TSTP Solution File: GRP573-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP573-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:48:06 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 19 RR)
% Number of literals : 19 ( 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(v,double_divide(w,u)),double_divide(w,identity))),double_divide(identity,identity)),v),
file('GRP573-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP573-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP573-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP573-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(inverse(a1),a1),identity),
file('GRP573-1.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(v,double_divide(w,u)),inverse(w))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
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(inverse(u),double_divide(double_divide(v,identity),inverse(u))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(54,plain,
equal(double_divide(double_divide(inverse(u),double_divide(inverse(v),inverse(u))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,51]),
[iquote('0:Rew:3.0,51.0')] ).
cnf(66,plain,
equal(double_divide(double_divide(inverse(inverse(u)),identity),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,54]),
[iquote('0:SpR:4.0,54.0')] ).
cnf(68,plain,
equal(double_divide(inverse(inverse(inverse(u))),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,66]),
[iquote('0:Rew:3.0,66.0')] ).
cnf(76,plain,
equal(double_divide(double_divide(inverse(identity),u),inverse(identity)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[68,54]),
[iquote('0:SpR:68.0,54.0')] ).
cnf(101,plain,
equal(inverse(inverse(inverse(inverse(identity)))),double_divide(identity,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[4,76]),
[iquote('0:SpR:4.0,76.0')] ).
cnf(104,plain,
equal(inverse(inverse(inverse(inverse(identity)))),identity),
inference(rew,[status(thm),theory(equality)],[4,101]),
[iquote('0:Rew:4.0,101.0')] ).
cnf(143,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[104,68]),
[iquote('0:SpR:104.0,68.0')] ).
cnf(146,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,143]),
[iquote('0:Rew:4.0,143.0')] ).
cnf(147,plain,
$false,
inference(mrr,[status(thm)],[146,14]),
[iquote('0:MRR:146.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP573-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n022.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 23:15:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 99 clauses, backtracked 0 clauses, performed 0 splits and kept 52 clauses.
% 0.19/0.42 SPASS allocated 63324 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 5, length 19 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_1
% 0.19/0.42
%------------------------------------------------------------------------------