TSTP Solution File: GRP522-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP522-1 : 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 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 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 : 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('GRP522-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP522-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP522-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP522-1.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,u)),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(8,plain,
equal(divide(multiply(inverse(u),u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
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(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(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(43,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.0,5.0')] ).
cnf(51,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[43,4]),
[iquote('0:Rew:43.0,4.0')] ).
cnf(65,plain,
equal(inverse(divide(divide(u,divide(v,inverse(divide(w,w)))),u)),v),
inference(spr,[status(thm),theory(equality)],[20,6]),
[iquote('0:SpR:20.0,6.0')] ).
cnf(83,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(84,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,83]),
[iquote('0:Rew:5.0,83.0')] ).
cnf(89,plain,
equal(inverse(divide(divide(u,multiply(v,divide(w,w))),u)),v),
inference(rew,[status(thm),theory(equality)],[5,65]),
[iquote('0:Rew:5.0,65.0')] ).
cnf(94,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[84,29]),
[iquote('0:SpR:84.0,29.0')] ).
cnf(102,plain,
equal(multiply(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[94,89]),
[iquote('0:Rew:94.0,89.0')] ).
cnf(107,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[102,39]),
[iquote('0:Rew:102.0,39.0')] ).
cnf(108,plain,
$false,
inference(unc,[status(thm)],[107,51]),
[iquote('0:UnC:107.0,51.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 : Tue Jun 14 07:48:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 86 clauses, backtracked 0 clauses, performed 0 splits and kept 63 clauses.
% 0.18/0.41 SPASS allocated 63252 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.41 0:00:00.03 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.01 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 3, length 21 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_2
% 0.18/0.41
%------------------------------------------------------------------------------