TSTP Solution File: GRP088-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP088-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:45:14 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of clauses : 52 ( 41 unt; 0 nHn; 52 RR)
% Number of literals : 72 ( 0 equ; 32 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 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(u,divide(v,divide(w,divide(u,v)))),w),
file('GRP088-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP088-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP088-1.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('GRP088-1.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(inverse(divide(u,divide(v,divide(divide(w,w),u)))),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(28,plain,
equal(divide(u,divide(inverse(v),divide(w,multiply(u,v)))),w),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(35,plain,
equal(divide(u,inverse(divide(v,divide(u,divide(w,w))))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(38,plain,
equal(inverse(divide(u,multiply(v,u))),v),
inference(rew,[status(thm),theory(equality)],[5,22,3]),
[iquote('0:Rew:5.0,22.0,3.0,22.0')] ).
cnf(41,plain,
equal(multiply(u,divide(v,divide(u,divide(w,w)))),v),
inference(rew,[status(thm),theory(equality)],[5,35]),
[iquote('0:Rew:5.0,35.0')] ).
cnf(53,plain,
equal(inverse(inverse(multiply(u,divide(v,v)))),u),
inference(spr,[status(thm),theory(equality)],[3,38]),
[iquote('0:SpR:3.0,38.0')] ).
cnf(58,plain,
equal(inverse(divide(u,inverse(inverse(u)))),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[10,38]),
[iquote('0:SpR:10.0,38.0')] ).
cnf(63,plain,
equal(inverse(multiply(u,inverse(u))),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[5,58]),
[iquote('0:Rew:5.0,58.0')] ).
cnf(64,plain,
equal(multiply(u,inverse(multiply(v,divide(w,w)))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[53,5]),
[iquote('0:SpR:53.0,5.0')] ).
cnf(76,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[63]),
[iquote('0:SpR:63.0,63.0')] ).
cnf(84,plain,
equal(divide(u,divide(u,divide(v,inverse(multiply(w,inverse(w)))))),v),
inference(spr,[status(thm),theory(equality)],[63,1]),
[iquote('0:SpR:63.0,1.0')] ).
cnf(87,plain,
equal(divide(u,divide(v,inverse(multiply(w,inverse(w))))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[63,1]),
[iquote('0:SpR:63.0,1.0')] ).
cnf(92,plain,
equal(divide(u,divide(u,multiply(v,multiply(w,inverse(w))))),v),
inference(rew,[status(thm),theory(equality)],[5,84]),
[iquote('0:Rew:5.0,84.0')] ).
cnf(93,plain,
equal(divide(u,multiply(v,multiply(w,inverse(w)))),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[5,87]),
[iquote('0:Rew:5.0,87.0')] ).
cnf(94,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[93,92]),
[iquote('0:Rew:93.0,92.0')] ).
cnf(103,plain,
equal(divide(u,divide(u,divide(v,divide(w,w)))),v),
inference(spr,[status(thm),theory(equality)],[76,1]),
[iquote('0:SpR:76.0,1.0')] ).
cnf(121,plain,
equal(divide(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[94,103]),
[iquote('0:Rew:94.0,103.0')] ).
cnf(122,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[121,41]),
[iquote('0:Rew:121.0,41.0')] ).
cnf(131,plain,
equal(inverse(divide(divide(u,u),v)),v),
inference(spr,[status(thm),theory(equality)],[94,3]),
[iquote('0:SpR:94.0,3.0')] ).
cnf(141,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,94]),
[iquote('0:SpR:5.0,94.0')] ).
cnf(148,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,131]),
[iquote('0:Rew:3.0,131.0')] ).
cnf(149,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)],[148,21]),
[iquote('0:Rew:148.0,21.3')] ).
cnf(150,plain,
equal(multiply(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[148,53]),
[iquote('0:Rew:148.0,53.0')] ).
cnf(172,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[150,64]),
[iquote('0:Rew:150.0,64.0')] ).
cnf(201,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)],[149]),
[iquote('0:Obv:149.3')] ).
cnf(239,plain,
equal(multiply(divide(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[94,122]),
[iquote('0:SpR:94.0,122.0')] ).
cnf(271,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[5,239]),
[iquote('0:SpR:5.0,239.0')] ).
cnf(278,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[172,271]),
[iquote('0:Rew:172.0,271.0')] ).
cnf(333,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[278,122]),
[iquote('0:SpR:278.0,122.0')] ).
cnf(342,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)],[333,201]),
[iquote('0:Rew:333.0,201.2')] ).
cnf(368,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)],[172,342,333]),
[iquote('0:Rew:172.0,342.1,333.0,342.1,172.0,342.1,333.0,342.1,333.0,342.0')] ).
cnf(369,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)],[368]),
[iquote('0:Obv:368.0')] ).
cnf(437,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[122,141]),
[iquote('0:SpR:122.0,141.0')] ).
cnf(491,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[5,437]),
[iquote('0:SpR:5.0,437.0')] ).
cnf(504,plain,
equal(divide(u,inverse(multiply(divide(v,multiply(u,w)),w))),v),
inference(rew,[status(thm),theory(equality)],[491,28]),
[iquote('0:Rew:491.0,28.0')] ).
cnf(516,plain,
equal(multiply(u,multiply(v,divide(w,multiply(u,v)))),w),
inference(rew,[status(thm),theory(equality)],[5,504,333]),
[iquote('0:Rew:5.0,504.0,333.0,504.0')] ).
cnf(534,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[278,516]),
[iquote('0:SpR:278.0,516.0')] ).
cnf(548,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)],[534,369]),
[iquote('0:Rew:534.0,369.1')] ).
cnf(556,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)],[333,548]),
[iquote('0:Rew:333.0,548.1')] ).
cnf(557,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[534,556]),
[iquote('0:Rew:534.0,556.1')] ).
cnf(558,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)],[333,557]),
[iquote('0:Rew:333.0,557.1')] ).
cnf(559,plain,
~ equal(divide(b1,b1),divide(a1,a1)),
inference(obv,[status(thm),theory(equality)],[558]),
[iquote('0:Obv:558.1')] ).
cnf(560,plain,
$false,
inference(unc,[status(thm)],[559,76]),
[iquote('0:UnC:559.0,76.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP088-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n014.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 03:34:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 407 clauses, backtracked 0 clauses, performed 0 splits and kept 111 clauses.
% 0.21/0.45 SPASS allocated 63495 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.21/0.45 0:00:00.03 for the input.
% 0.21/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.03 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 6, length 52 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms
% 0.21/0.45
%------------------------------------------------------------------------------