TSTP Solution File: RNG014-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG014-6 : 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 20:41:12 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,b))),
file('RNG014-6.p',unknown),
[] ).
cnf(2,axiom,
equal(add(additive_identity,u),u),
file('RNG014-6.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,additive_identity),u),
file('RNG014-6.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(u,additive_identity),additive_identity),
file('RNG014-6.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG014-6.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG014-6.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG014-6.p',unknown),
[] ).
cnf(11,axiom,
equal(add(u,v),add(v,u)),
file('RNG014-6.p',unknown),
[] ).
cnf(12,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG014-6.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(149,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(166,plain,
equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[3,149]),
[iquote('0:Rew:3.0,149.0')] ).
cnf(219,plain,
equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
inference(spr,[status(thm),theory(equality)],[8,166]),
[iquote('0:SpR:8.0,166.0')] ).
cnf(358,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(369,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
inference(rew,[status(thm),theory(equality)],[5,358]),
[iquote('0:Rew:5.0,358.0')] ).
cnf(677,plain,
equal(add(multiply(u,additive_inverse(v)),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[369,219]),
[iquote('0:SpR:369.0,219.0')] ).
cnf(705,plain,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,677,11,27]),
[iquote('0:Rew:2.0,677.0,11.0,677.0,27.0,677.0')] ).
cnf(706,plain,
$false,
inference(unc,[status(thm)],[705,1]),
[iquote('0:UnC:705.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG014-6 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.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 07:16:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 416 clauses, backtracked 0 clauses, performed 0 splits and kept 136 clauses.
% 0.20/0.48 SPASS allocated 64072 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.01 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.06 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 4, length 21 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : prove_equation left_additive_identity right_additive_identity right_multiplicative_zero right_additive_inverse additive_inverse_additive_inverse distribute1 commutativity_for_addition associativity_for_addition
% 0.20/0.48
%------------------------------------------------------------------------------