TSTP Solution File: REL003-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL003-1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Mon Jul 18 20:01:23 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 16 ( 10 unt; 2 nHn; 16 RR)
% Number of literals : 22 ( 0 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( equal(join(sk1,sk2),sk2)
| equal(join(converse(sk1),converse(sk2)),converse(sk2)) ),
file('REL003-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(join(sk1,sk2),sk2)
| ~ equal(join(converse(sk1),converse(sk2)),converse(sk2)) ),
file('REL003-1.p',unknown),
[] ).
cnf(10,axiom,
equal(converse(converse(u)),u),
file('REL003-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL003-1.p',unknown),
[] ).
cnf(17,plain,
( equal(converse(join(sk1,sk2)),converse(sk2))
| equal(join(sk1,sk2),sk2) ),
inference(rew,[status(thm),theory(equality)],[11,1]),
[iquote('0:Rew:11.0,1.1')] ).
cnf(19,plain,
( ~ equal(converse(join(sk1,sk2)),converse(sk2))
| ~ equal(join(sk1,sk2),sk2) ),
inference(rew,[status(thm),theory(equality)],[11,2]),
[iquote('0:Rew:11.0,2.1')] ).
cnf(212,plain,
equal(converse(join(sk1,sk2)),converse(sk2)),
inference(spt,[spt(split,[position(s1)])],[17]),
[iquote('1:Spt:17.0')] ).
cnf(213,plain,
( ~ equal(converse(sk2),converse(sk2))
| ~ equal(join(sk1,sk2),sk2) ),
inference(rew,[status(thm),theory(equality)],[212,19]),
[iquote('1:Rew:212.0,19.0')] ).
cnf(214,plain,
~ equal(join(sk1,sk2),sk2),
inference(obv,[status(thm),theory(equality)],[213]),
[iquote('1:Obv:213.0')] ).
cnf(215,plain,
equal(join(sk1,sk2),converse(converse(sk2))),
inference(spr,[status(thm),theory(equality)],[212,10]),
[iquote('1:SpR:212.0,10.0')] ).
cnf(221,plain,
equal(join(sk1,sk2),sk2),
inference(rew,[status(thm),theory(equality)],[10,215]),
[iquote('1:Rew:10.0,215.0')] ).
cnf(222,plain,
$false,
inference(mrr,[status(thm)],[221,214]),
[iquote('1:MRR:221.0,214.0')] ).
cnf(227,plain,
~ equal(converse(join(sk1,sk2)),converse(sk2)),
inference(spt,[spt(split,[position(sa)])],[222,212]),
[iquote('1:Spt:222.0,17.0,212.0')] ).
cnf(228,plain,
equal(join(sk1,sk2),sk2),
inference(spt,[spt(split,[position(s2)])],[17]),
[iquote('1:Spt:222.0,17.1')] ).
cnf(231,plain,
( ~ equal(converse(sk2),converse(sk2))
| ~ equal(sk2,sk2) ),
inference(rew,[status(thm),theory(equality)],[228,19]),
[iquote('1:Rew:228.0,19.1,228.0,19.0')] ).
cnf(232,plain,
$false,
inference(obv,[status(thm),theory(equality)],[231]),
[iquote('1:Obv:231.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL003-1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Fri Jul 8 09:54:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 142 clauses, backtracked 3 clauses, performed 1 splits and kept 80 clauses.
% 0.19/0.43 SPASS allocated 63394 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.02 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 2, length 16 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : goals_14 goals_17 converse_idempotence_8 converse_additivity_9
% 0.19/0.43
%------------------------------------------------------------------------------