TSTP Solution File: GRP550-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP550-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 11:48:00 EDT 2022
% Result : Unsatisfiable 0.16s 0.40s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 25 RR)
% Number of literals : 25 ( 0 equ; 3 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(divide(divide(identity,u),divide(divide(divide(v,u),w),v)),w),
file('GRP550-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP550-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP550-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP550-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP550-1.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(u),divide(divide(divide(v,u),w),v)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
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(multiply(identity,a2),a2),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.0')] ).
cnf(17,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,16]),
[iquote('0:Rew:13.0,16.0')] ).
cnf(30,plain,
equal(divide(inverse(u),divide(divide(identity,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(34,plain,
equal(divide(inverse(u),divide(identity,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(40,plain,
equal(divide(inverse(u),divide(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,30]),
[iquote('0:Rew:3.0,30.0')] ).
cnf(41,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[6,34,3]),
[iquote('0:Rew:6.0,34.0,3.0,34.0')] ).
cnf(50,plain,
equal(divide(u,identity),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[9,41]),
[iquote('0:SpR:9.0,41.0')] ).
cnf(51,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[15,50,13]),
[iquote('0:Rew:15.0,50.0,13.0,50.0')] ).
cnf(52,plain,
equal(divide(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[51,15]),
[iquote('0:Rew:51.0,15.0')] ).
cnf(58,plain,
equal(inverse(inverse(inverse(u))),divide(identity,u)),
inference(spr,[status(thm),theory(equality)],[51,41]),
[iquote('0:SpR:51.0,41.0')] ).
cnf(59,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[3,58]),
[iquote('0:Rew:3.0,58.0')] ).
cnf(96,plain,
equal(divide(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[4,40]),
[iquote('0:SpR:4.0,40.0')] ).
cnf(102,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[59,96,52]),
[iquote('0:Rew:59.0,96.0,52.0,96.0')] ).
cnf(103,plain,
$false,
inference(unc,[status(thm)],[102,17]),
[iquote('0:UnC:102.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP550-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jun 13 20:11:09 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.16/0.40
% 0.16/0.40 SPASS V 3.9
% 0.16/0.40 SPASS beiseite: Proof found.
% 0.16/0.40 % SZS status Theorem
% 0.16/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.40 SPASS derived 69 clauses, backtracked 0 clauses, performed 0 splits and kept 37 clauses.
% 0.16/0.40 SPASS allocated 63212 KBytes.
% 0.16/0.40 SPASS spent 0:00:00.07 on the problem.
% 0.16/0.40 0:00:00.04 for the input.
% 0.16/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.16/0.40 0:00:00.00 for inferences.
% 0.16/0.40 0:00:00.00 for the backtracking.
% 0.16/0.40 0:00:00.00 for the reduction.
% 0.16/0.40
% 0.16/0.40
% 0.16/0.40 Here is a proof with depth 3, length 25 :
% 0.16/0.40 % SZS output start Refutation
% See solution above
% 0.16/0.40 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.16/0.40
%------------------------------------------------------------------------------