TSTP Solution File: GRP101-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:45:18 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of clauses : 82 ( 74 unt; 0 nHn; 82 RR)
% Number of literals : 100 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(w,u)),double_divide(w,identity))),double_divide(identity,identity)),v),
file('GRP101-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP101-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP101-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP101-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP101-1.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(v,double_divide(w,u)),inverse(w))),inverse(identity)),v),
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(multiply(identity,a2),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ 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:12.0,5.2')] ).
cnf(15,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ 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(22,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(v,identity),inverse(u))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(24,plain,
equal(double_divide(double_divide(inverse(u),double_divide(inverse(v),inverse(u))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,22]),
[iquote('0:Rew:3.0,22.0')] ).
cnf(67,plain,
equal(double_divide(double_divide(inverse(inverse(u)),identity),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,24]),
[iquote('0:SpR:4.0,24.0')] ).
cnf(69,plain,
equal(double_divide(inverse(inverse(inverse(u))),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,67]),
[iquote('0:Rew:3.0,67.0')] ).
cnf(75,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(u,v),inverse(inverse(inverse(inverse(v)))))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[69,7]),
[iquote('0:SpR:69.0,7.0')] ).
cnf(77,plain,
equal(double_divide(double_divide(inverse(identity),u),inverse(identity)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[69,24]),
[iquote('0:SpR:69.0,24.0')] ).
cnf(79,plain,
equal(double_divide(inverse(inverse(multiply(u,v))),inverse(identity)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,69]),
[iquote('0:SpR:6.0,69.0')] ).
cnf(85,plain,
equal(inverse(inverse(double_divide(double_divide(u,v),inverse(inverse(inverse(inverse(v))))))),u),
inference(rew,[status(thm),theory(equality)],[77,75]),
[iquote('0:Rew:77.0,75.0')] ).
cnf(86,plain,
equal(inverse(multiply(inverse(inverse(inverse(inverse(u)))),double_divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[6,85]),
[iquote('0:Rew:6.0,85.0')] ).
cnf(100,plain,
equal(inverse(inverse(double_divide(inverse(u),inverse(identity)))),u),
inference(spr,[status(thm),theory(equality)],[77,24]),
[iquote('0:SpR:77.0,24.0')] ).
cnf(102,plain,
equal(inverse(inverse(inverse(inverse(identity)))),double_divide(identity,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[4,77]),
[iquote('0:SpR:4.0,77.0')] ).
cnf(104,plain,
equal(inverse(multiply(inverse(identity),inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[6,100]),
[iquote('0:Rew:6.0,100.0')] ).
cnf(105,plain,
equal(inverse(inverse(inverse(inverse(identity)))),identity),
inference(rew,[status(thm),theory(equality)],[4,102]),
[iquote('0:Rew:4.0,102.0')] ).
cnf(116,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(inverse(inverse(inverse(identity))),u)),identity)),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[105,7]),
[iquote('0:SpR:105.0,7.0')] ).
cnf(119,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[105,69]),
[iquote('0:SpR:105.0,69.0')] ).
cnf(123,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,119]),
[iquote('0:Rew:4.0,119.0')] ).
cnf(124,plain,
equal(multiply(inverse(u),u),identity),
inference(rew,[status(thm),theory(equality)],[123,12]),
[iquote('0:Rew:123.0,12.0')] ).
cnf(125,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(w,u)),inverse(w))),identity),v),
inference(rew,[status(thm),theory(equality)],[123,7]),
[iquote('0:Rew:123.0,7.0')] ).
cnf(128,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[123,15]),
[iquote('0:Rew:123.0,15.2')] ).
cnf(131,plain,
equal(double_divide(double_divide(identity,u),identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[123,77]),
[iquote('0:Rew:123.0,77.0')] ).
cnf(139,plain,
equal(double_divide(inverse(inverse(multiply(u,v))),identity),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[123,79]),
[iquote('0:Rew:123.0,79.0')] ).
cnf(141,plain,
equal(inverse(multiply(identity,inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[123,104]),
[iquote('0:Rew:123.0,104.0')] ).
cnf(148,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[13,141]),
[iquote('0:Rew:13.0,141.0')] ).
cnf(149,plain,
equal(inverse(multiply(u,double_divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[148,86]),
[iquote('0:Rew:148.0,86.0')] ).
cnf(164,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,131,3]),
[iquote('0:Rew:6.0,131.0,3.0,131.0')] ).
cnf(176,plain,
equal(inverse(inverse(inverse(multiply(u,v)))),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[3,139]),
[iquote('0:Rew:3.0,139.0')] ).
cnf(187,plain,
equal(multiply(double_divide(double_divide(u,double_divide(v,w)),inverse(v)),w),u),
inference(rew,[status(thm),theory(equality)],[6,125,3]),
[iquote('0:Rew:6.0,125.0,3.0,125.0')] ).
cnf(195,plain,
equal(double_divide(double_divide(u,multiply(double_divide(inverse(inverse(inverse(identity))),u),v)),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[6,116,3]),
[iquote('0:Rew:6.0,116.0,3.0,116.0')] ).
cnf(196,plain,
equal(double_divide(double_divide(u,multiply(double_divide(identity,u),v)),identity),v),
inference(rew,[status(thm),theory(equality)],[123,195]),
[iquote('0:Rew:123.0,195.0,123.0,195.0,123.0,195.0')] ).
cnf(197,plain,
equal(multiply(multiply(double_divide(identity,u),v),u),v),
inference(rew,[status(thm),theory(equality)],[6,196,3]),
[iquote('0:Rew:6.0,196.0,3.0,196.0')] ).
cnf(199,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[128]),
[iquote('0:Obv:128.2')] ).
cnf(221,plain,
equal(double_divide(inverse(inverse(inverse(u))),u),identity),
inference(spr,[status(thm),theory(equality)],[148,4]),
[iquote('0:SpR:148.0,4.0')] ).
cnf(223,plain,
equal(multiply(u,inverse(inverse(inverse(u)))),identity),
inference(spr,[status(thm),theory(equality)],[148,124]),
[iquote('0:SpR:148.0,124.0')] ).
cnf(231,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(u))),identity),
inference(spr,[status(thm),theory(equality)],[164,10]),
[iquote('0:SpR:164.0,10.0')] ).
cnf(261,plain,
equal(multiply(double_divide(identity,inverse(u)),v),inverse(inverse(inverse(double_divide(u,v))))),
inference(spr,[status(thm),theory(equality)],[221,187]),
[iquote('0:SpR:221.0,187.0')] ).
cnf(273,plain,
equal(multiply(double_divide(identity,inverse(u)),v),inverse(inverse(multiply(v,u)))),
inference(rew,[status(thm),theory(equality)],[6,261]),
[iquote('0:Rew:6.0,261.0')] ).
cnf(323,plain,
equal(multiply(u,double_divide(v,u)),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[149,148]),
[iquote('0:SpR:149.0,148.0')] ).
cnf(376,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),u),identity),
inference(spr,[status(thm),theory(equality)],[148,231]),
[iquote('0:SpR:148.0,231.0')] ).
cnf(391,plain,
equal(multiply(u,double_divide(identity,inverse(inverse(u)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[376,6]),
[iquote('0:SpR:376.0,6.0')] ).
cnf(405,plain,
equal(multiply(u,double_divide(identity,inverse(inverse(u)))),identity),
inference(rew,[status(thm),theory(equality)],[123,391]),
[iquote('0:Rew:123.0,391.0')] ).
cnf(493,plain,
equal(inverse(inverse(inverse(double_divide(identity,u)))),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[223,197]),
[iquote('0:SpR:223.0,197.0')] ).
cnf(494,plain,
equal(double_divide(identity,inverse(inverse(double_divide(identity,u)))),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[405,197]),
[iquote('0:SpR:405.0,197.0')] ).
cnf(500,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[148,493,164,6,13]),
[iquote('0:Rew:148.0,493.0,164.0,493.0,6.0,493.0,13.0,493.0')] ).
cnf(501,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[500,199]),
[iquote('0:Rew:500.0,199.0')] ).
cnf(506,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[500,13]),
[iquote('0:Rew:500.0,13.0')] ).
cnf(507,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[500,164]),
[iquote('0:Rew:500.0,164.0')] ).
cnf(513,plain,
equal(multiply(u,double_divide(v,u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[500,323]),
[iquote('0:Rew:500.0,323.0')] ).
cnf(516,plain,
equal(multiply(double_divide(identity,inverse(u)),v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[500,273]),
[iquote('0:Rew:500.0,273.0')] ).
cnf(518,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[500,176]),
[iquote('0:Rew:500.0,176.0')] ).
cnf(529,plain,
equal(double_divide(identity,inverse(multiply(u,identity))),multiply(identity,u)),
inference(rew,[status(thm),theory(equality)],[6,494]),
[iquote('0:Rew:6.0,494.0')] ).
cnf(530,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[507,529,506]),
[iquote('0:Rew:507.0,529.0,506.0,529.0')] ).
cnf(531,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[530,516]),
[iquote('0:Rew:530.0,516.0')] ).
cnf(533,plain,
equal(multiply(u,double_divide(double_divide(v,double_divide(w,u)),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[531,187]),
[iquote('0:Rew:531.0,187.0')] ).
cnf(534,plain,
equal(multiply(u,multiply(double_divide(identity,u),v)),v),
inference(rew,[status(thm),theory(equality)],[531,197]),
[iquote('0:Rew:531.0,197.0')] ).
cnf(547,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[501]),
[iquote('0:Obv:501.0')] ).
cnf(548,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[531,547]),
[iquote('0:Rew:531.0,547.1,531.0,547.0')] ).
cnf(549,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[548]),
[iquote('0:Obv:548.0')] ).
cnf(587,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[500,530]),
[iquote('0:SpR:500.0,530.0')] ).
cnf(597,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[587,534]),
[iquote('0:Rew:587.0,534.0')] ).
cnf(673,plain,
equal(inverse(multiply(u,v)),double_divide(u,v)),
inference(spr,[status(thm),theory(equality)],[531,518]),
[iquote('0:SpR:531.0,518.0')] ).
cnf(682,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[518,673]),
[iquote('0:Rew:518.0,673.0')] ).
cnf(684,plain,
equal(multiply(u,double_divide(inverse(v),double_divide(w,double_divide(v,u)))),w),
inference(rew,[status(thm),theory(equality)],[682,533]),
[iquote('0:Rew:682.0,533.0')] ).
cnf(749,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[682,513]),
[iquote('0:SpR:682.0,513.0')] ).
cnf(821,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[531,597]),
[iquote('0:SpR:531.0,597.0')] ).
cnf(913,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[749,597]),
[iquote('0:SpR:749.0,597.0')] ).
cnf(927,plain,
equal(multiply(u,multiply(v,inverse(double_divide(w,double_divide(v,u))))),w),
inference(rew,[status(thm),theory(equality)],[913,684]),
[iquote('0:Rew:913.0,684.0')] ).
cnf(940,plain,
equal(multiply(u,multiply(v,multiply(double_divide(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[6,927]),
[iquote('0:Rew:6.0,927.0')] ).
cnf(1075,plain,
equal(multiply(u,inverse(double_divide(v,w))),multiply(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[821,940]),
[iquote('0:SpR:821.0,940.0')] ).
cnf(1109,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[6,1075]),
[iquote('0:Rew:6.0,1075.0')] ).
cnf(1110,plain,
$false,
inference(unc,[status(thm)],[1109,549]),
[iquote('0:UnC:1109.0,549.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 23:38:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 680 clauses, backtracked 0 clauses, performed 0 splits and kept 183 clauses.
% 0.19/0.49 SPASS allocated 64221 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.08 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 9, length 82 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.19/0.50
%------------------------------------------------------------------------------