%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP484-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:47:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 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(u,double_divide(double_divide(double_divide(u,v),w),double_divide(v,identity))),double_divide(identity,identity)),w),
file('GRP484-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP484-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP484-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP484-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(inverse(a1),a1),identity),
file('GRP484-1.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(u,double_divide(double_divide(double_divide(u,v),w),inverse(v))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
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(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(14,plain,
~ equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.0')] ).
cnf(16,plain,
equal(multiply(multiply(u,v),double_divide(v,u)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(57,plain,
equal(double_divide(double_divide(u,double_divide(inverse(double_divide(u,v)),inverse(v))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(58,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(60,plain,
equal(double_divide(double_divide(u,double_divide(multiply(v,u),inverse(v))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,57]),
[iquote('0:Rew:6.0,57.0')] ).
cnf(73,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[4,58]),
[iquote('0:SpR:4.0,58.0')] ).
cnf(74,plain,
equal(double_divide(inverse(u),inverse(identity)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,73,13]),
[iquote('0:Rew:3.0,73.0,13.0,73.0')] ).
cnf(79,plain,
equal(multiply(inverse(identity),inverse(u)),inverse(inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[74,6]),
[iquote('0:SpR:74.0,6.0')] ).
cnf(84,plain,
equal(double_divide(multiply(u,v),inverse(identity)),inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[6,74]),
[iquote('0:SpR:6.0,74.0')] ).
cnf(108,plain,
equal(double_divide(multiply(u,double_divide(v,identity)),inverse(u)),double_divide(double_divide(v,identity),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[60,7]),
[iquote('0:SpR:60.0,7.0')] ).
cnf(116,plain,
equal(double_divide(double_divide(u,inverse(multiply(identity,u))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[84,60]),
[iquote('0:SpR:84.0,60.0')] ).
cnf(117,plain,
equal(double_divide(double_divide(u,inverse(inverse(inverse(u)))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[13,116]),
[iquote('0:Rew:13.0,116.0')] ).
cnf(120,plain,
equal(double_divide(multiply(u,inverse(v)),inverse(u)),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[74,108,3]),
[iquote('0:Rew:74.0,108.0,3.0,108.0')] ).
cnf(128,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),inverse(inverse(inverse(double_divide(u,identity))))),
inference(spr,[status(thm),theory(equality)],[117,7]),
[iquote('0:SpR:117.0,7.0')] ).
cnf(133,plain,
equal(inverse(inverse(inverse(inverse(u)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[74,128,3]),
[iquote('0:Rew:74.0,128.0,3.0,128.0')] ).
cnf(148,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(inverse(v)))),inverse(identity)),multiply(inverse(inverse(inverse(v))),u)),
inference(spr,[status(thm),theory(equality)],[133,58]),
[iquote('0:SpR:133.0,58.0')] ).
cnf(155,plain,
equal(multiply(inverse(inverse(inverse(u))),v),multiply(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[58,148]),
[iquote('0:Rew:58.0,148.0')] ).
cnf(204,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[120,6]),
[iquote('0:SpR:120.0,6.0')] ).
cnf(207,plain,
equal(multiply(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(v))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[120,16]),
[iquote('0:SpR:120.0,16.0')] ).
cnf(228,plain,
equal(multiply(inverse(u),inverse(inverse(u))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[155,207,204]),
[iquote('0:Rew:155.0,207.0,204.0,207.0')] ).
cnf(234,plain,
equal(inverse(inverse(inverse(inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[228,79]),
[iquote('0:SpR:228.0,79.0')] ).
cnf(242,plain,
equal(inverse(inverse(identity)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[133,234]),
[iquote('0:Rew:133.0,234.0')] ).
cnf(256,plain,
equal(double_divide(inverse(identity),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[242,4]),
[iquote('0:SpR:242.0,4.0')] ).
cnf(276,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[242,256,74]),
[iquote('0:Rew:242.0,256.0,74.0,256.0')] ).
cnf(277,plain,
$false,
inference(mrr,[status(thm)],[276,14]),
[iquote('0:MRR:276.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP484-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 13 11:36:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 206 clauses, backtracked 0 clauses, performed 0 splits and kept 87 clauses.
% 0.19/0.42 SPASS allocated 63499 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.42 0:00:00.03 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.02 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 7, length 35 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_1
% 0.19/0.42
%------------------------------------------------------------------------------