TSTP Solution File: GRP524-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:47:52 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 28 RR)
% Number of literals : 28 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,divide(v,divide(w,divide(u,v)))),w),
file('GRP524-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP524-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP524-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP524-1.p',unknown),
[] ).
cnf(5,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(17,plain,
equal(inverse(divide(u,divide(v,divide(divide(w,w),u)))),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(20,plain,
equal(divide(u,divide(divide(v,divide(w,u)),v)),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(25,plain,
equal(divide(u,divide(v,inverse(divide(u,v)))),divide(w,w)),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(29,plain,
equal(inverse(divide(u,multiply(v,u))),v),
inference(rew,[status(thm),theory(equality)],[5,17,3]),
[iquote('0:Rew:5.0,17.0,3.0,17.0')] ).
cnf(31,plain,
equal(divide(u,multiply(v,divide(u,v))),divide(w,w)),
inference(rew,[status(thm),theory(equality)],[5,25]),
[iquote('0:Rew:5.0,25.0')] ).
cnf(39,plain,
equal(inverse(inverse(multiply(u,divide(v,v)))),u),
inference(spr,[status(thm),theory(equality)],[3,29]),
[iquote('0:SpR:3.0,29.0')] ).
cnf(63,plain,
equal(multiply(u,inverse(multiply(v,divide(w,w)))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[39,5]),
[iquote('0:SpR:39.0,5.0')] ).
cnf(72,plain,
equal(inverse(divide(divide(u,divide(v,divide(w,w))),u)),v),
inference(spr,[status(thm),theory(equality)],[20,3]),
[iquote('0:SpR:20.0,3.0')] ).
cnf(91,plain,
equal(divide(u,inverse(divide(v,u))),v),
inference(spr,[status(thm),theory(equality)],[3,20]),
[iquote('0:SpR:3.0,20.0')] ).
cnf(92,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,91]),
[iquote('0:Rew:5.0,91.0')] ).
cnf(93,plain,
equal(divide(u,u),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[92,31]),
[iquote('0:Rew:92.0,31.0')] ).
cnf(102,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[92,29]),
[iquote('0:SpR:92.0,29.0')] ).
cnf(103,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[92,39]),
[iquote('0:SpR:92.0,39.0')] ).
cnf(111,plain,
equal(multiply(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[103,39]),
[iquote('0:Rew:103.0,39.0')] ).
cnf(127,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[111,63]),
[iquote('0:Rew:111.0,63.0')] ).
cnf(130,plain,
equal(divide(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[102,72]),
[iquote('0:Rew:102.0,72.0')] ).
cnf(162,plain,
equal(divide(u,divide(u,divide(v,divide(w,w)))),v),
inference(spr,[status(thm),theory(equality)],[93,1]),
[iquote('0:SpR:93.0,1.0')] ).
cnf(184,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[130,162]),
[iquote('0:Rew:130.0,162.0')] ).
cnf(256,plain,
equal(multiply(divide(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[184,92]),
[iquote('0:SpR:184.0,92.0')] ).
cnf(287,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[5,256]),
[iquote('0:SpR:5.0,256.0')] ).
cnf(294,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[127,287]),
[iquote('0:Rew:127.0,287.0')] ).
cnf(301,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[294,92]),
[iquote('0:SpR:294.0,92.0')] ).
cnf(309,plain,
$false,
inference(unc,[status(thm)],[301,4]),
[iquote('0:UnC:301.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n007.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jun 13 10:38:24 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 241 clauses, backtracked 0 clauses, performed 0 splits and kept 84 clauses.
% 0.20/0.43 SPASS allocated 63351 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.04 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.02 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 5, length 28 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_4
% 0.20/0.43
%------------------------------------------------------------------------------