TSTP Solution File: SET245-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET245-6 : 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 05:25:15 EDT 2022
% Result : Unsatisfiable 0.62s 0.82s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 7 unt; 5 nHn; 20 RR)
% Number of literals : 37 ( 0 equ; 15 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 : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(restrict(null_class,x__dfg,y__dfg),null_class),
file('SET245-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET245-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET245-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET245-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET245-6.p',unknown),
[] ).
cnf(29,axiom,
equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
file('SET245-6.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET245-6.p',unknown),
[] ).
cnf(161,plain,
( ~ member(regular(complement(u)),u)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[67,25]),
[iquote('0:Res:67.1,25.1')] ).
cnf(191,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[67,22]),
[iquote('0:Res:67.1,22.0')] ).
cnf(366,plain,
( ~ subclass(u,v)
| equal(u,null_class)
| member(regular(u),v) ),
inference(res,[status(thm),theory(equality)],[67,2]),
[iquote('0:Res:67.1,2.0')] ).
cnf(2022,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[366,161]),
[iquote('0:Res:366.2,161.0')] ).
cnf(2037,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[2022]),
[iquote('0:Obv:2022.1')] ).
cnf(2073,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[5,2037]),
[iquote('0:Res:5.0,2037.0')] ).
cnf(2112,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[2073,25]),
[iquote('0:SpL:2073.0,25.1')] ).
cnf(2157,plain,
( ~ subclass(u,universal_class)
| ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[366,2112]),
[iquote('0:Res:366.2,2112.0')] ).
cnf(2162,plain,
( ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(mrr,[status(thm)],[2157,5]),
[iquote('0:MRR:2157.0,5.0')] ).
cnf(2197,plain,
( equal(intersection(null_class,u),null_class)
| equal(intersection(null_class,u),null_class) ),
inference(res,[status(thm),theory(equality)],[191,2162]),
[iquote('0:Res:191.1,2162.0')] ).
cnf(2200,plain,
equal(intersection(null_class,u),null_class),
inference(obv,[status(thm),theory(equality)],[2197]),
[iquote('0:Obv:2197.0')] ).
cnf(2278,plain,
equal(restrict(null_class,u,v),null_class),
inference(spr,[status(thm),theory(equality)],[2200,29]),
[iquote('0:SpR:2200.0,29.0')] ).
cnf(2295,plain,
$false,
inference(unc,[status(thm)],[2278,1]),
[iquote('0:UnC:2278.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET245-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jul 11 02:08:23 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.62/0.82
% 0.62/0.82 SPASS V 3.9
% 0.62/0.82 SPASS beiseite: Proof found.
% 0.62/0.82 % SZS status Theorem
% 0.62/0.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.82 SPASS derived 1953 clauses, backtracked 204 clauses, performed 3 splits and kept 1441 clauses.
% 0.62/0.82 SPASS allocated 77811 KBytes.
% 0.62/0.82 SPASS spent 0:00:00.47 on the problem.
% 0.62/0.82 0:00:00.04 for the input.
% 0.62/0.82 0:00:00.00 for the FLOTTER CNF translation.
% 0.62/0.82 0:00:00.03 for inferences.
% 0.62/0.82 0:00:00.01 for the backtracking.
% 0.62/0.82 0:00:00.35 for the reduction.
% 0.62/0.82
% 0.62/0.82
% 0.62/0.82 Here is a proof with depth 7, length 20 :
% 0.62/0.82 % SZS output start Refutation
% See solution above
% 0.62/0.82 Formulae used in the proof : prove_restriction_with_null_class1_1 subclass_members class_elements_are_sets intersection1 complement1 restriction1 regularity1
% 0.62/0.82
%------------------------------------------------------------------------------