TSTP Solution File: SET079-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET079-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : Tue Jul 19 05:23:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.55s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 9 unt; 3 nHn; 20 RR)
% Number of literals : 33 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(x__dfg,universal_class),
file('SET079-6.p',unknown),
[] ).
cnf(2,axiom,
equal(singleton(x__dfg),null_class),
file('SET079-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET079-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET079-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET079-6.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET079-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET079-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET079-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET079-6.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(139,plain,
member(x__dfg,singleton(x__dfg)),
inference(spr,[status(thm),theory(equality)],[14,99]),
[iquote('0:SpR:14.0,99.0')] ).
cnf(347,plain,
member(x__dfg,null_class),
inference(rew,[status(thm),theory(equality)],[2,139]),
[iquote('0:Rew:2.0,139.0')] ).
cnf(523,plain,
( ~ subclass(null_class,u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[347,3]),
[iquote('0:Res:347.0,3.0')] ).
cnf(555,plain,
( ~ equal(u,null_class)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[8,523]),
[iquote('0:Res:8.1,523.0')] ).
cnf(573,plain,
( ~ equal(intersection(u,v),null_class)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[555,23]),
[iquote('0:Res:555.1,23.0')] ).
cnf(947,plain,
( ~ equal(null_class,null_class)
| equal(u,null_class)
| member(x__dfg,u) ),
inference(spl,[status(thm),theory(equality)],[69,573]),
[iquote('0:SpL:69.1,573.0')] ).
cnf(951,plain,
( equal(u,null_class)
| member(x__dfg,u) ),
inference(obv,[status(thm),theory(equality)],[947]),
[iquote('0:Obv:947.0')] ).
cnf(952,plain,
member(x__dfg,u),
inference(mrr,[status(thm)],[951,555]),
[iquote('0:MRR:951.0,555.0')] ).
cnf(953,plain,
$false,
inference(unc,[status(thm)],[952,108]),
[iquote('0:UnC:952.0,108.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET079-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % 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
% 0.12/0.34 % DateTime : Sat Jul 9 20:29:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.55
% 0.19/0.55 SPASS V 3.9
% 0.19/0.55 SPASS beiseite: Proof found.
% 0.19/0.55 % SZS status Theorem
% 0.19/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.55 SPASS derived 784 clauses, backtracked 26 clauses, performed 1 splits and kept 649 clauses.
% 0.19/0.55 SPASS allocated 76531 KBytes.
% 0.19/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.19/0.55 0:00:00.04 for the input.
% 0.19/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.55 0:00:00.01 for inferences.
% 0.19/0.55 0:00:00.00 for the backtracking.
% 0.19/0.55 0:00:00.11 for the reduction.
% 0.19/0.55
% 0.19/0.55
% 0.19/0.55 Here is a proof with depth 6, length 20 :
% 0.19/0.55 % SZS output start Refutation
% See solution above
% 0.19/0.55 Formulae used in the proof : prove_corollary_to_set_in_its_singleton_1 prove_corollary_to_set_in_its_singleton_2 subclass_members equal_implies_subclass2 unordered_pair2 singleton_set intersection1 complement1 regularity2
% 0.19/0.55
%------------------------------------------------------------------------------