TSTP Solution File: GRP093-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP093-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:45:16 EDT 2022
% Result : Unsatisfiable 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 56 ( 48 unt; 0 nHn; 56 RR)
% Number of literals : 72 ( 0 equ; 25 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 : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(identity,divide(divide(divide(u,v),w),u)),w),v),
file('GRP093-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP093-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP093-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP093-1.p',unknown),
[] ).
cnf(5,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('GRP093-1.p',unknown),
[] ).
cnf(6,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(7,plain,
equal(divide(inverse(divide(divide(divide(u,v),w),u)),w),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
cnf(16,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(identity,a2),a2) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.3')] ).
cnf(17,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(inverse(inverse(a2)),a2) ),
inference(rew,[status(thm),theory(equality)],[13,16,12]),
[iquote('0:Rew:13.0,16.3,12.0,16.1,12.0,16.1')] ).
cnf(18,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(inverse(inverse(a2)),a2) ),
inference(obv,[status(thm),theory(equality)],[17]),
[iquote('0:Obv:17.1')] ).
cnf(19,plain,
equal(multiply(inverse(divide(divide(divide(u,v),inverse(w)),u)),w),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(22,plain,
equal(divide(inverse(divide(divide(identity,u),v)),u),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(25,plain,
equal(divide(inverse(divide(identity,u)),divide(u,v)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(28,plain,
equal(divide(inverse(divide(inverse(u),v)),u),v),
inference(rew,[status(thm),theory(equality)],[3,22]),
[iquote('0:Rew:3.0,22.0')] ).
cnf(29,plain,
equal(divide(inverse(inverse(u)),divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[3,25]),
[iquote('0:Rew:3.0,25.0')] ).
cnf(31,plain,
equal(multiply(inverse(divide(multiply(divide(u,v),w),u)),w),v),
inference(rew,[status(thm),theory(equality)],[6,19]),
[iquote('0:Rew:6.0,19.0')] ).
cnf(57,plain,
equal(divide(inverse(divide(identity,u)),identity),u),
inference(spr,[status(thm),theory(equality)],[9,28]),
[iquote('0:SpR:9.0,28.0')] ).
cnf(63,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(rew,[status(thm),theory(equality)],[15,57,3]),
[iquote('0:Rew:15.0,57.0,3.0,57.0')] ).
cnf(71,plain,
equal(divide(inverse(u),inverse(v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[29,28]),
[iquote('0:SpR:29.0,28.0')] ).
cnf(74,plain,
equal(divide(inverse(inverse(identity)),inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[3,29]),
[iquote('0:SpR:3.0,29.0')] ).
cnf(76,plain,
equal(divide(inverse(inverse(u)),multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[6,29]),
[iquote('0:SpR:6.0,29.0')] ).
cnf(81,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,74,6,9]),
[iquote('0:Rew:13.0,74.0,6.0,74.0,9.0,74.0,9.0,74.0')] ).
cnf(82,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[81,18]),
[iquote('0:Rew:81.0,18.2')] ).
cnf(84,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[81,63]),
[iquote('0:Rew:81.0,63.0')] ).
cnf(85,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[81,29]),
[iquote('0:Rew:81.0,29.0')] ).
cnf(90,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[6,71]),
[iquote('0:Rew:6.0,71.0')] ).
cnf(93,plain,
equal(divide(u,divide(multiply(divide(v,w),u),v)),w),
inference(rew,[status(thm),theory(equality)],[90,31]),
[iquote('0:Rew:90.0,31.0')] ).
cnf(97,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[81,76]),
[iquote('0:Rew:81.0,76.0')] ).
cnf(102,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)],[82]),
[iquote('0:Obv:82.2')] ).
cnf(146,plain,
equal(divide(u,inverse(v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[81,90]),
[iquote('0:SpR:81.0,90.0')] ).
cnf(148,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,146]),
[iquote('0:Rew:6.0,146.0')] ).
cnf(149,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[148,102]),
[iquote('0:Rew:148.0,102.1')] ).
cnf(151,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)],[148,149]),
[iquote('0:Rew:148.0,149.0')] ).
cnf(152,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[151]),
[iquote('0:Obv:151.0')] ).
cnf(166,plain,
equal(divide(u,multiply(v,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[148,97]),
[iquote('0:SpR:148.0,97.0')] ).
cnf(198,plain,
equal(divide(multiply(divide(u,v),w),u),divide(w,v)),
inference(spr,[status(thm),theory(equality)],[93,85]),
[iquote('0:SpR:93.0,85.0')] ).
cnf(209,plain,
equal(divide(identity,divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[84,93]),
[iquote('0:SpR:84.0,93.0')] ).
cnf(215,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,209]),
[iquote('0:Rew:3.0,209.0')] ).
cnf(228,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[215,81]),
[iquote('0:SpR:215.0,81.0')] ).
cnf(259,plain,
equal(divide(divide(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[228,85]),
[iquote('0:SpR:228.0,85.0')] ).
cnf(266,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[97,228]),
[iquote('0:SpR:97.0,228.0')] ).
cnf(267,plain,
equal(divide(inverse(u),v),inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[166,228]),
[iquote('0:SpR:166.0,228.0')] ).
cnf(269,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[148,259,6]),
[iquote('0:Rew:148.0,259.0,6.0,259.0')] ).
cnf(282,plain,
equal(inverse(multiply(u,v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[266,267]),
[iquote('0:Rew:266.0,267.0')] ).
cnf(456,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[282,6]),
[iquote('0:SpR:282.0,6.0')] ).
cnf(490,plain,
equal(multiply(u,multiply(v,w)),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[6,456]),
[iquote('0:Rew:6.0,456.0')] ).
cnf(497,plain,
equal(multiply(divide(u,v),w),multiply(u,divide(w,v))),
inference(spr,[status(thm),theory(equality)],[198,269]),
[iquote('0:SpR:198.0,269.0')] ).
cnf(727,plain,
equal(multiply(u,multiply(v,w)),multiply(multiply(w,v),u)),
inference(spr,[status(thm),theory(equality)],[490,148]),
[iquote('0:SpR:490.0,148.0')] ).
cnf(859,plain,
equal(multiply(u,divide(v,inverse(w))),multiply(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[6,497]),
[iquote('0:SpR:6.0,497.0')] ).
cnf(876,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[6,859]),
[iquote('0:Rew:6.0,859.0')] ).
cnf(882,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[876,727]),
[iquote('0:Rew:876.0,727.0')] ).
cnf(892,plain,
$false,
inference(unc,[status(thm)],[882,152]),
[iquote('0:UnC:882.0,152.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP093-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 07:39:42 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.50
% 0.22/0.50 SPASS V 3.9
% 0.22/0.50 SPASS beiseite: Proof found.
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.50 SPASS derived 553 clauses, backtracked 0 clauses, performed 0 splits and kept 135 clauses.
% 0.22/0.50 SPASS allocated 63868 KBytes.
% 0.22/0.50 SPASS spent 0:00:00.12 on the problem.
% 0.22/0.50 0:00:00.04 for the input.
% 0.22/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.50 0:00:00.01 for inferences.
% 0.22/0.50 0:00:00.00 for the backtracking.
% 0.22/0.50 0:00:00.06 for the reduction.
% 0.22/0.50
% 0.22/0.50
% 0.22/0.50 Here is a proof with depth 7, length 56 :
% 0.22/0.50 % SZS output start Refutation
% See solution above
% 0.22/0.50 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.22/0.50
%------------------------------------------------------------------------------