TSTP Solution File: SET137-6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET137-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 05:24:25 EDT 2022
% Result : Unsatisfiable 24.62s 24.78s
% Output : Refutation 25.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 20
% Syntax : Number of clauses : 114 ( 55 unt; 27 nHn; 114 RR)
% Number of literals : 191 ( 0 equ; 55 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(union(singleton(u),v),set_builder(u,v)),
file('SET137-6.p',unknown),
[] ).
cnf(2,axiom,
member(u__dfg,x__dfg),
file('SET137-6.p',unknown),
[] ).
cnf(5,axiom,
equal(set_builder(u__dfg,set_builder(v__dfg,set_builder(w__dfg,null_class))),null_class),
file('SET137-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET137-6.p',unknown),
[] ).
cnf(7,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET137-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET137-6.p',unknown),
[] ).
cnf(9,axiom,
subclass(u,universal_class),
file('SET137-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET137-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET137-6.p',unknown),
[] ).
cnf(15,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET137-6.p',unknown),
[] ).
cnf(17,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET137-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET137-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET137-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET137-6.p',unknown),
[] ).
cnf(29,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET137-6.p',unknown),
[] ).
cnf(30,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET137-6.p',unknown),
[] ).
cnf(31,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET137-6.p',unknown),
[] ).
cnf(32,axiom,
equal(intersection(complement(intersection(u,v)),complement(intersection(complement(u),complement(v)))),symmetric_difference(u,v)),
file('SET137-6.p',unknown),
[] ).
cnf(48,axiom,
equal(union(u,singleton(u)),successor(u)),
file('SET137-6.p',unknown),
[] ).
cnf(71,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET137-6.p',unknown),
[] ).
cnf(97,plain,
equal(intersection(complement(intersection(u,v)),union(u,v)),symmetric_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[31,32]),
[iquote('0:Rew:31.0,32.0')] ).
cnf(113,plain,
( ~ subclass(x__dfg,u)
| member(u__dfg,u) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.0,6.1')] ).
cnf(153,plain,
member(u__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[9,113]),
[iquote('0:Res:9.0,113.0')] ).
cnf(205,plain,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[17,15]),
[iquote('0:SpR:17.0,15.1')] ).
cnf(211,plain,
( ~ member(regular(complement(u)),u)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[71,29]),
[iquote('0:Res:71.1,29.1')] ).
cnf(214,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[7,29]),
[iquote('0:Res:7.1,29.1')] ).
cnf(246,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[71,27]),
[iquote('0:Res:71.1,27.0')] ).
cnf(249,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[7,27]),
[iquote('0:Res:7.1,27.0')] ).
cnf(265,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[71,26]),
[iquote('0:Res:71.1,26.0')] ).
cnf(268,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[7,26]),
[iquote('0:Res:7.1,26.0')] ).
cnf(397,plain,
( ~ member(not_subclass_element(u,complement(v)),universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[30,8]),
[iquote('0:Res:30.2,8.0')] ).
cnf(439,plain,
( ~ subclass(universal_class,u)
| equal(universal_class,u) ),
inference(res,[status(thm),theory(equality)],[9,12]),
[iquote('0:Res:9.0,12.0')] ).
cnf(465,plain,
( ~ subclass(universal_class,u)
| member(u__dfg,u) ),
inference(res,[status(thm),theory(equality)],[153,6]),
[iquote('0:Res:153.0,6.0')] ).
cnf(484,plain,
( ~ subclass(u,v)
| equal(u,null_class)
| member(regular(u),v) ),
inference(res,[status(thm),theory(equality)],[71,6]),
[iquote('0:Res:71.1,6.0')] ).
cnf(487,plain,
( ~ subclass(u,v)
| subclass(u,w)
| member(not_subclass_element(u,w),v) ),
inference(res,[status(thm),theory(equality)],[7,6]),
[iquote('0:Res:7.1,6.0')] ).
cnf(527,plain,
( ~ equal(u,universal_class)
| member(u__dfg,u) ),
inference(res,[status(thm),theory(equality)],[11,465]),
[iquote('0:Res:11.1,465.0')] ).
cnf(559,plain,
( ~ equal(complement(u),universal_class)
| ~ member(u__dfg,u) ),
inference(res,[status(thm),theory(equality)],[527,29]),
[iquote('0:Res:527.1,29.1')] ).
cnf(718,plain,
( ~ member(u__dfg,universal_class)
| ~ equal(complement(singleton(u__dfg)),universal_class) ),
inference(res,[status(thm),theory(equality)],[205,559]),
[iquote('0:Res:205.1,559.1')] ).
cnf(723,plain,
~ equal(complement(singleton(u__dfg)),universal_class),
inference(mrr,[status(thm)],[718,153]),
[iquote('0:MRR:718.0,153.0')] ).
cnf(819,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[28,6]),
[iquote('0:Res:28.2,6.0')] ).
cnf(822,plain,
( ~ member(not_subclass_element(u,intersection(v,w)),w)
| ~ member(not_subclass_element(u,intersection(v,w)),v)
| subclass(u,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[28,8]),
[iquote('0:Res:28.2,8.0')] ).
cnf(1972,plain,
( ~ member(not_subclass_element(complement(complement(u)),v),universal_class)
| member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(res,[status(thm),theory(equality)],[30,214]),
[iquote('0:Res:30.2,214.0')] ).
cnf(2373,plain,
( ~ member(regular(intersection(complement(u),v)),u)
| equal(intersection(complement(u),v),null_class) ),
inference(res,[status(thm),theory(equality)],[265,29]),
[iquote('0:Res:265.1,29.1')] ).
cnf(2389,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[484,211]),
[iquote('0:Res:484.2,211.0')] ).
cnf(2402,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[2389]),
[iquote('0:Obv:2389.1')] ).
cnf(2412,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[9,2402]),
[iquote('0:Res:9.0,2402.0')] ).
cnf(2424,plain,
equal(complement(intersection(null_class,complement(u))),union(universal_class,u)),
inference(spr,[status(thm),theory(equality)],[2412,31]),
[iquote('0:SpR:2412.0,31.0')] ).
cnf(2445,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[2412,29]),
[iquote('0:SpL:2412.0,29.1')] ).
cnf(2526,plain,
( ~ subclass(u,universal_class)
| ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[484,2445]),
[iquote('0:Res:484.2,2445.0')] ).
cnf(2547,plain,
( ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(mrr,[status(thm)],[2526,9]),
[iquote('0:MRR:2526.0,9.0')] ).
cnf(2644,plain,
( equal(intersection(null_class,u),null_class)
| equal(intersection(null_class,u),null_class) ),
inference(res,[status(thm),theory(equality)],[265,2547]),
[iquote('0:Res:265.1,2547.0')] ).
cnf(2647,plain,
equal(intersection(null_class,u),null_class),
inference(obv,[status(thm),theory(equality)],[2644]),
[iquote('0:Obv:2644.0')] ).
cnf(2648,plain,
equal(union(universal_class,u),complement(null_class)),
inference(rew,[status(thm),theory(equality)],[2647,2424]),
[iquote('0:Rew:2647.0,2424.0')] ).
cnf(2798,plain,
( ~ member(u,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[2647,27]),
[iquote('0:SpL:2647.0,27.0')] ).
cnf(2820,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[2445,2798]),
[iquote('0:MRR:2445.0,2798.1')] ).
cnf(2924,plain,
equal(complement(null_class),successor(universal_class)),
inference(spr,[status(thm),theory(equality)],[2648,48]),
[iquote('0:SpR:2648.0,48.0')] ).
cnf(2925,plain,
equal(intersection(complement(intersection(universal_class,u)),complement(null_class)),symmetric_difference(universal_class,u)),
inference(spr,[status(thm),theory(equality)],[2648,97]),
[iquote('0:SpR:2648.0,97.0')] ).
cnf(2949,plain,
equal(intersection(complement(intersection(universal_class,u)),successor(universal_class)),symmetric_difference(universal_class,u)),
inference(rew,[status(thm),theory(equality)],[2924,2925]),
[iquote('0:Rew:2924.0,2925.0')] ).
cnf(2953,plain,
equal(complement(intersection(complement(u),successor(universal_class))),union(u,null_class)),
inference(spr,[status(thm),theory(equality)],[2924,31]),
[iquote('0:SpR:2924.0,31.0')] ).
cnf(3955,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[249,8]),
[iquote('0:Res:249.1,8.0')] ).
cnf(3959,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[3955]),
[iquote('0:Obv:3955.0')] ).
cnf(4038,plain,
( subclass(intersection(intersection(u,v),w),x)
| member(not_subclass_element(intersection(intersection(u,v),w),x),v) ),
inference(res,[status(thm),theory(equality)],[268,27]),
[iquote('0:Res:268.1,27.0')] ).
cnf(4049,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[268,8]),
[iquote('0:Res:268.1,8.0')] ).
cnf(4053,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[4049]),
[iquote('0:Obv:4049.0')] ).
cnf(4073,plain,
subclass(symmetric_difference(u,v),complement(intersection(u,v))),
inference(spr,[status(thm),theory(equality)],[97,4053]),
[iquote('0:SpR:97.0,4053.0')] ).
cnf(6257,plain,
( ~ subclass(u,universal_class)
| subclass(u,complement(v))
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[487,397]),
[iquote('0:Res:487.2,397.0')] ).
cnf(6261,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[6257]),
[iquote('0:Obv:6257.1')] ).
cnf(6262,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[6261,9]),
[iquote('0:MRR:6261.0,9.0')] ).
cnf(6297,plain,
subclass(u,complement(null_class)),
inference(res,[status(thm),theory(equality)],[6262,2820]),
[iquote('0:Res:6262.0,2820.0')] ).
cnf(6302,plain,
subclass(u,successor(universal_class)),
inference(rew,[status(thm),theory(equality)],[2924,6297]),
[iquote('0:Rew:2924.0,6297.0')] ).
cnf(6330,plain,
equal(successor(universal_class),universal_class),
inference(res,[status(thm),theory(equality)],[6302,439]),
[iquote('0:Res:6302.0,439.0')] ).
cnf(6358,plain,
equal(complement(null_class),universal_class),
inference(rew,[status(thm),theory(equality)],[6330,2924]),
[iquote('0:Rew:6330.0,2924.0')] ).
cnf(6387,plain,
equal(complement(intersection(complement(u),universal_class)),union(u,null_class)),
inference(rew,[status(thm),theory(equality)],[6330,2953]),
[iquote('0:Rew:6330.0,2953.0')] ).
cnf(6401,plain,
equal(intersection(complement(intersection(universal_class,u)),universal_class),symmetric_difference(universal_class,u)),
inference(rew,[status(thm),theory(equality)],[6330,2949]),
[iquote('0:Rew:6330.0,2949.0')] ).
cnf(8346,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[9,819]),
[iquote('0:Res:9.0,819.2')] ).
cnf(8356,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[8346]),
[iquote('0:Con:8346.1')] ).
cnf(8422,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[7,8356]),
[iquote('0:Res:7.1,8356.0')] ).
cnf(8578,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[1972,8422]),
[iquote('0:MRR:1972.0,8422.1')] ).
cnf(10369,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u))
| subclass(u,intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[7,822]),
[iquote('0:Res:7.1,822.0')] ).
cnf(10384,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u)) ),
inference(obv,[status(thm),theory(equality)],[10369]),
[iquote('0:Obv:10369.1')] ).
cnf(18728,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[8578,8]),
[iquote('0:Res:8578.0,8.0')] ).
cnf(18731,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[18728]),
[iquote('0:Obv:18728.0')] ).
cnf(18764,plain,
subclass(complement(union(u,null_class)),intersection(complement(u),universal_class)),
inference(spr,[status(thm),theory(equality)],[6387,18731]),
[iquote('0:SpR:6387.0,18731.0')] ).
cnf(19119,plain,
subclass(complement(set_builder(u,null_class)),intersection(complement(singleton(u)),universal_class)),
inference(spr,[status(thm),theory(equality)],[1,18764]),
[iquote('0:SpR:1.0,18764.0')] ).
cnf(21617,plain,
( subclass(u,intersection(universal_class,u))
| subclass(u,intersection(universal_class,u)) ),
inference(res,[status(thm),theory(equality)],[8422,10384]),
[iquote('0:Res:8422.1,10384.0')] ).
cnf(21619,plain,
( subclass(complement(complement(u)),intersection(u,complement(complement(u))))
| subclass(complement(complement(u)),intersection(u,complement(complement(u)))) ),
inference(res,[status(thm),theory(equality)],[8578,10384]),
[iquote('0:Res:8578.0,10384.0')] ).
cnf(21642,plain,
subclass(u,intersection(universal_class,u)),
inference(obv,[status(thm),theory(equality)],[21617]),
[iquote('0:Obv:21617.0')] ).
cnf(21667,plain,
subclass(complement(complement(u)),intersection(u,complement(complement(u)))),
inference(obv,[status(thm),theory(equality)],[21619]),
[iquote('0:Obv:21619.0')] ).
cnf(21709,plain,
( ~ subclass(intersection(universal_class,u),u)
| equal(intersection(universal_class,u),u) ),
inference(res,[status(thm),theory(equality)],[21642,12]),
[iquote('0:Res:21642.0,12.0')] ).
cnf(21953,plain,
equal(intersection(universal_class,u),u),
inference(mrr,[status(thm)],[21709,3959]),
[iquote('0:MRR:21709.0,3959.0')] ).
cnf(21957,plain,
equal(intersection(complement(u),universal_class),symmetric_difference(universal_class,u)),
inference(rew,[status(thm),theory(equality)],[21953,6401]),
[iquote('0:Rew:21953.0,6401.0')] ).
cnf(22309,plain,
subclass(complement(set_builder(u,null_class)),symmetric_difference(universal_class,singleton(u))),
inference(rew,[status(thm),theory(equality)],[21957,19119]),
[iquote('0:Rew:21957.0,19119.0')] ).
cnf(23635,plain,
subclass(symmetric_difference(universal_class,u),complement(u)),
inference(spr,[status(thm),theory(equality)],[21953,4073]),
[iquote('0:SpR:21953.0,4073.0')] ).
cnf(26183,plain,
( equal(intersection(complement(u),u),null_class)
| equal(intersection(complement(u),u),null_class) ),
inference(res,[status(thm),theory(equality)],[246,2373]),
[iquote('0:Res:246.1,2373.0')] ).
cnf(26187,plain,
equal(intersection(complement(u),u),null_class),
inference(obv,[status(thm),theory(equality)],[26183]),
[iquote('0:Obv:26183.0')] ).
cnf(30420,plain,
( ~ subclass(intersection(u,complement(complement(u))),complement(complement(u)))
| equal(intersection(u,complement(complement(u))),complement(complement(u))) ),
inference(res,[status(thm),theory(equality)],[21667,12]),
[iquote('0:Res:21667.0,12.0')] ).
cnf(30430,plain,
equal(intersection(u,complement(complement(u))),complement(complement(u))),
inference(mrr,[status(thm)],[30420,3959]),
[iquote('0:MRR:30420.0,3959.0')] ).
cnf(46362,plain,
( subclass(intersection(intersection(u,v),w),v)
| subclass(intersection(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[4038,8]),
[iquote('0:Res:4038.1,8.0')] ).
cnf(46378,plain,
subclass(intersection(intersection(u,v),w),v),
inference(obv,[status(thm),theory(equality)],[46362]),
[iquote('0:Obv:46362.0')] ).
cnf(47059,plain,
subclass(complement(complement(intersection(u,v))),v),
inference(spr,[status(thm),theory(equality)],[30430,46378]),
[iquote('0:SpR:30430.0,46378.0')] ).
cnf(47182,plain,
subclass(complement(union(u,v)),complement(v)),
inference(spr,[status(thm),theory(equality)],[31,47059]),
[iquote('0:SpR:31.0,47059.0')] ).
cnf(47268,plain,
subclass(complement(set_builder(u,v)),complement(v)),
inference(spr,[status(thm),theory(equality)],[1,47182]),
[iquote('0:SpR:1.0,47182.0')] ).
cnf(47476,plain,
subclass(complement(null_class),complement(set_builder(v__dfg,set_builder(w__dfg,null_class)))),
inference(spr,[status(thm),theory(equality)],[5,47268]),
[iquote('0:SpR:5.0,47268.0')] ).
cnf(47492,plain,
subclass(universal_class,complement(set_builder(v__dfg,set_builder(w__dfg,null_class)))),
inference(rew,[status(thm),theory(equality)],[6358,47476]),
[iquote('0:Rew:6358.0,47476.0')] ).
cnf(47582,plain,
equal(complement(set_builder(v__dfg,set_builder(w__dfg,null_class))),universal_class),
inference(res,[status(thm),theory(equality)],[47492,439]),
[iquote('0:Res:47492.0,439.0')] ).
cnf(47795,plain,
equal(intersection(universal_class,set_builder(v__dfg,set_builder(w__dfg,null_class))),null_class),
inference(spr,[status(thm),theory(equality)],[47582,26187]),
[iquote('0:SpR:47582.0,26187.0')] ).
cnf(47872,plain,
equal(set_builder(v__dfg,set_builder(w__dfg,null_class)),null_class),
inference(rew,[status(thm),theory(equality)],[21953,47795]),
[iquote('0:Rew:21953.0,47795.0')] ).
cnf(47873,plain,
equal(set_builder(u__dfg,null_class),null_class),
inference(rew,[status(thm),theory(equality)],[47872,5]),
[iquote('0:Rew:47872.0,5.0')] ).
cnf(48027,plain,
subclass(complement(null_class),symmetric_difference(universal_class,singleton(u__dfg))),
inference(spr,[status(thm),theory(equality)],[47873,22309]),
[iquote('0:SpR:47873.0,22309.0')] ).
cnf(48031,plain,
subclass(universal_class,symmetric_difference(universal_class,singleton(u__dfg))),
inference(rew,[status(thm),theory(equality)],[6358,48027]),
[iquote('0:Rew:6358.0,48027.0')] ).
cnf(48097,plain,
equal(symmetric_difference(universal_class,singleton(u__dfg)),universal_class),
inference(res,[status(thm),theory(equality)],[48031,439]),
[iquote('0:Res:48031.0,439.0')] ).
cnf(48441,plain,
subclass(universal_class,complement(singleton(u__dfg))),
inference(spr,[status(thm),theory(equality)],[48097,23635]),
[iquote('0:SpR:48097.0,23635.0')] ).
cnf(48482,plain,
( ~ subclass(complement(singleton(u__dfg)),universal_class)
| equal(complement(singleton(u__dfg)),universal_class) ),
inference(res,[status(thm),theory(equality)],[48441,12]),
[iquote('0:Res:48441.0,12.0')] ).
cnf(48502,plain,
$false,
inference(mrr,[status(thm)],[48482,9,723]),
[iquote('0:MRR:48482.0,48482.1,9.0,723.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET137-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 01:04:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 24.62/24.78
% 24.62/24.78 SPASS V 3.9
% 24.62/24.78 SPASS beiseite: Proof found.
% 24.62/24.78 % SZS status Theorem
% 24.62/24.78 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.62/24.78 SPASS derived 37137 clauses, backtracked 84 clauses, performed 7 splits and kept 14973 clauses.
% 24.62/24.78 SPASS allocated 116255 KBytes.
% 24.62/24.78 SPASS spent 0:0:24.39 on the problem.
% 24.62/24.78 0:00:00.04 for the input.
% 24.62/24.78 0:00:00.00 for the FLOTTER CNF translation.
% 24.62/24.78 0:00:00.37 for inferences.
% 24.62/24.78 0:00:01.13 for the backtracking.
% 24.62/24.78 0:0:22.49 for the reduction.
% 24.62/24.78
% 24.62/24.78
% 24.62/24.78 Here is a proof with depth 12, length 114 :
% 24.62/24.78 % SZS output start Refutation
% See solution above
% 25.02/25.17 Formulae used in the proof : definition_of_set_builder prove_member_of_triple_kludge1_1 prove_member_of_triple_kludge1_4 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair3 singleton_set intersection1 intersection2 intersection3 complement1 complement2 union symmetric_difference successor regularity1
% 25.02/25.17
%------------------------------------------------------------------------------