TSTP Solution File: GRP462-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP462-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:47:35 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 0 equ; 1 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,divide(divide(divide(identity,v),w),divide(divide(divide(u,u),u),w))),v),
file('GRP462-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP462-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP462-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP462-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP462-1.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(u,divide(divide(inverse(v),w),divide(inverse(u),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(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(28,plain,
equal(divide(u,divide(divide(inverse(v),divide(divide(inverse(w),x),divide(inverse(inverse(u)),x))),w)),v),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(31,plain,
equal(divide(u,divide(divide(inverse(v),inverse(u)),identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(35,plain,
equal(divide(u,divide(identity,divide(inverse(u),inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(38,plain,
equal(divide(u,identity),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(39,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[15,38]),
[iquote('0:Rew:15.0,38.0')] ).
cnf(40,plain,
equal(divide(u,identity),u),
inference(rew,[status(thm),theory(equality)],[39,15]),
[iquote('0:Rew:39.0,15.0')] ).
cnf(41,plain,
equal(divide(u,divide(multiply(inverse(v),u),identity)),v),
inference(rew,[status(thm),theory(equality)],[6,31]),
[iquote('0:Rew:6.0,31.0')] ).
cnf(42,plain,
equal(divide(u,multiply(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[40,41]),
[iquote('0:Rew:40.0,41.0')] ).
cnf(43,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[6,35,3]),
[iquote('0:Rew:6.0,35.0,3.0,35.0,6.0,35.0')] ).
cnf(69,plain,
equal(divide(identity,inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[39,42]),
[iquote('0:SpR:39.0,42.0')] ).
cnf(71,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,69,6]),
[iquote('0:Rew:13.0,69.0,6.0,69.0')] ).
cnf(74,plain,
equal(divide(u,divide(divide(inverse(v),divide(divide(inverse(w),x),divide(u,x))),w)),v),
inference(rew,[status(thm),theory(equality)],[71,28]),
[iquote('0:Rew:71.0,28.0')] ).
cnf(80,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[71,6]),
[iquote('0:SpR:71.0,6.0')] ).
cnf(82,plain,
equal(divide(u,multiply(v,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[71,42]),
[iquote('0:SpR:71.0,42.0')] ).
cnf(96,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(spr,[status(thm),theory(equality)],[71,43]),
[iquote('0:SpR:71.0,43.0')] ).
cnf(124,plain,
equal(divide(multiply(u,v),v),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[96,82]),
[iquote('0:SpR:96.0,82.0')] ).
cnf(138,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[71,124]),
[iquote('0:Rew:71.0,124.0')] ).
cnf(139,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[138,6]),
[iquote('0:SpR:138.0,6.0')] ).
cnf(148,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[80,139]),
[iquote('0:Rew:80.0,139.0')] ).
cnf(187,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[148,82]),
[iquote('0:SpR:148.0,82.0')] ).
cnf(207,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[6,187]),
[iquote('0:SpR:6.0,187.0')] ).
cnf(218,plain,
equal(divide(u,divide(divide(inverse(v),divide(inverse(multiply(w,x)),divide(u,w))),x)),v),
inference(rew,[status(thm),theory(equality)],[207,74]),
[iquote('0:Rew:207.0,74.0')] ).
cnf(236,plain,
equal(divide(u,inverse(multiply(v,multiply(inverse(multiply(divide(u,w),multiply(w,v))),x)))),x),
inference(rew,[status(thm),theory(equality)],[207,218]),
[iquote('0:Rew:207.0,218.0,207.0,218.0,207.0,218.0')] ).
cnf(237,plain,
equal(multiply(u,multiply(v,multiply(inverse(multiply(divide(u,w),multiply(w,v))),x))),x),
inference(rew,[status(thm),theory(equality)],[6,236]),
[iquote('0:Rew:6.0,236.0')] ).
cnf(527,plain,
equal(multiply(divide(u,v),multiply(v,w)),multiply(u,multiply(w,identity))),
inference(spr,[status(thm),theory(equality)],[12,237]),
[iquote('0:SpR:12.0,237.0')] ).
cnf(529,plain,
equal(multiply(multiply(divide(u,v),multiply(v,w)),x),multiply(u,multiply(w,x))),
inference(spr,[status(thm),theory(equality)],[96,237]),
[iquote('0:SpR:96.0,237.0')] ).
cnf(534,plain,
equal(multiply(divide(u,v),multiply(v,w)),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[39,527]),
[iquote('0:Rew:39.0,527.0')] ).
cnf(556,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[534,529]),
[iquote('0:Rew:534.0,529.0')] ).
cnf(557,plain,
$false,
inference(unc,[status(thm)],[556,5]),
[iquote('0:UnC:556.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP462-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 19:42:43 EDT 2022
% 0.13/0.34 % 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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 356 clauses, backtracked 0 clauses, performed 0 splits and kept 110 clauses.
% 0.19/0.46 SPASS allocated 63837 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.46 0:00:00.03 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 7, length 40 :
% 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_3
% 0.19/0.46
%------------------------------------------------------------------------------