%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP490-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:47:43 EDT 2022
% Result : Unsatisfiable 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 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(identity,u),double_divide(identity,double_divide(double_divide(double_divide(u,v),identity),double_divide(w,v)))),w),
file('GRP490-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP490-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP490-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP490-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(inverse(a1),a1),identity),
file('GRP490-1.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(identity,u),double_divide(identity,double_divide(multiply(v,u),double_divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[6,1,3]),
[iquote('0:Rew:6.0,1.0,3.0,1.0')] ).
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(14,plain,
~ equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.0')] ).
cnf(50,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(inverse(v),u),identity))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(58,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,inverse(multiply(inverse(v),u)))),v),
inference(rew,[status(thm),theory(equality)],[3,50]),
[iquote('0:Rew:3.0,50.0')] ).
cnf(70,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,inverse(inverse(identity)))),u),
inference(spr,[status(thm),theory(equality)],[12,58]),
[iquote('0:SpR:12.0,58.0')] ).
cnf(80,plain,
equal(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,70]),
[iquote('0:SpR:4.0,70.0')] ).
cnf(81,plain,
equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),identity),
inference(spr,[status(thm),theory(equality)],[3,70]),
[iquote('0:SpR:3.0,70.0')] ).
cnf(89,plain,
equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))),
inference(spr,[status(thm),theory(equality)],[80,70]),
[iquote('0:SpR:80.0,70.0')] ).
cnf(94,plain,
equal(double_divide(identity,inverse(inverse(identity))),identity),
inference(rew,[status(thm),theory(equality)],[81,89]),
[iquote('0:Rew:81.0,89.0')] ).
cnf(97,plain,
equal(double_divide(inverse(identity),identity),identity),
inference(rew,[status(thm),theory(equality)],[94,81]),
[iquote('0:Rew:94.0,81.0')] ).
cnf(101,plain,
equal(inverse(inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[3,97]),
[iquote('0:Rew:3.0,97.0')] ).
cnf(102,plain,
equal(double_divide(identity,identity),identity),
inference(rew,[status(thm),theory(equality)],[101,94]),
[iquote('0:Rew:101.0,94.0')] ).
cnf(103,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[3,102]),
[iquote('0:Rew:3.0,102.0')] ).
cnf(104,plain,
$false,
inference(mrr,[status(thm)],[103,14]),
[iquote('0:MRR:103.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP490-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 11:20:24 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.44
% 0.21/0.44 SPASS V 3.9
% 0.21/0.44 SPASS beiseite: Proof found.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.44 SPASS derived 78 clauses, backtracked 0 clauses, performed 0 splits and kept 46 clauses.
% 0.21/0.44 SPASS allocated 63262 KBytes.
% 0.21/0.44 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.44 0:00:00.03 for the input.
% 0.21/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.44 0:00:00.00 for inferences.
% 0.21/0.44 0:00:00.00 for the backtracking.
% 0.21/0.44 0:00:00.01 for the reduction.
% 0.21/0.44
% 0.21/0.44
% 0.21/0.44 Here is a proof with depth 4, length 21 :
% 0.21/0.44 % SZS output start Refutation
% See solution above
% 0.21/0.44 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_1
% 0.21/0.44
%------------------------------------------------------------------------------