,
equal(add(u,multiply(u,v)),multiply(add(v,multiplicative_identity),u)),
inference(spr,[status(thm),theory(equality)],[3,64]),
[iquote('0:SpR:3.0,64.0')] ).
cnf(100,plain,
equal(multiply(add(u,v),v),add(multiply(u,additive_identity),v)),
inference(spr,[status(thm),theory(equality)],[15,4]),
[iquote('0:SpR:15.0,4.0')] ).
cnf(101,plain,
equal(multiply(add(u,v),add(v,w)),add(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(108,plain,
equal(multiply(add(u,v),add(w,u)),add(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(110,plain,
equal(add(multiply(u,v),inverse(u)),multiply(multiplicative_identity,add(v,inverse(u)))),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(114,plain,
equal(multiply(u,add(v,u)),add(multiply(v,additive_identity),u)),
inference(rew,[status(thm),theory(equality)],[3,100]),
[iquote('0:Rew:3.0,100.0')] ).
cnf(120,plain,
equal(add(inverse(u),multiply(u,v)),add(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[2,110,13]),
[iquote('0:Rew:2.0,110.0,13.0,110.0')] ).
cnf(200,plain,
equal(multiply(add(u,multiply(v,w)),multiply(v,add(x,w))),add(multiply(u,multiply(v,x)),multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(205,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(216,plain,
equal(multiply(u,add(inverse(u),v)),add(additive_identity,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(230,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[15,205,2]),
[iquote('0:Rew:15.0,205.0,2.0,205.0')] ).
cnf(231,plain,
equal(multiply(u,add(inverse(u),v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[15,216]),
[iquote('0:Rew:15.0,216.0')] ).
cnf(250,plain,
equal(multiply(u,add(add(v,inverse(u)),w)),add(multiply(u,v),multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[230,7]),
[iquote('0:SpR:230.0,7.0')] ).
cnf(251,plain,
equal(multiply(u,add(v,add(w,inverse(u)))),add(multiply(u,v),multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[230,7]),
[iquote('0:SpR:230.0,7.0')] ).
cnf(257,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[15,230]),
[iquote('0:SpR:15.0,230.0')] ).
cnf(259,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[8,230]),
[iquote('0:SpR:8.0,230.0')] ).
cnf(263,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[12,259]),
[iquote('0:Rew:12.0,259.0')] ).
cnf(266,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[10,257]),
[iquote('0:Rew:10.0,257.0')] ).
cnf(269,plain,
equal(multiply(u,add(v,u)),add(additive_identity,u)),
inference(rew,[status(thm),theory(equality)],[266,114]),
[iquote('0:Rew:266.0,114.0')] ).
cnf(281,plain,
equal(multiply(u,add(v,u)),u),
inference(rew,[status(thm),theory(equality)],[15,269]),
[iquote('0:Rew:15.0,269.0')] ).
cnf(285,plain,
equal(multiply(u,add(add(v,inverse(u)),w)),multiply(u,add(v,w))),
inference(rew,[status(thm),theory(equality)],[7,250]),
[iquote('0:Rew:7.0,250.0')] ).
cnf(286,plain,
equal(multiply(u,add(v,add(w,inverse(u)))),multiply(u,add(v,w))),
inference(rew,[status(thm),theory(equality)],[7,251]),
[iquote('0:Rew:7.0,251.0')] ).
cnf(329,plain,
equal(add(u,multiply(v,u)),multiply(add(u,v),u)),
inference(spr,[status(thm),theory(equality)],[263,6]),
[iquote('0:SpR:263.0,6.0')] ).
cnf(331,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,u))),
inference(spr,[status(thm),theory(equality)],[263,7]),
[iquote('0:SpR:263.0,7.0')] ).
cnf(338,plain,
equal(multiply(add(u,multiplicative_identity),v),multiply(v,add(v,u))),
inference(rew,[status(thm),theory(equality)],[64,329,3]),
[iquote('0:Rew:64.0,329.0,3.0,329.0')] ).
cnf(340,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,u))),
inference(rew,[status(thm),theory(equality)],[2,331]),
[iquote('0:Rew:2.0,331.0')] ).
cnf(341,plain,
equal(multiply(add(u,multiplicative_identity),v),v),
inference(rew,[status(thm),theory(equality)],[75,340,281]),
[iquote('0:Rew:75.0,340.0,281.0,340.0')] ).
cnf(343,plain,
equal(add(u,multiply(v,u)),u),
inference(rew,[status(thm),theory(equality)],[341,64]),
[iquote('0:Rew:341.0,64.0')] ).
cnf(352,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[341,75]),
[iquote('0:Rew:341.0,75.0')] ).
cnf(358,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[341,338]),
[iquote('0:Rew:341.0,338.0')] ).
cnf(413,plain,
equal(add(add(u,multiply(v,w)),multiply(add(u,v),x)),multiply(add(u,v),add(add(u,w),x))),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(423,plain,
equal(add(u,multiply(v,inverse(u))),multiply(add(u,v),multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.0,5.0')] ).
cnf(426,plain,
equal(multiply(add(multiply(u,v),w),multiply(u,add(v,x))),add(multiply(u,v),multiply(w,multiply(u,x)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(430,plain,
equal(add(u,multiply(inverse(u),v)),multiply(multiplicative_identity,add(u,v))),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.0,5.0')] ).
cnf(440,plain,
equal(add(u,multiply(v,inverse(u))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[13,423,3]),
[iquote('0:Rew:13.0,423.0,3.0,423.0')] ).
cnf(441,plain,
equal(add(u,multiply(inverse(u),v)),add(u,v)),
inference(rew,[status(thm),theory(equality)],[13,430]),
[iquote('0:Rew:13.0,430.0')] ).
cnf(540,plain,
equal(multiply(u,add(add(v,u),w)),add(u,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[281,7]),
[iquote('0:SpR:281.0,7.0')] ).
cnf(556,plain,
equal(multiply(u,add(add(v,u),w)),u),
inference(rew,[status(thm),theory(equality)],[352,540]),
[iquote('0:Rew:352.0,540.0')] ).
cnf(596,plain,
equal(add(u,multiply(v,multiply(u,w))),multiply(add(u,v),u)),
inference(spr,[status(thm),theory(equality)],[352,5]),
[iquote('0:SpR:352.0,5.0')] ).
cnf(616,plain,
equal(add(u,multiply(v,multiply(u,w))),multiply(u,add(u,v))),
inference(rew,[status(thm),theory(equality)],[3,596]),
[iquote('0:Rew:3.0,596.0')] ).
cnf(617,plain,
equal(add(u,multiply(v,multiply(u,w))),u),
inference(rew,[status(thm),theory(equality)],[358,616]),
[iquote('0:Rew:358.0,616.0')] ).
cnf(627,plain,
equal(multiply(u,add(v,add(u,w))),add(multiply(u,v),u)),
inference(spr,[status(thm),theory(equality)],[358,7]),
[iquote('0:SpR:358.0,7.0')] ).
cnf(648,plain,
equal(multiply(u,add(v,add(u,w))),u),
inference(rew,[status(thm),theory(equality)],[352,627,2]),
[iquote('0:Rew:352.0,627.0,2.0,627.0')] ).
cnf(700,plain,
equal(multiply(u,add(v,add(inverse(u),w))),add(multiply(u,v),multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[231,7]),
[iquote('0:SpR:231.0,7.0')] ).
cnf(710,plain,
equal(multiply(u,inverse(inverse(u))),multiply(u,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[8,231]),
[iquote('0:SpR:8.0,231.0')] ).
cnf(712,plain,
equal(multiply(u,multiply(v,inverse(u))),multiply(u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[343,231]),
[iquote('0:SpR:343.0,231.0')] ).
cnf(720,plain,
equal(multiply(u,inverse(inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[12,710]),
[iquote('0:Rew:12.0,710.0')] ).
cnf(721,plain,
equal(multiply(u,multiply(v,inverse(u))),additive_identity),
inference(rew,[status(thm),theory(equality)],[10,712]),
[iquote('0:Rew:10.0,712.0')] ).
cnf(726,plain,
equal(multiply(u,add(v,add(inverse(u),w))),multiply(u,add(v,w))),
inference(rew,[status(thm),theory(equality)],[7,700]),
[iquote('0:Rew:7.0,700.0')] ).
cnf(730,plain,
equal(add(inverse(inverse(u)),u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[720,343]),
[iquote('0:SpR:720.0,343.0')] ).
cnf(742,plain,
equal(add(u,inverse(inverse(u))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[2,730]),
[iquote('0:Rew:2.0,730.0')] ).
cnf(990,plain,
equal(add(u,inverse(inverse(u))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[10,441]),
[iquote('0:SpR:10.0,441.0')] ).
cnf(1001,plain,
equal(add(u,add(v,inverse(u))),add(u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[281,441]),
[iquote('0:SpR:281.0,441.0')] ).
cnf(1005,plain,
equal(add(u,add(add(v,inverse(u)),w)),add(u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[556,441]),
[iquote('0:SpR:556.0,441.0')] ).
cnf(1010,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[742,990,14]),
[iquote('0:Rew:742.0,990.0,14.0,990.0')] ).
cnf(1053,plain,
equal(add(u,add(v,inverse(u))),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[8,1001]),
[iquote('0:Rew:8.0,1001.0')] ).
cnf(1068,plain,
equal(add(u,add(add(v,inverse(u)),w)),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[8,1005]),
[iquote('0:Rew:8.0,1005.0')] ).
cnf(1089,plain,
equal(multiply(inverse(u),multiply(v,u)),additive_identity),
inference(spr,[status(thm),theory(equality)],[1010,721]),
[iquote('0:SpR:1010.0,721.0')] ).
cnf(1117,plain,
equal(add(inverse(u),add(v,u)),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[1010,1053]),
[iquote('0:SpR:1010.0,1053.0')] ).
cnf(1194,plain,
equal(multiply(inverse(add(u,v)),v),additive_identity),
inference(spr,[status(thm),theory(equality)],[281,1089]),
[iquote('0:SpR:281.0,1089.0')] ).
cnf(1197,plain,
equal(multiply(inverse(add(add(u,v),w)),v),additive_identity),
inference(spr,[status(thm),theory(equality)],[556,1089]),
[iquote('0:SpR:556.0,1089.0')] ).
cnf(1205,plain,
equal(multiply(u,inverse(add(v,u))),additive_identity),
inference(rew,[status(thm),theory(equality)],[3,1194]),
[iquote('0:Rew:3.0,1194.0')] ).
cnf(1210,plain,
equal(multiply(u,inverse(add(add(v,u),w))),additive_identity),
inference(rew,[status(thm),theory(equality)],[3,1197]),
[iquote('0:Rew:3.0,1197.0')] ).
cnf(1237,plain,
equal(multiply(inverse(multiply(u,inverse(v))),add(v,u)),multiply(v,inverse(multiply(u,inverse(v))))),
inference(spr,[status(thm),theory(equality)],[440,70]),
[iquote('0:SpR:440.0,70.0')] ).
cnf(1239,plain,
equal(multiply(inverse(multiply(inverse(u),v)),add(u,v)),multiply(u,inverse(multiply(inverse(u),v)))),
inference(spr,[status(thm),theory(equality)],[441,70]),
[iquote('0:SpR:441.0,70.0')] ).
cnf(1261,plain,
equal(multiply(add(u,v),inverse(multiply(v,inverse(u)))),multiply(u,inverse(multiply(v,inverse(u))))),
inference(rew,[status(thm),theory(equality)],[3,1237]),
[iquote('0:Rew:3.0,1237.0')] ).
cnf(1262,plain,
equal(multiply(add(u,v),inverse(multiply(inverse(u),v))),multiply(u,inverse(multiply(inverse(u),v)))),
inference(rew,[status(thm),theory(equality)],[3,1239]),
[iquote('0:Rew:3.0,1239.0')] ).
cnf(1333,plain,
equal(add(inverse(multiply(u,v)),v),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[343,1117]),
[iquote('0:SpR:343.0,1117.0')] ).
cnf(1335,plain,
equal(add(inverse(multiply(u,v)),u),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[352,1117]),
[iquote('0:SpR:352.0,1117.0')] ).
cnf(1350,plain,
equal(add(u,inverse(multiply(v,u))),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[2,1333]),
[iquote('0:Rew:2.0,1333.0')] ).
cnf(1352,plain,
equal(add(u,inverse(multiply(u,v))),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[2,1335]),
[iquote('0:Rew:2.0,1335.0')] ).
cnf(1423,plain,
equal(add(u,inverse(add(v,inverse(u)))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[1205,441]),
[iquote('0:SpR:1205.0,441.0')] ).
cnf(1453,plain,
equal(add(u,inverse(add(v,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[14,1423]),
[iquote('0:Rew:14.0,1423.0')] ).
cnf(1580,plain,
equal(multiply(u,inverse(multiply(v,inverse(u)))),multiply(u,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[1350,231]),
[iquote('0:SpR:1350.0,231.0')] ).
cnf(1622,plain,
equal(multiply(u,inverse(multiply(v,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[12,1580]),
[iquote('0:Rew:12.0,1580.0')] ).
cnf(1623,plain,
equal(multiply(add(u,v),inverse(multiply(v,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[1622,1261]),
[iquote('0:Rew:1622.0,1261.0')] ).
cnf(1651,plain,
equal(multiply(u,inverse(multiply(inverse(u),v))),multiply(u,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[1352,231]),
[iquote('0:SpR:1352.0,231.0')] ).
cnf(1690,plain,
equal(multiply(u,inverse(multiply(inverse(u),v))),u),
inference(rew,[status(thm),theory(equality)],[12,1651]),
[iquote('0:Rew:12.0,1651.0')] ).
cnf(1691,plain,
equal(multiply(add(u,v),inverse(multiply(inverse(u),v))),u),
inference(rew,[status(thm),theory(equality)],[1690,1262]),
[iquote('0:Rew:1690.0,1262.0')] ).
cnf(2105,plain,
equal(multiply(add(inverse(u),v),add(w,inverse(u))),add(inverse(u),multiply(v,multiply(u,w)))),
inference(spr,[status(thm),theory(equality)],[120,5]),
[iquote('0:SpR:120.0,5.0')] ).
cnf(2172,plain,
equal(add(inverse(u),multiply(v,multiply(u,w))),add(multiply(v,w),inverse(u))),
inference(rew,[status(thm),theory(equality)],[108,2105]),
[iquote('0:Rew:108.0,2105.0')] ).
cnf(2803,plain,
equal(add(multiply(u,v),multiply(w,multiply(u,x))),multiply(u,add(v,multiply(w,multiply(u,x))))),
inference(spr,[status(thm),theory(equality)],[617,4]),
[iquote('0:SpR:617.0,4.0')] ).
cnf(2887,plain,
equal(multiply(add(multiply(u,v),w),multiply(u,add(v,x))),multiply(u,add(v,multiply(w,multiply(u,x))))),
inference(rew,[status(thm),theory(equality)],[2803,426]),
[iquote('0:Rew:2803.0,426.0')] ).
cnf(3227,plain,
equal(multiply(inverse(add(u,add(v,w))),v),additive_identity),
inference(spr,[status(thm),theory(equality)],[648,1089]),
[iquote('0:SpR:648.0,1089.0')] ).
cnf(3246,plain,
equal(add(u,add(v,add(inverse(u),w))),add(u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[648,441]),
[iquote('0:SpR:648.0,441.0')] ).
cnf(3317,plain,
equal(multiply(u,inverse(add(v,add(u,w)))),additive_identity),
inference(rew,[status(thm),theory(equality)],[3,3227]),
[iquote('0:Rew:3.0,3227.0')] ).
cnf(3322,plain,
equal(add(u,add(v,add(inverse(u),w))),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[8,3246]),
[iquote('0:Rew:8.0,3246.0')] ).
cnf(3443,plain,
equal(add(u,inverse(add(add(v,inverse(u)),w))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[1210,441]),
[iquote('0:SpR:1210.0,441.0')] ).
cnf(3529,plain,
equal(add(u,inverse(add(add(v,inverse(u)),w))),u),
inference(rew,[status(thm),theory(equality)],[14,3443]),
[iquote('0:Rew:14.0,3443.0')] ).
cnf(6433,plain,
equal(multiply(add(u,multiply(v,w)),multiply(v,add(w,x))),add(multiply(u,multiply(v,x)),multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[7,101]),
[iquote('0:SpR:7.0,101.0')] ).
cnf(8192,plain,
equal(multiply(u,add(inverse(add(v,add(u,w))),x)),add(additive_identity,multiply(u,x))),
inference(spr,[status(thm),theory(equality)],[3317,7]),
[iquote('0:SpR:3317.0,7.0')] ).
cnf(8204,plain,
equal(multiply(u,add(v,inverse(add(w,add(u,x))))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[3317,7]),
[iquote('0:SpR:3317.0,7.0')] ).
cnf(8210,plain,
equal(add(u,inverse(add(v,add(inverse(u),w)))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[3317,441]),
[iquote('0:SpR:3317.0,441.0')] ).
cnf(8349,plain,
equal(add(u,inverse(add(v,add(inverse(u),w)))),u),
inference(rew,[status(thm),theory(equality)],[14,8210]),
[iquote('0:Rew:14.0,8210.0')] ).
cnf(8353,plain,
equal(multiply(u,add(inverse(add(v,add(u,w))),x)),multiply(u,x)),
inference(rew,[status(thm),theory(equality)],[15,8192]),
[iquote('0:Rew:15.0,8192.0')] ).
cnf(8356,plain,
equal(multiply(u,add(v,inverse(add(w,add(u,x))))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[15,8204,2]),
[iquote('0:Rew:15.0,8204.0,2.0,8204.0')] ).
cnf(8978,plain,
equal(multiply(inverse(add(u,add(inverse(v),w))),multiplicative_identity),multiply(v,inverse(add(u,add(inverse(v),w))))),
inference(spr,[status(thm),theory(equality)],[3322,70]),
[iquote('0:SpR:3322.0,70.0')] ).
cnf(9152,plain,
equal(multiply(u,inverse(add(v,add(inverse(u),w)))),inverse(add(v,add(inverse(u),w)))),
inference(rew,[status(thm),theory(equality)],[13,8978,3]),
[iquote('0:Rew:13.0,8978.0,3.0,8978.0')] ).
cnf(25244,plain,
equal(add(add(u,inverse(v)),multiply(add(inverse(v),v),w)),multiply(add(inverse(v),v),add(add(inverse(v),u),w))),
inference(spr,[status(thm),theory(equality)],[120,413]),
[iquote('0:SpR:120.0,413.0')] ).
cnf(25365,plain,
equal(add(add(u,inverse(v)),w),add(add(inverse(v),u),w)),
inference(rew,[status(thm),theory(equality)],[13,25244,8,2]),
[iquote('0:Rew:13.0,25244.0,13.0,25244.0,8.0,25244.0,2.0,25244.0')] ).
cnf(26376,plain,
equal(multiply(add(u,v),inverse(multiply(u,inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[1623,68]),
[iquote('0:SpR:1623.0,68.0')] ).
cnf(26762,plain,
equal(multiply(add(u,v),inverse(multiply(inverse(v),u))),v),
inference(spr,[status(thm),theory(equality)],[1691,68]),
[iquote('0:SpR:1691.0,68.0')] ).
cnf(35811,plain,
equal(multiply(add(u,multiply(v,w)),multiply(v,add(w,x))),multiply(v,add(w,multiply(u,multiply(v,x))))),
inference(spr,[status(thm),theory(equality)],[2,2887]),
[iquote('0:SpR:2.0,2887.0')] ).
cnf(35889,plain,
equal(add(multiply(u,multiply(v,w)),multiply(v,x)),multiply(v,add(x,multiply(u,multiply(v,w))))),
inference(rew,[status(thm),theory(equality)],[6433,35811]),
[iquote('0:Rew:6433.0,35811.0')] ).
cnf(35890,plain,
equal(multiply(add(u,multiply(v,w)),multiply(v,add(x,w))),multiply(v,add(w,multiply(u,multiply(v,x))))),
inference(rew,[status(thm),theory(equality)],[35889,200]),
[iquote('0:Rew:35889.0,200.0')] ).
cnf(39258,plain,
equal(multiply(u,inverse(multiply(u,inverse(inverse(add(v,inverse(u))))))),inverse(add(v,inverse(u)))),
inference(spr,[status(thm),theory(equality)],[1453,26376]),
[iquote('0:SpR:1453.0,26376.0')] ).
cnf(39260,plain,
equal(multiply(u,inverse(multiply(u,inverse(inverse(add(v,add(inverse(u),w))))))),inverse(add(v,add(inverse(u),w)))),
inference(spr,[status(thm),theory(equality)],[8349,26376]),
[iquote('0:SpR:8349.0,26376.0')] ).
cnf(39262,plain,
equal(multiply(u,inverse(multiply(u,inverse(inverse(add(add(v,inverse(u)),w)))))),inverse(add(add(v,inverse(u)),w))),
inference(spr,[status(thm),theory(equality)],[3529,26376]),
[iquote('0:SpR:3529.0,26376.0')] ).
cnf(39497,plain,
equal(multiply(u,inverse(multiply(u,v))),inverse(add(v,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[230,39258,1010]),
[iquote('0:Rew:230.0,39258.0,1010.0,39258.0')] ).
cnf(39591,plain,
equal(multiply(u,inverse(multiply(u,add(add(v,inverse(u)),w)))),inverse(add(add(v,inverse(u)),w))),
inference(rew,[status(thm),theory(equality)],[1010,39262]),
[iquote('0:Rew:1010.0,39262.0')] ).
cnf(39592,plain,
equal(inverse(add(add(u,v),inverse(w))),inverse(add(add(u,inverse(w)),v))),
inference(rew,[status(thm),theory(equality)],[39497,39591,285]),
[iquote('0:Rew:39497.0,39591.0,285.0,39591.0')] ).
cnf(39593,plain,
equal(multiply(u,inverse(multiply(u,add(v,add(inverse(u),w))))),inverse(add(v,add(inverse(u),w)))),
inference(rew,[status(thm),theory(equality)],[1010,39260]),
[iquote('0:Rew:1010.0,39260.0')] ).
cnf(39594,plain,
equal(inverse(add(add(u,v),inverse(w))),inverse(add(u,add(inverse(w),v)))),
inference(rew,[status(thm),theory(equality)],[39497,39593,726]),
[iquote('0:Rew:39497.0,39593.0,726.0,39593.0')] ).
cnf(39596,plain,
equal(inverse(add(add(u,inverse(v)),w)),inverse(add(u,add(inverse(v),w)))),
inference(rew,[status(thm),theory(equality)],[39594,39592]),
[iquote('0:Rew:39594.0,39592.0')] ).
cnf(41606,plain,
equal(multiply(multiplicative_identity,inverse(multiply(inverse(add(add(u,inverse(v)),w)),v))),add(add(u,inverse(v)),w)),
inference(spr,[status(thm),theory(equality)],[1068,26762]),
[iquote('0:SpR:1068.0,26762.0')] ).
cnf(41860,plain,
equal(inverse(multiply(u,inverse(add(add(v,inverse(u)),w)))),add(add(v,inverse(u)),w)),
inference(rew,[status(thm),theory(equality)],[13,41606,3]),
[iquote('0:Rew:13.0,41606.0,3.0,41606.0')] ).
cnf(41861,plain,
equal(inverse(inverse(add(u,add(inverse(v),w)))),add(add(u,inverse(v)),w)),
inference(rew,[status(thm),theory(equality)],[9152,41860,39596]),
[iquote('0:Rew:9152.0,41860.0,39596.0,41860.0')] ).
cnf(41862,plain,
equal(add(add(u,inverse(v)),w),add(u,add(inverse(v),w))),
inference(rew,[status(thm),theory(equality)],[1010,41861]),
[iquote('0:Rew:1010.0,41861.0')] ).
cnf(41931,plain,
equal(add(add(inverse(u),v),w),add(v,add(inverse(u),w))),
inference(rew,[status(thm),theory(equality)],[41862,25365]),
[iquote('0:Rew:41862.0,25365.0')] ).
cnf(43946,plain,
equal(multiply(add(u,multiply(v,w)),multiply(v,add(x,add(inverse(v),w)))),multiply(v,add(add(inverse(v),w),multiply(u,multiply(v,x))))),
inference(spr,[status(thm),theory(equality)],[231,35890]),
[iquote('0:SpR:231.0,35890.0')] ).
cnf(43975,plain,
equal(multiply(add(u,additive_identity),multiply(v,add(w,inverse(add(x,add(v,y)))))),multiply(v,add(inverse(add(x,add(v,y))),multiply(u,multiply(v,w))))),
inference(spr,[status(thm),theory(equality)],[3317,35890]),
[iquote('0:SpR:3317.0,35890.0')] ).
cnf(44162,plain,
equal(multiply(add(u,multiply(v,w)),multiply(v,add(x,w))),multiply(v,add(w,multiply(u,x)))),
inference(rew,[status(thm),theory(equality)],[726,43946,286,2172,41931]),
[iquote('0:Rew:726.0,43946.0,286.0,43946.0,2172.0,43946.0,41931.0,43946.0')] ).
cnf(44163,plain,
equal(multiply(u,add(v,multiply(w,multiply(u,x)))),multiply(u,add(v,multiply(w,x)))),
inference(rew,[status(thm),theory(equality)],[35890,44162]),
[iquote('0:Rew:35890.0,44162.0')] ).
cnf(46102,plain,
equal(multiply(u,add(inverse(add(v,add(u,w))),multiply(x,multiply(u,y)))),multiply(x,multiply(u,add(y,inverse(add(v,add(u,w))))))),
inference(rew,[status(thm),theory(equality)],[14,43975]),
[iquote('0:Rew:14.0,43975.0')] ).
cnf(46103,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[8353,46102,44163,8356]),
[iquote('0:Rew:8353.0,46102.0,44163.0,46102.0,8356.0,46102.0')] ).
cnf(46111,plain,
~ equal(multiply(a,multiply(c,b)),multiply(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[46103,18]),
[iquote('0:Rew:46103.0,18.0')] ).
cnf(46305,plain,
~ equal(multiply(a,multiply(b,c)),multiply(a,multiply(b,c))),
inference(rew,[status(thm),theory(equality)],[3,46111]),
[iquote('0:Rew:3.0,46111.0')] ).
cnf(46306,plain,
$false,
inference(obv,[status(thm),theory(equality)],[46305]),
[iquote('0:Obv:46305.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : BOO007-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 1 17:38:16 EDT 2022
% 0.13/0.35 % CPUTime :
% 47.49/47.70
% 47.49/47.70 SPASS V 3.9
% 47.49/47.70 SPASS beiseite: Proof found.
% 47.49/47.70 % SZS status Theorem
% 47.49/47.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.49/47.70 SPASS derived 29150 clauses, backtracked 0 clauses, performed 0 splits and kept 6943 clauses.
% 47.49/47.70 SPASS allocated 112958 KBytes.
% 47.49/47.70 SPASS spent 0:0:47.29 on the problem.
% 47.49/47.70 0:00:00.04 for the input.
% 47.49/47.70 0:00:00.00 for the FLOTTER CNF translation.
% 47.49/47.70 0:00:00.18 for inferences.
% 47.49/47.70 0:00:00.00 for the backtracking.
% 47.49/47.70 0:0:47.02 for the reduction.
% 47.49/47.70
% 47.49/47.70
% 47.49/47.70 Here is a proof with depth 7, length 148 :
% 47.49/47.70 % SZS output start Refutation
% See solution above
% 47.89/48.12 Formulae used in the proof : prove_associativity commutativity_of_add commutativity_of_multiply distributivity1 distributivity2 distributivity3 distributivity4 additive_inverse1 multiplicative_inverse1 multiplicative_id1 multiplicative_id2 additive_id1 additive_id2
% 47.89/48.12
%------------------------------------------------------------------------------