%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET188-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 05:24:52 EDT 2022
% Result : Unsatisfiable 2.35s 2.54s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 39 ( 10 unt; 8 nHn; 39 RR)
% Number of literals : 79 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 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,
equal(intersection(complement(y__dfg),x__dfg),null_class),
file('SET188-6.p',unknown),
[] ).
cnf(2,axiom,
~ subclass(x__dfg,y__dfg),
file('SET188-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET188-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET188-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET188-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET188-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET188-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET188-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET188-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET188-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET188-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET188-6.p',unknown),
[] ).
cnf(117,plain,
~ member(not_subclass_element(x__dfg,y__dfg),y__dfg),
inference(res,[status(thm),theory(equality)],[5,2]),
[iquote('0:Res:5.1,2.0')] ).
cnf(118,plain,
member(not_subclass_element(x__dfg,y__dfg),x__dfg),
inference(res,[status(thm),theory(equality)],[4,2]),
[iquote('0:Res:4.1,2.0')] ).
cnf(158,plain,
( ~ member(regular(complement(u)),u)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[68,26]),
[iquote('0:Res:68.1,26.1')] ).
cnf(160,plain,
( subclass(u,u)
| subclass(u,u) ),
inference(res,[status(thm),theory(equality)],[4,5]),
[iquote('0:Res:4.1,5.0')] ).
cnf(161,plain,
subclass(u,u),
inference(obv,[status(thm),theory(equality)],[160]),
[iquote('0:Obv:160.0')] ).
cnf(167,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[68,24]),
[iquote('0:Res:68.1,24.0')] ).
cnf(359,plain,
( ~ subclass(x__dfg,u)
| member(not_subclass_element(x__dfg,y__dfg),u) ),
inference(res,[status(thm),theory(equality)],[118,3]),
[iquote('0:Res:118.0,3.0')] ).
cnf(363,plain,
( ~ subclass(u,v)
| equal(u,null_class)
| member(regular(u),v) ),
inference(res,[status(thm),theory(equality)],[68,3]),
[iquote('0:Res:68.1,3.0')] ).
cnf(1288,plain,
( ~ member(u,x__dfg)
| ~ member(u,complement(y__dfg))
| member(u,null_class) ),
inference(spr,[status(thm),theory(equality)],[1,25]),
[iquote('0:SpR:1.0,25.2')] ).
cnf(1299,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(3224,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[363,158]),
[iquote('0:Res:363.2,158.0')] ).
cnf(3240,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[3224]),
[iquote('0:Obv:3224.1')] ).
cnf(3252,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[6,3240]),
[iquote('0:Res:6.0,3240.0')] ).
cnf(3294,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[3252,26]),
[iquote('0:SpL:3252.0,26.1')] ).
cnf(3344,plain,
( ~ subclass(u,universal_class)
| ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[363,3294]),
[iquote('0:Res:363.2,3294.0')] ).
cnf(3349,plain,
( ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(mrr,[status(thm)],[3344,6]),
[iquote('0:MRR:3344.0,6.0')] ).
cnf(3409,plain,
( equal(intersection(u,null_class),null_class)
| equal(intersection(u,null_class),null_class) ),
inference(res,[status(thm),theory(equality)],[167,3349]),
[iquote('0:Res:167.1,3349.0')] ).
cnf(3412,plain,
equal(intersection(u,null_class),null_class),
inference(obv,[status(thm),theory(equality)],[3409]),
[iquote('0:Obv:3409.0')] ).
cnf(3501,plain,
( ~ member(u,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[3412,23]),
[iquote('0:SpL:3412.0,23.0')] ).
cnf(3516,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[3294,3501]),
[iquote('0:MRR:3294.0,3501.1')] ).
cnf(3519,plain,
( ~ member(u,x__dfg)
| ~ member(u,complement(y__dfg)) ),
inference(mrr,[status(thm)],[1288,3516]),
[iquote('0:MRR:1288.2,3516.0')] ).
cnf(3996,plain,
( ~ member(u,universal_class)
| ~ member(u,x__dfg)
| member(u,y__dfg) ),
inference(res,[status(thm),theory(equality)],[27,3519]),
[iquote('0:Res:27.2,3519.1')] ).
cnf(9731,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[6,1299]),
[iquote('0:Res:6.0,1299.2')] ).
cnf(9741,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[9731]),
[iquote('0:Con:9731.1')] ).
cnf(9744,plain,
( ~ member(u,x__dfg)
| member(u,y__dfg) ),
inference(mrr,[status(thm)],[3996,9741]),
[iquote('0:MRR:3996.0,9741.1')] ).
cnf(9786,plain,
( ~ subclass(x__dfg,x__dfg)
| member(not_subclass_element(x__dfg,y__dfg),y__dfg) ),
inference(res,[status(thm),theory(equality)],[359,9744]),
[iquote('0:Res:359.1,9744.0')] ).
cnf(9808,plain,
$false,
inference(mrr,[status(thm)],[9786,161,117]),
[iquote('0:MRR:9786.0,9786.1,161.0,117.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET188-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n026.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 02:41:12 EDT 2022
% 0.14/0.33 % CPUTime :
% 2.35/2.54
% 2.35/2.54 SPASS V 3.9
% 2.35/2.54 SPASS beiseite: Proof found.
% 2.35/2.54 % SZS status Theorem
% 2.35/2.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.35/2.54 SPASS derived 8305 clauses, backtracked 0 clauses, performed 2 splits and kept 3990 clauses.
% 2.35/2.54 SPASS allocated 84499 KBytes.
% 2.35/2.54 SPASS spent 0:00:02.14 on the problem.
% 2.35/2.54 0:00:00.04 for the input.
% 2.35/2.54 0:00:00.00 for the FLOTTER CNF translation.
% 2.35/2.54 0:00:00.10 for inferences.
% 2.35/2.54 0:00:00.04 for the backtracking.
% 2.35/2.54 0:00:01.90 for the reduction.
% 2.35/2.54
% 2.35/2.54
% 2.35/2.54 Here is a proof with depth 7, length 39 :
% 2.35/2.54 % SZS output start Refutation
% See solution above
% 2.35/2.54 Formulae used in the proof : prove_subclass_property6_1 prove_subclass_property6_2 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets intersection1 intersection2 intersection3 complement1 complement2 regularity1
% 2.35/2.54
%------------------------------------------------------------------------------