%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Tue Jul 19 05:27:06 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 8 unt; 1 nHn; 11 RR)
% Number of literals : 15 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(skc5,skc3),
file('SET581+3.p',unknown),
[] ).
cnf(2,axiom,
member(skc5,skc4),
file('SET581+3.p',unknown),
[] ).
cnf(3,axiom,
~ member(u,empty_set),
file('SET581+3.p',unknown),
[] ).
cnf(4,axiom,
~ not_equal(intersection(skc3,skc4),empty_set),
file('SET581+3.p',unknown),
[] ).
cnf(5,axiom,
( not_equal(u,v)
| equal(u,v) ),
file('SET581+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET581+3.p',unknown),
[] ).
cnf(18,plain,
( ~ member(skc5,u)
| member(skc5,intersection(u,skc4)) ),
inference(res,[status(thm),theory(equality)],[2,14]),
[iquote('0:Res:2.0,14.0')] ).
cnf(25,plain,
equal(intersection(skc3,skc4),empty_set),
inference(res,[status(thm),theory(equality)],[5,4]),
[iquote('0:Res:5.1,4.0')] ).
cnf(29,plain,
member(skc5,intersection(skc3,skc4)),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(35,plain,
member(skc5,empty_set),
inference(rew,[status(thm),theory(equality)],[25,29]),
[iquote('0:Rew:25.0,29.0')] ).
cnf(36,plain,
$false,
inference(mrr,[status(thm)],[35,3]),
[iquote('0:MRR:35.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jul 9 17:13:42 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 18 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.18/0.43 SPASS allocated 97746 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 2, length 11 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : prove_th24 empty_set_defn not_equal_defn intersection_defn
% 0.18/0.43
%------------------------------------------------------------------------------