TSTP Solution File: GRP095-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP095-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 54 ( 46 unt; 0 nHn; 54 RR)
% Number of literals : 70 ( 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 : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(identity,u),divide(divide(divide(v,u),w),v)),w),
file('GRP095-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP095-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP095-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP095-1.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('GRP095-1.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(u),divide(divide(divide(v,u),w),v)),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(21,plain,
equal(divide(inverse(u),divide(divide(identity,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(23,plain,
equal(divide(inverse(inverse(u)),divide(divide(multiply(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(24,plain,
equal(divide(inverse(u),divide(identity,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(27,plain,
equal(divide(identity,divide(divide(divide(u,identity),v),u)),v),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(28,plain,
equal(divide(inverse(u),divide(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,21]),
[iquote('0:Rew:3.0,21.0')] ).
cnf(29,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[6,24,3]),
[iquote('0:Rew:6.0,24.0,3.0,24.0')] ).
cnf(32,plain,
equal(inverse(divide(divide(divide(u,identity),v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,27]),
[iquote('0:Rew:3.0,27.0')] ).
cnf(33,plain,
equal(inverse(divide(divide(multiply(u,identity),v),u)),v),
inference(rew,[status(thm),theory(equality)],[15,32]),
[iquote('0:Rew:15.0,32.0')] ).
cnf(48,plain,
equal(divide(u,identity),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[9,29]),
[iquote('0:SpR:9.0,29.0')] ).
cnf(49,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[15,48,13]),
[iquote('0:Rew:15.0,48.0,13.0,48.0')] ).
cnf(50,plain,
equal(divide(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[49,15]),
[iquote('0:Rew:49.0,15.0')] ).
cnf(52,plain,
equal(inverse(divide(divide(inverse(inverse(u)),v),u)),v),
inference(rew,[status(thm),theory(equality)],[49,33]),
[iquote('0:Rew:49.0,33.0')] ).
cnf(56,plain,
equal(inverse(inverse(inverse(u))),divide(identity,u)),
inference(spr,[status(thm),theory(equality)],[49,29]),
[iquote('0:SpR:49.0,29.0')] ).
cnf(57,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[3,56]),
[iquote('0:Rew:3.0,56.0')] ).
cnf(94,plain,
equal(divide(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[4,28]),
[iquote('0:SpR:4.0,28.0')] ).
cnf(95,plain,
equal(divide(inverse(inverse(u)),multiply(inverse(v),u)),v),
inference(spr,[status(thm),theory(equality)],[6,28]),
[iquote('0:SpR:6.0,28.0')] ).
cnf(100,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[57,94,50]),
[iquote('0:Rew:57.0,94.0,50.0,94.0')] ).
cnf(101,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)],[100,18]),
[iquote('0:Rew:100.0,18.2')] ).
cnf(105,plain,
equal(divide(u,divide(divide(multiply(v,u),w),v)),w),
inference(rew,[status(thm),theory(equality)],[100,23]),
[iquote('0:Rew:100.0,23.0')] ).
cnf(106,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[100,52]),
[iquote('0:Rew:100.0,52.0')] ).
cnf(112,plain,
equal(divide(inverse(inverse(u)),divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[29,95]),
[iquote('0:Rew:29.0,95.0')] ).
cnf(113,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[100,112]),
[iquote('0:Rew:100.0,112.0')] ).
cnf(118,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)],[101]),
[iquote('0:Obv:101.2')] ).
cnf(120,plain,
equal(divide(u,inverse(v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[100,29]),
[iquote('0:SpR:100.0,29.0')] ).
cnf(128,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,120]),
[iquote('0:Rew:6.0,120.0')] ).
cnf(129,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)],[128,118]),
[iquote('0:Rew:128.0,118.1')] ).
cnf(134,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)],[128,129]),
[iquote('0:Rew:128.0,129.0')] ).
cnf(135,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[134]),
[iquote('0:Obv:134.0')] ).
cnf(156,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[6,113]),
[iquote('0:SpR:6.0,113.0')] ).
cnf(183,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[106,100]),
[iquote('0:SpR:106.0,100.0')] ).
cnf(237,plain,
equal(divide(u,divide(inverse(v),w)),multiply(multiply(w,u),v)),
inference(spr,[status(thm),theory(equality)],[156,105]),
[iquote('0:SpR:156.0,105.0')] ).
cnf(295,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[156,183]),
[iquote('0:SpR:156.0,183.0')] ).
cnf(306,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(multiply(v,u),w)),
inference(rew,[status(thm),theory(equality)],[295,237]),
[iquote('0:Rew:295.0,237.0')] ).
cnf(313,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[6,306]),
[iquote('0:Rew:6.0,306.0')] ).
cnf(588,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[313,128]),
[iquote('0:SpR:313.0,128.0')] ).
cnf(600,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[128,313]),
[iquote('0:SpR:128.0,313.0')] ).
cnf(609,plain,
~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[588,135]),
[iquote('0:Rew:588.0,135.0')] ).
cnf(610,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[313,600]),
[iquote('0:Rew:313.0,600.0')] ).
cnf(624,plain,
~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[610,609]),
[iquote('0:Rew:610.0,609.0')] ).
cnf(625,plain,
$false,
inference(obv,[status(thm),theory(equality)],[624]),
[iquote('0:Obv:624.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP095-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 12:06:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 349 clauses, backtracked 0 clauses, performed 0 splits and kept 103 clauses.
% 0.19/0.45 SPASS allocated 63652 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.45 0:00:00.03 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.04 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 5, length 54 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.19/0.45
%------------------------------------------------------------------------------