TSTP Solution File: SET082+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET082+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:23:44 EDT 2022
% Result : Theorem 0.57s 0.75s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 9 unt; 6 nHn; 20 RR)
% Number of literals : 35 ( 0 equ; 13 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('SET082+1.p',unknown),
[] ).
cnf(5,axiom,
~ member(skc3,universal_class),
file('SET082+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(singleton(skc3),null_class),
file('SET082+1.p',unknown),
[] ).
cnf(10,axiom,
member(unordered_pair(u,v),universal_class),
file('SET082+1.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET082+1.p',unknown),
[] ).
cnf(22,axiom,
( equal(u,null_class)
| member(skf9(u),u) ),
file('SET082+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET082+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET082+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ member(u,v)
| ~ member(w,u)
| member(w,sum_class(v)) ),
file('SET082+1.p',unknown),
[] ).
cnf(107,plain,
( ~ subclass(u,universal_class)
| ~ member(skc3,u) ),
inference(res,[status(thm),theory(equality)],[55,5]),
[iquote('0:Res:55.2,5.0')] ).
cnf(118,plain,
~ member(skc3,u),
inference(mrr,[status(thm)],[107,3]),
[iquote('0:MRR:107.0,3.0')] ).
cnf(125,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[14,10]),
[iquote('0:SpR:14.0,10.0')] ).
cnf(761,plain,
( ~ member(u,singleton(v))
| member(u,sum_class(universal_class)) ),
inference(res,[status(thm),theory(equality)],[125,66]),
[iquote('0:Res:125.0,66.0')] ).
cnf(868,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[14,63]),
[iquote('0:SpL:14.0,63.0')] ).
cnf(882,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[868]),
[iquote('0:Obv:868.1')] ).
cnf(930,plain,
( equal(singleton(u),null_class)
| equal(skf9(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[22,882]),
[iquote('0:Res:22.1,882.0')] ).
cnf(1778,plain,
( equal(singleton(u),null_class)
| member(skf9(singleton(u)),sum_class(universal_class)) ),
inference(res,[status(thm),theory(equality)],[22,761]),
[iquote('0:Res:22.1,761.0')] ).
cnf(1788,plain,
( equal(singleton(u),null_class)
| member(u,sum_class(universal_class)) ),
inference(rew,[status(thm),theory(equality)],[930,1778]),
[iquote('0:Rew:930.1,1778.1')] ).
cnf(1798,plain,
equal(singleton(skc3),null_class),
inference(res,[status(thm),theory(equality)],[1788,118]),
[iquote('0:Res:1788.1,118.0')] ).
cnf(1818,plain,
$false,
inference(mrr,[status(thm)],[1798,9]),
[iquote('0:MRR:1798.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET082+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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 22:14:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.75
% 0.57/0.75 SPASS V 3.9
% 0.57/0.75 SPASS beiseite: Proof found.
% 0.57/0.75 % SZS status Theorem
% 0.57/0.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.75 SPASS derived 1515 clauses, backtracked 4 clauses, performed 1 splits and kept 1028 clauses.
% 0.57/0.75 SPASS allocated 99151 KBytes.
% 0.57/0.75 SPASS spent 0:00:00.40 on the problem.
% 0.57/0.75 0:00:00.04 for the input.
% 0.57/0.75 0:00:00.05 for the FLOTTER CNF translation.
% 0.57/0.75 0:00:00.03 for inferences.
% 0.57/0.75 0:00:00.00 for the backtracking.
% 0.57/0.75 0:00:00.25 for the reduction.
% 0.57/0.75
% 0.57/0.75
% 0.57/0.75 Here is a proof with depth 4, length 20 :
% 0.57/0.75 % SZS output start Refutation
% See solution above
% 0.57/0.75 Formulae used in the proof : class_elements_are_sets singleton_is_null_class unordered_pair singleton_set_defn regularity infinity subclass_defn unordered_pair_defn sum_class_defn
% 0.57/0.75
%------------------------------------------------------------------------------