TSTP Solution File: GRP068-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP068-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:45:08 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 45 ( 40 unt; 0 nHn; 45 RR)
% Number of literals : 52 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,divide(divide(divide(identity,v),w),divide(divide(divide(u,u),u),w))),v),
file('GRP068-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP068-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP068-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP068-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP068-1.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(u,divide(divide(inverse(v),w),divide(inverse(u),w))),v),
inference(rew,[status(thm),theory(equality)],[3,1,4]),
[iquote('0:Rew:3.0,1.0,3.0,1.0,4.0,1.0')] ).
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(identity,a2),a2)
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.1')] ).
cnf(17,plain,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[16]),
[iquote('0:Obv:16.1')] ).
cnf(18,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[13,17]),
[iquote('0:Rew:13.0,17.0')] ).
cnf(20,plain,
equal(divide(u,divide(divide(inverse(v),divide(divide(inverse(w),x),divide(inverse(inverse(u)),x))),w)),v),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(24,plain,
equal(divide(u,divide(divide(inverse(v),inverse(u)),identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(27,plain,
equal(divide(u,divide(identity,divide(inverse(u),inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(29,plain,
equal(divide(u,identity),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(30,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[15,29]),
[iquote('0:Rew:15.0,29.0')] ).
cnf(31,plain,
equal(divide(u,identity),u),
inference(rew,[status(thm),theory(equality)],[30,15]),
[iquote('0:Rew:30.0,15.0')] ).
cnf(32,plain,
equal(divide(u,divide(multiply(inverse(v),u),identity)),v),
inference(rew,[status(thm),theory(equality)],[6,24]),
[iquote('0:Rew:6.0,24.0')] ).
cnf(33,plain,
equal(divide(u,multiply(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[31,32]),
[iquote('0:Rew:31.0,32.0')] ).
cnf(34,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[6,27,3]),
[iquote('0:Rew:6.0,27.0,3.0,27.0,6.0,27.0')] ).
cnf(59,plain,
equal(divide(identity,inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[30,33]),
[iquote('0:SpR:30.0,33.0')] ).
cnf(61,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,59,6]),
[iquote('0:Rew:13.0,59.0,6.0,59.0')] ).
cnf(62,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[61,18]),
[iquote('0:Rew:61.0,18.0')] ).
cnf(65,plain,
equal(divide(u,divide(divide(inverse(v),divide(divide(inverse(w),x),divide(u,x))),w)),v),
inference(rew,[status(thm),theory(equality)],[61,20]),
[iquote('0:Rew:61.0,20.0')] ).
cnf(68,plain,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[62]),
[iquote('0:Obv:62.0')] ).
cnf(72,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(74,plain,
equal(divide(u,multiply(v,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[61,33]),
[iquote('0:SpR:61.0,33.0')] ).
cnf(88,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(spr,[status(thm),theory(equality)],[61,34]),
[iquote('0:SpR:61.0,34.0')] ).
cnf(116,plain,
equal(divide(multiply(u,v),v),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[88,74]),
[iquote('0:SpR:88.0,74.0')] ).
cnf(130,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[61,116]),
[iquote('0:Rew:61.0,116.0')] ).
cnf(131,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[130,6]),
[iquote('0:SpR:130.0,6.0')] ).
cnf(140,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[72,131]),
[iquote('0:Rew:72.0,131.0')] ).
cnf(179,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[140,74]),
[iquote('0:SpR:140.0,74.0')] ).
cnf(199,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[6,179]),
[iquote('0:SpR:6.0,179.0')] ).
cnf(210,plain,
equal(divide(u,divide(divide(inverse(v),divide(inverse(multiply(w,x)),divide(u,w))),x)),v),
inference(rew,[status(thm),theory(equality)],[199,65]),
[iquote('0:Rew:199.0,65.0')] ).
cnf(228,plain,
equal(divide(u,inverse(multiply(v,multiply(inverse(multiply(divide(u,w),multiply(w,v))),x)))),x),
inference(rew,[status(thm),theory(equality)],[199,210]),
[iquote('0:Rew:199.0,210.0,199.0,210.0,199.0,210.0')] ).
cnf(229,plain,
equal(multiply(u,multiply(v,multiply(inverse(multiply(divide(u,w),multiply(w,v))),x))),x),
inference(rew,[status(thm),theory(equality)],[6,228]),
[iquote('0:Rew:6.0,228.0')] ).
cnf(519,plain,
equal(multiply(divide(u,v),multiply(v,w)),multiply(u,multiply(w,identity))),
inference(spr,[status(thm),theory(equality)],[12,229]),
[iquote('0:SpR:12.0,229.0')] ).
cnf(521,plain,
equal(multiply(multiply(divide(u,v),multiply(v,w)),x),multiply(u,multiply(w,x))),
inference(spr,[status(thm),theory(equality)],[88,229]),
[iquote('0:SpR:88.0,229.0')] ).
cnf(526,plain,
equal(multiply(divide(u,v),multiply(v,w)),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[30,519]),
[iquote('0:Rew:30.0,519.0')] ).
cnf(548,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[526,521]),
[iquote('0:Rew:526.0,521.0')] ).
cnf(549,plain,
$false,
inference(unc,[status(thm)],[548,68]),
[iquote('0:UnC:548.0,68.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP068-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.00/0.10 % Command : run_spass %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Tue Jun 14 10:45:57 EDT 2022
% 0.13/0.29 % CPUTime :
% 0.13/0.38
% 0.13/0.38 SPASS V 3.9
% 0.13/0.38 SPASS beiseite: Proof found.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 SPASS derived 353 clauses, backtracked 0 clauses, performed 0 splits and kept 112 clauses.
% 0.13/0.38 SPASS allocated 63840 KBytes.
% 0.13/0.38 SPASS spent 0:00:00.08 on the problem.
% 0.13/0.38 0:00:00.03 for the input.
% 0.13/0.38 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.38 0:00:00.00 for inferences.
% 0.13/0.38 0:00:00.00 for the backtracking.
% 0.13/0.38 0:00:00.03 for the reduction.
% 0.13/0.38
% 0.13/0.38
% 0.13/0.38 Here is a proof with depth 7, length 45 :
% 0.13/0.38 % SZS output start Refutation
% See solution above
% 0.13/0.38 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.13/0.38
%------------------------------------------------------------------------------