%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP513-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:47:49 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 19 RR)
% Number of literals : 19 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,multiply(multiply(v,w),inverse(multiply(u,w)))),v),
file('GRP513-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP513-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,multiply(multiply(v,multiply(multiply(w,x),inverse(multiply(u,x)))),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,multiply(v,inverse(multiply(u,multiply(multiply(v,w),inverse(multiply(x,w))))))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(13,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(20,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[13,3]),
[iquote('0:SpR:13.0,3.0')] ).
cnf(46,plain,
equal(multiply(multiply(u,v),multiply(w,inverse(multiply(w,v)))),u),
inference(spr,[status(thm),theory(equality)],[20,4]),
[iquote('0:SpR:20.0,4.0')] ).
cnf(52,plain,
equal(multiply(u,multiply(multiply(v,w),inverse(v))),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[20,3]),
[iquote('0:SpR:20.0,3.0')] ).
cnf(59,plain,
equal(multiply(multiply(u,v),multiply(w,inverse(u))),multiply(w,v)),
inference(spr,[status(thm),theory(equality)],[46,4]),
[iquote('0:SpR:46.0,4.0')] ).
cnf(162,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[59,52]),
[iquote('0:SpR:59.0,52.0')] ).
cnf(200,plain,
equal(multiply(u,multiply(multiply(v,inverse(v)),w)),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[162,52]),
[iquote('0:SpR:162.0,52.0')] ).
cnf(250,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[200,13]),
[iquote('0:SpR:200.0,13.0')] ).
cnf(251,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[200,20]),
[iquote('0:SpR:200.0,20.0')] ).
cnf(280,plain,
equal(multiply(multiply(multiply(u,inverse(u)),v),w),multiply(w,v)),
inference(spr,[status(thm),theory(equality)],[250,59]),
[iquote('0:SpR:250.0,59.0')] ).
cnf(284,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(spr,[status(thm),theory(equality)],[250,20]),
[iquote('0:SpR:250.0,20.0')] ).
cnf(289,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[284,280]),
[iquote('0:Rew:284.0,280.0')] ).
cnf(290,plain,
~ equal(multiply(inverse(a1),a1),multiply(b1,inverse(b1))),
inference(rew,[status(thm),theory(equality)],[289,2]),
[iquote('0:Rew:289.0,2.0')] ).
cnf(292,plain,
~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1))),
inference(rew,[status(thm),theory(equality)],[289,290]),
[iquote('0:Rew:289.0,290.0')] ).
cnf(293,plain,
$false,
inference(unc,[status(thm)],[292,251]),
[iquote('0:UnC:292.0,251.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP513-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n019.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 : Mon Jun 13 16:15:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 219 clauses, backtracked 0 clauses, performed 0 splits and kept 73 clauses.
% 0.19/0.45 SPASS allocated 63542 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.04 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 9, length 19 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : single_axiom prove_these_axioms_1
% 0.19/0.45
%------------------------------------------------------------------------------