%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP526-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:47:53 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 17 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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(divide(u,v),divide(w,v))),w),
file('GRP526-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP526-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP526-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP526-1.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(29,plain,
equal(divide(u,inverse(divide(v,u))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(30,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,29]),
[iquote('0:Rew:5.0,29.0')] ).
cnf(40,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(spr,[status(thm),theory(equality)],[5,30]),
[iquote('0:SpR:5.0,30.0')] ).
cnf(42,plain,
equal(multiply(u,inverse(u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[3,30]),
[iquote('0:SpR:3.0,30.0')] ).
cnf(47,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[42]),
[iquote('0:SpR:42.0,42.0')] ).
cnf(48,plain,
equal(multiply(inverse(inverse(u)),divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[42,40]),
[iquote('0:SpR:42.0,40.0')] ).
cnf(73,plain,
equal(multiply(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[47,30]),
[iquote('0:SpR:47.0,30.0')] ).
cnf(86,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[73,48]),
[iquote('0:Rew:73.0,48.0')] ).
cnf(90,plain,
equal(multiply(divide(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[86,10]),
[iquote('0:Rew:86.0,10.0')] ).
cnf(103,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(spr,[status(thm),theory(equality)],[5,90]),
[iquote('0:SpR:5.0,90.0')] ).
cnf(108,plain,
$false,
inference(unc,[status(thm)],[103,4]),
[iquote('0:UnC:103.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP526-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n020.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 09:31:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 84 clauses, backtracked 0 clauses, performed 0 splits and kept 44 clauses.
% 0.19/0.41 SPASS allocated 63204 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.03 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.01 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 4, length 17 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_2
% 0.19/0.41
%------------------------------------------------------------------------------