%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP552-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 24 ( 0 equ; 1 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('GRP552-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP552-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP552-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP552-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP552-1.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(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(inverse(u),divide(divide(identity,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(32,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(38,plain,
equal(divide(inverse(u),divide(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,28]),
[iquote('0:Rew:3.0,28.0')] ).
cnf(39,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[6,32,3]),
[iquote('0:Rew:6.0,32.0,3.0,32.0')] ).
cnf(48,plain,
equal(divide(u,identity),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[9,39]),
[iquote('0:SpR:9.0,39.0')] ).
cnf(49,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[15,48,13]),
[iquote('0:Rew:15.0,48.0,13.0,48.0')] ).
cnf(50,plain,
equal(divide(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[49,15]),
[iquote('0:Rew:49.0,15.0')] ).
cnf(56,plain,
equal(inverse(inverse(inverse(u))),divide(identity,u)),
inference(spr,[status(thm),theory(equality)],[49,39]),
[iquote('0:SpR:49.0,39.0')] ).
cnf(57,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[3,56]),
[iquote('0:Rew:3.0,56.0')] ).
cnf(94,plain,
equal(divide(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[4,38]),
[iquote('0:SpR:4.0,38.0')] ).
cnf(100,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[57,94,50]),
[iquote('0:Rew:57.0,94.0,50.0,94.0')] ).
cnf(118,plain,
equal(divide(u,inverse(v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[100,39]),
[iquote('0:SpR:100.0,39.0')] ).
cnf(126,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,118]),
[iquote('0:Rew:6.0,118.0')] ).
cnf(127,plain,
$false,
inference(unc,[status(thm)],[126,5]),
[iquote('0:UnC:126.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP552-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 15:39:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.40
% 0.18/0.40 SPASS V 3.9
% 0.18/0.40 SPASS beiseite: Proof found.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.40 SPASS derived 82 clauses, backtracked 0 clauses, performed 0 splits and kept 39 clauses.
% 0.18/0.40 SPASS allocated 63224 KBytes.
% 0.18/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.40 0:00:00.03 for the input.
% 0.18/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40 0:00:00.00 for inferences.
% 0.18/0.40 0:00:00.00 for the backtracking.
% 0.18/0.40 0:00:00.01 for the reduction.
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 Here is a proof with depth 3, length 24 :
% 0.18/0.40 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.18/0.41
%------------------------------------------------------------------------------