TSTP Solution File: GRP097-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP097-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:45:17 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 50 ( 40 unt; 0 nHn; 50 RR)
% Number of literals : 66 ( 0 equ; 27 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 : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,inverse(divide(divide(v,w),divide(u,w)))),v),
file('GRP097-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP097-1.p',unknown),
[] ).
cnf(3,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('GRP097-1.p',unknown),
[] ).
cnf(4,plain,
equal(multiply(u,divide(divide(v,w),divide(u,w))),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(7,plain,
equal(multiply(u,divide(divide(v,inverse(w)),multiply(u,w))),v),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(9,plain,
equal(multiply(u,divide(multiply(v,w),multiply(u,w))),v),
inference(rew,[status(thm),theory(equality)],[2,7]),
[iquote('0:Rew:2.0,7.0')] ).
cnf(12,plain,
equal(multiply(u,divide(multiply(v,divide(multiply(w,x),multiply(u,x))),w)),v),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(25,plain,
equal(multiply(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[9,12]),
[iquote('0:SpR:9.0,12.0')] ).
cnf(26,plain,
equal(multiply(u,multiply(multiply(v,divide(multiply(inverse(w),x),multiply(u,x))),w)),v),
inference(spr,[status(thm),theory(equality)],[2,12]),
[iquote('0:SpR:2.0,12.0')] ).
cnf(33,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[25,12]),
[iquote('0:SpR:25.0,12.0')] ).
cnf(35,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(spr,[status(thm),theory(equality)],[2,25]),
[iquote('0:SpR:2.0,25.0')] ).
cnf(48,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(spr,[status(thm),theory(equality)],[2,33]),
[iquote('0:SpR:2.0,33.0')] ).
cnf(70,plain,
equal(multiply(inverse(divide(u,u)),v),v),
inference(spr,[status(thm),theory(equality)],[25,48]),
[iquote('0:SpR:25.0,48.0')] ).
cnf(120,plain,
equal(divide(multiply(u,v),multiply(inverse(divide(w,w)),v)),u),
inference(spr,[status(thm),theory(equality)],[70,9]),
[iquote('0:SpR:70.0,9.0')] ).
cnf(141,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[70,120]),
[iquote('0:Rew:70.0,120.0')] ).
cnf(151,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[141,2]),
[iquote('0:SpR:141.0,2.0')] ).
cnf(154,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[141,33]),
[iquote('0:SpR:141.0,33.0')] ).
cnf(159,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[25,141]),
[iquote('0:SpR:25.0,141.0')] ).
cnf(160,plain,
equal(divide(u,divide(u,v)),v),
inference(spr,[status(thm),theory(equality)],[33,141]),
[iquote('0:SpR:33.0,141.0')] ).
cnf(165,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[48,141]),
[iquote('0:SpR:48.0,141.0')] ).
cnf(166,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(multiply(a2,multiply(inverse(b2),b2)),a2) ),
inference(rew,[status(thm),theory(equality)],[154,3]),
[iquote('0:Rew:154.0,3.3')] ).
cnf(167,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[154,35]),
[iquote('0:Rew:154.0,35.0')] ).
cnf(170,plain,
equal(multiply(u,multiply(v,multiply(w,divide(multiply(inverse(v),x),multiply(u,x))))),w),
inference(rew,[status(thm),theory(equality)],[154,26]),
[iquote('0:Rew:154.0,26.0')] ).
cnf(179,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[154,151]),
[iquote('0:Rew:154.0,151.0')] ).
cnf(186,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[167,166,154]),
[iquote('0:Rew:167.0,166.3,154.0,166.3,154.0,166.2,154.0,166.1,154.0,166.1,154.0,166.0')] ).
cnf(187,plain,
( ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[186]),
[iquote('0:Obv:186.3')] ).
cnf(188,plain,
equal(divide(multiply(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[154,141]),
[iquote('0:SpR:154.0,141.0')] ).
cnf(235,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[159,160]),
[iquote('0:SpR:159.0,160.0')] ).
cnf(249,plain,
equal(divide(multiply(u,v),multiply(w,v)),divide(u,w)),
inference(spr,[status(thm),theory(equality)],[9,188]),
[iquote('0:SpR:9.0,188.0')] ).
cnf(263,plain,
equal(multiply(u,multiply(v,multiply(w,divide(inverse(v),u)))),w),
inference(rew,[status(thm),theory(equality)],[249,170]),
[iquote('0:Rew:249.0,170.0')] ).
cnf(429,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[179,188]),
[iquote('0:SpR:179.0,188.0')] ).
cnf(445,plain,
( ~ equal(multiply(a1,inverse(a1)),divide(b1,b1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[429,187]),
[iquote('0:Rew:429.0,187.0')] ).
cnf(466,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[429,445]),
[iquote('0:Rew:429.0,445.0')] ).
cnf(476,plain,
equal(divide(u,multiply(v,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[154,165]),
[iquote('0:SpR:154.0,165.0')] ).
cnf(478,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[33,165]),
[iquote('0:SpR:33.0,165.0')] ).
cnf(481,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[48,165]),
[iquote('0:SpR:48.0,165.0')] ).
cnf(497,plain,
equal(multiply(u,multiply(v,multiply(w,inverse(multiply(u,v))))),w),
inference(rew,[status(thm),theory(equality)],[481,263]),
[iquote('0:Rew:481.0,263.0')] ).
cnf(504,plain,
equal(multiply(u,multiply(v,divide(w,multiply(u,v)))),w),
inference(rew,[status(thm),theory(equality)],[429,497]),
[iquote('0:Rew:429.0,497.0')] ).
cnf(652,plain,
equal(multiply(u,divide(v,w)),divide(u,divide(w,v))),
inference(spr,[status(thm),theory(equality)],[478,2]),
[iquote('0:SpR:478.0,2.0')] ).
cnf(672,plain,
equal(multiply(u,divide(v,divide(multiply(u,v),w))),w),
inference(rew,[status(thm),theory(equality)],[652,504]),
[iquote('0:Rew:652.0,504.0')] ).
cnf(698,plain,
equal(divide(u,divide(divide(multiply(u,v),w),v)),w),
inference(rew,[status(thm),theory(equality)],[652,672]),
[iquote('0:Rew:652.0,672.0')] ).
cnf(817,plain,
equal(divide(u,divide(inverse(v),w)),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[476,698]),
[iquote('0:SpR:476.0,698.0')] ).
cnf(868,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[481,817]),
[iquote('0:Rew:481.0,817.0')] ).
cnf(869,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,868]),
[iquote('0:Rew:2.0,868.0')] ).
cnf(870,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)],[869,466]),
[iquote('0:Rew:869.0,466.1')] ).
cnf(883,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)],[154,870]),
[iquote('0:Rew:154.0,870.1')] ).
cnf(884,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)],[869,883]),
[iquote('0:Rew:869.0,883.1')] ).
cnf(885,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)],[154,884]),
[iquote('0:Rew:154.0,884.1')] ).
cnf(886,plain,
~ equal(divide(b1,b1),divide(a1,a1)),
inference(obv,[status(thm),theory(equality)],[885]),
[iquote('0:Obv:885.1')] ).
cnf(887,plain,
$false,
inference(unc,[status(thm)],[886,235]),
[iquote('0:UnC:886.0,235.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP097-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n006.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 08:39:56 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/sandbox2/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 610 clauses, backtracked 0 clauses, performed 0 splits and kept 192 clauses.
% 0.20/0.50 SPASS allocated 64044 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.50 0:00:00.03 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 10, length 50 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 0.20/0.50
%------------------------------------------------------------------------------