TSTP Solution File: SET065-7 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET065-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 05:23:27 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
~ member(null_class,universal_class),
file('SET065-7.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET065-7.p',unknown),
[] ).
cnf(20,axiom,
subclass(u,universal_class),
file('SET065-7.p',unknown),
[] ).
cnf(63,axiom,
( ~ inductive(u)
| member(null_class,u) ),
file('SET065-7.p',unknown),
[] ).
cnf(66,axiom,
inductive(omega),
file('SET065-7.p',unknown),
[] ).
cnf(119,plain,
( ~ subclass(u,universal_class)
| ~ member(null_class,u) ),
inference(res,[status(thm),theory(equality)],[17,16]),
[iquote('0:Res:17.2,16.0')] ).
cnf(120,plain,
~ member(null_class,u),
inference(mrr,[status(thm)],[119,20]),
[iquote('0:MRR:119.0,20.0')] ).
cnf(121,plain,
~ inductive(u),
inference(mrr,[status(thm)],[63,120]),
[iquote('0:MRR:63.1,120.0')] ).
cnf(122,plain,
$false,
inference(unc,[status(thm)],[121,66]),
[iquote('0:UnC:121.0,66.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET065-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.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 19:39:23 EDT 2022
% 0.13/0.34 % 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/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 11 clauses, backtracked 0 clauses, performed 0 splits and kept 112 clauses.
% 0.19/0.43 SPASS allocated 75755 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 0:00:00.01 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 1, length 9 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : prove_null_class_is_a_set_1 subclass_members class_elements_are_sets inductive1 omega_is_inductive1
% 0.19/0.43
%------------------------------------------------------------------------------