TSTP Solution File: GRP446-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP446-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:47:31 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 22 RR)
% Number of literals : 22 ( 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(divide(u,divide(divide(divide(divide(u,u),v),w),divide(divide(divide(u,u),u),w))),v),
file('GRP446-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP446-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP446-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP446-1.p',unknown),
[] ).
cnf(5,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(6,plain,
equal(divide(u,divide(divide(inverse(v),w),divide(inverse(u),w))),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,u)),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(9,plain,
equal(divide(multiply(inverse(u),u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(24,plain,
equal(divide(divide(u,u),divide(divide(inverse(v),w),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(27,plain,
equal(divide(u,inverse(divide(inverse(u),inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(28,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[5,27]),
[iquote('0:Rew:5.0,27.0,5.0,27.0')] ).
cnf(29,plain,
equal(inverse(multiply(divide(inverse(u),v),v)),u),
inference(rew,[status(thm),theory(equality)],[3,24,5]),
[iquote('0:Rew:3.0,24.0,5.0,24.0')] ).
cnf(36,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[28]),
[iquote('0:SpR:28.0,28.0')] ).
cnf(39,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(42,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[39,4]),
[iquote('0:Rew:39.0,4.0')] ).
cnf(105,plain,
equal(inverse(multiply(inverse(u),u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[7,29]),
[iquote('0:SpR:7.0,29.0')] ).
cnf(164,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[105]),
[iquote('0:SpR:105.0,105.0')] ).
cnf(187,plain,
equal(divide(u,u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[164,5]),
[iquote('0:SpR:164.0,5.0')] ).
cnf(250,plain,
equal(multiply(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[187,28]),
[iquote('0:SpR:187.0,28.0')] ).
cnf(362,plain,
equal(multiply(u,divide(v,v)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[250,36]),
[iquote('0:SpR:250.0,36.0')] ).
cnf(373,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[250,362]),
[iquote('0:Rew:250.0,362.0')] ).
cnf(374,plain,
$false,
inference(unc,[status(thm)],[373,42]),
[iquote('0:UnC:373.0,42.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP446-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 03:47:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.46
% 0.20/0.46 SPASS V 3.9
% 0.20/0.46 SPASS beiseite: Proof found.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 SPASS derived 248 clauses, backtracked 0 clauses, performed 0 splits and kept 89 clauses.
% 0.20/0.46 SPASS allocated 63667 KBytes.
% 0.20/0.46 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.46 0:00:00.03 for the input.
% 0.20/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.46 0:00:00.00 for inferences.
% 0.20/0.46 0:00:00.00 for the backtracking.
% 0.20/0.46 0:00:00.03 for the reduction.
% 0.20/0.46
% 0.20/0.46
% 0.20/0.46 Here is a proof with depth 7, length 22 :
% 0.20/0.46 % SZS output start Refutation
% See solution above
% 0.20/0.46 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_2
% 0.20/0.46
%------------------------------------------------------------------------------