TSTP Solution File: GRP578-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP578-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:48:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 52 RR)
% Number of literals : 52 ( 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(double_divide(v,u),w),double_divide(v,identity))),double_divide(identity,identity)),w),
file('GRP578-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP578-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP578-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP578-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP578-1.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(double_divide(v,u),w),inverse(v))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
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(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(14,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,5]),
[iquote('0:Rew:13.0,5.0')] ).
cnf(53,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,v),inverse(u))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(57,plain,
equal(double_divide(double_divide(u,double_divide(inverse(double_divide(v,u)),inverse(v))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(58,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(60,plain,
equal(double_divide(double_divide(u,double_divide(multiply(u,v),inverse(v))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,57]),
[iquote('0:Rew:6.0,57.0')] ).
cnf(73,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[4,58]),
[iquote('0:SpR:4.0,58.0')] ).
cnf(74,plain,
equal(double_divide(inverse(u),inverse(identity)),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[3,73]),
[iquote('0:Rew:3.0,73.0')] ).
cnf(83,plain,
equal(double_divide(multiply(u,v),inverse(identity)),multiply(double_divide(v,u),identity)),
inference(spr,[status(thm),theory(equality)],[6,74]),
[iquote('0:SpR:6.0,74.0')] ).
cnf(109,plain,
equal(double_divide(double_divide(double_divide(multiply(u,v),inverse(v)),double_divide(identity,inverse(u))),inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[60,7]),
[iquote('0:SpR:60.0,7.0')] ).
cnf(125,plain,
equal(multiply(double_divide(multiply(u,v),inverse(v)),u),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[58,109]),
[iquote('0:Rew:58.0,109.0')] ).
cnf(135,plain,
equal(multiply(double_divide(inverse(identity),inverse(u)),inverse(u)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[12,125]),
[iquote('0:SpR:12.0,125.0')] ).
cnf(162,plain,
equal(multiply(identity,inverse(inverse(identity))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,135]),
[iquote('0:SpR:4.0,135.0')] ).
cnf(164,plain,
equal(inverse(inverse(inverse(inverse(identity)))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[13,162]),
[iquote('0:Rew:13.0,162.0')] ).
cnf(167,plain,
equal(double_divide(inverse(inverse(inverse(identity))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[164,4]),
[iquote('0:SpR:164.0,4.0')] ).
cnf(177,plain,
equal(multiply(inverse(inverse(identity)),identity),identity),
inference(rew,[status(thm),theory(equality)],[74,167]),
[iquote('0:Rew:74.0,167.0')] ).
cnf(196,plain,
equal(double_divide(double_divide(inverse(double_divide(identity,u)),identity),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,53]),
[iquote('0:SpR:4.0,53.0')] ).
cnf(198,plain,
equal(double_divide(double_divide(inverse(identity),multiply(identity,u)),inverse(identity)),double_divide(identity,inverse(u))),
inference(spr,[status(thm),theory(equality)],[58,53]),
[iquote('0:SpR:58.0,53.0')] ).
cnf(202,plain,
equal(multiply(multiply(u,identity),identity),u),
inference(rew,[status(thm),theory(equality)],[74,196,3,6]),
[iquote('0:Rew:74.0,196.0,3.0,196.0,6.0,196.0')] ).
cnf(204,plain,
equal(double_divide(double_divide(inverse(identity),inverse(inverse(u))),inverse(identity)),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[13,198]),
[iquote('0:Rew:13.0,198.0')] ).
cnf(215,plain,
equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),double_divide(identity,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[177,83]),
[iquote('0:SpR:177.0,83.0')] ).
cnf(222,plain,
equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),identity),
inference(rew,[status(thm),theory(equality)],[4,215]),
[iquote('0:Rew:4.0,215.0')] ).
cnf(244,plain,
equal(double_divide(identity,inverse(inverse(identity))),multiply(identity,identity)),
inference(spr,[status(thm),theory(equality)],[222,202]),
[iquote('0:SpR:222.0,202.0')] ).
cnf(248,plain,
equal(double_divide(identity,inverse(inverse(identity))),inverse(inverse(identity))),
inference(rew,[status(thm),theory(equality)],[13,244]),
[iquote('0:Rew:13.0,244.0')] ).
cnf(259,plain,
equal(multiply(inverse(inverse(identity)),identity),inverse(inverse(inverse(identity)))),
inference(spr,[status(thm),theory(equality)],[248,6]),
[iquote('0:SpR:248.0,6.0')] ).
cnf(267,plain,
equal(inverse(inverse(inverse(identity))),identity),
inference(rew,[status(thm),theory(equality)],[177,259]),
[iquote('0:Rew:177.0,259.0')] ).
cnf(307,plain,
equal(multiply(double_divide(inverse(identity),identity),identity),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[267,135]),
[iquote('0:SpR:267.0,135.0')] ).
cnf(317,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[177,307,3]),
[iquote('0:Rew:177.0,307.0,3.0,307.0')] ).
cnf(321,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),identity),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[317,58]),
[iquote('0:Rew:317.0,58.0')] ).
cnf(322,plain,
equal(double_divide(inverse(u),identity),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[317,74]),
[iquote('0:Rew:317.0,74.0')] ).
cnf(367,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),identity),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[317,204]),
[iquote('0:Rew:317.0,204.0')] ).
cnf(390,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,322]),
[iquote('0:Rew:3.0,322.0')] ).
cnf(391,plain,
equal(inverse(inverse(multiply(u,identity))),u),
inference(rew,[status(thm),theory(equality)],[390,202]),
[iquote('0:Rew:390.0,202.0')] ).
cnf(394,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[390,391]),
[iquote('0:Rew:390.0,391.0')] ).
cnf(436,plain,
equal(multiply(double_divide(identity,inverse(u)),v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,321,3]),
[iquote('0:Rew:6.0,321.0,3.0,321.0')] ).
cnf(455,plain,
equal(multiply(inverse(inverse(u)),identity),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,367,3]),
[iquote('0:Rew:6.0,367.0,3.0,367.0')] ).
cnf(456,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[394,455,390]),
[iquote('0:Rew:394.0,455.0,390.0,455.0')] ).
cnf(457,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[456,436]),
[iquote('0:Rew:456.0,436.0')] ).
cnf(564,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(spr,[status(thm),theory(equality)],[456,6]),
[iquote('0:SpR:456.0,6.0')] ).
cnf(570,plain,
equal(multiply(identity,inverse(u)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[457,564]),
[iquote('0:Rew:457.0,564.0')] ).
cnf(571,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[13,570]),
[iquote('0:Rew:13.0,570.0')] ).
cnf(572,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[571,394]),
[iquote('0:Rew:571.0,394.0')] ).
cnf(574,plain,
$false,
inference(unc,[status(thm)],[572,14]),
[iquote('0:UnC:572.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP578-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 23:53:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 301 clauses, backtracked 0 clauses, performed 0 splits and kept 132 clauses.
% 0.19/0.46 SPASS allocated 63772 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.04 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 9, length 52 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.19/0.46
%------------------------------------------------------------------------------