%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 18 ( 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(u,divide(divide(u,v),divide(w,v))),w),
file('GRP525-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP525-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP525-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP525-1.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(72,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(73,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,72]),
[iquote('0:Rew:5.0,72.0')] ).
cnf(94,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(spr,[status(thm),theory(equality)],[5,73]),
[iquote('0:SpR:5.0,73.0')] ).
cnf(96,plain,
equal(multiply(u,inverse(u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[3,73]),
[iquote('0:SpR:3.0,73.0')] ).
cnf(110,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[96]),
[iquote('0:SpR:96.0,96.0')] ).
cnf(123,plain,
equal(divide(u,divide(divide(u,v),multiply(w,inverse(w)))),v),
inference(spr,[status(thm),theory(equality)],[96,1]),
[iquote('0:SpR:96.0,1.0')] ).
cnf(126,plain,
equal(divide(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[96,1]),
[iquote('0:SpR:96.0,1.0')] ).
cnf(128,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[126,123]),
[iquote('0:Rew:126.0,123.0')] ).
cnf(265,plain,
equal(multiply(divide(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[128,73]),
[iquote('0:SpR:128.0,73.0')] ).
cnf(374,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[265,94]),
[iquote('0:SpR:265.0,94.0')] ).
cnf(384,plain,
~ equal(multiply(inverse(a1),a1),divide(b1,b1)),
inference(rew,[status(thm),theory(equality)],[374,4]),
[iquote('0:Rew:374.0,4.0')] ).
cnf(404,plain,
~ equal(divide(b1,b1),divide(a1,a1)),
inference(rew,[status(thm),theory(equality)],[374,384]),
[iquote('0:Rew:374.0,384.0')] ).
cnf(405,plain,
$false,
inference(unc,[status(thm)],[404,110]),
[iquote('0:UnC:404.0,110.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.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 08:58:22 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 308 clauses, backtracked 0 clauses, performed 0 splits and kept 88 clauses.
% 0.18/0.42 SPASS allocated 63378 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 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 5, length 18 :
% 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
%------------------------------------------------------------------------------