TSTP Solution File: GRP076-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP076-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:45:11 EDT 2022
% Result : Unsatisfiable 0.14s 0.43s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of clauses : 78 ( 72 unt; 0 nHn; 78 RR)
% Number of literals : 88 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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(u,double_divide(double_divide(double_divide(u,v),w),double_divide(v,identity))),double_divide(identity,identity)),w),
file('GRP076-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP076-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP076-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP076-1.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('GRP076-1.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(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(17,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(21,plain,
equal(double_divide(double_divide(double_divide(double_divide(u,identity),v),w),inverse(v)),double_divide(double_divide(u,w),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(24,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(identity,v),inverse(inverse(u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(25,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(inverse(u),v),inverse(identity))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(26,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),inverse(double_divide(u,v))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(27,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(28,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,26]),
[iquote('0:Rew:6.0,26.0')] ).
cnf(29,plain,
equal(double_divide(double_divide(u,double_divide(multiply(v,u),inverse(v))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,27]),
[iquote('0:Rew:6.0,27.0')] ).
cnf(30,plain,
equal(double_divide(double_divide(double_divide(inverse(u),v),w),inverse(v)),double_divide(double_divide(u,w),inverse(identity))),
inference(rew,[status(thm),theory(equality)],[3,21]),
[iquote('0:Rew:3.0,21.0')] ).
cnf(70,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(u,identity))),inverse(identity)),double_divide(identity,inverse(v))),
inference(spr,[status(thm),theory(equality)],[28,7]),
[iquote('0:SpR:28.0,7.0')] ).
cnf(74,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[4,28]),
[iquote('0:SpR:4.0,28.0')] ).
cnf(75,plain,
equal(double_divide(inverse(u),inverse(identity)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,74,13]),
[iquote('0:Rew:3.0,74.0,13.0,74.0')] ).
cnf(77,plain,
equal(double_divide(double_divide(u,multiply(v,inverse(u))),inverse(identity)),double_divide(identity,inverse(v))),
inference(rew,[status(thm),theory(equality)],[3,70]),
[iquote('0:Rew:3.0,70.0')] ).
cnf(80,plain,
equal(multiply(inverse(identity),inverse(u)),inverse(inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[75,6]),
[iquote('0:SpR:75.0,6.0')] ).
cnf(85,plain,
equal(double_divide(multiply(u,v),inverse(identity)),inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[6,75]),
[iquote('0:SpR:6.0,75.0')] ).
cnf(120,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)],[29,7]),
[iquote('0:SpR:29.0,7.0')] ).
cnf(129,plain,
equal(double_divide(double_divide(u,inverse(multiply(identity,u))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[85,29]),
[iquote('0:SpR:85.0,29.0')] ).
cnf(130,plain,
equal(double_divide(double_divide(u,inverse(inverse(inverse(u)))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[13,129]),
[iquote('0:Rew:13.0,129.0')] ).
cnf(133,plain,
equal(double_divide(multiply(u,inverse(v)),inverse(u)),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[75,120,3]),
[iquote('0:Rew:75.0,120.0,3.0,120.0')] ).
cnf(141,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),inverse(inverse(inverse(double_divide(u,identity))))),
inference(spr,[status(thm),theory(equality)],[130,7]),
[iquote('0:SpR:130.0,7.0')] ).
cnf(146,plain,
equal(inverse(inverse(inverse(inverse(u)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[75,141,3]),
[iquote('0:Rew:75.0,141.0,3.0,141.0')] ).
cnf(156,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)],[146,28]),
[iquote('0:SpR:146.0,28.0')] ).
cnf(168,plain,
equal(multiply(inverse(inverse(inverse(u))),v),multiply(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[28,156]),
[iquote('0:Rew:28.0,156.0')] ).
cnf(204,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(double_divide(v,identity)))),double_divide(double_divide(v,u),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[24,7]),
[iquote('0:SpR:24.0,7.0')] ).
cnf(214,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(inverse(v)))),double_divide(double_divide(v,u),inverse(identity))),
inference(rew,[status(thm),theory(equality)],[3,204]),
[iquote('0:Rew:3.0,204.0')] ).
cnf(218,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[133,6]),
[iquote('0:SpR:133.0,6.0')] ).
cnf(221,plain,
equal(multiply(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(v))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[133,17]),
[iquote('0:SpR:133.0,17.0')] ).
cnf(242,plain,
equal(multiply(inverse(u),inverse(inverse(u))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[168,221,218]),
[iquote('0:Rew:168.0,221.0,218.0,221.0')] ).
cnf(249,plain,
equal(double_divide(inverse(identity),inverse(inverse(u))),inverse(inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[242,133]),
[iquote('0:SpR:242.0,133.0')] ).
cnf(250,plain,
equal(inverse(inverse(inverse(inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[242,80]),
[iquote('0:SpR:242.0,80.0')] ).
cnf(257,plain,
equal(inverse(inverse(identity)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[146,250]),
[iquote('0:Rew:146.0,250.0')] ).
cnf(273,plain,
equal(double_divide(inverse(identity),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[257,4]),
[iquote('0:SpR:257.0,4.0')] ).
cnf(293,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[257,273,75]),
[iquote('0:Rew:257.0,273.0,75.0,273.0')] ).
cnf(295,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(u,v),w),inverse(v))),identity),w),
inference(rew,[status(thm),theory(equality)],[293,7]),
[iquote('0:Rew:293.0,7.0')] ).
cnf(298,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)],[293,15]),
[iquote('0:Rew:293.0,15.1')] ).
cnf(308,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(inverse(u),v),identity)),identity),v),
inference(rew,[status(thm),theory(equality)],[293,25]),
[iquote('0:Rew:293.0,25.0')] ).
cnf(310,plain,
equal(double_divide(double_divide(double_divide(inverse(u),v),w),inverse(v)),double_divide(double_divide(u,w),identity)),
inference(rew,[status(thm),theory(equality)],[293,30]),
[iquote('0:Rew:293.0,30.0')] ).
cnf(315,plain,
equal(double_divide(double_divide(u,multiply(v,inverse(u))),identity),double_divide(identity,inverse(v))),
inference(rew,[status(thm),theory(equality)],[293,77]),
[iquote('0:Rew:293.0,77.0')] ).
cnf(326,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(inverse(v)))),double_divide(double_divide(v,u),identity)),
inference(rew,[status(thm),theory(equality)],[293,214]),
[iquote('0:Rew:293.0,214.0')] ).
cnf(332,plain,
equal(double_divide(identity,inverse(inverse(u))),inverse(inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[293,249]),
[iquote('0:Rew:293.0,249.0')] ).
cnf(374,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(rew,[status(thm),theory(equality)],[6,308,3]),
[iquote('0:Rew:6.0,308.0,3.0,308.0,6.0,308.0,3.0,308.0')] ).
cnf(382,plain,
equal(multiply(multiply(u,inverse(v)),v),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,315,3]),
[iquote('0:Rew:6.0,315.0,3.0,315.0')] ).
cnf(383,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[374,382]),
[iquote('0:Rew:374.0,382.0')] ).
cnf(385,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[383,332]),
[iquote('0:Rew:383.0,332.0')] ).
cnf(396,plain,
equal(multiply(double_divide(double_divide(double_divide(u,v),w),inverse(v)),u),w),
inference(rew,[status(thm),theory(equality)],[6,295,3]),
[iquote('0:Rew:6.0,295.0,3.0,295.0')] ).
cnf(402,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(inverse(v)))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,326,3]),
[iquote('0:Rew:6.0,326.0,3.0,326.0')] ).
cnf(403,plain,
equal(double_divide(double_divide(identity,u),inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[385,402]),
[iquote('0:Rew:385.0,402.0')] ).
cnf(411,plain,
equal(double_divide(double_divide(double_divide(inverse(u),v),w),inverse(v)),multiply(w,u)),
inference(rew,[status(thm),theory(equality)],[6,310,3]),
[iquote('0:Rew:6.0,310.0,3.0,310.0')] ).
cnf(435,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[298]),
[iquote('0:Obv:298.1')] ).
cnf(474,plain,
equal(multiply(double_divide(double_divide(u,v),inverse(inverse(u))),identity),v),
inference(spr,[status(thm),theory(equality)],[383,396]),
[iquote('0:SpR:383.0,396.0')] ).
cnf(494,plain,
equal(double_divide(identity,inverse(u)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[385,383]),
[iquote('0:SpR:385.0,383.0')] ).
cnf(503,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[383,494]),
[iquote('0:Rew:383.0,494.0')] ).
cnf(506,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[503,435]),
[iquote('0:Rew:503.0,435.0')] ).
cnf(513,plain,
equal(multiply(double_divide(double_divide(u,v),u),identity),v),
inference(rew,[status(thm),theory(equality)],[503,474]),
[iquote('0:Rew:503.0,474.0')] ).
cnf(519,plain,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[506]),
[iquote('0:Obv:506.0')] ).
cnf(522,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[503,383]),
[iquote('0:SpR:503.0,383.0')] ).
cnf(530,plain,
equal(double_divide(inverse(u),inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[522,403]),
[iquote('0:Rew:522.0,403.0')] ).
cnf(574,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[522,6]),
[iquote('0:SpR:522.0,6.0')] ).
cnf(578,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[503,574]),
[iquote('0:Rew:503.0,574.0')] ).
cnf(582,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[578,513]),
[iquote('0:Rew:578.0,513.0')] ).
cnf(599,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[582]),
[iquote('0:SpR:582.0,582.0')] ).
cnf(613,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(spr,[status(thm),theory(equality)],[599,6]),
[iquote('0:SpR:599.0,6.0')] ).
cnf(644,plain,
equal(double_divide(double_divide(double_divide(inverse(u),inverse(v)),w),v),multiply(w,u)),
inference(spr,[status(thm),theory(equality)],[503,411]),
[iquote('0:SpR:503.0,411.0')] ).
cnf(669,plain,
equal(double_divide(double_divide(multiply(u,v),w),v),multiply(w,u)),
inference(rew,[status(thm),theory(equality)],[530,644]),
[iquote('0:Rew:530.0,644.0')] ).
cnf(1720,plain,
equal(inverse(double_divide(multiply(u,v),w)),multiply(multiply(w,u),v)),
inference(spr,[status(thm),theory(equality)],[669,613]),
[iquote('0:SpR:669.0,613.0')] ).
cnf(1787,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,1720]),
[iquote('0:Rew:6.0,1720.0')] ).
cnf(1788,plain,
$false,
inference(unc,[status(thm)],[1787,519]),
[iquote('0:UnC:1787.0,519.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP076-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.00/0.10 % Command : run_spass %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Tue Jun 14 02:15:27 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.14/0.43
% 0.14/0.43 SPASS V 3.9
% 0.14/0.43 SPASS beiseite: Proof found.
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.43 SPASS derived 1016 clauses, backtracked 0 clauses, performed 0 splits and kept 219 clauses.
% 0.14/0.43 SPASS allocated 64951 KBytes.
% 0.14/0.43 SPASS spent 0:00:00.13 on the problem.
% 0.14/0.43 0:00:00.03 for the input.
% 0.14/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.43 0:00:00.01 for inferences.
% 0.14/0.43 0:00:00.00 for the backtracking.
% 0.14/0.43 0:00:00.08 for the reduction.
% 0.14/0.43
% 0.14/0.43
% 0.14/0.43 Here is a proof with depth 7, length 78 :
% 0.14/0.43 % SZS output start Refutation
% See solution above
% 0.14/0.45 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.14/0.45
%------------------------------------------------------------------------------