TSTP Solution File: RNG018-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG018-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 30 RR)
% Number of literals : 30 ( 0 equ; 7 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(multiply(add(x__dfg,y__dfg),additive_inverse(z__dfg)),add(additive_inverse(multiply(x__dfg,z__dfg)),additive_inverse(multiply(y__dfg,z__dfg)))),
file('RNG018-6.p',unknown),
[] ).
cnf(2,axiom,
equal(add(additive_identity,u),u),
file('RNG018-6.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,additive_identity),u),
file('RNG018-6.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(u,additive_identity),additive_identity),
file('RNG018-6.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG018-6.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG018-6.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG018-6.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG018-6.p',unknown),
[] ).
cnf(11,axiom,
equal(add(u,v),add(v,u)),
file('RNG018-6.p',unknown),
[] ).
cnf(12,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG018-6.p',unknown),
[] ).
cnf(19,plain,
~ equal(add(multiply(x__dfg,additive_inverse(z__dfg)),multiply(y__dfg,additive_inverse(z__dfg))),add(additive_inverse(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(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(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(186,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(246,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[186,76]),
[iquote('0:SpR:186.0,76.0')] ).
cnf(366,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(377,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
inference(rew,[status(thm),theory(equality)],[5,366]),
[iquote('0:Rew:5.0,366.0')] ).
cnf(391,plain,
equal(add(additive_inverse(u),v),additive_inverse(add(u,additive_inverse(v)))),
inference(spr,[status(thm),theory(equality)],[246,11]),
[iquote('0:SpR:246.0,11.0')] ).
cnf(440,plain,
~ equal(add(multiply(x__dfg,additive_inverse(z__dfg)),multiply(y__dfg,additive_inverse(z__dfg))),additive_inverse(add(multiply(x__dfg,z__dfg),additive_inverse(additive_inverse(multiply(y__dfg,z__dfg)))))),
inference(rew,[status(thm),theory(equality)],[391,19]),
[iquote('0:Rew:391.0,19.0')] ).
cnf(492,plain,
~ equal(add(multiply(x__dfg,additive_inverse(z__dfg)),multiply(y__dfg,additive_inverse(z__dfg))),additive_inverse(add(multiply(x__dfg,z__dfg),multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[8,440]),
[iquote('0:Rew:8.0,440.0')] ).
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)],[377,186]),
[iquote('0:SpR:377.0,186.0')] ).
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(additive_inverse(multiply(x__dfg,z__dfg)),multiply(y__dfg,additive_inverse(z__dfg))),additive_inverse(add(multiply(x__dfg,z__dfg),multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[702,492]),
[iquote('0:Rew:702.0,492.0')] ).
cnf(766,plain,
~ equal(additive_inverse(add(multiply(x__dfg,z__dfg),additive_inverse(additive_inverse(multiply(y__dfg,z__dfg))))),additive_inverse(add(multiply(x__dfg,z__dfg),multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[391,704,702]),
[iquote('0:Rew:391.0,704.0,702.0,704.0')] ).
cnf(767,plain,
~ equal(additive_inverse(add(multiply(x__dfg,z__dfg),multiply(y__dfg,z__dfg))),additive_inverse(add(multiply(x__dfg,z__dfg),multiply(y__dfg,z__dfg)))),
inference(rew,[status(thm),theory(equality)],[8,766]),
[iquote('0:Rew:8.0,766.0')] ).
cnf(768,plain,
$false,
inference(obv,[status(thm),theory(equality)],[767]),
[iquote('0:Obv:767.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : RNG018-6 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 13:19:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.47
% 0.18/0.47 SPASS V 3.9
% 0.18/0.47 SPASS beiseite: Proof found.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 425 clauses, backtracked 0 clauses, performed 0 splits and kept 132 clauses.
% 0.18/0.47 SPASS allocated 64125 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.47 0:00:00.04 for the input.
% 0.18/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.47 0:00:00.01 for inferences.
% 0.18/0.47 0:00:00.00 for the backtracking.
% 0.18/0.47 0:00:00.07 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 5, length 30 :
% 0.18/0.47 % SZS output start Refutation
% See solution above
% 0.18/0.47 Formulae used in the proof : prove_distributivity left_additive_identity right_additive_identity right_multiplicative_zero right_additive_inverse additive_inverse_additive_inverse distribute1 distribute2 commutativity_for_addition associativity_for_addition
% 0.18/0.47
%------------------------------------------------------------------------------