%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET596+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 05:27:15 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 10 unt; 0 nHn; 12 RR)
% Number of literals : 14 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 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,
subset(skc5,skc3),
file('SET596+3.p',unknown),
[] ).
cnf(4,axiom,
equal(intersection(skc3,skc4),empty_set),
file('SET596+3.p',unknown),
[] ).
cnf(5,axiom,
~ equal(intersection(skc5,skc4),empty_set),
file('SET596+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ subset(u,empty_set)
| equal(u,empty_set) ),
file('SET596+3.p',unknown),
[] ).
cnf(10,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET596+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ subset(u,v)
| subset(intersection(u,w),intersection(v,w)) ),
file('SET596+3.p',unknown),
[] ).
cnf(24,plain,
~ equal(intersection(skc4,skc5),empty_set),
inference(rew,[status(thm),theory(equality)],[10,5]),
[iquote('0:Rew:10.0,5.0')] ).
cnf(26,plain,
subset(intersection(skc5,u),intersection(skc3,u)),
inference(res,[status(thm),theory(equality)],[1,16]),
[iquote('0:Res:1.0,16.0')] ).
cnf(34,plain,
~ subset(intersection(skc4,skc5),empty_set),
inference(res,[status(thm),theory(equality)],[7,24]),
[iquote('0:Res:7.1,24.0')] ).
cnf(46,plain,
subset(intersection(skc5,skc4),empty_set),
inference(spr,[status(thm),theory(equality)],[4,26]),
[iquote('0:SpR:4.0,26.0')] ).
cnf(47,plain,
subset(intersection(skc4,skc5),empty_set),
inference(rew,[status(thm),theory(equality)],[10,46]),
[iquote('0:Rew:10.0,46.0')] ).
cnf(48,plain,
$false,
inference(mrr,[status(thm)],[47,34]),
[iquote('0:MRR:47.0,34.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET596+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 19:17:43 EDT 2022
% 0.13/0.34 % 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 16 clauses, backtracked 0 clauses, performed 0 splits and kept 28 clauses.
% 0.19/0.45 SPASS allocated 97841 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 0:00:00.04 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 0:00:00.00 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 2, length 12 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : prove_th55 subset_of_empty_set_is_empty_set commutativity_of_intersection intersection_of_subset
% 0.19/0.45
%------------------------------------------------------------------------------