TSTP Solution File: SET497-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET497-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 05:26:36 EDT 2022
% Result : Unsatisfiable 0.53s 0.70s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 13 unt; 13 nHn; 36 RR)
% Number of literals : 67 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
member(z__dfg,z__dfg),
file('SET497-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET497-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET497-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET497-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET497-6.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET497-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET497-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET497-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET497-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET497-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET497-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(z__dfg,u)
| member(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[2,3]),
[iquote('0:Res:2.0,3.1')] ).
cnf(121,plain,
~ member(z__dfg,complement(z__dfg)),
inference(res,[status(thm),theory(equality)],[2,26]),
[iquote('0:Res:2.0,26.1')] ).
cnf(122,plain,
( ~ member(z__dfg,u)
| member(z__dfg,intersection(u,z__dfg)) ),
inference(res,[status(thm),theory(equality)],[2,25]),
[iquote('0:Res:2.0,25.1')] ).
cnf(143,plain,
member(z__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[6,117]),
[iquote('0:Res:6.0,117.0')] ).
cnf(182,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(227,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(684,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(697,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[684]),
[iquote('0:Obv:684.1')] ).
cnf(703,plain,
( equal(singleton(u),null_class)
| equal(regular(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[68,697]),
[iquote('0:Res:68.1,697.0')] ).
cnf(798,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[703,68]),
[iquote('0:SpR:703.1,68.1')] ).
cnf(799,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| equal(intersection(singleton(u),u),null_class) ),
inference(spr,[status(thm),theory(equality)],[703,69]),
[iquote('0:SpR:703.1,69.1')] ).
cnf(801,plain,
( equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[798]),
[iquote('0:Obv:798.0')] ).
cnf(802,plain,
( equal(singleton(u),null_class)
| equal(intersection(singleton(u),u),null_class) ),
inference(obv,[status(thm),theory(equality)],[799]),
[iquote('0:Obv:799.0')] ).
cnf(2325,plain,
( ~ member(z__dfg,singleton(z__dfg))
| equal(singleton(z__dfg),null_class)
| member(z__dfg,null_class) ),
inference(spr,[status(thm),theory(equality)],[802,122]),
[iquote('0:SpR:802.1,122.1')] ).
cnf(2340,plain,
( equal(singleton(z__dfg),null_class)
| member(z__dfg,null_class) ),
inference(mrr,[status(thm)],[2325,801]),
[iquote('0:MRR:2325.0,801.1')] ).
cnf(2341,plain,
member(z__dfg,null_class),
inference(spt,[spt(split,[position(s1)])],[2340]),
[iquote('1:Spt:2340.1')] ).
cnf(2346,plain,
( equal(u,null_class)
| member(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[2341,227]),
[iquote('1:Res:2341.0,227.0')] ).
cnf(2360,plain,
equal(complement(z__dfg),null_class),
inference(res,[status(thm),theory(equality)],[2346,121]),
[iquote('1:Res:2346.1,121.0')] ).
cnf(2377,plain,
~ member(z__dfg,null_class),
inference(rew,[status(thm),theory(equality)],[2360,121]),
[iquote('1:Rew:2360.0,121.0')] ).
cnf(2381,plain,
$false,
inference(mrr,[status(thm)],[2377,2341]),
[iquote('1:MRR:2377.0,2341.0')] ).
cnf(2424,plain,
~ member(z__dfg,null_class),
inference(spt,[spt(split,[position(sa)])],[2381,2341]),
[iquote('1:Spt:2381.0,2340.1,2341.0')] ).
cnf(2425,plain,
equal(singleton(z__dfg),null_class),
inference(spt,[spt(split,[position(s2)])],[2340]),
[iquote('1:Spt:2381.0,2340.0')] ).
cnf(2436,plain,
( ~ member(z__dfg,universal_class)
| member(z__dfg,null_class) ),
inference(spr,[status(thm),theory(equality)],[2425,182]),
[iquote('1:SpR:2425.0,182.1')] ).
cnf(2460,plain,
member(z__dfg,null_class),
inference(mrr,[status(thm)],[2436,143]),
[iquote('1:MRR:2436.0,143.0')] ).
cnf(2461,plain,
$false,
inference(mrr,[status(thm)],[2460,2424]),
[iquote('1:MRR:2460.0,2424.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET497-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 : Sat Jul 9 16:37:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.53/0.70
% 0.53/0.70 SPASS V 3.9
% 0.53/0.70 SPASS beiseite: Proof found.
% 0.53/0.70 % SZS status Theorem
% 0.53/0.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.70 SPASS derived 2170 clauses, backtracked 85 clauses, performed 2 splits and kept 1078 clauses.
% 0.53/0.70 SPASS allocated 77735 KBytes.
% 0.53/0.70 SPASS spent 0:00:00.34 on the problem.
% 0.53/0.70 0:00:00.04 for the input.
% 0.53/0.70 0:00:00.00 for the FLOTTER CNF translation.
% 0.53/0.70 0:00:00.03 for inferences.
% 0.53/0.70 0:00:00.00 for the backtracking.
% 0.53/0.70 0:00:00.24 for the reduction.
% 0.53/0.70
% 0.53/0.70
% 0.53/0.70 Here is a proof with depth 7, length 36 :
% 0.53/0.70 % SZS output start Refutation
% See solution above
% 0.53/0.70 Formulae used in the proof : prove_russell_class1_2 subclass_members class_elements_are_sets unordered_pair_member unordered_pair3 singleton_set intersection1 intersection3 complement1 regularity1 regularity2
% 0.53/0.70
%------------------------------------------------------------------------------