%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP546-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:47:59 EDT 2022
% Result : Unsatisfiable 0.12s 0.40s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 23 RR)
% Number of literals : 23 ( 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,divide(u,v)),divide(divide(v,w),u)),w),
file('GRP546-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP546-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP546-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP546-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP546-1.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(divide(u,v)),divide(divide(v,w),u)),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(31,plain,
equal(divide(inverse(divide(u,v)),divide(identity,u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(35,plain,
equal(divide(inverse(divide(divide(u,v),u)),identity),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(38,plain,
equal(divide(inverse(identity),divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(42,plain,
equal(multiply(inverse(divide(u,v)),u),v),
inference(rew,[status(thm),theory(equality)],[6,31,3]),
[iquote('0:Rew:6.0,31.0,3.0,31.0')] ).
cnf(43,plain,
equal(multiply(inverse(divide(divide(u,v),u)),identity),v),
inference(rew,[status(thm),theory(equality)],[15,35]),
[iquote('0:Rew:15.0,35.0')] ).
cnf(44,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,38,9]),
[iquote('0:Rew:3.0,38.0,9.0,38.0')] ).
cnf(45,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[44,43]),
[iquote('0:Rew:44.0,43.0')] ).
cnf(68,plain,
equal(inverse(divide(identity,u)),u),
inference(spr,[status(thm),theory(equality)],[42,45]),
[iquote('0:SpR:42.0,45.0')] ).
cnf(75,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,68]),
[iquote('0:Rew:3.0,68.0')] ).
cnf(76,plain,
$false,
inference(unc,[status(thm)],[75,17]),
[iquote('0:UnC:75.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP546-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 21:00:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.40
% 0.12/0.40 SPASS V 3.9
% 0.12/0.40 SPASS beiseite: Proof found.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40 SPASS derived 48 clauses, backtracked 0 clauses, performed 0 splits and kept 29 clauses.
% 0.12/0.40 SPASS allocated 63176 KBytes.
% 0.12/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.40 0:00:00.03 for the input.
% 0.12/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.40 0:00:00.00 for inferences.
% 0.12/0.40 0:00:00.00 for the backtracking.
% 0.12/0.40 0:00:00.00 for the reduction.
% 0.12/0.40
% 0.12/0.40
% 0.12/0.40 Here is a proof with depth 2, length 23 :
% 0.12/0.40 % SZS output start Refutation
% See solution above
% 0.12/0.40 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.12/0.40
%------------------------------------------------------------------------------