TSTP Solution File: RNG016-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG016-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 56 RR)
% Number of literals : 56 ( 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 : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(multiply(add(x__dfg,additive_inverse(y__dfg)),z__dfg),add(multiply(x__dfg,z__dfg),additive_inverse(multiply(y__dfg,z__dfg)))),
file('RNG016-6.p',unknown),
[] ).
cnf(2,axiom,
equal(add(additive_identity,u),u),
file('RNG016-6.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,additive_identity),u),
file('RNG016-6.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(additive_identity,u),additive_identity),
file('RNG016-6.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(u,additive_identity),additive_identity),
file('RNG016-6.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG016-6.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG016-6.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG016-6.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG016-6.p',unknown),
[] ).
cnf(11,axiom,
equal(add(u,v),add(v,u)),
file('RNG016-6.p',unknown),
[] ).
cnf(12,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG016-6.p',unknown),
[] ).
cnf(16,axiom,
equal(add(multiply(u,v),additive_inverse(multiply(v,u))),commutator(v,u)),
file('RNG016-6.p',unknown),
[] ).
cnf(18,plain,
~ equal(add(multiply(x__dfg,z__dfg),multiply(additive_inverse(y__dfg),z__dfg)),add(multiply(x__dfg,z__dfg),additive_inverse(multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[10,1]),
[iquote('0:Rew:10.0,1.0')] ).
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(multiply(x__dfg,z__dfg),add(commutator(z__dfg,additive_inverse(y__dfg)),multiply(z__dfg,additive_inverse(y__dfg)))),add(multiply(x__dfg,z__dfg),additive_inverse(multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[163,18]),
[iquote('0:Rew:163.0,18.0')] ).
cnf(171,plain,
~ equal(add(commutator(z__dfg,additive_inverse(y__dfg)),add(multiply(x__dfg,z__dfg),multiply(z__dfg,additive_inverse(y__dfg)))),add(multiply(x__dfg,z__dfg),additive_inverse(multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[77,165]),
[iquote('0:Rew:77.0,165.0')] ).
cnf(188,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(220,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(229,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),additive_identity),
inference(rew,[status(thm),theory(equality)],[4,220]),
[iquote('0:Rew:4.0,220.0')] ).
cnf(248,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[188,76]),
[iquote('0:SpR:188.0,76.0')] ).
cnf(308,plain,
equal(add(multiply(additive_inverse(u),v),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[229,188]),
[iquote('0:SpR:229.0,188.0')] ).
cnf(325,plain,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,308,11,28]),
[iquote('0:Rew:2.0,308.0,11.0,308.0,28.0,308.0')] ).
cnf(347,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)],[325,16]),
[iquote('0:SpR:325.0,16.0')] ).
cnf(368,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(379,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
inference(rew,[status(thm),theory(equality)],[5,368]),
[iquote('0:Rew:5.0,368.0')] ).
cnf(393,plain,
equal(add(additive_inverse(u),v),additive_inverse(add(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[248,11]),
[iquote('0:SpR:248.0,11.0')] ).
cnf(396,plain,
equal(add(additive_inverse(add(u,additive_inverse(v))),w),add(v,add(additive_inverse(u),w))),
inference(spr,[status(thm),theory(equality)],[248,12]),
[iquote('0:SpR:248.0,12.0')] ).
cnf(404,plain,
equal(additive_inverse(add(multiply(u,v),additive_inverse(multiply(v,u)))),commutator(u,v)),
inference(spr,[status(thm),theory(equality)],[248,16]),
[iquote('0:SpR:248.0,16.0')] ).
cnf(441,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)],[393,347]),
[iquote('0:Rew:393.0,347.0')] ).
cnf(462,plain,
equal(additive_inverse(commutator(u,v)),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[16,404]),
[iquote('0:Rew:16.0,404.0')] ).
cnf(471,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)],[393,396]),
[iquote('0:Rew:393.0,396.0,393.0,396.0')] ).
cnf(472,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)],[12,471]),
[iquote('0:Rew:12.0,471.0')] ).
cnf(473,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)],[393,472]),
[iquote('0:Rew:393.0,472.0')] ).
cnf(474,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)],[8,473]),
[iquote('0:Rew:8.0,473.0')] ).
cnf(491,plain,
equal(additive_inverse(add(multiply(u,v),multiply(v,additive_inverse(u)))),commutator(v,additive_inverse(u))),
inference(rew,[status(thm),theory(equality)],[8,441]),
[iquote('0:Rew:8.0,441.0')] ).
cnf(494,plain,
equal(add(commutator(u,v),commutator(v,u)),additive_identity),
inference(spr,[status(thm),theory(equality)],[462,7]),
[iquote('0:SpR:462.0,7.0')] ).
cnf(573,plain,
equal(add(commutator(u,v),add(commutator(v,u),w)),add(additive_identity,w)),
inference(spr,[status(thm),theory(equality)],[494,12]),
[iquote('0:SpR:494.0,12.0')] ).
cnf(598,plain,
equal(add(commutator(u,v),add(commutator(v,u),w)),w),
inference(rew,[status(thm),theory(equality)],[2,573]),
[iquote('0:Rew:2.0,573.0')] ).
cnf(674,plain,
equal(add(multiply(u,additive_inverse(v)),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[379,188]),
[iquote('0:SpR:379.0,188.0')] ).
cnf(702,plain,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,674,11,28]),
[iquote('0:Rew:2.0,674.0,11.0,674.0,28.0,674.0')] ).
cnf(704,plain,
~ equal(add(commutator(z__dfg,additive_inverse(y__dfg)),add(multiply(x__dfg,z__dfg),additive_inverse(multiply(z__dfg,y__dfg)))),add(multiply(x__dfg,z__dfg),additive_inverse(multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[702,171]),
[iquote('0:Rew:702.0,171.0')] ).
cnf(706,plain,
equal(additive_inverse(add(multiply(u,v),additive_inverse(multiply(v,u)))),commutator(v,additive_inverse(u))),
inference(rew,[status(thm),theory(equality)],[702,491]),
[iquote('0:Rew:702.0,491.0')] ).
cnf(739,plain,
equal(commutator(u,additive_inverse(v)),additive_inverse(commutator(u,v))),
inference(rew,[status(thm),theory(equality)],[16,706]),
[iquote('0:Rew:16.0,706.0')] ).
cnf(770,plain,
~ equal(additive_inverse(additive_inverse(add(multiply(x__dfg,z__dfg),additive_inverse(multiply(y__dfg,z__dfg))))),add(multiply(x__dfg,z__dfg),additive_inverse(multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[598,704,474,393,739,163]),
[iquote('0:Rew:598.0,704.0,474.0,704.0,393.0,704.0,739.0,704.0,163.0,704.0')] ).
cnf(771,plain,
~ equal(add(multiply(x__dfg,z__dfg),additive_inverse(multiply(y__dfg,z__dfg))),add(multiply(x__dfg,z__dfg),additive_inverse(multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[8,770]),
[iquote('0:Rew:8.0,770.0')] ).
cnf(772,plain,
$false,
inference(obv,[status(thm),theory(equality)],[771]),
[iquote('0:Obv:771.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG016-6 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.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 16:19:01 EDT 2022
% 0.12/0.33 % 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 425 clauses, backtracked 0 clauses, performed 0 splits and kept 132 clauses.
% 0.19/0.48 SPASS allocated 64126 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.48 0:00:00.03 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.01 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.07 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 7, length 56 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.48 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
% 0.19/0.48
%------------------------------------------------------------------------------