TSTP Solution File: GRP514-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP514-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:47:50 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 4 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('GRP514-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP514-1.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(170,plain,
equal(multiply(u,multiply(v,inverse(w))),multiply(v,multiply(u,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[20,59]),
[iquote('0:SpR:20.0,59.0')] ).
cnf(198,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)],[198,13]),
[iquote('0:SpR:198.0,13.0')] ).
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(a2,multiply(inverse(b2),b2)),a2),
inference(rew,[status(thm),theory(equality)],[289,2]),
[iquote('0:Rew:289.0,2.0')] ).
cnf(292,plain,
~ equal(multiply(b2,multiply(a2,inverse(b2))),a2),
inference(rew,[status(thm),theory(equality)],[170,290,289]),
[iquote('0:Rew:170.0,290.0,289.0,290.0')] ).
cnf(293,plain,
~ equal(a2,a2),
inference(rew,[status(thm),theory(equality)],[20,292]),
[iquote('0:Rew:20.0,292.0')] ).
cnf(294,plain,
$false,
inference(obv,[status(thm),theory(equality)],[293]),
[iquote('0:Obv:293.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP514-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 13:41:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 219 clauses, backtracked 0 clauses, performed 0 splits and kept 73 clauses.
% 0.20/0.45 SPASS allocated 63543 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.20/0.45 0:00:00.03 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.04 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 9, length 20 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : single_axiom prove_these_axioms_2
% 0.20/0.45
%------------------------------------------------------------------------------