TSTP Solution File: RNG017-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG017-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 20:41:13 EDT 2022
% Result : Unsatisfiable 0.14s 0.42s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 60 RR)
% Number of literals : 60 ( 0 equ; 11 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(multiply(additive_inverse(x__dfg),add(y__dfg,z__dfg)),add(additive_inverse(multiply(x__dfg,y__dfg)),additive_inverse(multiply(x__dfg,z__dfg)))),
file('RNG017-6.p',unknown),
[] ).
cnf(2,axiom,
equal(add(additive_identity,u),u),
file('RNG017-6.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,additive_identity),u),
file('RNG017-6.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(additive_identity,u),additive_identity),
file('RNG017-6.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(u,additive_identity),additive_identity),
file('RNG017-6.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG017-6.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG017-6.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG017-6.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG017-6.p',unknown),
[] ).
cnf(11,axiom,
equal(add(u,v),add(v,u)),
file('RNG017-6.p',unknown),
[] ).
cnf(12,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG017-6.p',unknown),
[] ).
cnf(16,axiom,
equal(add(multiply(u,v),additive_inverse(multiply(v,u))),commutator(v,u)),
file('RNG017-6.p',unknown),
[] ).
cnf(19,plain,
~ equal(add(multiply(additive_inverse(x__dfg),y__dfg),multiply(additive_inverse(x__dfg),z__dfg)),add(additive_inverse(multiply(x__dfg,y__dfg)),additive_inverse(multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[9,1]),
[iquote('0:Rew:9.0,1.0')] ).
cnf(28,plain,
equal(additive_inverse(additive_identity),additive_identity),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(65,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(70,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[11,12]),
[iquote('0:SpR:11.0,12.0')] ).
cnf(72,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(76,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[2,72]),
[iquote('0:Rew:2.0,72.0')] ).
cnf(77,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[12,70]),
[iquote('0:Rew:12.0,70.0')] ).
cnf(87,plain,
equal(add(u,add(v,additive_inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[11,76]),
[iquote('0:SpR:11.0,76.0')] ).
cnf(121,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),add(v,additive_identity)),
inference(spr,[status(thm),theory(equality)],[65,76]),
[iquote('0:SpR:65.0,76.0')] ).
cnf(137,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[3,121]),
[iquote('0:Rew:3.0,121.0')] ).
cnf(149,plain,
equal(add(multiply(u,v),commutator(u,v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[16,87]),
[iquote('0:SpR:16.0,87.0')] ).
cnf(163,plain,
equal(add(commutator(u,v),multiply(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[11,149]),
[iquote('0:Rew:11.0,149.0')] ).
cnf(165,plain,
~ equal(add(add(commutator(y__dfg,additive_inverse(x__dfg)),multiply(y__dfg,additive_inverse(x__dfg))),multiply(additive_inverse(x__dfg),z__dfg)),add(additive_inverse(multiply(x__dfg,y__dfg)),additive_inverse(multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[163,19]),
[iquote('0:Rew:163.0,19.0')] ).
cnf(172,plain,
~ equal(add(commutator(y__dfg,additive_inverse(x__dfg)),add(multiply(y__dfg,additive_inverse(x__dfg)),multiply(additive_inverse(x__dfg),z__dfg))),add(additive_inverse(multiply(x__dfg,y__dfg)),additive_inverse(multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[12,165]),
[iquote('0:Rew:12.0,165.0')] ).
cnf(173,plain,
~ equal(add(commutator(y__dfg,additive_inverse(x__dfg)),add(commutator(z__dfg,additive_inverse(x__dfg)),add(multiply(y__dfg,additive_inverse(x__dfg)),multiply(z__dfg,additive_inverse(x__dfg))))),add(additive_inverse(multiply(x__dfg,y__dfg)),additive_inverse(multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[77,172,163]),
[iquote('0:Rew:77.0,172.0,163.0,172.0')] ).
cnf(189,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[8,137]),
[iquote('0:SpR:8.0,137.0')] ).
cnf(221,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(230,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),additive_identity),
inference(rew,[status(thm),theory(equality)],[4,221]),
[iquote('0:Rew:4.0,221.0')] ).
cnf(249,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[189,76]),
[iquote('0:SpR:189.0,76.0')] ).
cnf(253,plain,
equal(add(u,additive_inverse(add(u,v))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[11,189]),
[iquote('0:SpR:11.0,189.0')] ).
cnf(309,plain,
equal(add(multiply(additive_inverse(u),v),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[230,189]),
[iquote('0:SpR:230.0,189.0')] ).
cnf(326,plain,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,309,11,28]),
[iquote('0:Rew:2.0,309.0,11.0,309.0,28.0,309.0')] ).
cnf(348,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)],[326,16]),
[iquote('0:SpR:326.0,16.0')] ).
cnf(364,plain,
equal(add(multiply(additive_inverse(u),v),multiply(additive_inverse(u),w)),additive_inverse(multiply(u,add(v,w)))),
inference(spr,[status(thm),theory(equality)],[9,326]),
[iquote('0:SpR:9.0,326.0')] ).
cnf(369,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(380,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
inference(rew,[status(thm),theory(equality)],[5,369]),
[iquote('0:Rew:5.0,369.0')] ).
cnf(385,plain,
equal(add(additive_inverse(multiply(u,v)),additive_inverse(multiply(u,w))),additive_inverse(add(multiply(u,v),multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[326,364,9]),
[iquote('0:Rew:326.0,364.0,326.0,364.0,9.0,364.0')] ).
cnf(386,plain,
~ equal(add(commutator(y__dfg,additive_inverse(x__dfg)),add(commutator(z__dfg,additive_inverse(x__dfg)),add(multiply(y__dfg,additive_inverse(x__dfg)),multiply(z__dfg,additive_inverse(x__dfg))))),additive_inverse(add(multiply(x__dfg,y__dfg),multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[385,173]),
[iquote('0:Rew:385.0,173.0')] ).
cnf(395,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(398,plain,
equal(add(additive_inverse(add(u,additive_inverse(v))),w),add(v,add(additive_inverse(u),w))),
inference(spr,[status(thm),theory(equality)],[249,12]),
[iquote('0:SpR:249.0,12.0')] ).
cnf(406,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(443,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)],[395,348]),
[iquote('0:Rew:395.0,348.0')] ).
cnf(464,plain,
equal(additive_inverse(commutator(u,v)),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[16,406]),
[iquote('0:Rew:16.0,406.0')] ).
cnf(473,plain,
equal(additive_inverse(add(add(u,additive_inverse(v)),additive_inverse(w))),add(v,additive_inverse(add(u,additive_inverse(w))))),
inference(rew,[status(thm),theory(equality)],[395,398]),
[iquote('0:Rew:395.0,398.0,395.0,398.0')] ).
cnf(474,plain,
equal(additive_inverse(add(u,add(additive_inverse(v),additive_inverse(w)))),add(v,additive_inverse(add(u,additive_inverse(w))))),
inference(rew,[status(thm),theory(equality)],[12,473]),
[iquote('0:Rew:12.0,473.0')] ).
cnf(475,plain,
equal(additive_inverse(add(u,additive_inverse(add(v,additive_inverse(additive_inverse(w)))))),add(v,additive_inverse(add(u,additive_inverse(w))))),
inference(rew,[status(thm),theory(equality)],[395,474]),
[iquote('0:Rew:395.0,474.0')] ).
cnf(476,plain,
equal(additive_inverse(add(u,additive_inverse(add(v,w)))),add(v,additive_inverse(add(u,additive_inverse(w))))),
inference(rew,[status(thm),theory(equality)],[8,475]),
[iquote('0:Rew:8.0,475.0')] ).
cnf(493,plain,
equal(additive_inverse(add(multiply(u,v),multiply(v,additive_inverse(u)))),commutator(v,additive_inverse(u))),
inference(rew,[status(thm),theory(equality)],[8,443]),
[iquote('0:Rew:8.0,443.0')] ).
cnf(676,plain,
equal(add(multiply(u,additive_inverse(v)),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[380,189]),
[iquote('0:SpR:380.0,189.0')] ).
cnf(704,plain,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,676,11,28]),
[iquote('0:Rew:2.0,676.0,11.0,676.0,28.0,676.0')] ).
cnf(706,plain,
~ equal(add(commutator(y__dfg,additive_inverse(x__dfg)),add(commutator(z__dfg,additive_inverse(x__dfg)),add(additive_inverse(multiply(y__dfg,x__dfg)),multiply(z__dfg,additive_inverse(x__dfg))))),additive_inverse(add(multiply(x__dfg,y__dfg),multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[704,386]),
[iquote('0:Rew:704.0,386.0')] ).
cnf(708,plain,
equal(additive_inverse(add(multiply(u,v),additive_inverse(multiply(v,u)))),commutator(v,additive_inverse(u))),
inference(rew,[status(thm),theory(equality)],[704,493]),
[iquote('0:Rew:704.0,493.0')] ).
cnf(741,plain,
equal(commutator(u,additive_inverse(v)),additive_inverse(commutator(u,v))),
inference(rew,[status(thm),theory(equality)],[16,708]),
[iquote('0:Rew:16.0,708.0')] ).
cnf(774,plain,
~ equal(additive_inverse(add(commutator(y__dfg,x__dfg),additive_inverse(additive_inverse(add(commutator(z__dfg,x__dfg),additive_inverse(additive_inverse(add(add(commutator(x__dfg,y__dfg),multiply(x__dfg,y__dfg)),additive_inverse(additive_inverse(add(commutator(x__dfg,z__dfg),multiply(x__dfg,z__dfg)))))))))))),additive_inverse(add(multiply(x__dfg,y__dfg),multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[395,706,741,163,704]),
[iquote('0:Rew:395.0,706.0,741.0,706.0,395.0,706.0,741.0,706.0,395.0,706.0,163.0,706.0,163.0,706.0,704.0,706.0')] ).
cnf(775,plain,
~ equal(additive_inverse(add(additive_inverse(commutator(x__dfg,y__dfg)),add(additive_inverse(commutator(x__dfg,z__dfg)),add(commutator(x__dfg,y__dfg),add(multiply(x__dfg,y__dfg),add(commutator(x__dfg,z__dfg),multiply(x__dfg,z__dfg))))))),additive_inverse(add(multiply(x__dfg,y__dfg),multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[464,774,8,12]),
[iquote('0:Rew:464.0,774.0,8.0,774.0,464.0,774.0,8.0,774.0,12.0,774.0,8.0,774.0')] ).
cnf(776,plain,
~ equal(additive_inverse(additive_inverse(additive_inverse(add(commutator(x__dfg,y__dfg),additive_inverse(add(commutator(x__dfg,y__dfg),add(commutator(x__dfg,z__dfg),additive_inverse(add(commutator(x__dfg,z__dfg),add(multiply(x__dfg,y__dfg),multiply(x__dfg,z__dfg))))))))))),additive_inverse(add(multiply(x__dfg,y__dfg),multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[476,775,395,77]),
[iquote('0:Rew:476.0,775.0,395.0,775.0,476.0,775.0,395.0,775.0,77.0,775.0')] ).
cnf(777,plain,
~ equal(additive_inverse(add(multiply(x__dfg,y__dfg),multiply(x__dfg,z__dfg))),additive_inverse(add(multiply(x__dfg,y__dfg),multiply(x__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[8,776,253]),
[iquote('0:Rew:8.0,776.0,8.0,776.0,253.0,776.0,253.0,776.0')] ).
cnf(778,plain,
$false,
inference(obv,[status(thm),theory(equality)],[777]),
[iquote('0:Obv:777.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : RNG017-6 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.10 % Command : run_spass %d %s
% 0.10/0.29 % Computer : n026.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Mon May 30 21:38:10 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.14/0.42
% 0.14/0.42 SPASS V 3.9
% 0.14/0.42 SPASS beiseite: Proof found.
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 SPASS derived 426 clauses, backtracked 0 clauses, performed 0 splits and kept 133 clauses.
% 0.14/0.42 SPASS allocated 64167 KBytes.
% 0.14/0.42 SPASS spent 0:00:00.12 on the problem.
% 0.14/0.42 0:00:00.03 for the input.
% 0.14/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.42 0:00:00.00 for inferences.
% 0.14/0.42 0:00:00.00 for the backtracking.
% 0.14/0.42 0:00:00.07 for the reduction.
% 0.14/0.42
% 0.14/0.42
% 0.14/0.42 Here is a proof with depth 5, length 60 :
% 0.14/0.42 % SZS output start Refutation
% See solution above
% 0.14/0.43 Formulae used in the proof : prove_distributivity 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
% 0.14/0.43
%------------------------------------------------------------------------------