%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP078-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 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 11:45:12 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of clauses : 66 ( 60 unt; 0 nHn; 66 RR)
% Number of literals : 76 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 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('GRP078-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP078-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP078-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP078-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP078-1.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(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(multiply(identity,a2),a2)
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.1')] ).
cnf(15,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[13,14]),
[iquote('0:Rew:13.0,14.0')] ).
cnf(21,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(22,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(identity,u),inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(24,plain,
equal(double_divide(identity,double_divide(identity,double_divide(multiply(u,inverse(identity)),double_divide(v,u)))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(26,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,inverse(multiply(inverse(v),u)))),v),
inference(rew,[status(thm),theory(equality)],[3,21]),
[iquote('0:Rew:3.0,21.0')] ).
cnf(27,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(inverse(inverse(u)),inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[13,22]),
[iquote('0:Rew:13.0,22.0')] ).
cnf(67,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(multiply(inverse(v),w))),u),v))),double_divide(identity,w)),
inference(spr,[status(thm),theory(equality)],[26,7]),
[iquote('0:SpR:26.0,7.0')] ).
cnf(71,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,inverse(inverse(identity)))),u),
inference(spr,[status(thm),theory(equality)],[12,26]),
[iquote('0:SpR:12.0,26.0')] ).
cnf(78,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),u),v))),double_divide(identity,v)),
inference(spr,[status(thm),theory(equality)],[71,7]),
[iquote('0:SpR:71.0,7.0')] ).
cnf(81,plain,
equal(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,71]),
[iquote('0:SpR:4.0,71.0')] ).
cnf(82,plain,
equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),identity),
inference(spr,[status(thm),theory(equality)],[3,71]),
[iquote('0:SpR:3.0,71.0')] ).
cnf(91,plain,
equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))),
inference(spr,[status(thm),theory(equality)],[81,71]),
[iquote('0:SpR:81.0,71.0')] ).
cnf(95,plain,
equal(double_divide(identity,inverse(inverse(identity))),identity),
inference(rew,[status(thm),theory(equality)],[82,91]),
[iquote('0:Rew:82.0,91.0')] ).
cnf(96,plain,
equal(double_divide(double_divide(identity,u),identity),u),
inference(rew,[status(thm),theory(equality)],[95,71]),
[iquote('0:Rew:95.0,71.0')] ).
cnf(98,plain,
equal(double_divide(inverse(identity),identity),identity),
inference(rew,[status(thm),theory(equality)],[95,82]),
[iquote('0:Rew:95.0,82.0')] ).
cnf(100,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(identity,u),v))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[95,78]),
[iquote('0:Rew:95.0,78.0')] ).
cnf(102,plain,
equal(inverse(inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[3,98]),
[iquote('0:Rew:3.0,98.0')] ).
cnf(103,plain,
equal(double_divide(identity,identity),identity),
inference(rew,[status(thm),theory(equality)],[102,95]),
[iquote('0:Rew:102.0,95.0')] ).
cnf(104,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[3,103]),
[iquote('0:Rew:3.0,103.0')] ).
cnf(107,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[104,15]),
[iquote('0:Rew:104.0,15.1')] ).
cnf(108,plain,
equal(double_divide(identity,double_divide(identity,double_divide(multiply(u,identity),double_divide(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[104,24]),
[iquote('0:Rew:104.0,24.0')] ).
cnf(115,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[6,96,3]),
[iquote('0:Rew:6.0,96.0,3.0,96.0')] ).
cnf(120,plain,
equal(double_divide(identity,double_divide(identity,double_divide(u,double_divide(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[115,108]),
[iquote('0:Rew:115.0,108.0')] ).
cnf(122,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(inverse(inverse(u)),v))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[13,100]),
[iquote('0:Rew:13.0,100.0')] ).
cnf(123,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[122,27]),
[iquote('0:Rew:122.0,27.0')] ).
cnf(126,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(multiply(inverse(v),w),u),v))),double_divide(identity,w)),
inference(rew,[status(thm),theory(equality)],[123,67]),
[iquote('0:Rew:123.0,67.0')] ).
cnf(139,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[107]),
[iquote('0:Obv:107.1')] ).
cnf(162,plain,
equal(double_divide(identity,multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,123]),
[iquote('0:SpR:6.0,123.0')] ).
cnf(192,plain,
equal(multiply(double_divide(identity,double_divide(u,double_divide(v,u))),identity),inverse(v)),
inference(spr,[status(thm),theory(equality)],[120,6]),
[iquote('0:SpR:120.0,6.0')] ).
cnf(201,plain,
equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[3,120]),
[iquote('0:SpR:3.0,120.0')] ).
cnf(207,plain,
equal(double_divide(identity,double_divide(identity,u)),u),
inference(rew,[status(thm),theory(equality)],[123,201]),
[iquote('0:Rew:123.0,201.0')] ).
cnf(208,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[207,120]),
[iquote('0:Rew:207.0,120.0')] ).
cnf(217,plain,
equal(double_divide(identity,double_divide(u,double_divide(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[115,192]),
[iquote('0:Rew:115.0,192.0')] ).
cnf(218,plain,
equal(double_divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[208,217]),
[iquote('0:Rew:208.0,217.0')] ).
cnf(219,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[218,123]),
[iquote('0:Rew:218.0,123.0')] ).
cnf(220,plain,
equal(double_divide(inverse(u),double_divide(identity,double_divide(multiply(v,u),double_divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[218,7]),
[iquote('0:Rew:218.0,7.0')] ).
cnf(226,plain,
equal(double_divide(double_divide(identity,u),inverse(double_divide(multiply(multiply(inverse(v),w),u),v))),double_divide(identity,w)),
inference(rew,[status(thm),theory(equality)],[218,126]),
[iquote('0:Rew:218.0,126.0')] ).
cnf(230,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[218,162]),
[iquote('0:Rew:218.0,162.0')] ).
cnf(236,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[219,139]),
[iquote('0:Rew:219.0,139.0')] ).
cnf(249,plain,
equal(double_divide(inverse(u),inverse(double_divide(multiply(v,u),double_divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[218,220]),
[iquote('0:Rew:218.0,220.0')] ).
cnf(250,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,w),multiply(w,u))),v),
inference(rew,[status(thm),theory(equality)],[6,249]),
[iquote('0:Rew:6.0,249.0')] ).
cnf(256,plain,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[236]),
[iquote('0:Obv:236.0')] ).
cnf(257,plain,
equal(double_divide(double_divide(identity,u),multiply(v,multiply(multiply(inverse(v),w),u))),double_divide(identity,w)),
inference(rew,[status(thm),theory(equality)],[6,226]),
[iquote('0:Rew:6.0,226.0')] ).
cnf(258,plain,
equal(double_divide(inverse(u),multiply(v,multiply(multiply(inverse(v),w),u))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[218,257]),
[iquote('0:Rew:218.0,257.0,218.0,257.0')] ).
cnf(306,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[208]),
[iquote('0:SpR:208.0,208.0')] ).
cnf(318,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[306,6]),
[iquote('0:SpR:306.0,6.0')] ).
cnf(362,plain,
equal(double_divide(inverse(u),multiply(v,multiply(w,u))),double_divide(w,v)),
inference(spr,[status(thm),theory(equality)],[306,250]),
[iquote('0:SpR:306.0,250.0')] ).
cnf(388,plain,
equal(double_divide(multiply(inverse(u),v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[362,258]),
[iquote('0:Rew:362.0,258.0')] ).
cnf(514,plain,
equal(inverse(double_divide(inverse(u),v)),double_divide(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[318,388]),
[iquote('0:SpR:318.0,388.0')] ).
cnf(530,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(rew,[status(thm),theory(equality)],[6,514]),
[iquote('0:Rew:6.0,514.0')] ).
cnf(533,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[530,362]),
[iquote('0:Rew:530.0,362.0')] ).
cnf(537,plain,
equal(multiply(u,double_divide(multiply(v,u),w)),double_divide(v,w)),
inference(rew,[status(thm),theory(equality)],[230,533]),
[iquote('0:Rew:230.0,533.0')] ).
cnf(865,plain,
equal(double_divide(u,double_divide(v,multiply(u,w))),multiply(w,v)),
inference(spr,[status(thm),theory(equality)],[208,537]),
[iquote('0:SpR:208.0,537.0')] ).
cnf(1479,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[865,318]),
[iquote('0:SpR:865.0,318.0')] ).
cnf(1550,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,1479]),
[iquote('0:Rew:6.0,1479.0')] ).
cnf(1551,plain,
$false,
inference(unc,[status(thm)],[1550,256]),
[iquote('0:UnC:1550.0,256.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP078-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 16:26:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 875 clauses, backtracked 0 clauses, performed 0 splits and kept 148 clauses.
% 0.20/0.50 SPASS allocated 64484 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.08 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 5, length 66 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.20/0.51
%------------------------------------------------------------------------------