%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET073-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 05:23:35 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 14 ( 8 unt; 3 nHn; 14 RR)
% Number of literals : 21 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(x__dfg,universal_class),
file('SET073-6.p',unknown),
[] ).
cnf(2,axiom,
equal(unordered_pair(x__dfg,y__dfg),null_class),
file('SET073-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET073-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET073-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET073-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET073-6.p',unknown),
[] ).
cnf(99,plain,
member(x__dfg,unordered_pair(x__dfg,u)),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.0')] ).
cnf(108,plain,
~ member(x__dfg,complement(universal_class)),
inference(res,[status(thm),theory(equality)],[1,26]),
[iquote('0:Res:1.0,26.1')] ).
cnf(334,plain,
member(x__dfg,null_class),
inference(spr,[status(thm),theory(equality)],[2,99]),
[iquote('0:SpR:2.0,99.0')] ).
cnf(351,plain,
( ~ member(u,null_class)
| equal(v,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[69,23]),
[iquote('0:SpL:69.1,23.0')] ).
cnf(456,plain,
( equal(u,null_class)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[334,351]),
[iquote('0:Res:334.0,351.0')] ).
cnf(461,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[456,108]),
[iquote('0:Res:456.1,108.0')] ).
cnf(469,plain,
~ member(x__dfg,null_class),
inference(rew,[status(thm),theory(equality)],[461,108]),
[iquote('0:Rew:461.0,108.0')] ).
cnf(470,plain,
$false,
inference(mrr,[status(thm)],[469,334]),
[iquote('0:MRR:469.0,334.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET073-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jul 10 11:03:12 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 349 clauses, backtracked 21 clauses, performed 1 splits and kept 330 clauses.
% 0.19/0.47 SPASS allocated 76108 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.01 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.05 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 4, length 14 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : prove_corollary_to_unordered_pair_axiom1_1 prove_corollary_to_unordered_pair_axiom1_2 unordered_pair2 intersection1 complement1 regularity2
% 0.19/0.47
%------------------------------------------------------------------------------