%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG024-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 20:41:14 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 30 RR)
% Number of literals : 30 ( 0 equ; 1 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 : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(associator(x__dfg,y__dfg,y__dfg),additive_identity),
file('RNG024-6.p',unknown),
[] ).
cnf(2,axiom,
equal(add(additive_identity,u),u),
file('RNG024-6.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,additive_identity),u),
file('RNG024-6.p',unknown),
[] ).
cnf(7,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG024-6.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG024-6.p',unknown),
[] ).
cnf(11,axiom,
equal(add(u,v),add(v,u)),
file('RNG024-6.p',unknown),
[] ).
cnf(12,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG024-6.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(multiply(u,v),v),multiply(u,multiply(v,v))),
file('RNG024-6.p',unknown),
[] ).
cnf(15,axiom,
equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
file('RNG024-6.p',unknown),
[] ).
cnf(16,axiom,
equal(add(multiply(u,v),additive_inverse(multiply(v,u))),commutator(v,u)),
file('RNG024-6.p',unknown),
[] ).
cnf(18,plain,
equal(add(additive_inverse(multiply(u,multiply(v,w))),multiply(multiply(u,v),w)),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[11,15]),
[iquote('0:Rew:11.0,15.0')] ).
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(133,plain,
equal(add(commutator(u,multiply(v,u)),multiply(u,multiply(v,u))),multiply(v,multiply(u,u))),
inference(rew,[status(thm),theory(equality)],[132,13]),
[iquote('0:Rew:132.0,13.0')] ).
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(248,plain,
equal(add(u,additive_inverse(v)),additive_inverse(add(v,additive_inverse(u)))),
inference(spr,[status(thm),theory(equality)],[219,75]),
[iquote('0:SpR:219.0,75.0')] ).
cnf(396,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(407,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(446,plain,
equal(additive_inverse(add(multiply(u,multiply(v,w)),additive_inverse(multiply(multiply(u,v),w)))),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[396,18]),
[iquote('0:Rew:396.0,18.0')] ).
cnf(465,plain,
equal(additive_inverse(commutator(u,v)),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[16,407]),
[iquote('0:Rew:16.0,407.0')] ).
cnf(881,plain,
equal(additive_inverse(add(add(commutator(u,multiply(v,u)),multiply(u,multiply(v,u))),additive_inverse(multiply(multiply(v,u),u)))),associator(v,u,u)),
inference(spr,[status(thm),theory(equality)],[133,446]),
[iquote('0:SpR:133.0,446.0')] ).
cnf(948,plain,
equal(associator(u,v,v),additive_identity),
inference(rew,[status(thm),theory(equality)],[27,881,7,465,16,12]),
[iquote('0:Rew:27.0,881.0,7.0,881.0,465.0,881.0,16.0,881.0,12.0,881.0')] ).
cnf(949,plain,
$false,
inference(unc,[status(thm)],[948,1]),
[iquote('0:UnC:948.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG024-6 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n020.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 09:08:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 508 clauses, backtracked 0 clauses, performed 0 splits and kept 166 clauses.
% 0.19/0.52 SPASS allocated 64875 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.52 0:00:00.04 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.10 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 5, length 30 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.52 Formulae used in the proof : prove_right_alternative left_additive_identity right_additive_identity right_additive_inverse additive_inverse_additive_inverse commutativity_for_addition associativity_for_addition right_alternative associator commutator
% 0.19/0.52
%------------------------------------------------------------------------------