TSTP Solution File: RNG029-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG029-3 : TPTP v8.1.0. Bugfixed v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 20:41:16 EDT 2022
% Result : Unsatisfiable 28.86s 29.07s
% Output : Refutation 29.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 72 RR)
% Number of literals : 72 ( 0 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(multiply(multiply(u,v),w),v),multiply(u,multiply(v,multiply(w,v)))),
file('RNG029-3.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(multiply(u,multiply(v,u)),w),multiply(u,multiply(v,multiply(u,w)))),
file('RNG029-3.p',unknown),
[] ).
cnf(3,axiom,
equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
file('RNG029-3.p',unknown),
[] ).
cnf(5,axiom,
equal(additive_inverse(associator(u,v,w)),associator(v,u,w)),
file('RNG029-3.p',unknown),
[] ).
cnf(6,axiom,
equal(additive_inverse(associator(u,v,w)),associator(w,v,u)),
file('RNG029-3.p',unknown),
[] ).
cnf(7,axiom,
~ equal(multiply(cx,multiply(multiply(cy,cz),cx)),multiply(multiply(cx,cy),multiply(cz,cx))),
file('RNG029-3.p',unknown),
[] ).
cnf(8,axiom,
equal(add(additive_identity,u),u),
file('RNG029-3.p',unknown),
[] ).
cnf(11,axiom,
equal(add(additive_inverse(u),u),additive_identity),
file('RNG029-3.p',unknown),
[] ).
cnf(12,axiom,
equal(additive_inverse(add(u,v)),add(additive_inverse(u),additive_inverse(v))),
file('RNG029-3.p',unknown),
[] ).
cnf(13,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG029-3.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG029-3.p',unknown),
[] ).
cnf(18,axiom,
equal(additive_inverse(multiply(u,v)),multiply(additive_inverse(u),v)),
file('RNG029-3.p',unknown),
[] ).
cnf(19,axiom,
equal(additive_inverse(multiply(u,v)),multiply(u,additive_inverse(v))),
file('RNG029-3.p',unknown),
[] ).
cnf(21,axiom,
equal(add(u,v),add(v,u)),
file('RNG029-3.p',unknown),
[] ).
cnf(22,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG029-3.p',unknown),
[] ).
cnf(25,plain,
equal(add(u,additive_inverse(u)),additive_identity),
inference(rew,[status(thm),theory(equality)],[21,11]),
[iquote('0:Rew:21.0,11.0')] ).
cnf(26,plain,
equal(multiply(u,additive_inverse(v)),multiply(additive_inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[19,18]),
[iquote('0:Rew:19.0,18.0')] ).
cnf(27,plain,
equal(associator(u,v,w),associator(v,w,u)),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(28,plain,
equal(add(multiply(multiply(u,v),w),multiply(u,multiply(v,additive_inverse(w)))),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[19,3]),
[iquote('0:Rew:19.0,3.0,19.0,3.0')] ).
cnf(46,plain,
equal(add(u,additive_identity),u),
inference(spr,[status(thm),theory(equality)],[21,8]),
[iquote('0:SpR:21.0,8.0')] ).
cnf(63,plain,
equal(multiply(additive_inverse(u),additive_inverse(v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[13,26]),
[iquote('0:SpR:13.0,26.0')] ).
cnf(73,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
inference(spr,[status(thm),theory(equality)],[19,25]),
[iquote('0:SpR:19.0,25.0')] ).
cnf(74,plain,
equal(multiply(multiply(u,v),additive_inverse(w)),multiply(multiply(u,additive_inverse(v)),w)),
inference(spr,[status(thm),theory(equality)],[19,26]),
[iquote('0:SpR:19.0,26.0')] ).
cnf(75,plain,
equal(multiply(u,multiply(v,additive_inverse(w))),multiply(additive_inverse(u),multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[19,26]),
[iquote('0:SpR:19.0,26.0')] ).
cnf(92,plain,
equal(multiply(additive_inverse(u),multiply(v,additive_inverse(w))),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[19,63]),
[iquote('0:SpR:19.0,63.0')] ).
cnf(137,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),additive_identity),
inference(spr,[status(thm),theory(equality)],[26,73]),
[iquote('0:SpR:26.0,73.0')] ).
cnf(160,plain,
equal(multiply(additive_inverse(u),associator(v,w,x)),multiply(u,associator(x,w,v))),
inference(spr,[status(thm),theory(equality)],[6,26]),
[iquote('0:SpR:6.0,26.0')] ).
cnf(653,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[21,22]),
[iquote('0:SpR:21.0,22.0')] ).
cnf(660,plain,
equal(add(multiply(u,v),add(multiply(additive_inverse(u),v),w)),add(additive_identity,w)),
inference(spr,[status(thm),theory(equality)],[137,22]),
[iquote('0:SpR:137.0,22.0')] ).
cnf(687,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[22,653]),
[iquote('0:Rew:22.0,653.0')] ).
cnf(711,plain,
equal(add(multiply(u,v),add(multiply(additive_inverse(u),v),w)),w),
inference(rew,[status(thm),theory(equality)],[8,660]),
[iquote('0:Rew:8.0,660.0')] ).
cnf(1645,plain,
equal(add(additive_inverse(multiply(multiply(u,v),w)),additive_inverse(multiply(u,multiply(v,additive_inverse(w))))),additive_inverse(associator(u,v,w))),
inference(spr,[status(thm),theory(equality)],[28,12]),
[iquote('0:SpR:28.0,12.0')] ).
cnf(1654,plain,
equal(add(multiply(multiply(u,v),additive_inverse(w)),multiply(u,multiply(v,w))),associator(u,v,additive_inverse(w))),
inference(spr,[status(thm),theory(equality)],[13,28]),
[iquote('0:SpR:13.0,28.0')] ).
cnf(1662,plain,
equal(add(multiply(multiply(u,v),w),multiply(u,multiply(additive_inverse(v),w))),associator(u,v,w)),
inference(spr,[status(thm),theory(equality)],[26,28]),
[iquote('0:SpR:26.0,28.0')] ).
cnf(1665,plain,
equal(add(multiply(multiply(u,additive_inverse(v)),w),multiply(u,multiply(v,w))),associator(u,additive_inverse(v),w)),
inference(spr,[status(thm),theory(equality)],[63,28]),
[iquote('0:SpR:63.0,28.0')] ).
cnf(1675,plain,
equal(add(multiply(multiply(additive_inverse(u),v),w),multiply(u,additive_inverse(multiply(v,additive_inverse(w))))),associator(additive_inverse(u),v,w)),
inference(spr,[status(thm),theory(equality)],[26,28]),
[iquote('0:SpR:26.0,28.0')] ).
cnf(1688,plain,
equal(add(multiply(multiply(u,additive_inverse(v)),w),multiply(additive_inverse(u),multiply(v,additive_inverse(w)))),associator(additive_inverse(u),v,w)),
inference(spr,[status(thm),theory(equality)],[26,28]),
[iquote('0:SpR:26.0,28.0')] ).
cnf(1703,plain,
equal(add(multiply(u,multiply(v,multiply(w,v))),multiply(multiply(u,v),multiply(w,additive_inverse(v)))),associator(multiply(u,v),w,v)),
inference(spr,[status(thm),theory(equality)],[1,28]),
[iquote('0:SpR:1.0,28.0')] ).
cnf(1724,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(u,v),additive_inverse(w))),associator(u,v,additive_inverse(w))),
inference(rew,[status(thm),theory(equality)],[21,1654]),
[iquote('0:Rew:21.0,1654.0')] ).
cnf(1726,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(u,additive_inverse(v)),w)),associator(u,additive_inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[21,1665]),
[iquote('0:Rew:21.0,1665.0')] ).
cnf(1737,plain,
equal(add(multiply(multiply(u,additive_inverse(v)),w),multiply(u,multiply(v,w))),associator(additive_inverse(u),v,w)),
inference(rew,[status(thm),theory(equality)],[92,1688]),
[iquote('0:Rew:92.0,1688.0')] ).
cnf(1738,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(u,additive_inverse(v)),w)),associator(additive_inverse(u),v,w)),
inference(rew,[status(thm),theory(equality)],[21,1737]),
[iquote('0:Rew:21.0,1737.0')] ).
cnf(1739,plain,
equal(associator(u,additive_inverse(v),w),associator(additive_inverse(u),v,w)),
inference(rew,[status(thm),theory(equality)],[1726,1738]),
[iquote('0:Rew:1726.0,1738.0')] ).
cnf(1741,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(additive_inverse(u),v),w)),associator(additive_inverse(u),v,w)),
inference(rew,[status(thm),theory(equality)],[21,1675,13,19]),
[iquote('0:Rew:21.0,1675.0,13.0,1675.0,19.0,1675.0')] ).
cnf(1747,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(u,v),additive_inverse(w))),associator(w,v,u)),
inference(rew,[status(thm),theory(equality)],[21,1645,19,13,6]),
[iquote('0:Rew:21.0,1645.0,19.0,1645.0,13.0,1645.0,19.0,1645.0,19.0,1645.0,6.0,1645.0')] ).
cnf(1748,plain,
equal(associator(u,v,additive_inverse(w)),associator(w,v,u)),
inference(rew,[status(thm),theory(equality)],[1724,1747]),
[iquote('0:Rew:1724.0,1747.0')] ).
cnf(1750,plain,
equal(add(multiply(u,multiply(v,multiply(w,v))),multiply(multiply(u,v),multiply(w,additive_inverse(v)))),associator(v,multiply(u,v),w)),
inference(rew,[status(thm),theory(equality)],[27,1703]),
[iquote('0:Rew:27.0,1703.0')] ).
cnf(1869,plain,
equal(associator(additive_inverse(u),v,w),associator(u,w,v)),
inference(spr,[status(thm),theory(equality)],[1748,27]),
[iquote('0:SpR:1748.0,27.0')] ).
cnf(1870,plain,
equal(associator(u,v,w),associator(v,additive_inverse(u),w)),
inference(spr,[status(thm),theory(equality)],[1748,27]),
[iquote('0:SpR:1748.0,27.0')] ).
cnf(1907,plain,
equal(associator(u,additive_inverse(v),w),associator(u,w,v)),
inference(rew,[status(thm),theory(equality)],[1869,1739]),
[iquote('0:Rew:1869.0,1739.0')] ).
cnf(1908,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(additive_inverse(u),v),w)),associator(u,w,v)),
inference(rew,[status(thm),theory(equality)],[1869,1741]),
[iquote('0:Rew:1869.0,1741.0')] ).
cnf(2008,plain,
equal(associator(u,additive_inverse(v),additive_inverse(w)),associator(u,v,w)),
inference(spr,[status(thm),theory(equality)],[1907]),
[iquote('0:SpR:1907.0,1907.0')] ).
cnf(3920,plain,
equal(associator(u,additive_inverse(v),multiply(w,additive_inverse(x))),associator(u,v,multiply(w,x))),
inference(spr,[status(thm),theory(equality)],[19,2008]),
[iquote('0:SpR:19.0,2008.0')] ).
cnf(4036,plain,
equal(multiply(u,multiply(multiply(v,additive_inverse(w)),x)),multiply(additive_inverse(u),multiply(multiply(v,w),x))),
inference(spr,[status(thm),theory(equality)],[74,75]),
[iquote('0:SpR:74.0,75.0')] ).
cnf(19495,plain,
equal(add(multiply(multiply(u,v),multiply(w,additive_inverse(x))),multiply(u,multiply(additive_inverse(additive_inverse(v)),multiply(w,x)))),associator(u,v,multiply(w,additive_inverse(x)))),
inference(spr,[status(thm),theory(equality)],[75,1662]),
[iquote('0:SpR:75.0,1662.0')] ).
cnf(19588,plain,
equal(add(multiply(u,multiply(v,multiply(u,w))),multiply(u,multiply(additive_inverse(multiply(v,u)),w))),associator(u,multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[2,1662]),
[iquote('0:SpR:2.0,1662.0')] ).
cnf(19717,plain,
equal(add(multiply(u,multiply(v,multiply(u,w))),multiply(u,multiply(multiply(v,additive_inverse(u)),w))),associator(u,multiply(v,u),w)),
inference(rew,[status(thm),theory(equality)],[19,19588]),
[iquote('0:Rew:19.0,19588.0')] ).
cnf(19718,plain,
equal(add(multiply(u,multiply(v,multiply(u,w))),multiply(additive_inverse(u),multiply(multiply(v,u),w))),associator(u,multiply(v,u),w)),
inference(rew,[status(thm),theory(equality)],[4036,19717]),
[iquote('0:Rew:4036.0,19717.0')] ).
cnf(19775,plain,
equal(add(multiply(u,multiply(v,multiply(w,x))),multiply(multiply(u,v),multiply(w,additive_inverse(x)))),associator(u,v,multiply(w,additive_inverse(x)))),
inference(rew,[status(thm),theory(equality)],[21,19495,13]),
[iquote('0:Rew:21.0,19495.0,13.0,19495.0')] ).
cnf(19778,plain,
equal(associator(u,v,multiply(w,additive_inverse(v))),associator(v,multiply(u,v),w)),
inference(rew,[status(thm),theory(equality)],[19775,1750]),
[iquote('0:Rew:19775.0,1750.0')] ).
cnf(20554,plain,
equal(associator(u,multiply(v,u),w),associator(u,additive_inverse(v),multiply(w,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[19778,1870]),
[iquote('0:SpR:19778.0,1870.0')] ).
cnf(20733,plain,
equal(associator(u,multiply(v,u),w),associator(u,v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[3920,20554]),
[iquote('0:Rew:3920.0,20554.0')] ).
cnf(21383,plain,
equal(multiply(multiply(additive_inverse(additive_inverse(u)),v),w),add(multiply(u,multiply(v,w)),associator(additive_inverse(u),w,v))),
inference(spr,[status(thm),theory(equality)],[1908,711]),
[iquote('0:SpR:1908.0,711.0')] ).
cnf(21551,plain,
equal(multiply(multiply(u,v),w),add(associator(u,v,w),multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[13,21383,21,1869]),
[iquote('0:Rew:13.0,21383.0,21.0,21383.0,1869.0,21383.0')] ).
cnf(21556,plain,
~ equal(multiply(multiply(cx,cy),multiply(cz,cx)),multiply(cx,add(associator(cy,cz,cx),multiply(cy,multiply(cz,cx))))),
inference(rew,[status(thm),theory(equality)],[21551,7]),
[iquote('0:Rew:21551.0,7.0')] ).
cnf(22027,plain,
equal(add(multiply(u,multiply(v,multiply(u,w))),multiply(additive_inverse(u),add(associator(v,u,w),multiply(v,multiply(u,w))))),associator(u,multiply(v,u),w)),
inference(rew,[status(thm),theory(equality)],[21551,19718]),
[iquote('0:Rew:21551.0,19718.0')] ).
cnf(22362,plain,
~ equal(multiply(multiply(cx,cy),multiply(cz,cx)),add(multiply(cx,associator(cx,cy,cz)),multiply(cx,multiply(cy,multiply(cz,cx))))),
inference(rew,[status(thm),theory(equality)],[14,21556,27]),
[iquote('0:Rew:14.0,21556.0,27.0,21556.0')] ).
cnf(22363,plain,
~ equal(add(associator(cx,multiply(cy,cx),cz),multiply(cx,multiply(cy,multiply(cz,cx)))),add(multiply(cx,associator(cx,cy,cz)),multiply(cx,multiply(cy,multiply(cz,cx))))),
inference(rew,[status(thm),theory(equality)],[20733,22362,21551]),
[iquote('0:Rew:20733.0,22362.0,21551.0,22362.0')] ).
cnf(22819,plain,
equal(multiply(u,associator(v,u,w)),associator(u,multiply(w,u),v)),
inference(rew,[status(thm),theory(equality)],[46,22027,137,687,160,14]),
[iquote('0:Rew:46.0,22027.0,137.0,22027.0,687.0,22027.0,160.0,22027.0,14.0,22027.0')] ).
cnf(22820,plain,
~ equal(add(multiply(cx,associator(cz,cx,cy)),multiply(cx,multiply(cy,multiply(cz,cx)))),add(multiply(cx,associator(cx,cy,cz)),multiply(cx,multiply(cy,multiply(cz,cx))))),
inference(rew,[status(thm),theory(equality)],[22819,22363]),
[iquote('0:Rew:22819.0,22363.0')] ).
cnf(23037,plain,
~ equal(add(multiply(cx,associator(cx,cy,cz)),multiply(cx,multiply(cy,multiply(cz,cx)))),add(multiply(cx,associator(cx,cy,cz)),multiply(cx,multiply(cy,multiply(cz,cx))))),
inference(rew,[status(thm),theory(equality)],[27,22820]),
[iquote('0:Rew:27.0,22820.0')] ).
cnf(23038,plain,
$false,
inference(obv,[status(thm),theory(equality)],[23037]),
[iquote('0:Obv:23037.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG029-3 : TPTP v8.1.0. Bugfixed v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 19:52:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 28.86/29.07
% 28.86/29.07 SPASS V 3.9
% 28.86/29.07 SPASS beiseite: Proof found.
% 28.86/29.07 % SZS status Theorem
% 28.86/29.07 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.86/29.07 SPASS derived 14177 clauses, backtracked 0 clauses, performed 0 splits and kept 3958 clauses.
% 28.86/29.07 SPASS allocated 106014 KBytes.
% 28.86/29.07 SPASS spent 0:0:28.71 on the problem.
% 28.86/29.07 0:00:00.03 for the input.
% 28.86/29.07 0:00:00.00 for the FLOTTER CNF translation.
% 28.86/29.07 0:00:00.10 for inferences.
% 28.86/29.07 0:00:00.00 for the backtracking.
% 28.86/29.07 0:0:28.54 for the reduction.
% 28.86/29.07
% 28.86/29.07
% 28.86/29.07 Here is a proof with depth 4, length 72 :
% 28.86/29.07 % SZS output start Refutation
% See solution above
% 29.24/29.43 Formulae used in the proof : right_moufang left_moufang associator associator_skew_symmetry1 associator_skew_symmetry2 prove_middle_law left_additive_identity add_inverse sum_of_inverses additive_inverse_additive_inverse multiply_over_add1 inverse_product1 inverse_product2 commutativity_for_addition associativity_for_addition
% 29.24/29.43
%------------------------------------------------------------------------------