TSTP Solution File: SET510-6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET510-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 05:26:41 EDT 2022
% Result : Unsatisfiable 3.72s 4.01s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 21
% Syntax : Number of clauses : 113 ( 47 unt; 31 nHn; 113 RR)
% Number of literals : 200 ( 0 equ; 66 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(singleton(universal_class),null_class),
file('SET510-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET510-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET510-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET510-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET510-6.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET510-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET510-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET510-6.p',unknown),
[] ).
cnf(12,axiom,
member(unordered_pair(u,v),universal_class),
file('SET510-6.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET510-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET510-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET510-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET510-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET510-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET510-6.p',unknown),
[] ).
cnf(27,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET510-6.p',unknown),
[] ).
cnf(28,axiom,
equal(intersection(complement(intersection(u,v)),complement(intersection(complement(u),complement(v)))),symmetric_difference(u,v)),
file('SET510-6.p',unknown),
[] ).
cnf(44,axiom,
equal(union(u,singleton(u)),successor(u)),
file('SET510-6.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET510-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET510-6.p',unknown),
[] ).
cnf(71,axiom,
( ~ member(u,universal_class)
| equal(u,null_class)
| member(apply(choice,u),u) ),
file('SET510-6.p',unknown),
[] ).
cnf(114,plain,
equal(intersection(complement(intersection(u,v)),union(u,v)),symmetric_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[27,28]),
[iquote('0:Rew:27.0,28.0')] ).
cnf(131,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.0,12.0')] ).
cnf(161,plain,
( ~ member(regular(complement(u)),u)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[67,25]),
[iquote('0:Res:67.1,25.1')] ).
cnf(170,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[3,23]),
[iquote('0:Res:3.1,23.0')] ).
cnf(191,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[67,22]),
[iquote('0:Res:67.1,22.0')] ).
cnf(192,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[3,22]),
[iquote('0:Res:3.1,22.0')] ).
cnf(317,plain,
( ~ subclass(universal_class,u)
| equal(universal_class,u) ),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.0,8.0')] ).
cnf(353,plain,
( ~ subclass(u,v)
| equal(u,null_class)
| member(regular(u),v) ),
inference(res,[status(thm),theory(equality)],[67,2]),
[iquote('0:Res:67.1,2.0')] ).
cnf(533,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(544,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[533]),
[iquote('0:Obv:533.1')] ).
cnf(548,plain,
( equal(singleton(u),null_class)
| equal(regular(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[67,544]),
[iquote('0:Res:67.1,544.0')] ).
cnf(549,plain,
( subclass(singleton(u),v)
| equal(not_subclass_element(singleton(u),v),u) ),
inference(res,[status(thm),theory(equality)],[3,544]),
[iquote('0:Res:3.1,544.0')] ).
cnf(553,plain,
( ~ member(singleton(u),universal_class)
| equal(singleton(u),null_class)
| equal(apply(choice,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[71,544]),
[iquote('0:Res:71.2,544.0')] ).
cnf(555,plain,
( equal(singleton(u),null_class)
| equal(apply(choice,singleton(u)),u) ),
inference(mrr,[status(thm)],[553,131]),
[iquote('0:MRR:553.0,131.0')] ).
cnf(623,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[548,67]),
[iquote('0:SpR:548.1,67.1')] ).
cnf(624,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| equal(intersection(singleton(u),u),null_class) ),
inference(spr,[status(thm),theory(equality)],[548,68]),
[iquote('0:SpR:548.1,68.1')] ).
cnf(628,plain,
( equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[623]),
[iquote('0:Obv:623.0')] ).
cnf(629,plain,
( equal(singleton(u),null_class)
| equal(intersection(singleton(u),u),null_class) ),
inference(obv,[status(thm),theory(equality)],[624]),
[iquote('0:Obv:624.0')] ).
cnf(789,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[24,2]),
[iquote('0:Res:24.2,2.0')] ).
cnf(887,plain,
( ~ member(u,v)
| ~ member(u,singleton(v))
| equal(singleton(v),null_class)
| member(u,null_class) ),
inference(spr,[status(thm),theory(equality)],[629,24]),
[iquote('0:SpR:629.1,24.2')] ).
cnf(1292,plain,
( subclass(singleton(u),v)
| subclass(singleton(u),v)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[549,3]),
[iquote('0:SpR:549.1,3.1')] ).
cnf(1298,plain,
( subclass(singleton(u),v)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[1292]),
[iquote('0:Obv:1292.0')] ).
cnf(1299,plain,
( subclass(null_class,u)
| member(v,singleton(v)) ),
inference(rew,[status(thm),theory(equality)],[628,1298]),
[iquote('0:Rew:628.0,1298.0')] ).
cnf(1304,plain,
member(u,singleton(u)),
inference(spt,[spt(split,[position(s1)])],[1299]),
[iquote('1:Spt:1299.1')] ).
cnf(1309,plain,
( ~ subclass(singleton(u),v)
| member(u,v) ),
inference(res,[status(thm),theory(equality)],[1304,2]),
[iquote('1:Res:1304.0,2.0')] ).
cnf(1574,plain,
member(u,universal_class),
inference(res,[status(thm),theory(equality)],[5,1309]),
[iquote('1:Res:5.0,1309.0')] ).
cnf(1576,plain,
( ~ equal(u,singleton(v))
| member(v,u) ),
inference(res,[status(thm),theory(equality)],[7,1309]),
[iquote('1:Res:7.1,1309.0')] ).
cnf(1585,plain,
( equal(u,null_class)
| member(apply(choice,u),u) ),
inference(mrr,[status(thm)],[71,1574]),
[iquote('1:MRR:71.0,1574.0')] ).
cnf(1634,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[1574,161]),
[iquote('1:Res:1574.0,161.0')] ).
cnf(1670,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[1634,25]),
[iquote('1:SpL:1634.0,25.1')] ).
cnf(1672,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[1670,1574]),
[iquote('1:MRR:1670.0,1574.0')] ).
cnf(1674,plain,
( ~ member(u,v)
| ~ member(u,singleton(v))
| equal(singleton(v),null_class) ),
inference(mrr,[status(thm)],[887,1672]),
[iquote('1:MRR:887.3,1672.0')] ).
cnf(2591,plain,
~ equal(singleton(u),null_class),
inference(res,[status(thm),theory(equality)],[1576,1672]),
[iquote('1:Res:1576.1,1672.0')] ).
cnf(2610,plain,
equal(apply(choice,singleton(u)),u),
inference(mrr,[status(thm)],[555,2591]),
[iquote('1:MRR:555.0,2591.0')] ).
cnf(2613,plain,
( ~ member(u,v)
| ~ member(u,singleton(v)) ),
inference(mrr,[status(thm)],[1674,2591]),
[iquote('1:MRR:1674.2,2591.0')] ).
cnf(3760,plain,
( ~ member(apply(choice,singleton(u)),u)
| equal(singleton(u),null_class) ),
inference(res,[status(thm),theory(equality)],[1585,2613]),
[iquote('1:Res:1585.1,2613.1')] ).
cnf(3774,plain,
( ~ member(u,u)
| equal(singleton(u),null_class) ),
inference(rew,[status(thm),theory(equality)],[2610,3760]),
[iquote('1:Rew:2610.0,3760.0')] ).
cnf(3775,plain,
~ member(u,u),
inference(mrr,[status(thm)],[3774,2591]),
[iquote('1:MRR:3774.1,2591.0')] ).
cnf(3776,plain,
$false,
inference(unc,[status(thm)],[3775,1574]),
[iquote('1:UnC:3775.0,1574.0')] ).
cnf(3779,plain,
subclass(null_class,u),
inference(spt,[spt(split,[position(s2)])],[1299]),
[iquote('1:Spt:3776.0,1299.0')] ).
cnf(3784,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[3779,8]),
[iquote('1:Res:3779.0,8.0')] ).
cnf(4634,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[353,161]),
[iquote('0:Res:353.2,161.0')] ).
cnf(4649,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[4634]),
[iquote('0:Obv:4634.1')] ).
cnf(4659,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[5,4649]),
[iquote('0:Res:5.0,4649.0')] ).
cnf(4671,plain,
equal(complement(intersection(null_class,complement(u))),union(universal_class,u)),
inference(spr,[status(thm),theory(equality)],[4659,27]),
[iquote('0:SpR:4659.0,27.0')] ).
cnf(4673,plain,
equal(complement(intersection(complement(u),null_class)),union(u,universal_class)),
inference(spr,[status(thm),theory(equality)],[4659,27]),
[iquote('0:SpR:4659.0,27.0')] ).
cnf(4686,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[4659,25]),
[iquote('0:SpL:4659.0,25.1')] ).
cnf(5527,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[170,4]),
[iquote('0:Res:170.1,4.0')] ).
cnf(5530,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[5527]),
[iquote('0:Obv:5527.0')] ).
cnf(5568,plain,
equal(intersection(u,null_class),null_class),
inference(res,[status(thm),theory(equality)],[5530,3784]),
[iquote('1:Res:5530.0,3784.0')] ).
cnf(5572,plain,
equal(union(u,universal_class),complement(null_class)),
inference(rew,[status(thm),theory(equality)],[5568,4673]),
[iquote('1:Rew:5568.0,4673.0')] ).
cnf(5776,plain,
equal(intersection(complement(null_class),union(u,null_class)),symmetric_difference(u,null_class)),
inference(spr,[status(thm),theory(equality)],[5568,114]),
[iquote('1:SpR:5568.0,114.0')] ).
cnf(5799,plain,
( ~ member(u,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[5568,22]),
[iquote('1:SpL:5568.0,22.0')] ).
cnf(5819,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[4686,5799]),
[iquote('1:MRR:4686.0,5799.1')] ).
cnf(5854,plain,
equal(intersection(null_class,u),null_class),
inference(res,[status(thm),theory(equality)],[191,5819]),
[iquote('1:Res:191.1,5819.0')] ).
cnf(5868,plain,
equal(union(universal_class,u),complement(null_class)),
inference(rew,[status(thm),theory(equality)],[5854,4671]),
[iquote('1:Rew:5854.0,4671.0')] ).
cnf(5929,plain,
equal(intersection(complement(intersection(u,universal_class)),complement(null_class)),symmetric_difference(u,universal_class)),
inference(spr,[status(thm),theory(equality)],[5572,114]),
[iquote('1:SpR:5572.0,114.0')] ).
cnf(5970,plain,
equal(complement(null_class),successor(universal_class)),
inference(spr,[status(thm),theory(equality)],[5868,44]),
[iquote('1:SpR:5868.0,44.0')] ).
cnf(5978,plain,
equal(union(universal_class,u),successor(universal_class)),
inference(rew,[status(thm),theory(equality)],[5970,5868]),
[iquote('1:Rew:5970.0,5868.0')] ).
cnf(6002,plain,
equal(intersection(successor(universal_class),union(u,null_class)),symmetric_difference(u,null_class)),
inference(rew,[status(thm),theory(equality)],[5970,5776]),
[iquote('1:Rew:5970.0,5776.0')] ).
cnf(6004,plain,
equal(intersection(complement(intersection(u,universal_class)),successor(universal_class)),symmetric_difference(u,universal_class)),
inference(rew,[status(thm),theory(equality)],[5970,5929]),
[iquote('1:Rew:5970.0,5929.0')] ).
cnf(6009,plain,
( ~ member(u,universal_class)
| member(u,null_class)
| member(u,successor(universal_class)) ),
inference(spr,[status(thm),theory(equality)],[5970,26]),
[iquote('1:SpR:5970.0,26.2')] ).
cnf(6027,plain,
( ~ member(u,universal_class)
| member(u,successor(universal_class)) ),
inference(mrr,[status(thm)],[6009,5819]),
[iquote('1:MRR:6009.1,5819.0')] ).
cnf(6531,plain,
( ~ member(not_subclass_element(u,successor(universal_class)),universal_class)
| subclass(u,successor(universal_class)) ),
inference(res,[status(thm),theory(equality)],[6027,4]),
[iquote('1:Res:6027.1,4.0')] ).
cnf(6672,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[192,4]),
[iquote('0:Res:192.1,4.0')] ).
cnf(6676,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[6672]),
[iquote('0:Obv:6672.0')] ).
cnf(6694,plain,
subclass(symmetric_difference(u,v),complement(intersection(u,v))),
inference(spr,[status(thm),theory(equality)],[114,6676]),
[iquote('0:SpR:114.0,6676.0')] ).
cnf(7418,plain,
equal(intersection(successor(universal_class),successor(universal_class)),symmetric_difference(universal_class,null_class)),
inference(spr,[status(thm),theory(equality)],[5978,6002]),
[iquote('1:SpR:5978.0,6002.0')] ).
cnf(7469,plain,
( ~ member(u,successor(universal_class))
| ~ member(u,successor(universal_class))
| member(u,symmetric_difference(universal_class,null_class)) ),
inference(spr,[status(thm),theory(equality)],[7418,24]),
[iquote('1:SpR:7418.0,24.2')] ).
cnf(7489,plain,
( ~ member(u,successor(universal_class))
| member(u,symmetric_difference(universal_class,null_class)) ),
inference(obv,[status(thm),theory(equality)],[7469]),
[iquote('1:Obv:7469.0')] ).
cnf(7892,plain,
( ~ member(not_subclass_element(u,symmetric_difference(universal_class,null_class)),successor(universal_class))
| subclass(u,symmetric_difference(universal_class,null_class)) ),
inference(res,[status(thm),theory(equality)],[7489,4]),
[iquote('1:Res:7489.1,4.0')] ).
cnf(9024,plain,
( equal(singleton(universal_class),null_class)
| equal(intersection(complement(null_class),successor(universal_class)),symmetric_difference(singleton(universal_class),universal_class)) ),
inference(spr,[status(thm),theory(equality)],[629,6004]),
[iquote('1:SpR:629.1,6004.0')] ).
cnf(9042,plain,
( equal(singleton(universal_class),null_class)
| equal(symmetric_difference(singleton(universal_class),universal_class),symmetric_difference(universal_class,null_class)) ),
inference(rew,[status(thm),theory(equality)],[7418,9024,5970]),
[iquote('1:Rew:7418.0,9024.1,5970.0,9024.1')] ).
cnf(9043,plain,
equal(symmetric_difference(singleton(universal_class),universal_class),symmetric_difference(universal_class,null_class)),
inference(mrr,[status(thm)],[9042,1]),
[iquote('1:MRR:9042.0,1.0')] ).
cnf(9052,plain,
subclass(symmetric_difference(universal_class,null_class),complement(intersection(singleton(universal_class),universal_class))),
inference(spr,[status(thm),theory(equality)],[9043,6694]),
[iquote('1:SpR:9043.0,6694.0')] ).
cnf(9060,plain,
( ~ subclass(complement(intersection(singleton(universal_class),universal_class)),symmetric_difference(universal_class,null_class))
| equal(complement(intersection(singleton(universal_class),universal_class)),symmetric_difference(universal_class,null_class)) ),
inference(res,[status(thm),theory(equality)],[9052,8]),
[iquote('1:Res:9052.0,8.0')] ).
cnf(11271,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[5,789]),
[iquote('0:Res:5.0,789.2')] ).
cnf(11281,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[11271]),
[iquote('0:Con:11271.1')] ).
cnf(11324,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[3,11281]),
[iquote('0:Res:3.1,11281.0')] ).
cnf(12432,plain,
subclass(u,successor(universal_class)),
inference(mrr,[status(thm)],[6531,11324]),
[iquote('1:MRR:6531.0,11324.1')] ).
cnf(12502,plain,
equal(successor(universal_class),universal_class),
inference(res,[status(thm),theory(equality)],[12432,317]),
[iquote('1:Res:12432.0,317.0')] ).
cnf(12711,plain,
( ~ member(not_subclass_element(u,symmetric_difference(universal_class,null_class)),universal_class)
| subclass(u,symmetric_difference(universal_class,null_class)) ),
inference(rew,[status(thm),theory(equality)],[12502,7892]),
[iquote('1:Rew:12502.0,7892.0')] ).
cnf(12906,plain,
subclass(u,symmetric_difference(universal_class,null_class)),
inference(mrr,[status(thm)],[12711,11324]),
[iquote('1:MRR:12711.0,11324.1')] ).
cnf(12907,plain,
equal(complement(intersection(singleton(universal_class),universal_class)),symmetric_difference(universal_class,null_class)),
inference(mrr,[status(thm)],[9060,12906]),
[iquote('1:MRR:9060.0,12906.0')] ).
cnf(13195,plain,
equal(symmetric_difference(universal_class,null_class),universal_class),
inference(res,[status(thm),theory(equality)],[12906,317]),
[iquote('1:Res:12906.0,317.0')] ).
cnf(13215,plain,
equal(complement(intersection(singleton(universal_class),universal_class)),universal_class),
inference(rew,[status(thm),theory(equality)],[13195,12907]),
[iquote('1:Rew:13195.0,12907.0')] ).
cnf(13433,plain,
( ~ member(u,intersection(singleton(universal_class),universal_class))
| ~ member(u,universal_class) ),
inference(spl,[status(thm),theory(equality)],[13215,25]),
[iquote('1:SpL:13215.0,25.1')] ).
cnf(13448,plain,
~ member(u,intersection(singleton(universal_class),universal_class)),
inference(mrr,[status(thm)],[13433,11281]),
[iquote('1:MRR:13433.1,11281.1')] ).
cnf(13629,plain,
( ~ member(u,universal_class)
| ~ member(u,singleton(universal_class)) ),
inference(res,[status(thm),theory(equality)],[24,13448]),
[iquote('1:Res:24.2,13448.0')] ).
cnf(13666,plain,
~ member(u,singleton(universal_class)),
inference(mrr,[status(thm)],[13629,11281]),
[iquote('1:MRR:13629.0,11281.1')] ).
cnf(13683,plain,
( ~ member(singleton(universal_class),universal_class)
| equal(singleton(universal_class),null_class) ),
inference(res,[status(thm),theory(equality)],[71,13666]),
[iquote('1:Res:71.2,13666.0')] ).
cnf(13707,plain,
$false,
inference(mrr,[status(thm)],[13683,131,1]),
[iquote('1:MRR:13683.0,13683.1,131.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET510-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.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 : Sun Jul 10 20:37:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.72/4.01
% 3.72/4.01 SPASS V 3.9
% 3.72/4.01 SPASS beiseite: Proof found.
% 3.72/4.01 % SZS status Theorem
% 3.72/4.01 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/4.01 SPASS derived 11134 clauses, backtracked 1237 clauses, performed 5 splits and kept 6186 clauses.
% 3.72/4.01 SPASS allocated 85949 KBytes.
% 3.72/4.01 SPASS spent 0:00:03.66 on the problem.
% 3.72/4.01 0:00:00.04 for the input.
% 3.72/4.01 0:00:00.00 for the FLOTTER CNF translation.
% 3.72/4.01 0:00:00.12 for inferences.
% 3.72/4.01 0:00:00.12 for the backtracking.
% 3.72/4.01 0:00:03.28 for the reduction.
% 3.72/4.01
% 3.72/4.01
% 3.72/4.01 Here is a proof with depth 11, length 113 :
% 3.72/4.01 % SZS output start Refutation
% See solution above
% 3.84/4.08 Formulae used in the proof : prove_corollary_to_singleton_is_null_class_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair_member unordered_pairs_in_universal singleton_set intersection1 intersection2 intersection3 complement1 complement2 union symmetric_difference successor regularity1 regularity2 choice2
% 3.84/4.08
%------------------------------------------------------------------------------