%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% 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 : 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(u,divide(divide(u,v),divide(w,v))),w),
file('GRP528-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP528-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP528-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP528-1.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(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(54,plain,
equal(divide(u,divide(divide(u,v),multiply(w,inverse(w)))),v),
inference(spr,[status(thm),theory(equality)],[42,1]),
[iquote('0:SpR:42.0,1.0')] ).
cnf(57,plain,
equal(divide(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[42,1]),
[iquote('0:SpR:42.0,1.0')] ).
cnf(59,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[57,54]),
[iquote('0:Rew:57.0,54.0')] ).
cnf(132,plain,
equal(multiply(divide(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[59,30]),
[iquote('0:SpR:59.0,30.0')] ).
cnf(206,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[132,40]),
[iquote('0:SpR:132.0,40.0')] ).
cnf(218,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[206,40]),
[iquote('0:Rew:206.0,40.0')] ).
cnf(240,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[218,30]),
[iquote('0:SpR:218.0,30.0')] ).
cnf(245,plain,
$false,
inference(unc,[status(thm)],[240,4]),
[iquote('0:UnC:240.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 06:11:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 195 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.20/0.43 SPASS allocated 63272 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.04 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.01 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 5, length 17 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_4
% 0.20/0.43
%------------------------------------------------------------------------------