TSTP Solution File: SET516-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET516-6 : 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 05:26:43 EDT 2022
% Result : Unsatisfiable 0.60s 0.77s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of clauses : 79 ( 27 unt; 18 nHn; 79 RR)
% Number of literals : 141 ( 0 equ; 53 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(singleton(x__dfg),x__dfg),
file('SET516-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET516-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET516-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET516-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET516-6.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET516-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET516-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET516-6.p',unknown),
[] ).
cnf(12,axiom,
member(unordered_pair(u,v),universal_class),
file('SET516-6.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET516-6.p',unknown),
[] ).
cnf(20,axiom,
( ~ member(ordered_pair(u,v),element_relation)
| member(u,v) ),
file('SET516-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET516-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET516-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET516-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET516-6.p',unknown),
[] ).
cnf(30,axiom,
equal(intersection(cross_product(u,v),w),restrict(w,u,v)),
file('SET516-6.p',unknown),
[] ).
cnf(53,axiom,
member(omega,universal_class),
file('SET516-6.p',unknown),
[] ).
cnf(56,axiom,
equal(complement(image(element_relation,complement(u))),power_class(u)),
file('SET516-6.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET516-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET516-6.p',unknown),
[] ).
cnf(77,axiom,
equal(complement(domain_of(intersection(u,identity_relation))),diagonalise(u)),
file('SET516-6.p',unknown),
[] ).
cnf(123,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.0,12.0')] ).
cnf(125,plain,
member(x__dfg,universal_class),
inference(spr,[status(thm),theory(equality)],[1,123]),
[iquote('0:SpR:1.0,123.0')] ).
cnf(132,plain,
equal(complement(image(element_relation,diagonalise(u))),power_class(domain_of(intersection(u,identity_relation)))),
inference(spr,[status(thm),theory(equality)],[77,56]),
[iquote('0:SpR:77.0,56.0')] ).
cnf(154,plain,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[13,11]),
[iquote('0:SpR:13.0,11.1')] ).
cnf(155,plain,
( ~ member(x__dfg,universal_class)
| member(x__dfg,x__dfg) ),
inference(spr,[status(thm),theory(equality)],[1,154]),
[iquote('0:SpR:1.0,154.1')] ).
cnf(156,plain,
member(x__dfg,x__dfg),
inference(mrr,[status(thm)],[155,125]),
[iquote('0:MRR:155.0,125.0')] ).
cnf(163,plain,
( subclass(u,u)
| subclass(u,u) ),
inference(res,[status(thm),theory(equality)],[3,4]),
[iquote('0:Res:3.1,4.0')] ).
cnf(164,plain,
subclass(u,u),
inference(obv,[status(thm),theory(equality)],[163]),
[iquote('0:Obv:163.0')] ).
cnf(172,plain,
( ~ member(u,null_class)
| equal(v,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[68,22]),
[iquote('0:SpL:68.1,22.0')] ).
cnf(229,plain,
( ~ member(u,restrict(v,w,x))
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[30,23]),
[iquote('0:SpL:30.0,23.0')] ).
cnf(371,plain,
( ~ subclass(universal_class,u)
| member(omega,u) ),
inference(res,[status(thm),theory(equality)],[53,2]),
[iquote('0:Res:53.0,2.0')] ).
cnf(374,plain,
( ~ subclass(universal_class,u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[125,2]),
[iquote('0:Res:125.0,2.0')] ).
cnf(389,plain,
( ~ subclass(x__dfg,u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[156,2]),
[iquote('0:Res:156.0,2.0')] ).
cnf(400,plain,
( ~ subclass(universal_class,complement(u))
| ~ member(omega,u) ),
inference(res,[status(thm),theory(equality)],[371,25]),
[iquote('0:Res:371.1,25.1')] ).
cnf(414,plain,
( ~ subclass(universal_class,restrict(u,v,w))
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[374,229]),
[iquote('0:Res:374.1,229.0')] ).
cnf(422,plain,
( ~ subclass(x__dfg,complement(u))
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[389,25]),
[iquote('0:Res:389.1,25.1')] ).
cnf(425,plain,
( ~ subclass(x__dfg,null_class)
| equal(u,null_class)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[389,172]),
[iquote('0:Res:389.1,172.0')] ).
cnf(495,plain,
( ~ subclass(universal_class,power_class(domain_of(intersection(u,identity_relation))))
| ~ member(omega,image(element_relation,diagonalise(u))) ),
inference(spl,[status(thm),theory(equality)],[132,400]),
[iquote('0:SpL:132.0,400.0')] ).
cnf(510,plain,
( ~ equal(complement(u),x__dfg)
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[7,422]),
[iquote('0:Res:7.1,422.0')] ).
cnf(546,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[13,9]),
[iquote('0:SpL:13.0,9.0')] ).
cnf(560,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[546]),
[iquote('0:Obv:546.1')] ).
cnf(562,plain,
( ~ member(u,x__dfg)
| equal(u,x__dfg) ),
inference(spl,[status(thm),theory(equality)],[1,560]),
[iquote('0:SpL:1.0,560.0')] ).
cnf(570,plain,
( ~ subclass(x__dfg,singleton(u))
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[389,560]),
[iquote('0:Res:389.1,560.0')] ).
cnf(575,plain,
( equal(null_class,x__dfg)
| equal(regular(x__dfg),x__dfg) ),
inference(res,[status(thm),theory(equality)],[67,562]),
[iquote('0:Res:67.1,562.0')] ).
cnf(576,plain,
( subclass(x__dfg,u)
| equal(not_subclass_element(x__dfg,u),x__dfg) ),
inference(res,[status(thm),theory(equality)],[3,562]),
[iquote('0:Res:3.1,562.0')] ).
cnf(584,plain,
equal(null_class,x__dfg),
inference(spt,[spt(split,[position(s1)])],[575]),
[iquote('1:Spt:575.0')] ).
cnf(618,plain,
( ~ subclass(x__dfg,null_class)
| equal(u,x__dfg)
| member(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[584,425]),
[iquote('1:Rew:584.0,425.1')] ).
cnf(675,plain,
( ~ subclass(x__dfg,x__dfg)
| equal(u,x__dfg)
| member(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[584,618]),
[iquote('1:Rew:584.0,618.0')] ).
cnf(676,plain,
( equal(u,x__dfg)
| member(x__dfg,u) ),
inference(mrr,[status(thm)],[675,164]),
[iquote('1:MRR:675.0,164.0')] ).
cnf(725,plain,
( equal(singleton(u),x__dfg)
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[676,560]),
[iquote('1:Res:676.1,560.0')] ).
cnf(735,plain,
( ~ subclass(x__dfg,x__dfg)
| equal(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[725,570]),
[iquote('1:Rew:725.0,570.0')] ).
cnf(740,plain,
equal(x__dfg,u),
inference(mrr,[status(thm)],[735,164]),
[iquote('1:MRR:735.0,164.0')] ).
cnf(754,plain,
( ~ member(x__dfg,element_relation)
| member(u,v) ),
inference(rew,[status(thm),theory(equality)],[740,20]),
[iquote('1:Rew:740.0,20.0')] ).
cnf(770,plain,
( ~ member(x__dfg,u)
| subclass(v,u) ),
inference(rew,[status(thm),theory(equality)],[740,4]),
[iquote('1:Rew:740.0,4.0')] ).
cnf(847,plain,
subclass(u,x__dfg),
inference(rew,[status(thm),theory(equality)],[740,5]),
[iquote('1:Rew:740.0,5.0')] ).
cnf(879,plain,
( ~ subclass(universal_class,power_class(domain_of(intersection(u,identity_relation))))
| ~ member(x__dfg,image(element_relation,diagonalise(u))) ),
inference(rew,[status(thm),theory(equality)],[740,495]),
[iquote('1:Rew:740.0,495.1')] ).
cnf(955,plain,
( ~ subclass(universal_class,x__dfg)
| member(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[740,414]),
[iquote('1:Rew:740.0,414.0')] ).
cnf(1095,plain,
member(x__dfg,u),
inference(mrr,[status(thm)],[955,847]),
[iquote('1:MRR:955.0,847.0')] ).
cnf(1097,plain,
subclass(u,v),
inference(mrr,[status(thm)],[770,1095]),
[iquote('1:MRR:770.0,1095.0')] ).
cnf(1098,plain,
member(u,v),
inference(mrr,[status(thm)],[754,1095]),
[iquote('1:MRR:754.0,1095.0')] ).
cnf(1168,plain,
$false,
inference(mrr,[status(thm)],[879,1097,1098]),
[iquote('1:MRR:879.0,879.1,1097.0,1098.0')] ).
cnf(1172,plain,
~ equal(null_class,x__dfg),
inference(spt,[spt(split,[position(sa)])],[1168,584]),
[iquote('1:Spt:1168.0,575.0,584.0')] ).
cnf(1173,plain,
equal(regular(x__dfg),x__dfg),
inference(spt,[spt(split,[position(s2)])],[575]),
[iquote('1:Spt:1168.0,575.1')] ).
cnf(1297,plain,
( equal(null_class,x__dfg)
| equal(intersection(x__dfg,x__dfg),null_class) ),
inference(spr,[status(thm),theory(equality)],[1173,68]),
[iquote('1:SpR:1173.0,68.1')] ).
cnf(1298,plain,
equal(intersection(x__dfg,x__dfg),null_class),
inference(mrr,[status(thm)],[1297,1172]),
[iquote('1:MRR:1297.0,1172.0')] ).
cnf(1514,plain,
( ~ member(x__dfg,u)
| subclass(x__dfg,u)
| subclass(x__dfg,u) ),
inference(spl,[status(thm),theory(equality)],[576,4]),
[iquote('0:SpL:576.1,4.0')] ).
cnf(1519,plain,
( ~ member(x__dfg,u)
| subclass(x__dfg,u) ),
inference(obv,[status(thm),theory(equality)],[1514]),
[iquote('0:Obv:1514.1')] ).
cnf(2412,plain,
( ~ member(u,x__dfg)
| ~ member(u,x__dfg)
| member(u,null_class) ),
inference(spr,[status(thm),theory(equality)],[1298,24]),
[iquote('1:SpR:1298.0,24.2')] ).
cnf(2424,plain,
( ~ member(u,x__dfg)
| member(u,null_class) ),
inference(obv,[status(thm),theory(equality)],[2412]),
[iquote('1:Obv:2412.0')] ).
cnf(2430,plain,
( ~ member(x__dfg,x__dfg)
| subclass(x__dfg,null_class) ),
inference(res,[status(thm),theory(equality)],[2424,1519]),
[iquote('1:Res:2424.1,1519.0')] ).
cnf(2432,plain,
( ~ member(x__dfg,x__dfg)
| ~ equal(complement(null_class),x__dfg) ),
inference(res,[status(thm),theory(equality)],[2424,510]),
[iquote('1:Res:2424.1,510.1')] ).
cnf(2434,plain,
subclass(x__dfg,null_class),
inference(mrr,[status(thm)],[2430,156]),
[iquote('1:MRR:2430.0,156.0')] ).
cnf(2435,plain,
( equal(u,null_class)
| member(x__dfg,u) ),
inference(mrr,[status(thm)],[425,2434]),
[iquote('1:MRR:425.0,2434.0')] ).
cnf(2442,plain,
~ equal(complement(null_class),x__dfg),
inference(mrr,[status(thm)],[2432,156]),
[iquote('1:MRR:2432.0,156.0')] ).
cnf(2471,plain,
( equal(singleton(u),null_class)
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[2435,560]),
[iquote('1:Res:2435.1,560.0')] ).
cnf(2508,plain,
( ~ subclass(x__dfg,null_class)
| equal(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[2471,570]),
[iquote('1:Rew:2471.0,570.0')] ).
cnf(2514,plain,
equal(x__dfg,u),
inference(mrr,[status(thm)],[2508,2434]),
[iquote('1:MRR:2508.0,2434.0')] ).
cnf(2515,plain,
$false,
inference(unc,[status(thm)],[2514,2442]),
[iquote('1:UnC:2514.0,2442.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET516-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 19:00:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/0.77
% 0.60/0.77 SPASS V 3.9
% 0.60/0.77 SPASS beiseite: Proof found.
% 0.60/0.77 % SZS status Theorem
% 0.60/0.77 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.77 SPASS derived 2314 clauses, backtracked 429 clauses, performed 4 splits and kept 1599 clauses.
% 0.60/0.77 SPASS allocated 77727 KBytes.
% 0.60/0.77 SPASS spent 0:00:00.40 on the problem.
% 0.60/0.77 0:00:00.04 for the input.
% 0.60/0.77 0:00:00.00 for the FLOTTER CNF translation.
% 0.60/0.77 0:00:00.03 for inferences.
% 0.60/0.77 0:00:00.01 for the backtracking.
% 0.60/0.77 0:00:00.29 for the reduction.
% 0.60/0.77
% 0.60/0.77
% 0.60/0.77 Here is a proof with depth 7, length 79 :
% 0.60/0.77 % SZS output start Refutation
% See solution above
% 0.60/0.77 Formulae used in the proof : prove_corollary_to_no_class_belongs_to_itself_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 unordered_pair_member unordered_pair3 unordered_pairs_in_universal singleton_set element_relation2 intersection1 intersection2 intersection3 complement1 restriction2 omega_in_universal power_class_definition regularity1 regularity2 diagonalisation
% 0.60/0.77
%------------------------------------------------------------------------------