TSTP Solution File: SET517-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET517-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 : 22
% Syntax : Number of clauses : 81 ( 29 unt; 18 nHn; 81 RR)
% Number of literals : 143 ( 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 : 24 ( 24 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(singleton(member_of(x__dfg)),x__dfg),
file('SET517-6.p',unknown),
[] ).
cnf(2,axiom,
equal(member_of(x__dfg),x__dfg),
file('SET517-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET517-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET517-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET517-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET517-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET517-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET517-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET517-6.p',unknown),
[] ).
cnf(13,axiom,
member(unordered_pair(u,v),universal_class),
file('SET517-6.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET517-6.p',unknown),
[] ).
cnf(21,axiom,
( ~ member(ordered_pair(u,v),element_relation)
| member(u,v) ),
file('SET517-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET517-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET517-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET517-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET517-6.p',unknown),
[] ).
cnf(31,axiom,
equal(intersection(cross_product(u,v),w),restrict(w,u,v)),
file('SET517-6.p',unknown),
[] ).
cnf(54,axiom,
member(omega,universal_class),
file('SET517-6.p',unknown),
[] ).
cnf(57,axiom,
equal(complement(image(element_relation,complement(u))),power_class(u)),
file('SET517-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET517-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET517-6.p',unknown),
[] ).
cnf(78,axiom,
equal(complement(domain_of(intersection(u,identity_relation))),diagonalise(u)),
file('SET517-6.p',unknown),
[] ).
cnf(115,plain,
equal(singleton(x__dfg),x__dfg),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(130,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[14,13]),
[iquote('0:SpR:14.0,13.0')] ).
cnf(132,plain,
member(x__dfg,universal_class),
inference(spr,[status(thm),theory(equality)],[115,130]),
[iquote('0:SpR:115.0,130.0')] ).
cnf(139,plain,
equal(complement(image(element_relation,diagonalise(u))),power_class(domain_of(intersection(u,identity_relation)))),
inference(spr,[status(thm),theory(equality)],[78,57]),
[iquote('0:SpR:78.0,57.0')] ).
cnf(161,plain,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[14,12]),
[iquote('0:SpR:14.0,12.1')] ).
cnf(163,plain,
( ~ member(x__dfg,universal_class)
| member(x__dfg,x__dfg) ),
inference(spr,[status(thm),theory(equality)],[115,161]),
[iquote('0:SpR:115.0,161.1')] ).
cnf(164,plain,
member(x__dfg,x__dfg),
inference(mrr,[status(thm)],[163,132]),
[iquote('0:MRR:163.0,132.0')] ).
cnf(170,plain,
( subclass(u,u)
| subclass(u,u) ),
inference(res,[status(thm),theory(equality)],[4,5]),
[iquote('0:Res:4.1,5.0')] ).
cnf(171,plain,
subclass(u,u),
inference(obv,[status(thm),theory(equality)],[170]),
[iquote('0:Obv:170.0')] ).
cnf(196,plain,
( ~ member(u,null_class)
| equal(v,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[69,23]),
[iquote('0:SpL:69.1,23.0')] ).
cnf(231,plain,
( ~ member(u,restrict(v,w,x))
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[31,24]),
[iquote('0:SpL:31.0,24.0')] ).
cnf(374,plain,
( ~ subclass(universal_class,u)
| member(omega,u) ),
inference(res,[status(thm),theory(equality)],[54,3]),
[iquote('0:Res:54.0,3.0')] ).
cnf(377,plain,
( ~ subclass(universal_class,u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[132,3]),
[iquote('0:Res:132.0,3.0')] ).
cnf(392,plain,
( ~ subclass(x__dfg,u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[164,3]),
[iquote('0:Res:164.0,3.0')] ).
cnf(402,plain,
( ~ subclass(universal_class,complement(u))
| ~ member(omega,u) ),
inference(res,[status(thm),theory(equality)],[374,26]),
[iquote('0:Res:374.1,26.1')] ).
cnf(416,plain,
( ~ subclass(universal_class,restrict(u,v,w))
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[377,231]),
[iquote('0:Res:377.1,231.0')] ).
cnf(424,plain,
( ~ subclass(x__dfg,complement(u))
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[392,26]),
[iquote('0:Res:392.1,26.1')] ).
cnf(427,plain,
( ~ subclass(x__dfg,null_class)
| equal(u,null_class)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[392,196]),
[iquote('0:Res:392.1,196.0')] ).
cnf(493,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)],[139,402]),
[iquote('0:SpL:139.0,402.0')] ).
cnf(511,plain,
( ~ equal(complement(u),x__dfg)
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[8,424]),
[iquote('0:Res:8.1,424.0')] ).
cnf(568,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[14,10]),
[iquote('0:SpL:14.0,10.0')] ).
cnf(582,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[568]),
[iquote('0:Obv:568.1')] ).
cnf(612,plain,
( ~ member(u,x__dfg)
| equal(u,x__dfg) ),
inference(spl,[status(thm),theory(equality)],[115,582]),
[iquote('0:SpL:115.0,582.0')] ).
cnf(620,plain,
( ~ subclass(x__dfg,singleton(u))
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[392,582]),
[iquote('0:Res:392.1,582.0')] ).
cnf(625,plain,
( equal(null_class,x__dfg)
| equal(regular(x__dfg),x__dfg) ),
inference(res,[status(thm),theory(equality)],[68,612]),
[iquote('0:Res:68.1,612.0')] ).
cnf(626,plain,
( subclass(x__dfg,u)
| equal(not_subclass_element(x__dfg,u),x__dfg) ),
inference(res,[status(thm),theory(equality)],[4,612]),
[iquote('0:Res:4.1,612.0')] ).
cnf(634,plain,
equal(null_class,x__dfg),
inference(spt,[spt(split,[position(s1)])],[625]),
[iquote('1:Spt:625.0')] ).
cnf(668,plain,
( ~ subclass(x__dfg,null_class)
| equal(u,x__dfg)
| member(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[634,427]),
[iquote('1:Rew:634.0,427.1')] ).
cnf(728,plain,
( ~ subclass(x__dfg,x__dfg)
| equal(u,x__dfg)
| member(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[634,668]),
[iquote('1:Rew:634.0,668.0')] ).
cnf(729,plain,
( equal(u,x__dfg)
| member(x__dfg,u) ),
inference(mrr,[status(thm)],[728,171]),
[iquote('1:MRR:728.0,171.0')] ).
cnf(788,plain,
( equal(singleton(u),x__dfg)
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[729,582]),
[iquote('1:Res:729.1,582.0')] ).
cnf(799,plain,
( ~ subclass(x__dfg,x__dfg)
| equal(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[788,620]),
[iquote('1:Rew:788.0,620.0')] ).
cnf(803,plain,
equal(x__dfg,u),
inference(mrr,[status(thm)],[799,171]),
[iquote('1:MRR:799.0,171.0')] ).
cnf(818,plain,
( ~ member(x__dfg,element_relation)
| member(u,v) ),
inference(rew,[status(thm),theory(equality)],[803,21]),
[iquote('1:Rew:803.0,21.0')] ).
cnf(833,plain,
( ~ member(x__dfg,u)
| subclass(v,u) ),
inference(rew,[status(thm),theory(equality)],[803,5]),
[iquote('1:Rew:803.0,5.0')] ).
cnf(916,plain,
subclass(u,x__dfg),
inference(rew,[status(thm),theory(equality)],[803,6]),
[iquote('1:Rew:803.0,6.0')] ).
cnf(948,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)],[803,493]),
[iquote('1:Rew:803.0,493.1')] ).
cnf(1028,plain,
( ~ subclass(universal_class,x__dfg)
| member(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[803,416]),
[iquote('1:Rew:803.0,416.0')] ).
cnf(1185,plain,
member(x__dfg,u),
inference(mrr,[status(thm)],[1028,916]),
[iquote('1:MRR:1028.0,916.0')] ).
cnf(1187,plain,
subclass(u,v),
inference(mrr,[status(thm)],[833,1185]),
[iquote('1:MRR:833.0,1185.0')] ).
cnf(1188,plain,
member(u,v),
inference(mrr,[status(thm)],[818,1185]),
[iquote('1:MRR:818.0,1185.0')] ).
cnf(1260,plain,
$false,
inference(mrr,[status(thm)],[948,1187,1188]),
[iquote('1:MRR:948.0,948.1,1187.0,1188.0')] ).
cnf(1264,plain,
~ equal(null_class,x__dfg),
inference(spt,[spt(split,[position(sa)])],[1260,634]),
[iquote('1:Spt:1260.0,625.0,634.0')] ).
cnf(1265,plain,
equal(regular(x__dfg),x__dfg),
inference(spt,[spt(split,[position(s2)])],[625]),
[iquote('1:Spt:1260.0,625.1')] ).
cnf(1396,plain,
( equal(null_class,x__dfg)
| equal(intersection(x__dfg,x__dfg),null_class) ),
inference(spr,[status(thm),theory(equality)],[1265,69]),
[iquote('1:SpR:1265.0,69.1')] ).
cnf(1397,plain,
equal(intersection(x__dfg,x__dfg),null_class),
inference(mrr,[status(thm)],[1396,1264]),
[iquote('1:MRR:1396.0,1264.0')] ).
cnf(1633,plain,
( ~ member(x__dfg,u)
| subclass(x__dfg,u)
| subclass(x__dfg,u) ),
inference(spl,[status(thm),theory(equality)],[626,5]),
[iquote('0:SpL:626.1,5.0')] ).
cnf(1638,plain,
( ~ member(x__dfg,u)
| subclass(x__dfg,u) ),
inference(obv,[status(thm),theory(equality)],[1633]),
[iquote('0:Obv:1633.1')] ).
cnf(2547,plain,
( ~ member(u,x__dfg)
| ~ member(u,x__dfg)
| member(u,null_class) ),
inference(spr,[status(thm),theory(equality)],[1397,25]),
[iquote('1:SpR:1397.0,25.2')] ).
cnf(2559,plain,
( ~ member(u,x__dfg)
| member(u,null_class) ),
inference(obv,[status(thm),theory(equality)],[2547]),
[iquote('1:Obv:2547.0')] ).
cnf(2565,plain,
( ~ member(x__dfg,x__dfg)
| subclass(x__dfg,null_class) ),
inference(res,[status(thm),theory(equality)],[2559,1638]),
[iquote('1:Res:2559.1,1638.0')] ).
cnf(2566,plain,
( ~ member(x__dfg,x__dfg)
| ~ equal(complement(null_class),x__dfg) ),
inference(res,[status(thm),theory(equality)],[2559,511]),
[iquote('1:Res:2559.1,511.1')] ).
cnf(2569,plain,
subclass(x__dfg,null_class),
inference(mrr,[status(thm)],[2565,164]),
[iquote('1:MRR:2565.0,164.0')] ).
cnf(2570,plain,
( equal(u,null_class)
| member(x__dfg,u) ),
inference(mrr,[status(thm)],[427,2569]),
[iquote('1:MRR:427.0,2569.0')] ).
cnf(2576,plain,
~ equal(complement(null_class),x__dfg),
inference(mrr,[status(thm)],[2566,164]),
[iquote('1:MRR:2566.0,164.0')] ).
cnf(2611,plain,
( equal(singleton(u),null_class)
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[2570,582]),
[iquote('1:Res:2570.1,582.0')] ).
cnf(2644,plain,
( ~ subclass(x__dfg,null_class)
| equal(x__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[2611,620]),
[iquote('1:Rew:2611.0,620.0')] ).
cnf(2650,plain,
equal(x__dfg,u),
inference(mrr,[status(thm)],[2644,2569]),
[iquote('1:MRR:2644.0,2569.0')] ).
cnf(2651,plain,
$false,
inference(unc,[status(thm)],[2650,2576]),
[iquote('1:UnC:2650.0,2576.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET517-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n006.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 19:19:06 EDT 2022
% 0.13/0.33 % 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 2438 clauses, backtracked 456 clauses, performed 4 splits and kept 1662 clauses.
% 0.60/0.77 SPASS allocated 77801 KBytes.
% 0.60/0.77 SPASS spent 0:00:00.42 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 0:00:00.30 for the reduction.
% 0.60/0.77
% 0.60/0.77
% 0.60/0.77 Here is a proof with depth 7, length 81 :
% 0.60/0.77 % SZS output start Refutation
% See solution above
% 0.60/0.77 Formulae used in the proof : prove_not_singleton_of_set_1 prove_not_singleton_of_set_2 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
%------------------------------------------------------------------------------