TSTP Solution File: GRP091-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP091-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:45:15 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of clauses : 50 ( 42 unt; 0 nHn; 50 RR)
% Number of literals : 66 ( 0 equ; 26 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(u,divide(divide(u,v),w)),v),w),
file('GRP091-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP091-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP091-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP091-1.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('GRP091-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[4,3]),
[iquote('0:Rew:4.0,3.0')] ).
cnf(7,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,2,4]),
[iquote('0:Rew:6.0,2.0,4.0,2.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
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(divide(u,divide(divide(u,inverse(v)),w)),v),w),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(23,plain,
equal(divide(divide(u,divide(identity,v)),u),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(29,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[7,23,6]),
[iquote('0:Rew:7.0,23.0,6.0,23.0')] ).
cnf(33,plain,
equal(multiply(divide(u,divide(multiply(u,v),w)),v),w),
inference(rew,[status(thm),theory(equality)],[7,19]),
[iquote('0:Rew:7.0,19.0')] ).
cnf(54,plain,
equal(multiply(multiply(identity,u),identity),u),
inference(spr,[status(thm),theory(equality)],[29,15]),
[iquote('0:SpR:29.0,15.0')] ).
cnf(55,plain,
equal(divide(identity,inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[12,29]),
[iquote('0:SpR:12.0,29.0')] ).
cnf(57,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,55,7]),
[iquote('0:Rew:13.0,55.0,7.0,55.0')] ).
cnf(58,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[57,13]),
[iquote('0:Rew:57.0,13.0')] ).
cnf(59,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)],[57,18]),
[iquote('0:Rew:57.0,18.2')] ).
cnf(60,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[58,54]),
[iquote('0:Rew:58.0,54.0')] ).
cnf(61,plain,
equal(divide(u,identity),u),
inference(rew,[status(thm),theory(equality)],[60,15]),
[iquote('0:Rew:60.0,15.0')] ).
cnf(64,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)],[59]),
[iquote('0:Obv:59.2')] ).
cnf(67,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[57,7]),
[iquote('0:SpR:57.0,7.0')] ).
cnf(80,plain,
equal(divide(divide(u,divide(u,v)),identity),v),
inference(spr,[status(thm),theory(equality)],[61,1]),
[iquote('0:SpR:61.0,1.0')] ).
cnf(84,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[61,80]),
[iquote('0:Rew:61.0,80.0')] ).
cnf(111,plain,
equal(divide(multiply(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[29,84]),
[iquote('0:SpR:29.0,84.0')] ).
cnf(113,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[7,84]),
[iquote('0:SpR:7.0,84.0')] ).
cnf(125,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[111,7]),
[iquote('0:SpR:111.0,7.0')] ).
cnf(132,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[67,125]),
[iquote('0:Rew:67.0,125.0')] ).
cnf(139,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[29,132]),
[iquote('0:SpR:29.0,132.0')] ).
cnf(141,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[84,132]),
[iquote('0:SpR:84.0,132.0')] ).
cnf(145,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)],[139,64]),
[iquote('0:Rew:139.0,64.1')] ).
cnf(149,plain,
equal(multiply(u,divide(v,divide(multiply(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[139,33]),
[iquote('0:Rew:139.0,33.0')] ).
cnf(153,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)],[139,145]),
[iquote('0:Rew:139.0,145.0')] ).
cnf(154,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[153]),
[iquote('0:Obv:153.0')] ).
cnf(182,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[67,139]),
[iquote('0:SpR:67.0,139.0')] ).
cnf(198,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[141,113]),
[iquote('0:SpR:141.0,113.0')] ).
cnf(339,plain,
equal(divide(u,divide(v,w)),multiply(divide(w,v),u)),
inference(spr,[status(thm),theory(equality)],[198,182]),
[iquote('0:SpR:198.0,182.0')] ).
cnf(365,plain,
equal(multiply(u,multiply(divide(v,multiply(w,u)),w)),v),
inference(rew,[status(thm),theory(equality)],[339,149]),
[iquote('0:Rew:339.0,149.0')] ).
cnf(374,plain,
equal(multiply(u,multiply(v,divide(w,multiply(v,u)))),w),
inference(rew,[status(thm),theory(equality)],[139,365]),
[iquote('0:Rew:139.0,365.0')] ).
cnf(428,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[29,374]),
[iquote('0:SpR:29.0,374.0')] ).
cnf(432,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[111,374]),
[iquote('0:SpR:111.0,374.0')] ).
cnf(450,plain,
~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[432,154]),
[iquote('0:Rew:432.0,154.0')] ).
cnf(794,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[139,428]),
[iquote('0:SpR:139.0,428.0')] ).
cnf(805,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[428,794]),
[iquote('0:Rew:428.0,794.0')] ).
cnf(806,plain,
$false,
inference(unc,[status(thm)],[805,450]),
[iquote('0:UnC:805.0,450.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP091-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 00:38:18 EDT 2022
% 0.13/0.34 % 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 474 clauses, backtracked 0 clauses, performed 0 splits and kept 115 clauses.
% 0.20/0.47 SPASS allocated 63747 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 0:00:00.01 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 8, length 50 :
% 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
%------------------------------------------------------------------------------