TSTP Solution File: GRP564-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP564-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:48:03 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(divide(u,inverse(v)),w),divide(u,w)),v),
file('GRP564-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP564-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP564-1.p',unknown),
[] ).
cnf(4,plain,
equal(divide(divide(multiply(u,v),w),divide(u,w)),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(6,plain,
equal(divide(divide(multiply(divide(multiply(u,v),w),x),divide(u,w)),v),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(8,plain,
equal(divide(divide(multiply(u,v),inverse(w)),multiply(u,w)),v),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(10,plain,
equal(divide(multiply(multiply(u,v),w),multiply(u,w)),v),
inference(rew,[status(thm),theory(equality)],[2,8]),
[iquote('0:Rew:2.0,8.0')] ).
cnf(15,plain,
equal(multiply(divide(multiply(divide(multiply(u,inverse(v)),w),x),divide(u,w)),v),x),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(23,plain,
equal(divide(divide(multiply(u,v),divide(multiply(w,u),multiply(w,x))),x),v),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.0')] ).
cnf(53,plain,
equal(divide(divide(u,divide(divide(multiply(v,inverse(w)),x),divide(v,x))),u),w),
inference(spr,[status(thm),theory(equality)],[15,6]),
[iquote('0:SpR:15.0,6.0')] ).
cnf(74,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[2,53,4]),
[iquote('0:Rew:2.0,53.0,4.0,53.0')] ).
cnf(82,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[74,4]),
[iquote('0:SpR:74.0,4.0')] ).
cnf(98,plain,
equal(multiply(divide(u,u),v),v),
inference(spr,[status(thm),theory(equality)],[82,74]),
[iquote('0:SpR:82.0,74.0')] ).
cnf(119,plain,
equal(divide(multiply(u,v),multiply(divide(w,w),v)),u),
inference(spr,[status(thm),theory(equality)],[98,10]),
[iquote('0:SpR:98.0,10.0')] ).
cnf(138,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[98,119]),
[iquote('0:Rew:98.0,119.0')] ).
cnf(155,plain,
equal(multiply(divide(multiply(u,v),divide(u,inverse(w))),w),v),
inference(spr,[status(thm),theory(equality)],[138,15]),
[iquote('0:SpR:138.0,15.0')] ).
cnf(164,plain,
equal(divide(multiply(u,v),multiply(u,w)),divide(v,w)),
inference(spr,[status(thm),theory(equality)],[138,23]),
[iquote('0:SpR:138.0,23.0')] ).
cnf(191,plain,
equal(multiply(divide(multiply(u,v),multiply(u,w)),w),v),
inference(rew,[status(thm),theory(equality)],[2,155]),
[iquote('0:Rew:2.0,155.0')] ).
cnf(192,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[164,191]),
[iquote('0:Rew:164.0,191.0')] ).
cnf(384,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[74,192]),
[iquote('0:SpR:74.0,192.0')] ).
cnf(392,plain,
$false,
inference(unc,[status(thm)],[384,3]),
[iquote('0:UnC:384.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : GRP564-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.05/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 14:16:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 331 clauses, backtracked 0 clauses, performed 0 splits and kept 152 clauses.
% 0.20/0.48 SPASS allocated 63858 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.48 0:00:00.03 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.07 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 8, length 21 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : single_axiom multiply prove_these_axioms_4
% 0.20/0.48
%------------------------------------------------------------------------------