TSTP Solution File: RNG013-6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG013-6 : TPTP v8.1.0. Released v1.0.0.
% 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 20:41:12 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 47 RR)
% Number of literals : 47 ( 0 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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(multiply(additive_inverse(a),b),additive_inverse(multiply(a,b))),
file('RNG013-6.p',unknown),
[] ).
cnf(2,axiom,
equal(add(additive_identity,u),u),
file('RNG013-6.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,additive_identity),u),
file('RNG013-6.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(additive_identity,u),additive_identity),
file('RNG013-6.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(u,additive_identity),additive_identity),
file('RNG013-6.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG013-6.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG013-6.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG013-6.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG013-6.p',unknown),
[] ).
cnf(11,axiom,
equal(add(u,v),add(v,u)),
file('RNG013-6.p',unknown),
[] ).
cnf(12,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG013-6.p',unknown),
[] ).
cnf(16,axiom,
equal(add(multiply(u,v),additive_inverse(multiply(v,u))),commutator(v,u)),
file('RNG013-6.p',unknown),
[] ).
cnf(27,plain,
equal(additive_inverse(additive_identity),additive_identity),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(64,plain,
equal(add(u,add(v,additive_inverse(add(u,v)))),additive_identity),
inference(spr,[status(thm),theory(equality)],[12,7]),
[iquote('0:SpR:12.0,7.0')] ).
cnf(71,plain,
equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[7,12]),
[iquote('0:SpR:7.0,12.0')] ).
cnf(75,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[2,71]),
[iquote('0:Rew:2.0,71.0')] ).
cnf(86,plain,
equal(add(u,add(v,additive_inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[11,75]),
[iquote('0:SpR:11.0,75.0')] ).
cnf(118,plain,
equal(add(multiply(u,v),commutator(u,v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[16,86]),
[iquote('0:SpR:16.0,86.0')] ).
cnf(132,plain,
equal(add(commutator(u,v),multiply(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[11,118]),
[iquote('0:Rew:11.0,118.0')] ).
cnf(134,plain,
~ equal(add(commutator(b,additive_inverse(a)),multiply(b,additive_inverse(a))),additive_inverse(multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[132,1]),
[iquote('0:Rew:132.0,1.0')] ).
cnf(150,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),add(v,additive_identity)),
inference(spr,[status(thm),theory(equality)],[64,75]),
[iquote('0:SpR:64.0,75.0')] ).
cnf(167,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[3,150]),
[iquote('0:Rew:3.0,150.0')] ).
cnf(185,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),multiply(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[7,10]),
[iquote('0:SpR:7.0,10.0')] ).
cnf(195,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),additive_identity),
inference(rew,[status(thm),theory(equality)],[4,185]),
[iquote('0:Rew:4.0,185.0')] ).
cnf(220,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[8,167]),
[iquote('0:SpR:8.0,167.0')] ).
cnf(249,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[220,75]),
[iquote('0:SpR:220.0,75.0')] ).
cnf(253,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[11,220]),
[iquote('0:SpR:11.0,220.0')] ).
cnf(312,plain,
equal(add(multiply(additive_inverse(u),v),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[195,220]),
[iquote('0:SpR:195.0,220.0')] ).
cnf(329,plain,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,312,11,27]),
[iquote('0:Rew:2.0,312.0,11.0,312.0,27.0,312.0')] ).
cnf(359,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[7,9]),
[iquote('0:SpR:7.0,9.0')] ).
cnf(370,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
inference(rew,[status(thm),theory(equality)],[5,359]),
[iquote('0:Rew:5.0,359.0')] ).
cnf(384,plain,
equal(add(additive_inverse(multiply(u,v)),additive_inverse(multiply(v,additive_inverse(u)))),commutator(v,additive_inverse(u))),
inference(spr,[status(thm),theory(equality)],[329,16]),
[iquote('0:SpR:329.0,16.0')] ).
cnf(397,plain,
equal(add(additive_inverse(u),v),additive_inverse(add(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[249,11]),
[iquote('0:SpR:249.0,11.0')] ).
cnf(408,plain,
equal(additive_inverse(add(multiply(u,v),additive_inverse(multiply(v,u)))),commutator(u,v)),
inference(spr,[status(thm),theory(equality)],[249,16]),
[iquote('0:SpR:249.0,16.0')] ).
cnf(445,plain,
equal(additive_inverse(add(multiply(u,v),additive_inverse(additive_inverse(multiply(v,additive_inverse(u)))))),commutator(v,additive_inverse(u))),
inference(rew,[status(thm),theory(equality)],[397,384]),
[iquote('0:Rew:397.0,384.0')] ).
cnf(466,plain,
equal(additive_inverse(commutator(u,v)),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[16,408]),
[iquote('0:Rew:16.0,408.0')] ).
cnf(495,plain,
equal(additive_inverse(add(multiply(u,v),multiply(v,additive_inverse(u)))),commutator(v,additive_inverse(u))),
inference(rew,[status(thm),theory(equality)],[8,445]),
[iquote('0:Rew:8.0,445.0')] ).
cnf(605,plain,
equal(add(multiply(u,additive_inverse(v)),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[370,220]),
[iquote('0:SpR:370.0,220.0')] ).
cnf(632,plain,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,605,11,27]),
[iquote('0:Rew:2.0,605.0,11.0,605.0,27.0,605.0')] ).
cnf(633,plain,
~ equal(add(commutator(b,additive_inverse(a)),additive_inverse(multiply(b,a))),additive_inverse(multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[632,134]),
[iquote('0:Rew:632.0,134.0')] ).
cnf(635,plain,
equal(additive_inverse(add(multiply(u,v),additive_inverse(multiply(v,u)))),commutator(v,additive_inverse(u))),
inference(rew,[status(thm),theory(equality)],[632,495]),
[iquote('0:Rew:632.0,495.0')] ).
cnf(667,plain,
equal(commutator(u,additive_inverse(v)),additive_inverse(commutator(u,v))),
inference(rew,[status(thm),theory(equality)],[16,635]),
[iquote('0:Rew:16.0,635.0')] ).
cnf(671,plain,
~ equal(additive_inverse(add(commutator(b,a),additive_inverse(additive_inverse(add(commutator(a,b),multiply(a,b)))))),additive_inverse(multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[397,633,667,132]),
[iquote('0:Rew:397.0,633.0,667.0,633.0,132.0,633.0')] ).
cnf(672,plain,
~ equal(additive_inverse(add(additive_inverse(commutator(a,b)),add(commutator(a,b),multiply(a,b)))),additive_inverse(multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[466,671,8]),
[iquote('0:Rew:466.0,671.0,8.0,671.0')] ).
cnf(673,plain,
~ equal(additive_inverse(additive_inverse(add(commutator(a,b),additive_inverse(add(commutator(a,b),multiply(a,b)))))),additive_inverse(multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[397,672]),
[iquote('0:Rew:397.0,672.0')] ).
cnf(674,plain,
~ equal(additive_inverse(multiply(a,b)),additive_inverse(multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[8,673,253]),
[iquote('0:Rew:8.0,673.0,253.0,673.0')] ).
cnf(675,plain,
$false,
inference(obv,[status(thm),theory(equality)],[674]),
[iquote('0:Obv:674.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG013-6 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 12:32:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 386 clauses, backtracked 0 clauses, performed 0 splits and kept 117 clauses.
% 0.19/0.48 SPASS allocated 63914 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.48 0:00:00.04 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.00 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.06 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 5, length 47 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.48 Formulae used in the proof : prove_equation left_additive_identity right_additive_identity left_multiplicative_zero right_multiplicative_zero right_additive_inverse additive_inverse_additive_inverse distribute1 distribute2 commutativity_for_addition associativity_for_addition commutator
% 0.19/0.48
%------------------------------------------------------------------------------