TSTP Solution File: GRP453-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP453-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:47:32 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 43 RR)
% Number of literals : 43 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(divide(u,u),divide(u,divide(v,divide(divide(divide(u,u),u),w)))),w),v),
file('GRP453-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP453-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP453-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP453-1.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(6,plain,
equal(divide(inverse(divide(u,divide(v,divide(inverse(u),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,u)),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(11,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(12,plain,
equal(divide(inverse(inverse(divide(u,u))),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(53,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),divide(x,v))),w),x),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(57,plain,
equal(divide(inverse(divide(divide(u,u),divide(v,inverse(w)))),w),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(60,plain,
equal(divide(inverse(divide(u,inverse(divide(inverse(u),v)))),v),divide(w,w)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(70,plain,
equal(divide(inverse(inverse(multiply(u,v))),v),u),
inference(rew,[status(thm),theory(equality)],[3,57,5]),
[iquote('0:Rew:3.0,57.0,5.0,57.0')] ).
cnf(75,plain,
equal(divide(inverse(multiply(u,divide(inverse(u),v))),v),divide(w,w)),
inference(rew,[status(thm),theory(equality)],[5,60]),
[iquote('0:Rew:5.0,60.0')] ).
cnf(87,plain,
equal(multiply(inverse(inverse(multiply(u,inverse(v)))),v),u),
inference(spr,[status(thm),theory(equality)],[70,5]),
[iquote('0:SpR:70.0,5.0')] ).
cnf(91,plain,
equal(divide(inverse(inverse(inverse(inverse(u)))),u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[11,70]),
[iquote('0:SpR:11.0,70.0')] ).
cnf(96,plain,
equal(inverse(inverse(multiply(u,inverse(v)))),divide(inverse(inverse(u)),v)),
inference(spr,[status(thm),theory(equality)],[87,70]),
[iquote('0:SpR:87.0,70.0')] ).
cnf(102,plain,
equal(multiply(divide(inverse(inverse(u)),v),v),u),
inference(rew,[status(thm),theory(equality)],[96,87]),
[iquote('0:Rew:96.0,87.0')] ).
cnf(105,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[102,11]),
[iquote('0:SpR:102.0,11.0')] ).
cnf(110,plain,
equal(divide(u,u),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[105,91]),
[iquote('0:Rew:105.0,91.0')] ).
cnf(158,plain,
equal(multiply(u,inverse(inverse(inverse(v)))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[105,5]),
[iquote('0:SpR:105.0,5.0')] ).
cnf(165,plain,
equal(multiply(divide(u,v),v),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[105,102]),
[iquote('0:SpR:105.0,102.0')] ).
cnf(514,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),x)),w),inverse(inverse(multiply(x,v)))),
inference(spr,[status(thm),theory(equality)],[70,53]),
[iquote('0:SpR:70.0,53.0')] ).
cnf(516,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),divide(x,x))),w),inverse(multiply(y,divide(inverse(y),v)))),
inference(spr,[status(thm),theory(equality)],[75,53]),
[iquote('0:SpR:75.0,53.0')] ).
cnf(520,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),x)),w),inverse(divide(y,divide(x,divide(inverse(y),v))))),
inference(spr,[status(thm),theory(equality)],[6,53]),
[iquote('0:SpR:6.0,53.0')] ).
cnf(606,plain,
equal(inverse(divide(u,divide(v,divide(inverse(u),w)))),inverse(inverse(multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[514,520]),
[iquote('0:Rew:514.0,520.0')] ).
cnf(611,plain,
equal(inverse(inverse(multiply(divide(u,u),v))),inverse(multiply(w,divide(inverse(w),v)))),
inference(rew,[status(thm),theory(equality)],[514,516]),
[iquote('0:Rew:514.0,516.0')] ).
cnf(612,plain,
equal(inverse(multiply(u,divide(inverse(u),v))),v),
inference(rew,[status(thm),theory(equality)],[105,611,11]),
[iquote('0:Rew:105.0,611.0,11.0,611.0')] ).
cnf(787,plain,
equal(divide(inverse(u),divide(inverse(v),u)),v),
inference(spr,[status(thm),theory(equality)],[612,70]),
[iquote('0:SpR:612.0,70.0')] ).
cnf(799,plain,
equal(inverse(multiply(u,divide(v,v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[110,612]),
[iquote('0:SpR:110.0,612.0')] ).
cnf(855,plain,
equal(inverse(divide(inverse(u),inverse(divide(v,v)))),u),
inference(spr,[status(thm),theory(equality)],[787,12]),
[iquote('0:SpR:787.0,12.0')] ).
cnf(874,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[70,787]),
[iquote('0:SpR:70.0,787.0')] ).
cnf(924,plain,
equal(inverse(inverse(multiply(u,inverse(v)))),inverse(multiply(v,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[874,96]),
[iquote('0:Rew:874.0,96.0')] ).
cnf(926,plain,
equal(inverse(divide(u,divide(v,inverse(multiply(w,u))))),inverse(inverse(multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[874,606]),
[iquote('0:Rew:874.0,606.0')] ).
cnf(936,plain,
equal(inverse(multiply(inverse(u),divide(v,v))),u),
inference(rew,[status(thm),theory(equality)],[5,855]),
[iquote('0:Rew:5.0,855.0')] ).
cnf(937,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[799,936]),
[iquote('0:Rew:799.0,936.0')] ).
cnf(939,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[937,165]),
[iquote('0:Rew:937.0,165.0')] ).
cnf(957,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[937,158]),
[iquote('0:Rew:937.0,158.0')] ).
cnf(1023,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[937,924,957]),
[iquote('0:Rew:937.0,924.0,957.0,924.0,957.0,924.0')] ).
cnf(1070,plain,
equal(inverse(divide(u,multiply(v,multiply(w,u)))),inverse(inverse(multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[5,926]),
[iquote('0:Rew:5.0,926.0')] ).
cnf(1071,plain,
equal(divide(multiply(u,multiply(v,w)),w),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[1023,1070,937]),
[iquote('0:Rew:1023.0,1070.0,937.0,1070.0')] ).
cnf(1490,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1071,939]),
[iquote('0:SpR:1071.0,939.0')] ).
cnf(1509,plain,
$false,
inference(unc,[status(thm)],[1490,4]),
[iquote('0:UnC:1490.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP453-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n028.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 : Mon Jun 13 05:27:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 1054 clauses, backtracked 0 clauses, performed 0 splits and kept 250 clauses.
% 0.19/0.52 SPASS allocated 64521 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.52 0:00:00.03 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.10 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 6, length 43 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.52 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_3
% 0.19/0.52
%------------------------------------------------------------------------------