TSTP Solution File: GRP523-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP523-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 0 equ; 2 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(u,divide(v,divide(w,divide(u,v)))),w),
file('GRP523-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP523-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP523-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP523-1.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(10,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(21,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(27,plain,
equal(divide(u,divide(inverse(v),divide(w,multiply(u,v)))),w),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(34,plain,
equal(divide(u,inverse(divide(v,divide(u,divide(w,w))))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(37,plain,
equal(inverse(divide(u,multiply(v,u))),v),
inference(rew,[status(thm),theory(equality)],[5,21,3]),
[iquote('0:Rew:5.0,21.0,3.0,21.0')] ).
cnf(40,plain,
equal(multiply(u,divide(v,divide(u,divide(w,w)))),v),
inference(rew,[status(thm),theory(equality)],[5,34]),
[iquote('0:Rew:5.0,34.0')] ).
cnf(52,plain,
equal(inverse(inverse(multiply(u,divide(v,v)))),u),
inference(spr,[status(thm),theory(equality)],[3,37]),
[iquote('0:SpR:3.0,37.0')] ).
cnf(57,plain,
equal(inverse(divide(u,inverse(inverse(u)))),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[10,37]),
[iquote('0:SpR:10.0,37.0')] ).
cnf(62,plain,
equal(inverse(multiply(u,inverse(u))),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[5,57]),
[iquote('0:Rew:5.0,57.0')] ).
cnf(63,plain,
equal(multiply(u,inverse(multiply(v,divide(w,w)))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[52,5]),
[iquote('0:SpR:52.0,5.0')] ).
cnf(75,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[62]),
[iquote('0:SpR:62.0,62.0')] ).
cnf(83,plain,
equal(divide(u,divide(u,divide(v,inverse(multiply(w,inverse(w)))))),v),
inference(spr,[status(thm),theory(equality)],[62,1]),
[iquote('0:SpR:62.0,1.0')] ).
cnf(86,plain,
equal(divide(u,divide(v,inverse(multiply(w,inverse(w))))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[62,1]),
[iquote('0:SpR:62.0,1.0')] ).
cnf(91,plain,
equal(divide(u,divide(u,multiply(v,multiply(w,inverse(w))))),v),
inference(rew,[status(thm),theory(equality)],[5,83]),
[iquote('0:Rew:5.0,83.0')] ).
cnf(92,plain,
equal(divide(u,multiply(v,multiply(w,inverse(w)))),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[5,86]),
[iquote('0:Rew:5.0,86.0')] ).
cnf(93,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[92,91]),
[iquote('0:Rew:92.0,91.0')] ).
cnf(102,plain,
equal(divide(u,divide(u,divide(v,divide(w,w)))),v),
inference(spr,[status(thm),theory(equality)],[75,1]),
[iquote('0:SpR:75.0,1.0')] ).
cnf(120,plain,
equal(divide(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[93,102]),
[iquote('0:Rew:93.0,102.0')] ).
cnf(121,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[120,40]),
[iquote('0:Rew:120.0,40.0')] ).
cnf(130,plain,
equal(inverse(divide(divide(u,u),v)),v),
inference(spr,[status(thm),theory(equality)],[93,3]),
[iquote('0:SpR:93.0,3.0')] ).
cnf(140,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,93]),
[iquote('0:SpR:5.0,93.0')] ).
cnf(147,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,130]),
[iquote('0:Rew:3.0,130.0')] ).
cnf(148,plain,
equal(multiply(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[147,52]),
[iquote('0:Rew:147.0,52.0')] ).
cnf(170,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[148,63]),
[iquote('0:Rew:148.0,63.0')] ).
cnf(236,plain,
equal(multiply(divide(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[93,121]),
[iquote('0:SpR:93.0,121.0')] ).
cnf(268,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[5,236]),
[iquote('0:SpR:5.0,236.0')] ).
cnf(275,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[170,268]),
[iquote('0:Rew:170.0,268.0')] ).
cnf(282,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[275,121]),
[iquote('0:SpR:275.0,121.0')] ).
cnf(288,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[282,4]),
[iquote('0:Rew:282.0,4.0')] ).
cnf(379,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[121,140]),
[iquote('0:SpR:121.0,140.0')] ).
cnf(477,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[5,379]),
[iquote('0:SpR:5.0,379.0')] ).
cnf(490,plain,
equal(divide(u,inverse(multiply(divide(v,multiply(u,w)),w))),v),
inference(rew,[status(thm),theory(equality)],[477,27]),
[iquote('0:Rew:477.0,27.0')] ).
cnf(502,plain,
equal(multiply(u,multiply(v,divide(w,multiply(u,v)))),w),
inference(rew,[status(thm),theory(equality)],[5,490,282]),
[iquote('0:Rew:5.0,490.0,282.0,490.0')] ).
cnf(543,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[275,502]),
[iquote('0:SpR:275.0,502.0')] ).
cnf(558,plain,
$false,
inference(unc,[status(thm)],[543,288]),
[iquote('0:UnC:543.0,288.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP523-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n010.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 09:48:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 414 clauses, backtracked 0 clauses, performed 0 splits and kept 104 clauses.
% 0.20/0.44 SPASS allocated 63485 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.44 0:00:00.03 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.03 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 6, length 40 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_3
% 0.20/0.44
%------------------------------------------------------------------------------