TSTP Solution File: GRP094-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP094-1 : 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 11:45:16 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of clauses : 69 ( 61 unt; 0 nHn; 69 RR)
% Number of literals : 85 ( 0 equ; 27 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 : 17 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(identity,divide(u,v)),divide(divide(v,w),u)),w),
file('GRP094-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP094-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP094-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP094-1.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('GRP094-1.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(u,v)),divide(divide(v,w),u)),w),
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(20,plain,
equal(divide(inverse(divide(u,inverse(divide(v,w)))),divide(x,u)),divide(divide(w,x),v)),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(22,plain,
equal(divide(inverse(divide(u,v)),divide(identity,u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(24,plain,
equal(divide(inverse(divide(u,v)),divide(multiply(v,w),u)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(25,plain,
equal(divide(inverse(divide(divide(u,v),u)),identity),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(26,plain,
equal(divide(inverse(divide(inverse(u),v)),multiply(divide(v,w),u)),w),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(27,plain,
equal(divide(inverse(identity),divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(28,plain,
equal(divide(inverse(inverse(u)),divide(divide(u,v),identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(30,plain,
equal(multiply(inverse(divide(u,v)),u),v),
inference(rew,[status(thm),theory(equality)],[6,22,3]),
[iquote('0:Rew:6.0,22.0,3.0,22.0')] ).
cnf(31,plain,
equal(multiply(inverse(divide(divide(u,v),u)),identity),v),
inference(rew,[status(thm),theory(equality)],[15,25]),
[iquote('0:Rew:15.0,25.0')] ).
cnf(32,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,27,9]),
[iquote('0:Rew:3.0,27.0,9.0,27.0')] ).
cnf(33,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[32,31]),
[iquote('0:Rew:32.0,31.0')] ).
cnf(34,plain,
equal(divide(u,identity),u),
inference(rew,[status(thm),theory(equality)],[33,15]),
[iquote('0:Rew:33.0,15.0')] ).
cnf(36,plain,
equal(divide(inverse(inverse(u)),divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[34,28]),
[iquote('0:Rew:34.0,28.0')] ).
cnf(38,plain,
equal(divide(inverse(multiply(u,divide(v,w))),divide(x,u)),divide(divide(w,x),v)),
inference(rew,[status(thm),theory(equality)],[6,20]),
[iquote('0:Rew:6.0,20.0')] ).
cnf(54,plain,
equal(inverse(divide(identity,u)),u),
inference(spr,[status(thm),theory(equality)],[30,33]),
[iquote('0:SpR:30.0,33.0')] ).
cnf(60,plain,
equal(multiply(inverse(u),inverse(divide(v,w))),divide(divide(w,u),v)),
inference(spr,[status(thm),theory(equality)],[7,30]),
[iquote('0:SpR:7.0,30.0')] ).
cnf(61,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,54]),
[iquote('0:Rew:3.0,54.0')] ).
cnf(62,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)],[61,18]),
[iquote('0:Rew:61.0,18.2')] ).
cnf(64,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[61,36]),
[iquote('0:Rew:61.0,36.0')] ).
cnf(67,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)],[62]),
[iquote('0:Obv:62.2')] ).
cnf(70,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[61,6]),
[iquote('0:SpR:61.0,6.0')] ).
cnf(73,plain,
equal(divide(inverse(u),divide(v,w)),divide(divide(w,u),v)),
inference(rew,[status(thm),theory(equality)],[70,60]),
[iquote('0:Rew:70.0,60.0')] ).
cnf(76,plain,
equal(divide(divide(u,multiply(u,divide(v,w))),x),divide(divide(w,x),v)),
inference(rew,[status(thm),theory(equality)],[73,38]),
[iquote('0:Rew:73.0,38.0')] ).
cnf(79,plain,
equal(divide(divide(u,divide(u,v)),multiply(v,w)),inverse(w)),
inference(rew,[status(thm),theory(equality)],[73,24]),
[iquote('0:Rew:73.0,24.0')] ).
cnf(84,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[64,79]),
[iquote('0:Rew:64.0,79.0')] ).
cnf(86,plain,
equal(divide(inverse(divide(u,v)),w),divide(divide(v,w),u)),
inference(rew,[status(thm),theory(equality)],[84,76]),
[iquote('0:Rew:84.0,76.0')] ).
cnf(87,plain,
equal(divide(divide(u,multiply(divide(u,v),w)),inverse(w)),v),
inference(rew,[status(thm),theory(equality)],[86,26]),
[iquote('0:Rew:86.0,26.0')] ).
cnf(88,plain,
equal(multiply(divide(u,multiply(divide(u,v),w)),w),v),
inference(rew,[status(thm),theory(equality)],[6,87]),
[iquote('0:Rew:6.0,87.0')] ).
cnf(92,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[64,30]),
[iquote('0:SpR:64.0,30.0')] ).
cnf(111,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[64,32]),
[iquote('0:SpR:64.0,32.0')] ).
cnf(119,plain,
equal(divide(divide(u,v),w),divide(divide(u,w),v)),
inference(rew,[status(thm),theory(equality)],[111,86]),
[iquote('0:Rew:111.0,86.0')] ).
cnf(141,plain,
equal(divide(u,inverse(v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[61,92]),
[iquote('0:SpR:61.0,92.0')] ).
cnf(143,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,141]),
[iquote('0:Rew:6.0,141.0')] ).
cnf(144,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)],[143,67]),
[iquote('0:Rew:143.0,67.1')] ).
cnf(146,plain,
equal(multiply(u,divide(v,multiply(divide(v,w),u))),w),
inference(rew,[status(thm),theory(equality)],[143,88]),
[iquote('0:Rew:143.0,88.0')] ).
cnf(150,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)],[143,144]),
[iquote('0:Rew:143.0,144.0')] ).
cnf(151,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[150]),
[iquote('0:Obv:150.0')] ).
cnf(224,plain,
equal(divide(divide(u,inverse(v)),w),multiply(divide(u,w),v)),
inference(spr,[status(thm),theory(equality)],[119,6]),
[iquote('0:SpR:119.0,6.0')] ).
cnf(248,plain,
equal(divide(divide(u,v),divide(u,w)),divide(w,v)),
inference(spr,[status(thm),theory(equality)],[64,119]),
[iquote('0:SpR:64.0,119.0')] ).
cnf(268,plain,
equal(divide(multiply(u,v),w),multiply(divide(u,w),v)),
inference(rew,[status(thm),theory(equality)],[6,224]),
[iquote('0:Rew:6.0,224.0')] ).
cnf(284,plain,
equal(divide(u,divide(v,w)),multiply(divide(w,v),u)),
inference(spr,[status(thm),theory(equality)],[111,92]),
[iquote('0:SpR:111.0,92.0')] ).
cnf(304,plain,
equal(multiply(divide(u,v),divide(v,w)),divide(u,w)),
inference(rew,[status(thm),theory(equality)],[284,248]),
[iquote('0:Rew:284.0,248.0')] ).
cnf(428,plain,
equal(multiply(u,divide(v,multiply(inverse(w),u))),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[84,146]),
[iquote('0:SpR:84.0,146.0')] ).
cnf(463,plain,
equal(multiply(u,divide(v,divide(u,w))),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[92,428]),
[iquote('0:Rew:92.0,428.0')] ).
cnf(464,plain,
equal(multiply(u,multiply(divide(v,u),w)),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[284,463]),
[iquote('0:Rew:284.0,463.0')] ).
cnf(701,plain,
equal(multiply(multiply(divide(u,divide(v,w)),x),v),multiply(w,multiply(x,u))),
inference(spr,[status(thm),theory(equality)],[464]),
[iquote('0:SpR:464.0,464.0')] ).
cnf(710,plain,
equal(multiply(u,multiply(multiply(divide(v,u),w),x)),multiply(x,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[268,464]),
[iquote('0:SpR:268.0,464.0')] ).
cnf(716,plain,
equal(multiply(divide(u,v),w),multiply(u,divide(w,v))),
inference(spr,[status(thm),theory(equality)],[304,464]),
[iquote('0:SpR:304.0,464.0')] ).
cnf(726,plain,
equal(divide(u,divide(v,w)),multiply(w,divide(u,v))),
inference(rew,[status(thm),theory(equality)],[716,284]),
[iquote('0:Rew:716.0,284.0')] ).
cnf(760,plain,
equal(multiply(u,multiply(divide(v,divide(u,w)),x)),multiply(w,multiply(x,v))),
inference(rew,[status(thm),theory(equality)],[143,701]),
[iquote('0:Rew:143.0,701.0')] ).
cnf(761,plain,
equal(multiply(u,multiply(multiply(v,divide(w,u)),x)),multiply(v,multiply(x,w))),
inference(rew,[status(thm),theory(equality)],[726,760]),
[iquote('0:Rew:726.0,760.0')] ).
cnf(763,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[761,710,716]),
[iquote('0:Rew:761.0,710.0,716.0,710.0')] ).
cnf(764,plain,
~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[763,151]),
[iquote('0:Rew:763.0,151.0')] ).
cnf(765,plain,
~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[143,764]),
[iquote('0:Rew:143.0,764.0')] ).
cnf(766,plain,
$false,
inference(obv,[status(thm),theory(equality)],[765]),
[iquote('0:Obv:765.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP094-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 09:02:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 442 clauses, backtracked 0 clauses, performed 0 splits and kept 124 clauses.
% 0.20/0.47 SPASS allocated 63735 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.20/0.47 0:00:00.03 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.05 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 3, length 69 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.20/0.47
%------------------------------------------------------------------------------