TSTP Solution File: SET067+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET067+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 05:23:28 EDT 2022
% Result : Theorem 18.32s 18.49s
% Output : Refutation 18.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 27 ( 11 unt; 7 nHn; 27 RR)
% Number of literals : 49 ( 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
subclass(u,universal_class),
file('SET067+1.p',unknown),
[] ).
cnf(8,axiom,
member(unordered_pair(u,v),universal_class),
file('SET067+1.p',unknown),
[] ).
cnf(11,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET067+1.p',unknown),
[] ).
cnf(21,axiom,
~ subclass(unordered_pair(skc5,skc5),unordered_pair(skc5,skc4)),
file('SET067+1.p',unknown),
[] ).
cnf(22,axiom,
( subclass(u,v)
| member(skf5(v,u),u) ),
file('SET067+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ member(skf5(u,v),u)
| subclass(w,u) ),
file('SET067+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET067+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET067+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ member(u,v)
| ~ member(w,u)
| member(w,sum_class(v)) ),
file('SET067+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ equal(u,v)
| ~ member(u,universal_class)
| member(u,unordered_pair(v,w)) ),
file('SET067+1.p',unknown),
[] ).
cnf(91,plain,
~ subclass(singleton(skc5),unordered_pair(skc5,skc4)),
inference(rew,[status(thm),theory(equality)],[11,21]),
[iquote('0:Rew:11.0,21.0')] ).
cnf(98,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[11,8]),
[iquote('0:SpR:11.0,8.0')] ).
cnf(649,plain,
( ~ member(u,singleton(v))
| member(u,sum_class(universal_class)) ),
inference(res,[status(thm),theory(equality)],[98,65]),
[iquote('0:Res:98.0,65.0')] ).
cnf(814,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[11,62]),
[iquote('0:SpL:11.0,62.0')] ).
cnf(829,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[814]),
[iquote('0:Obv:814.1')] ).
cnf(928,plain,
( subclass(singleton(u),v)
| equal(skf5(v,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[22,829]),
[iquote('0:Res:22.1,829.0')] ).
cnf(1194,plain,
( subclass(singleton(u),v)
| member(skf5(v,singleton(u)),sum_class(universal_class)) ),
inference(res,[status(thm),theory(equality)],[22,649]),
[iquote('0:Res:22.1,649.0')] ).
cnf(1204,plain,
( subclass(singleton(u),v)
| member(u,sum_class(universal_class)) ),
inference(rew,[status(thm),theory(equality)],[928,1194]),
[iquote('0:Rew:928.1,1194.1')] ).
cnf(1241,plain,
member(skc5,sum_class(universal_class)),
inference(res,[status(thm),theory(equality)],[1204,91]),
[iquote('0:Res:1204.0,91.0')] ).
cnf(1263,plain,
( ~ subclass(sum_class(universal_class),u)
| member(skc5,u) ),
inference(res,[status(thm),theory(equality)],[1241,54]),
[iquote('0:Res:1241.0,54.0')] ).
cnf(1266,plain,
member(skc5,universal_class),
inference(res,[status(thm),theory(equality)],[3,1263]),
[iquote('0:Res:3.0,1263.0')] ).
cnf(32694,plain,
( ~ member(u,v)
| subclass(singleton(u),v)
| subclass(w,v) ),
inference(spl,[status(thm),theory(equality)],[928,36]),
[iquote('0:SpL:928.1,36.0')] ).
cnf(32708,plain,
( ~ member(u,v)
| subclass(singleton(u),v) ),
inference(con,[status(thm)],[32694]),
[iquote('0:Con:32694.2')] ).
cnf(32821,plain,
~ member(skc5,unordered_pair(skc5,skc4)),
inference(res,[status(thm),theory(equality)],[32708,91]),
[iquote('0:Res:32708.1,91.0')] ).
cnf(32823,plain,
( ~ equal(skc5,skc5)
| ~ member(skc5,universal_class) ),
inference(res,[status(thm),theory(equality)],[70,32821]),
[iquote('0:Res:70.2,32821.0')] ).
cnf(32828,plain,
~ member(skc5,universal_class),
inference(obv,[status(thm),theory(equality)],[32823]),
[iquote('0:Obv:32823.0')] ).
cnf(32829,plain,
$false,
inference(mrr,[status(thm)],[32828,1266]),
[iquote('0:MRR:32828.0,1266.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET067+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n029.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 11:02:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 18.32/18.49
% 18.32/18.49 SPASS V 3.9
% 18.32/18.49 SPASS beiseite: Proof found.
% 18.32/18.49 % SZS status Theorem
% 18.32/18.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.32/18.49 SPASS derived 26913 clauses, backtracked 2381 clauses, performed 6 splits and kept 12070 clauses.
% 18.32/18.49 SPASS allocated 120328 KBytes.
% 18.32/18.49 SPASS spent 0:0:17.87 on the problem.
% 18.32/18.49 0:00:00.03 for the input.
% 18.32/18.49 0:00:00.06 for the FLOTTER CNF translation.
% 18.32/18.49 0:00:00.26 for inferences.
% 18.32/18.49 0:00:00.55 for the backtracking.
% 18.32/18.49 0:0:16.72 for the reduction.
% 18.32/18.49
% 18.32/18.49
% 18.32/18.49 Here is a proof with depth 6, length 27 :
% 18.32/18.49 % SZS output start Refutation
% See solution above
% 18.32/18.49 Formulae used in the proof : class_elements_are_sets unordered_pair singleton_set_defn pair_contains_other subclass_defn unordered_pair_defn sum_class_defn
% 18.32/18.49
%------------------------------------------------------------------------------