TSTP Solution File: RNG008-5 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG008-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 : Mon Jul 18 20:41:11 EDT 2022
% Result : Unsatisfiable 230.14s 230.32s
% Output : Refutation 233.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 24
% Syntax : Number of clauses : 155 ( 64 unt; 0 nHn; 155 RR)
% Number of literals : 302 ( 0 equ; 148 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
sum__dfg(additive_inverse(additive_inverse(u)),additive_identity,u),
file('RNG008-5.p',unknown),
[] ).
cnf(3,axiom,
product(u,additive_identity,additive_identity),
file('RNG008-5.p',unknown),
[] ).
cnf(4,axiom,
product(additive_identity,u,additive_identity),
file('RNG008-5.p',unknown),
[] ).
cnf(5,axiom,
sum__dfg(additive_inverse(u),additive_inverse(v),additive_inverse(add(u,v))),
file('RNG008-5.p',unknown),
[] ).
cnf(6,axiom,
product(u,additive_inverse(v),additive_inverse(multiply(u,v))),
file('RNG008-5.p',unknown),
[] ).
cnf(7,axiom,
product(u,u,u),
file('RNG008-5.p',unknown),
[] ).
cnf(8,axiom,
product(a,b,c),
file('RNG008-5.p',unknown),
[] ).
cnf(9,axiom,
~ product(b,a,c),
file('RNG008-5.p',unknown),
[] ).
cnf(10,axiom,
sum__dfg(additive_identity,u,u),
file('RNG008-5.p',unknown),
[] ).
cnf(11,axiom,
sum__dfg(u,additive_identity,u),
file('RNG008-5.p',unknown),
[] ).
cnf(12,axiom,
product(u,v,multiply(u,v)),
file('RNG008-5.p',unknown),
[] ).
cnf(13,axiom,
sum__dfg(u,v,add(u,v)),
file('RNG008-5.p',unknown),
[] ).
cnf(14,axiom,
sum__dfg(additive_inverse(u),u,additive_identity),
file('RNG008-5.p',unknown),
[] ).
cnf(15,axiom,
sum__dfg(u,additive_inverse(u),additive_identity),
file('RNG008-5.p',unknown),
[] ).
cnf(16,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(17,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(18,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(20,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(22,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,z)
| ~ product(x1,y,v)
| ~ product(x1,x,u)
| product(x1,z,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(23,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,u)
| ~ product(y,v,z)
| ~ product(x,v,x1)
| sum__dfg(x1,z,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(24,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,z)
| ~ product(y,x1,v)
| ~ product(x,x1,u)
| product(z,x1,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(25,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(26,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('RNG008-5.p',unknown),
[] ).
cnf(33,plain,
sum__dfg(additive_identity,additive_inverse(additive_inverse(u)),u),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.0')] ).
cnf(36,plain,
sum__dfg(u,v,add(v,u)),
inference(res,[status(thm),theory(equality)],[13,18]),
[iquote('0:Res:13.0,18.0')] ).
cnf(41,plain,
( ~ sum__dfg(additive_identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[10,25]),
[iquote('0:Res:10.0,25.0')] ).
cnf(43,plain,
( ~ sum__dfg(u,additive_identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[11,25]),
[iquote('0:Res:11.0,25.0')] ).
cnf(47,plain,
( ~ sum__dfg(u,v,w)
| equal(w,add(u,v)) ),
inference(res,[status(thm),theory(equality)],[13,25]),
[iquote('0:Res:13.0,25.0')] ).
cnf(48,plain,
( ~ sum__dfg(u,v,w)
| equal(w,add(v,u)) ),
inference(res,[status(thm),theory(equality)],[36,25]),
[iquote('0:Res:36.0,25.0')] ).
cnf(52,plain,
( ~ product(additive_identity,u,v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[4,26]),
[iquote('0:Res:4.0,26.0')] ).
cnf(53,plain,
( ~ product(u,additive_identity,v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[3,26]),
[iquote('0:Res:3.0,26.0')] ).
cnf(54,plain,
( ~ product(u,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[7,26]),
[iquote('0:Res:7.0,26.0')] ).
cnf(55,plain,
( ~ product(u,v,w)
| equal(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[12,26]),
[iquote('0:Res:12.0,26.0')] ).
cnf(71,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(w,u,x)
| sum__dfg(x,v,w) ),
inference(res,[status(thm),theory(equality)],[11,17]),
[iquote('0:Res:11.0,17.0')] ).
cnf(73,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(additive_inverse(w),u,x)
| sum__dfg(x,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[14,17]),
[iquote('0:Res:14.0,17.0')] ).
cnf(75,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,u,y)
| sum__dfg(y,v,add(x,w)) ),
inference(res,[status(thm),theory(equality)],[13,17]),
[iquote('0:Res:13.0,17.0')] ).
cnf(102,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,u,additive_identity)
| sum__dfg(x,w,v) ),
inference(res,[status(thm),theory(equality)],[10,16]),
[iquote('0:Res:10.0,16.0')] ).
cnf(135,plain,
( ~ product(u,v,w)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[7,20]),
[iquote('0:Res:7.0,20.0')] ).
cnf(136,plain,
( ~ product(u,v,w)
| ~ product(x,u,y)
| product(y,v,multiply(x,w)) ),
inference(res,[status(thm),theory(equality)],[12,20]),
[iquote('0:Res:12.0,20.0')] ).
cnf(143,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(res,[status(thm),theory(equality)],[12,53]),
[iquote('0:Res:12.0,53.0')] ).
cnf(158,plain,
equal(additive_inverse(additive_inverse(u)),u),
inference(res,[status(thm),theory(equality)],[33,41]),
[iquote('0:Res:33.0,41.0')] ).
cnf(161,plain,
equal(add(additive_identity,u),u),
inference(res,[status(thm),theory(equality)],[13,41]),
[iquote('0:Res:13.0,41.0')] ).
cnf(162,plain,
equal(add(u,additive_identity),u),
inference(res,[status(thm),theory(equality)],[36,41]),
[iquote('0:Res:36.0,41.0')] ).
cnf(206,plain,
product(u,v,additive_inverse(multiply(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[158,6]),
[iquote('0:SpR:158.0,6.0')] ).
cnf(212,plain,
( ~ product(u,v,w)
| ~ product(x,u,additive_identity)
| product(x,w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[4,19]),
[iquote('0:Res:4.0,19.0')] ).
cnf(215,plain,
( ~ product(u,v,w)
| ~ product(x,u,y)
| product(x,w,multiply(y,v)) ),
inference(res,[status(thm),theory(equality)],[12,19]),
[iquote('0:Res:12.0,19.0')] ).
cnf(252,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ product(v,w,x)
| ~ product(u,w,y)
| sum__dfg(y,x,additive_identity) ),
inference(res,[status(thm),theory(equality)],[4,23]),
[iquote('0:Res:4.0,23.0')] ).
cnf(257,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,additive_inverse(x),y)
| ~ product(u,additive_inverse(x),z)
| sum__dfg(z,y,additive_inverse(multiply(w,x))) ),
inference(res,[status(thm),theory(equality)],[6,23]),
[iquote('0:Res:6.0,23.0')] ).
cnf(290,plain,
equal(multiply(u,u),u),
inference(res,[status(thm),theory(equality)],[12,54]),
[iquote('0:Res:12.0,54.0')] ).
cnf(296,plain,
product(additive_inverse(u),u,additive_inverse(additive_inverse(u))),
inference(spr,[status(thm),theory(equality)],[290,206]),
[iquote('0:SpR:290.0,206.0')] ).
cnf(299,plain,
product(additive_inverse(u),u,u),
inference(rew,[status(thm),theory(equality)],[158,296]),
[iquote('0:Rew:158.0,296.0')] ).
cnf(371,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,additive_inverse(y))
| ~ product(u,x,y)
| product(w,x,additive_identity) ),
inference(res,[status(thm),theory(equality)],[15,24]),
[iquote('0:Res:15.0,24.0')] ).
cnf(374,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,additive_inverse(y))
| ~ product(u,x,additive_inverse(z))
| product(w,x,additive_inverse(add(z,y))) ),
inference(res,[status(thm),theory(equality)],[5,24]),
[iquote('0:Res:5.0,24.0')] ).
cnf(417,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,v,additive_inverse(y))
| ~ product(x,u,y)
| product(x,w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[15,22]),
[iquote('0:Res:15.0,22.0')] ).
cnf(420,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,v,additive_inverse(y))
| ~ product(x,u,additive_inverse(z))
| product(x,w,additive_inverse(add(z,y))) ),
inference(res,[status(thm),theory(equality)],[5,22]),
[iquote('0:Res:5.0,22.0')] ).
cnf(509,plain,
equal(add(u,v),add(v,u)),
inference(res,[status(thm),theory(equality)],[36,47]),
[iquote('0:Res:36.0,47.0')] ).
cnf(1256,plain,
( ~ product(u,a,additive_identity)
| product(u,c,additive_identity) ),
inference(res,[status(thm),theory(equality)],[8,212]),
[iquote('0:Res:8.0,212.0')] ).
cnf(1271,plain,
( ~ product(u,a,additive_identity)
| equal(multiply(u,c),additive_identity) ),
inference(res,[status(thm),theory(equality)],[1256,55]),
[iquote('0:Res:1256.1,55.0')] ).
cnf(1358,plain,
( ~ sum__dfg(u,additive_inverse(v),w)
| sum__dfg(w,v,u) ),
inference(res,[status(thm),theory(equality)],[14,71]),
[iquote('0:Res:14.0,71.0')] ).
cnf(1383,plain,
( ~ sum__dfg(u,v,additive_identity)
| sum__dfg(u,additive_identity,additive_inverse(v)) ),
inference(res,[status(thm),theory(equality)],[15,102]),
[iquote('0:Res:15.0,102.0')] ).
cnf(1455,plain,
( ~ product(multiply(u,v),u,w)
| product(w,v,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[12,135]),
[iquote('0:Res:12.0,135.0')] ).
cnf(1612,plain,
( ~ sum__dfg(additive_identity,u,v)
| sum__dfg(additive_inverse(v),u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[11,73]),
[iquote('0:Res:11.0,73.1')] ).
cnf(1757,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(w,x,add(u,add(v,x))) ),
inference(res,[status(thm),theory(equality)],[13,75]),
[iquote('0:Res:13.0,75.0')] ).
cnf(1794,plain,
( ~ product(u,a,v)
| product(v,b,multiply(u,c)) ),
inference(res,[status(thm),theory(equality)],[8,136]),
[iquote('0:Res:8.0,136.0')] ).
cnf(1804,plain,
( ~ product(u,v,w)
| product(w,x,multiply(u,multiply(v,x))) ),
inference(res,[status(thm),theory(equality)],[12,136]),
[iquote('0:Res:12.0,136.0')] ).
cnf(1839,plain,
( ~ product(u,a,v)
| product(u,c,multiply(v,b)) ),
inference(res,[status(thm),theory(equality)],[8,215]),
[iquote('0:Res:8.0,215.0')] ).
cnf(1848,plain,
( ~ product(u,v,w)
| product(u,v,multiply(w,v)) ),
inference(res,[status(thm),theory(equality)],[7,215]),
[iquote('0:Res:7.0,215.0')] ).
cnf(2126,plain,
( ~ sum__dfg(u,v,additive_identity)
| sum__dfg(additive_identity,u,additive_inverse(v)) ),
inference(res,[status(thm),theory(equality)],[1383,18]),
[iquote('0:Res:1383.1,18.0')] ).
cnf(2131,plain,
( ~ sum__dfg(u,v,additive_identity)
| equal(additive_inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[1383,43]),
[iquote('0:Res:1383.1,43.0')] ).
cnf(2163,plain,
( ~ sum__dfg(additive_identity,u,v)
| equal(add(additive_inverse(v),u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[1612,47]),
[iquote('0:Res:1612.1,47.0')] ).
cnf(2169,plain,
( ~ sum__dfg(additive_identity,u,v)
| sum__dfg(u,additive_inverse(v),additive_identity) ),
inference(res,[status(thm),theory(equality)],[1612,18]),
[iquote('0:Res:1612.1,18.0')] ).
cnf(2170,plain,
( ~ sum__dfg(additive_identity,u,v)
| equal(additive_inverse(u),additive_inverse(v)) ),
inference(res,[status(thm),theory(equality)],[1612,2131]),
[iquote('0:Res:1612.1,2131.0')] ).
cnf(2700,plain,
( ~ sum__dfg(u,v,additive_identity)
| equal(additive_inverse(u),additive_inverse(additive_inverse(v))) ),
inference(res,[status(thm),theory(equality)],[2126,2170]),
[iquote('0:Res:2126.1,2170.0')] ).
cnf(2710,plain,
( ~ sum__dfg(u,v,additive_identity)
| equal(additive_inverse(u),v) ),
inference(rew,[status(thm),theory(equality)],[158,2700]),
[iquote('0:Rew:158.0,2700.1')] ).
cnf(2714,plain,
( ~ product(u,v,w)
| ~ product(additive_inverse(u),v,x)
| sum__dfg(x,w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[14,252]),
[iquote('0:Res:14.0,252.0')] ).
cnf(3694,plain,
sum__dfg(add(u,additive_inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[13,1358]),
[iquote('0:Res:13.0,1358.0')] ).
cnf(3695,plain,
sum__dfg(add(additive_inverse(u),v),u,v),
inference(res,[status(thm),theory(equality)],[36,1358]),
[iquote('0:Res:36.0,1358.0')] ).
cnf(3696,plain,
( ~ sum__dfg(additive_identity,u,v)
| sum__dfg(additive_identity,v,u) ),
inference(res,[status(thm),theory(equality)],[2169,1358]),
[iquote('0:Res:2169.1,1358.0')] ).
cnf(3723,plain,
equal(add(u,add(v,additive_inverse(u))),v),
inference(res,[status(thm),theory(equality)],[3694,48]),
[iquote('0:Res:3694.0,48.0')] ).
cnf(3811,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(res,[status(thm),theory(equality)],[3695,48]),
[iquote('0:Res:3695.0,48.0')] ).
cnf(4356,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,additive_inverse(x),multiply(v,x))
| product(w,additive_inverse(x),additive_identity) ),
inference(res,[status(thm),theory(equality)],[6,371]),
[iquote('0:Res:6.0,371.1')] ).
cnf(4982,plain,
( ~ sum__dfg(u,additive_inverse(v),w)
| ~ product(x,u,multiply(x,v))
| product(x,w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[6,417]),
[iquote('0:Res:6.0,417.1')] ).
cnf(6201,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,additive_inverse(x),y)
| sum__dfg(y,additive_inverse(multiply(v,x)),additive_inverse(multiply(w,x))) ),
inference(res,[status(thm),theory(equality)],[6,257]),
[iquote('0:Res:6.0,257.1')] ).
cnf(6254,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,additive_inverse(x),additive_inverse(y))
| product(w,additive_inverse(x),additive_inverse(add(y,multiply(v,x)))) ),
inference(res,[status(thm),theory(equality)],[6,374]),
[iquote('0:Res:6.0,374.1')] ).
cnf(6293,plain,
( ~ sum__dfg(u,additive_inverse(v),w)
| ~ product(x,u,additive_inverse(y))
| product(x,w,additive_inverse(add(y,multiply(x,v)))) ),
inference(res,[status(thm),theory(equality)],[6,420]),
[iquote('0:Res:6.0,420.1')] ).
cnf(6378,plain,
( ~ product(u,a,v)
| equal(multiply(u,c),multiply(v,b)) ),
inference(res,[status(thm),theory(equality)],[1794,55]),
[iquote('0:Res:1794.1,55.0')] ).
cnf(10823,plain,
product(multiply(multiply(u,v),u),v,multiply(u,v)),
inference(res,[status(thm),theory(equality)],[12,1455]),
[iquote('0:Res:12.0,1455.0')] ).
cnf(10899,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(w,additive_inverse(u),v) ),
inference(spr,[status(thm),theory(equality)],[3723,1757]),
[iquote('0:SpR:3723.0,1757.1')] ).
cnf(11049,plain,
equal(multiply(multiply(multiply(u,v),u),v),multiply(u,v)),
inference(res,[status(thm),theory(equality)],[10823,55]),
[iquote('0:Res:10823.0,55.0')] ).
cnf(11480,plain,
( ~ sum__dfg(u,v,additive_identity)
| sum__dfg(additive_identity,v,additive_inverse(u)) ),
inference(res,[status(thm),theory(equality)],[10899,3696]),
[iquote('0:Res:10899.1,3696.0')] ).
cnf(11853,plain,
( ~ product(u,v,w)
| equal(multiply(u,multiply(v,x)),multiply(w,x)) ),
inference(res,[status(thm),theory(equality)],[1804,55]),
[iquote('0:Res:1804.1,55.0')] ).
cnf(15011,plain,
( ~ sum__dfg(additive_identity,additive_inverse(u),v)
| equal(add(u,additive_identity),additive_inverse(v)) ),
inference(spr,[status(thm),theory(equality)],[2163,3723]),
[iquote('0:SpR:2163.1,3723.0')] ).
cnf(15069,plain,
( ~ sum__dfg(additive_identity,additive_inverse(u),v)
| equal(u,additive_inverse(v)) ),
inference(rew,[status(thm),theory(equality)],[162,15011]),
[iquote('0:Rew:162.0,15011.1')] ).
cnf(15308,plain,
( ~ sum__dfg(u,additive_inverse(v),additive_identity)
| equal(v,additive_inverse(additive_inverse(u))) ),
inference(res,[status(thm),theory(equality)],[11480,15069]),
[iquote('0:Res:11480.1,15069.0')] ).
cnf(15324,plain,
( ~ sum__dfg(u,additive_inverse(v),additive_identity)
| equal(v,u) ),
inference(rew,[status(thm),theory(equality)],[158,15308]),
[iquote('0:Rew:158.0,15308.1')] ).
cnf(17785,plain,
( ~ product(u,u,v)
| sum__dfg(u,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[299,2714]),
[iquote('0:Res:299.0,2714.1')] ).
cnf(23870,plain,
sum__dfg(u,u,additive_identity),
inference(res,[status(thm),theory(equality)],[7,17785]),
[iquote('0:Res:7.0,17785.0')] ).
cnf(24067,plain,
equal(add(u,u),additive_identity),
inference(res,[status(thm),theory(equality)],[23870,48]),
[iquote('0:Res:23870.0,48.0')] ).
cnf(24086,plain,
equal(additive_inverse(u),u),
inference(res,[status(thm),theory(equality)],[23870,2710]),
[iquote('0:Res:23870.0,2710.0')] ).
cnf(24287,plain,
( ~ sum__dfg(u,v,additive_identity)
| equal(v,u) ),
inference(rew,[status(thm),theory(equality)],[24086,15324]),
[iquote('0:Rew:24086.0,15324.0')] ).
cnf(24364,plain,
equal(add(u,add(u,v)),v),
inference(rew,[status(thm),theory(equality)],[24086,3811]),
[iquote('0:Rew:24086.0,3811.0')] ).
cnf(24596,plain,
( ~ sum__dfg(u,additive_inverse(v),w)
| ~ product(x,u,y)
| product(x,w,additive_inverse(add(y,multiply(x,v)))) ),
inference(rew,[status(thm),theory(equality)],[24086,6293]),
[iquote('0:Rew:24086.0,6293.1')] ).
cnf(24617,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,additive_inverse(x),y)
| product(w,additive_inverse(x),additive_inverse(add(y,multiply(v,x)))) ),
inference(rew,[status(thm),theory(equality)],[24086,6254]),
[iquote('0:Rew:24086.0,6254.1')] ).
cnf(24863,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,x,multiply(v,x))
| product(w,additive_inverse(x),additive_identity) ),
inference(rew,[status(thm),theory(equality)],[24086,4356]),
[iquote('0:Rew:24086.0,4356.1')] ).
cnf(24888,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,x,y)
| sum__dfg(y,additive_inverse(multiply(v,x)),additive_inverse(multiply(w,x))) ),
inference(rew,[status(thm),theory(equality)],[24086,6201]),
[iquote('0:Rew:24086.0,6201.1')] ).
cnf(27011,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,u,multiply(x,v))
| product(x,w,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[24086,4982]),
[iquote('0:Rew:24086.0,4982.0')] ).
cnf(28999,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,x,multiply(v,x))
| product(w,x,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[24086,24863]),
[iquote('0:Rew:24086.0,24863.2')] ).
cnf(29405,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,u,y)
| product(x,w,add(y,multiply(x,v))) ),
inference(rew,[status(thm),theory(equality)],[24086,24596]),
[iquote('0:Rew:24086.0,24596.2,24086.0,24596.0')] ).
cnf(29456,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,x,y)
| sum__dfg(y,multiply(v,x),multiply(w,x)) ),
inference(rew,[status(thm),theory(equality)],[24086,24888]),
[iquote('0:Rew:24086.0,24888.2,24086.0,24888.2')] ).
cnf(29524,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,x,y)
| product(w,x,add(y,multiply(v,x))) ),
inference(rew,[status(thm),theory(equality)],[24086,24617]),
[iquote('0:Rew:24086.0,24617.2,24086.0,24617.2,24086.0,24617.1')] ).
cnf(32507,plain,
( ~ product(u,a,u)
| ~ sum__dfg(c,b,v)
| product(u,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[1839,27011]),
[iquote('0:Res:1839.1,27011.1')] ).
cnf(33111,plain,
( ~ product(u,v,w)
| ~ sum__dfg(u,w,x)
| product(x,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[1848,28999]),
[iquote('0:Res:1848.1,28999.1')] ).
cnf(34938,plain,
( ~ product(u,v,w)
| product(u,add(v,x),add(w,multiply(u,x))) ),
inference(res,[status(thm),theory(equality)],[13,29405]),
[iquote('0:Res:13.0,29405.0')] ).
cnf(35093,plain,
( ~ product(u,v,w)
| sum__dfg(w,multiply(x,v),multiply(add(u,x),v)) ),
inference(res,[status(thm),theory(equality)],[13,29456]),
[iquote('0:Res:13.0,29456.0')] ).
cnf(35346,plain,
( ~ product(additive_identity,u,v)
| product(w,u,add(v,multiply(w,u))) ),
inference(res,[status(thm),theory(equality)],[10,29524]),
[iquote('0:Res:10.0,29524.0')] ).
cnf(49280,plain,
equal(multiply(multiply(u,a),b),multiply(u,c)),
inference(res,[status(thm),theory(equality)],[12,6378]),
[iquote('0:Res:12.0,6378.0')] ).
cnf(49362,plain,
equal(multiply(multiply(b,c),a),multiply(b,a)),
inference(spr,[status(thm),theory(equality)],[49280,11049]),
[iquote('0:SpR:49280.0,11049.0')] ).
cnf(79555,plain,
( ~ product(additive_identity,u,multiply(v,u))
| product(v,u,additive_identity) ),
inference(spr,[status(thm),theory(equality)],[24067,35346]),
[iquote('0:SpR:24067.0,35346.1')] ).
cnf(97177,plain,
( ~ sum__dfg(c,b,u)
| product(a,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,32507]),
[iquote('0:Res:7.0,32507.0')] ).
cnf(97195,plain,
( ~ sum__dfg(c,b,u)
| equal(multiply(a,u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[97177,55]),
[iquote('0:Res:97177.1,55.0')] ).
cnf(98003,plain,
equal(multiply(a,add(c,b)),additive_identity),
inference(res,[status(thm),theory(equality)],[13,97195]),
[iquote('0:Res:13.0,97195.0')] ).
cnf(98035,plain,
equal(multiply(a,add(b,c)),additive_identity),
inference(rew,[status(thm),theory(equality)],[509,98003]),
[iquote('0:Rew:509.0,98003.0')] ).
cnf(109885,plain,
equal(multiply(a,multiply(b,u)),multiply(c,u)),
inference(res,[status(thm),theory(equality)],[8,11853]),
[iquote('0:Res:8.0,11853.0')] ).
cnf(109918,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(res,[status(thm),theory(equality)],[12,11853]),
[iquote('0:Res:12.0,11853.0')] ).
cnf(110256,plain,
equal(multiply(b,multiply(c,a)),multiply(b,a)),
inference(rew,[status(thm),theory(equality)],[109918,49362]),
[iquote('0:Rew:109918.0,49362.0')] ).
cnf(110262,plain,
product(multiply(u,multiply(v,u)),v,multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[109918,10823]),
[iquote('0:Rew:109918.0,10823.0')] ).
cnf(111042,plain,
product(multiply(add(b,c),additive_identity),a,multiply(add(b,c),a)),
inference(spr,[status(thm),theory(equality)],[98035,110262]),
[iquote('0:SpR:98035.0,110262.0')] ).
cnf(111116,plain,
product(additive_identity,a,multiply(add(b,c),a)),
inference(rew,[status(thm),theory(equality)],[143,111042]),
[iquote('0:Rew:143.0,111042.0')] ).
cnf(111187,plain,
product(add(b,c),a,additive_identity),
inference(res,[status(thm),theory(equality)],[111116,79555]),
[iquote('0:Res:111116.0,79555.0')] ).
cnf(111237,plain,
equal(multiply(add(b,c),c),additive_identity),
inference(res,[status(thm),theory(equality)],[111187,1271]),
[iquote('0:Res:111187.0,1271.0')] ).
cnf(114792,plain,
( ~ sum__dfg(a,c,u)
| product(u,b,additive_identity) ),
inference(res,[status(thm),theory(equality)],[8,33111]),
[iquote('0:Res:8.0,33111.0')] ).
cnf(114931,plain,
( ~ sum__dfg(a,c,u)
| equal(multiply(u,b),additive_identity) ),
inference(res,[status(thm),theory(equality)],[114792,55]),
[iquote('0:Res:114792.1,55.0')] ).
cnf(118063,plain,
equal(multiply(add(a,c),b),additive_identity),
inference(res,[status(thm),theory(equality)],[13,114931]),
[iquote('0:Res:13.0,114931.0')] ).
cnf(118137,plain,
product(multiply(b,additive_identity),add(a,c),multiply(b,add(a,c))),
inference(spr,[status(thm),theory(equality)],[118063,110262]),
[iquote('0:SpR:118063.0,110262.0')] ).
cnf(118168,plain,
product(additive_identity,add(a,c),multiply(b,add(a,c))),
inference(rew,[status(thm),theory(equality)],[143,118137]),
[iquote('0:Rew:143.0,118137.0')] ).
cnf(118401,plain,
equal(multiply(b,add(a,c)),additive_identity),
inference(res,[status(thm),theory(equality)],[118168,52]),
[iquote('0:Res:118168.0,52.0')] ).
cnf(118557,plain,
equal(multiply(c,add(a,c)),multiply(a,additive_identity)),
inference(spr,[status(thm),theory(equality)],[118401,109885]),
[iquote('0:SpR:118401.0,109885.0')] ).
cnf(118590,plain,
equal(multiply(c,add(a,c)),additive_identity),
inference(rew,[status(thm),theory(equality)],[143,118557]),
[iquote('0:Rew:143.0,118557.0')] ).
cnf(118604,plain,
product(c,add(a,c),additive_identity),
inference(spr,[status(thm),theory(equality)],[118590,12]),
[iquote('0:SpR:118590.0,12.0')] ).
cnf(118690,plain,
( ~ product(c,add(a,c),u)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[118604,26]),
[iquote('0:Res:118604.0,26.0')] ).
cnf(131700,plain,
( ~ product(c,a,u)
| equal(add(u,multiply(c,c)),additive_identity) ),
inference(res,[status(thm),theory(equality)],[34938,118690]),
[iquote('0:Res:34938.1,118690.0')] ).
cnf(131711,plain,
( ~ product(c,a,u)
| equal(add(u,c),additive_identity) ),
inference(rew,[status(thm),theory(equality)],[290,131700]),
[iquote('0:Rew:290.0,131700.1')] ).
cnf(131793,plain,
equal(add(multiply(c,a),c),additive_identity),
inference(res,[status(thm),theory(equality)],[12,131711]),
[iquote('0:Res:12.0,131711.0')] ).
cnf(131799,plain,
equal(add(c,multiply(c,a)),additive_identity),
inference(rew,[status(thm),theory(equality)],[509,131793]),
[iquote('0:Rew:509.0,131793.0')] ).
cnf(131814,plain,
equal(multiply(c,a),add(c,additive_identity)),
inference(spr,[status(thm),theory(equality)],[131799,24364]),
[iquote('0:SpR:131799.0,24364.0')] ).
cnf(132336,plain,
equal(multiply(c,a),c),
inference(rew,[status(thm),theory(equality)],[161,131814,509]),
[iquote('0:Rew:161.0,131814.0,509.0,131814.0')] ).
cnf(132369,plain,
equal(multiply(b,c),multiply(b,a)),
inference(rew,[status(thm),theory(equality)],[132336,110256]),
[iquote('0:Rew:132336.0,110256.0')] ).
cnf(134041,plain,
( ~ product(b,c,u)
| sum__dfg(u,multiply(c,c),additive_identity) ),
inference(spr,[status(thm),theory(equality)],[111237,35093]),
[iquote('0:SpR:111237.0,35093.1')] ).
cnf(134212,plain,
( ~ product(b,c,u)
| sum__dfg(u,c,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[290,134041]),
[iquote('0:Rew:290.0,134041.1')] ).
cnf(136155,plain,
sum__dfg(multiply(b,c),c,additive_identity),
inference(res,[status(thm),theory(equality)],[12,134212]),
[iquote('0:Res:12.0,134212.0')] ).
cnf(136171,plain,
sum__dfg(multiply(b,a),c,additive_identity),
inference(rew,[status(thm),theory(equality)],[132369,136155]),
[iquote('0:Rew:132369.0,136155.0')] ).
cnf(136223,plain,
equal(multiply(b,a),c),
inference(res,[status(thm),theory(equality)],[136171,24287]),
[iquote('0:Res:136171.0,24287.0')] ).
cnf(136604,plain,
product(b,a,c),
inference(spr,[status(thm),theory(equality)],[136223,12]),
[iquote('0:SpR:136223.0,12.0')] ).
cnf(136690,plain,
$false,
inference(mrr,[status(thm)],[136604,9]),
[iquote('0:MRR:136604.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG008-5 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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 May 30 17:50:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 230.14/230.32
% 230.14/230.32 SPASS V 3.9
% 230.14/230.32 SPASS beiseite: Proof found.
% 230.14/230.32 % SZS status Theorem
% 230.14/230.32 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 230.14/230.32 SPASS derived 105334 clauses, backtracked 0 clauses, performed 0 splits and kept 26891 clauses.
% 230.14/230.32 SPASS allocated 132187 KBytes.
% 230.14/230.32 SPASS spent 0:3:49.85 on the problem.
% 230.14/230.32 0:00:00.03 for the input.
% 230.14/230.32 0:00:00.00 for the FLOTTER CNF translation.
% 230.14/230.32 0:00:01.00 for inferences.
% 230.14/230.32 0:00:00.00 for the backtracking.
% 230.14/230.32 0:3:48.16 for the reduction.
% 230.14/230.32
% 230.14/230.32
% 230.14/230.32 Here is a proof with depth 14, length 155 :
% 230.14/230.32 % SZS output start Refutation
% See solution above
% 233.67/233.89 Formulae used in the proof : additive_inverse_additive_inverse multiply_additive_id1 multiply_additive_id2 distribute_additive_inverse multiply_additive_inverse x_squared_is_x a_times_b_is_c prove_b_times_a_is_c additive_identity1 additive_identity2 closure_of_multiplication closure_of_addition left_inverse right_inverse associativity_of_addition1 associativity_of_addition2 commutativity_of_addition associativity_of_multiplication1 associativity_of_multiplication2 distributivity2 distributivity3 distributivity4 addition_is_well_defined multiplication_is_well_defined
% 233.67/233.89
%------------------------------------------------------------------------------