TSTP Solution File: GRP529-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP529-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:47:54 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 26 RR)
% Number of literals : 26 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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(divide(u,divide(v,w)),divide(u,v)),w),
file('GRP529-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP529-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP529-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP529-1.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(51,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(52,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(63,plain,
equal(divide(divide(u,inverse(v)),divide(u,divide(w,w))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(74,plain,
equal(divide(multiply(u,v),divide(u,divide(w,w))),v),
inference(rew,[status(thm),theory(equality)],[5,63]),
[iquote('0:Rew:5.0,63.0')] ).
cnf(100,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[3,52]),
[iquote('0:SpR:3.0,52.0')] ).
cnf(102,plain,
equal(multiply(divide(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[100,10]),
[iquote('0:Rew:100.0,10.0')] ).
cnf(130,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[100,5]),
[iquote('0:SpR:100.0,5.0')] ).
cnf(135,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[52,100]),
[iquote('0:SpR:52.0,100.0')] ).
cnf(140,plain,
equal(divide(u,inverse(divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[135,51]),
[iquote('0:Rew:135.0,51.0')] ).
cnf(141,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,140]),
[iquote('0:Rew:5.0,140.0')] ).
cnf(152,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[141,102]),
[iquote('0:SpR:141.0,102.0')] ).
cnf(155,plain,
equal(multiply(u,inverse(u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[3,141]),
[iquote('0:SpR:3.0,141.0')] ).
cnf(159,plain,
equal(divide(u,divide(v,w)),multiply(divide(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,141]),
[iquote('0:SpR:1.0,141.0')] ).
cnf(161,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[152,74]),
[iquote('0:Rew:152.0,74.0')] ).
cnf(163,plain,
equal(divide(u,u),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[130,155]),
[iquote('0:Rew:130.0,155.0')] ).
cnf(172,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[159,152]),
[iquote('0:Rew:159.0,152.0')] ).
cnf(253,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[161,172]),
[iquote('0:SpR:161.0,172.0')] ).
cnf(255,plain,
~ equal(multiply(inverse(a1),a1),multiply(b1,inverse(b1))),
inference(rew,[status(thm),theory(equality)],[253,4]),
[iquote('0:Rew:253.0,4.0')] ).
cnf(287,plain,
~ equal(divide(b1,b1),divide(a1,a1)),
inference(rew,[status(thm),theory(equality)],[130,255,253]),
[iquote('0:Rew:130.0,255.0,253.0,255.0,130.0,255.0')] ).
cnf(288,plain,
$false,
inference(unc,[status(thm)],[287,163]),
[iquote('0:UnC:287.0,163.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP529-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 13:26:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 211 clauses, backtracked 0 clauses, performed 0 splits and kept 82 clauses.
% 0.18/0.42 SPASS allocated 63361 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.02 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 3, length 26 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_1
% 0.18/0.42
%------------------------------------------------------------------------------