TSTP Solution File: GRP090-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP090-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:45:15 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of clauses : 56 ( 46 unt; 0 nHn; 56 RR)
% Number of literals : 75 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(u,divide(v,w)),divide(u,v)),w),
file('GRP090-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP090-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP090-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP090-1.p',unknown),
[] ).
cnf(5,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(8,plain,
equal(divide(multiply(inverse(u),u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(10,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(19,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.0,5.0')] ).
cnf(21,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(inverse(inverse(a2)),a2) ),
inference(rew,[status(thm),theory(equality)],[19,4]),
[iquote('0:Rew:19.0,4.3')] ).
cnf(22,plain,
equal(divide(u,divide(divide(v,divide(w,u)),v)),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(23,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(31,plain,
equal(divide(divide(u,multiply(v,w)),divide(u,v)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(32,plain,
equal(divide(divide(u,inverse(v)),divide(u,divide(w,w))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(39,plain,
equal(divide(multiply(u,v),divide(u,divide(w,w))),v),
inference(rew,[status(thm),theory(equality)],[5,32]),
[iquote('0:Rew:5.0,32.0')] ).
cnf(56,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[3,23]),
[iquote('0:SpR:3.0,23.0')] ).
cnf(57,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[56,21]),
[iquote('0:Rew:56.0,21.3')] ).
cnf(61,plain,
equal(multiply(divide(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[56,10]),
[iquote('0:Rew:56.0,10.0')] ).
cnf(66,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[57]),
[iquote('0:Obv:57.3')] ).
cnf(67,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[56,5]),
[iquote('0:SpR:56.0,5.0')] ).
cnf(71,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[23,56]),
[iquote('0:SpR:23.0,56.0')] ).
cnf(74,plain,
equal(divide(u,inverse(divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[71,22]),
[iquote('0:Rew:71.0,22.0')] ).
cnf(75,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,74]),
[iquote('0:Rew:5.0,74.0')] ).
cnf(83,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[75,61]),
[iquote('0:SpR:75.0,61.0')] ).
cnf(86,plain,
equal(multiply(u,inverse(u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[3,75]),
[iquote('0:SpR:3.0,75.0')] ).
cnf(89,plain,
equal(divide(u,divide(v,w)),multiply(divide(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,75]),
[iquote('0:SpR:1.0,75.0')] ).
cnf(91,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[83,39]),
[iquote('0:Rew:83.0,39.0')] ).
cnf(93,plain,
equal(divide(u,u),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[67,86]),
[iquote('0:Rew:67.0,86.0')] ).
cnf(96,plain,
equal(multiply(divide(divide(u,divide(v,w)),u),v),w),
inference(rew,[status(thm),theory(equality)],[89,1]),
[iquote('0:Rew:89.0,1.0')] ).
cnf(100,plain,
equal(multiply(divide(divide(u,multiply(v,w)),u),v),inverse(w)),
inference(rew,[status(thm),theory(equality)],[89,31]),
[iquote('0:Rew:89.0,31.0')] ).
cnf(101,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[89,83]),
[iquote('0:Rew:89.0,83.0')] ).
cnf(104,plain,
equal(multiply(divide(multiply(divide(u,v),w),u),v),w),
inference(rew,[status(thm),theory(equality)],[89,96]),
[iquote('0:Rew:89.0,96.0')] ).
cnf(106,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[71,100]),
[iquote('0:Rew:71.0,100.0')] ).
cnf(118,plain,
equal(multiply(multiply(multiply(divide(inverse(u),v),w),u),v),w),
inference(spr,[status(thm),theory(equality)],[5,104]),
[iquote('0:SpR:5.0,104.0')] ).
cnf(172,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[91,101]),
[iquote('0:SpR:91.0,101.0')] ).
cnf(179,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[172,66]),
[iquote('0:Rew:172.0,66.2')] ).
cnf(180,plain,
equal(multiply(multiply(u,multiply(divide(inverse(u),v),w)),v),w),
inference(rew,[status(thm),theory(equality)],[172,118]),
[iquote('0:Rew:172.0,118.0')] ).
cnf(182,plain,
equal(multiply(u,inverse(multiply(u,v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[172,106]),
[iquote('0:Rew:172.0,106.0')] ).
cnf(202,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[67,182]),
[iquote('0:Rew:67.0,182.0')] ).
cnf(208,plain,
equal(multiply(u,multiply(v,multiply(divide(inverse(v),u),w))),w),
inference(rew,[status(thm),theory(equality)],[172,180]),
[iquote('0:Rew:172.0,180.0')] ).
cnf(211,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[67,179,172]),
[iquote('0:Rew:67.0,179.1,172.0,179.1,67.0,179.1,172.0,179.1,172.0,179.0')] ).
cnf(212,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[211]),
[iquote('0:Obv:211.0')] ).
cnf(252,plain,
equal(divide(multiply(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[172,91]),
[iquote('0:SpR:172.0,91.0')] ).
cnf(299,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[67,172]),
[iquote('0:SpR:67.0,172.0')] ).
cnf(383,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[202,71]),
[iquote('0:SpR:202.0,71.0')] ).
cnf(400,plain,
equal(multiply(u,multiply(v,multiply(inverse(multiply(u,v)),w))),w),
inference(rew,[status(thm),theory(equality)],[383,208]),
[iquote('0:Rew:383.0,208.0')] ).
cnf(406,plain,
equal(multiply(u,multiply(v,divide(w,multiply(u,v)))),w),
inference(rew,[status(thm),theory(equality)],[299,400]),
[iquote('0:Rew:299.0,400.0')] ).
cnf(414,plain,
equal(divide(inverse(u),v),divide(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[299,67]),
[iquote('0:SpR:299.0,67.0')] ).
cnf(422,plain,
equal(inverse(multiply(u,v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[383,414]),
[iquote('0:Rew:383.0,414.0,383.0,414.0')] ).
cnf(531,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[422,5]),
[iquote('0:SpR:422.0,5.0')] ).
cnf(563,plain,
equal(multiply(u,multiply(v,w)),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[5,531]),
[iquote('0:Rew:5.0,531.0')] ).
cnf(588,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[252,406]),
[iquote('0:SpR:252.0,406.0')] ).
cnf(601,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[588,212]),
[iquote('0:Rew:588.0,212.1')] ).
cnf(619,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[172,601]),
[iquote('0:Rew:172.0,601.1')] ).
cnf(620,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[563,619,588]),
[iquote('0:Rew:563.0,619.1,588.0,619.1')] ).
cnf(621,plain,
~ equal(divide(b1,b1),divide(a1,a1)),
inference(obv,[status(thm),theory(equality)],[620]),
[iquote('0:Obv:620.1')] ).
cnf(622,plain,
$false,
inference(unc,[status(thm)],[621,93]),
[iquote('0:UnC:621.0,93.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : GRP090-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.09/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 02:38:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 400 clauses, backtracked 0 clauses, performed 0 splits and kept 108 clauses.
% 0.21/0.47 SPASS allocated 63576 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.10 on the problem.
% 0.21/0.47 0:00:00.04 for the input.
% 0.21/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.00 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.03 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 6, length 56 :
% 0.21/0.47 % SZS output start Refutation
% See solution above
% 0.21/0.47 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms
% 0.21/0.47
%------------------------------------------------------------------------------