TSTP Solution File: GRP455-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP455-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 : Sat Jul 16 11:47:33 EDT 2022
% Result : Unsatisfiable 0.12s 0.42s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 24 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(identity,divide(u,divide(v,divide(divide(divide(u,u),u),w)))),w),v),
file('GRP455-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP455-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP455-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP455-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP455-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,divide(v,divide(inverse(u),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[3,1,4]),
[iquote('0:Rew:3.0,1.0,3.0,1.0,4.0,1.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
cnf(16,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,5]),
[iquote('0:Rew:13.0,5.0')] ).
cnf(32,plain,
equal(divide(inverse(divide(identity,divide(u,divide(identity,v)))),v),u),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(33,plain,
equal(divide(inverse(divide(u,divide(v,identity))),inverse(u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(39,plain,
equal(multiply(inverse(divide(u,multiply(v,identity))),u),v),
inference(rew,[status(thm),theory(equality)],[6,33,15]),
[iquote('0:Rew:6.0,33.0,15.0,33.0')] ).
cnf(41,plain,
equal(divide(inverse(inverse(multiply(u,v))),v),u),
inference(rew,[status(thm),theory(equality)],[3,32,6]),
[iquote('0:Rew:3.0,32.0,6.0,32.0,3.0,32.0')] ).
cnf(49,plain,
equal(multiply(inverse(inverse(multiply(u,identity))),identity),u),
inference(spr,[status(thm),theory(equality)],[41,15]),
[iquote('0:SpR:41.0,15.0')] ).
cnf(56,plain,
equal(divide(inverse(inverse(u)),identity),inverse(inverse(multiply(u,identity)))),
inference(spr,[status(thm),theory(equality)],[49,41]),
[iquote('0:SpR:49.0,41.0')] ).
cnf(63,plain,
equal(multiply(inverse(inverse(u)),identity),inverse(inverse(multiply(u,identity)))),
inference(rew,[status(thm),theory(equality)],[15,56]),
[iquote('0:Rew:15.0,56.0')] ).
cnf(64,plain,
equal(inverse(inverse(multiply(multiply(u,identity),identity))),u),
inference(rew,[status(thm),theory(equality)],[63,49]),
[iquote('0:Rew:63.0,49.0')] ).
cnf(96,plain,
equal(multiply(inverse(identity),multiply(u,identity)),u),
inference(spr,[status(thm),theory(equality)],[4,39]),
[iquote('0:SpR:4.0,39.0')] ).
cnf(101,plain,
equal(inverse(inverse(multiply(u,identity))),u),
inference(rew,[status(thm),theory(equality)],[13,96,9]),
[iquote('0:Rew:13.0,96.0,9.0,96.0')] ).
cnf(102,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[101,64]),
[iquote('0:Rew:101.0,64.0')] ).
cnf(110,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[102,101]),
[iquote('0:Rew:102.0,101.0')] ).
cnf(112,plain,
$false,
inference(unc,[status(thm)],[110,16]),
[iquote('0:UnC:110.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : GRP455-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.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 Jun 13 09:40:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.42
% 0.12/0.42 SPASS V 3.9
% 0.12/0.42 SPASS beiseite: Proof found.
% 0.12/0.42 % SZS status Theorem
% 0.12/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.42 SPASS derived 82 clauses, backtracked 0 clauses, performed 0 splits and kept 51 clauses.
% 0.12/0.42 SPASS allocated 63271 KBytes.
% 0.12/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.42 0:00:00.03 for the input.
% 0.12/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.42 0:00:00.00 for inferences.
% 0.12/0.42 0:00:00.00 for the backtracking.
% 0.12/0.42 0:00:00.01 for the reduction.
% 0.12/0.42
% 0.12/0.42
% 0.12/0.42 Here is a proof with depth 4, length 24 :
% 0.12/0.42 % SZS output start Refutation
% See solution above
% 0.12/0.42 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.12/0.42
%------------------------------------------------------------------------------