TSTP Solution File: SET168-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET168-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 05:24:42 EDT 2022
% Result : Unsatisfiable 7.56s 7.76s
% Output : Refutation 7.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 32 ( 13 unt; 6 nHn; 32 RR)
% Number of literals : 58 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(x__dfg,z__dfg),
file('SET168-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(x__dfg,union(y__dfg,z__dfg)),
file('SET168-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET168-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET168-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET168-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET168-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET168-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET168-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET168-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET168-6.p',unknown),
[] ).
cnf(28,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET168-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(z__dfg,u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.1')] ).
cnf(121,plain,
~ member(x__dfg,complement(z__dfg)),
inference(res,[status(thm),theory(equality)],[1,26]),
[iquote('0:Res:1.0,26.1')] ).
cnf(129,plain,
( ~ subclass(u,union(y__dfg,z__dfg))
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.2,2.0')] ).
cnf(141,plain,
member(x__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[6,117]),
[iquote('0:Res:6.0,117.0')] ).
cnf(182,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[4,26]),
[iquote('0:Res:4.1,26.1')] ).
cnf(1220,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[25,3]),
[iquote('0:Res:25.2,3.0')] ).
cnf(2706,plain,
( ~ member(not_subclass_element(complement(complement(u)),v),universal_class)
| member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(res,[status(thm),theory(equality)],[27,182]),
[iquote('0:Res:27.2,182.0')] ).
cnf(10242,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[6,1220]),
[iquote('0:Res:6.0,1220.2')] ).
cnf(10252,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[10242]),
[iquote('0:Con:10242.1')] ).
cnf(10314,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[4,10252]),
[iquote('0:Res:4.1,10252.0')] ).
cnf(10431,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[2706,10314]),
[iquote('0:MRR:2706.0,10314.1')] ).
cnf(20278,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[10431,5]),
[iquote('0:Res:10431.0,5.0')] ).
cnf(20281,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[20278]),
[iquote('0:Obv:20278.0')] ).
cnf(20318,plain,
subclass(complement(union(u,v)),intersection(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[28,20281]),
[iquote('0:SpR:28.0,20281.0')] ).
cnf(20338,plain,
~ member(x__dfg,complement(complement(union(y__dfg,z__dfg)))),
inference(res,[status(thm),theory(equality)],[20281,129]),
[iquote('0:Res:20281.0,129.0')] ).
cnf(20361,plain,
( ~ member(x__dfg,universal_class)
| member(x__dfg,complement(union(y__dfg,z__dfg))) ),
inference(res,[status(thm),theory(equality)],[27,20338]),
[iquote('0:Res:27.2,20338.0')] ).
cnf(20362,plain,
member(x__dfg,complement(union(y__dfg,z__dfg))),
inference(mrr,[status(thm)],[20361,141]),
[iquote('0:MRR:20361.0,141.0')] ).
cnf(20405,plain,
( ~ subclass(complement(union(y__dfg,z__dfg)),u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[20362,3]),
[iquote('0:Res:20362.0,3.0')] ).
cnf(20934,plain,
member(x__dfg,intersection(complement(y__dfg),complement(z__dfg))),
inference(res,[status(thm),theory(equality)],[20318,20405]),
[iquote('0:Res:20318.0,20405.0')] ).
cnf(20960,plain,
member(x__dfg,complement(z__dfg)),
inference(res,[status(thm),theory(equality)],[20934,24]),
[iquote('0:Res:20934.0,24.0')] ).
cnf(20962,plain,
$false,
inference(mrr,[status(thm)],[20960,121]),
[iquote('0:MRR:20960.0,121.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET168-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 19:36:45 EDT 2022
% 0.13/0.33 % CPUTime :
% 7.56/7.76
% 7.56/7.76 SPASS V 3.9
% 7.56/7.76 SPASS beiseite: Proof found.
% 7.56/7.76 % SZS status Theorem
% 7.56/7.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.56/7.76 SPASS derived 17146 clauses, backtracked 164 clauses, performed 4 splits and kept 7926 clauses.
% 7.56/7.76 SPASS allocated 94796 KBytes.
% 7.56/7.76 SPASS spent 0:00:07.26 on the problem.
% 7.56/7.76 0:00:00.04 for the input.
% 7.56/7.76 0:00:00.00 for the FLOTTER CNF translation.
% 7.56/7.76 0:00:00.22 for inferences.
% 7.56/7.76 0:00:00.61 for the backtracking.
% 7.56/7.76 0:00:06.22 for the reduction.
% 7.56/7.76
% 7.56/7.76
% 7.56/7.76 Here is a proof with depth 8, length 32 :
% 7.56/7.76 % SZS output start Refutation
% See solution above
% 7.56/7.76 Formulae used in the proof : prove_members_of_union3_1 prove_members_of_union3_2 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets intersection2 intersection3 complement1 complement2 union
% 7.56/7.76
%------------------------------------------------------------------------------