TSTP Solution File: GRP581-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP581-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:48:08 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 15 RR)
% Number of literals : 15 ( 0 equ; 2 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(identity,identity)),w),
file('GRP581-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP581-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP581-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP581-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(inverse(a1),a1),identity),
file('GRP581-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(14,plain,
~ equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.0')] ).
cnf(51,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,u),double_divide(v,inverse(u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(107,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,u),identity)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,51]),
[iquote('0:SpR:4.0,51.0')] ).
cnf(114,plain,
equal(double_divide(double_divide(identity,multiply(u,identity)),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[6,107,3]),
[iquote('0:Rew:6.0,107.0,3.0,107.0')] ).
cnf(143,plain,
equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[12,114]),
[iquote('0:SpR:12.0,114.0')] ).
cnf(145,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,143]),
[iquote('0:Rew:4.0,143.0,4.0,143.0')] ).
cnf(146,plain,
$false,
inference(mrr,[status(thm)],[145,14]),
[iquote('0:MRR:145.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP581-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.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 Jun 13 04:33:27 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 94 clauses, backtracked 0 clauses, performed 0 splits and kept 46 clauses.
% 0.18/0.42 SPASS allocated 63319 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.42 0:00:00.04 for the input.
% 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.01 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 3, length 15 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_1
% 0.18/0.42
%------------------------------------------------------------------------------