TSTP Solution File: SET189-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET189-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:24:53 EDT 2022
% Result : Unsatisfiable 2.42s 2.61s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of clauses : 42 ( 10 unt; 9 nHn; 42 RR)
% Number of literals : 86 ( 0 equ; 42 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('SET189-6.p',unknown),
[] ).
cnf(2,axiom,
subclass(y__dfg,x__dfg),
file('SET189-6.p',unknown),
[] ).
cnf(3,axiom,
~ equal(x__dfg,y__dfg),
file('SET189-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET189-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET189-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET189-6.p',unknown),
[] ).
cnf(7,axiom,
subclass(u,universal_class),
file('SET189-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET189-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET189-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET189-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET189-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET189-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET189-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET189-6.p',unknown),
[] ).
cnf(119,plain,
( ~ subclass(x__dfg,y__dfg)
| equal(x__dfg,y__dfg) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.0')] ).
cnf(131,plain,
~ subclass(x__dfg,y__dfg),
inference(mrr,[status(thm)],[119,3]),
[iquote('0:MRR:119.1,3.0')] ).
cnf(182,plain,
( ~ member(regular(complement(u)),u)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[69,27]),
[iquote('0:Res:69.1,27.1')] ).
cnf(194,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[69,25]),
[iquote('0:Res:69.1,25.0')] ).
cnf(202,plain,
( ~ member(u,null_class)
| member(u,complement(y__dfg)) ),
inference(spl,[status(thm),theory(equality)],[1,24]),
[iquote('0:SpL:1.0,24.0')] ).
cnf(224,plain,
( ~ member(u,null_class)
| ~ member(u,y__dfg) ),
inference(res,[status(thm),theory(equality)],[202,27]),
[iquote('0:Res:202.1,27.1')] ).
cnf(415,plain,
( ~ subclass(u,v)
| equal(u,null_class)
| member(regular(u),v) ),
inference(res,[status(thm),theory(equality)],[69,4]),
[iquote('0:Res:69.1,4.0')] ).
cnf(830,plain,
( ~ member(u,x__dfg)
| ~ member(u,complement(y__dfg))
| member(u,null_class) ),
inference(spr,[status(thm),theory(equality)],[1,26]),
[iquote('0:SpR:1.0,26.2')] ).
cnf(840,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[26,4]),
[iquote('0:Res:26.2,4.0')] ).
cnf(1914,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[415,182]),
[iquote('0:Res:415.2,182.0')] ).
cnf(1932,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[1914]),
[iquote('0:Obv:1914.1')] ).
cnf(1988,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[7,1932]),
[iquote('0:Res:7.0,1932.0')] ).
cnf(2016,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[1988,27]),
[iquote('0:SpL:1988.0,27.1')] ).
cnf(2086,plain,
( ~ subclass(u,universal_class)
| ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[415,2016]),
[iquote('0:Res:415.2,2016.0')] ).
cnf(2090,plain,
( ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(mrr,[status(thm)],[2086,7]),
[iquote('0:MRR:2086.0,7.0')] ).
cnf(2109,plain,
( equal(intersection(u,null_class),null_class)
| equal(intersection(u,null_class),null_class) ),
inference(res,[status(thm),theory(equality)],[194,2090]),
[iquote('0:Res:194.1,2090.0')] ).
cnf(2112,plain,
equal(intersection(u,null_class),null_class),
inference(obv,[status(thm),theory(equality)],[2109]),
[iquote('0:Obv:2109.0')] ).
cnf(2205,plain,
( ~ member(u,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[2112,24]),
[iquote('0:SpL:2112.0,24.0')] ).
cnf(2220,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[224,2205]),
[iquote('0:MRR:224.1,2205.1')] ).
cnf(2223,plain,
( ~ member(u,x__dfg)
| ~ member(u,complement(y__dfg)) ),
inference(mrr,[status(thm)],[830,2220]),
[iquote('0:MRR:830.2,2220.0')] ).
cnf(2581,plain,
( ~ member(u,universal_class)
| ~ member(u,x__dfg)
| member(u,y__dfg) ),
inference(res,[status(thm),theory(equality)],[28,2223]),
[iquote('0:Res:28.2,2223.1')] ).
cnf(7909,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[7,840]),
[iquote('0:Res:7.0,840.2')] ).
cnf(7921,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[7909]),
[iquote('0:Con:7909.1')] ).
cnf(7924,plain,
( ~ member(u,x__dfg)
| member(u,y__dfg) ),
inference(mrr,[status(thm)],[2581,7921]),
[iquote('0:MRR:2581.0,7921.1')] ).
cnf(7957,plain,
( subclass(x__dfg,u)
| member(not_subclass_element(x__dfg,u),y__dfg) ),
inference(res,[status(thm),theory(equality)],[5,7924]),
[iquote('0:Res:5.1,7924.0')] ).
cnf(8883,plain,
( subclass(x__dfg,y__dfg)
| subclass(x__dfg,y__dfg) ),
inference(res,[status(thm),theory(equality)],[7957,6]),
[iquote('0:Res:7957.1,6.0')] ).
cnf(8885,plain,
subclass(x__dfg,y__dfg),
inference(obv,[status(thm),theory(equality)],[8883]),
[iquote('0:Obv:8883.0')] ).
cnf(8886,plain,
$false,
inference(mrr,[status(thm)],[8885,131]),
[iquote('0:MRR:8885.0,131.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET189-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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
% 0.12/0.33 % DateTime : Mon Jul 11 10:42:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.42/2.61
% 2.42/2.61 SPASS V 3.9
% 2.42/2.61 SPASS beiseite: Proof found.
% 2.42/2.61 % SZS status Theorem
% 2.42/2.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.42/2.61 SPASS derived 7243 clauses, backtracked 39 clauses, performed 3 splits and kept 3849 clauses.
% 2.42/2.61 SPASS allocated 83660 KBytes.
% 2.42/2.61 SPASS spent 0:00:02.21 on the problem.
% 2.42/2.61 0:00:00.04 for the input.
% 2.42/2.61 0:00:00.00 for the FLOTTER CNF translation.
% 2.42/2.61 0:00:00.08 for inferences.
% 2.42/2.61 0:00:00.03 for the backtracking.
% 2.42/2.61 0:00:01.99 for the reduction.
% 2.42/2.61
% 2.42/2.61
% 2.42/2.61 Here is a proof with depth 7, length 42 :
% 2.42/2.61 % SZS output start Refutation
% See solution above
% 2.42/2.61 Formulae used in the proof : prove_corollary_to_subclass_property6_1 prove_corollary_to_subclass_property6_2 prove_corollary_to_subclass_property6_3 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal intersection1 intersection2 intersection3 complement1 complement2 regularity1
% 2.42/2.61
%------------------------------------------------------------------------------