TSTP Solution File: SET103+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET103+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 05:24:05 EDT 2022
% Result : Theorem 0.50s 0.71s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 11 unt; 6 nHn; 22 RR)
% Number of literals : 37 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
subclass(u,universal_class),
file('SET103+1.p',unknown),
[] ).
cnf(5,axiom,
~ member(skc4,universal_class),
file('SET103+1.p',unknown),
[] ).
cnf(9,axiom,
member(unordered_pair(u,v),universal_class),
file('SET103+1.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET103+1.p',unknown),
[] ).
cnf(21,axiom,
( equal(u,null_class)
| member(skf9(u),u) ),
file('SET103+1.p',unknown),
[] ).
cnf(54,axiom,
~ equal(unordered_pair(singleton(skc5),unordered_pair(skc5,null_class)),ordered_pair(skc5,skc4)),
file('SET103+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET103+1.p',unknown),
[] ).
cnf(57,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('SET103+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET103+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ member(u,v)
| ~ member(w,u)
| member(w,sum_class(v)) ),
file('SET103+1.p',unknown),
[] ).
cnf(107,plain,
( ~ subclass(u,universal_class)
| ~ member(skc4,u) ),
inference(res,[status(thm),theory(equality)],[55,5]),
[iquote('0:Res:55.2,5.0')] ).
cnf(115,plain,
~ member(skc4,u),
inference(mrr,[status(thm)],[107,3]),
[iquote('0:MRR:107.0,3.0')] ).
cnf(122,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[13,9]),
[iquote('0:SpR:13.0,9.0')] ).
cnf(779,plain,
( ~ member(u,singleton(v))
| member(u,sum_class(universal_class)) ),
inference(res,[status(thm),theory(equality)],[122,66]),
[iquote('0:Res:122.0,66.0')] ).
cnf(884,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[13,63]),
[iquote('0:SpL:13.0,63.0')] ).
cnf(898,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[884]),
[iquote('0:Obv:884.1')] ).
cnf(1207,plain,
( equal(singleton(u),null_class)
| equal(skf9(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[21,898]),
[iquote('0:Res:21.1,898.0')] ).
cnf(1773,plain,
( equal(singleton(u),null_class)
| member(skf9(singleton(u)),sum_class(universal_class)) ),
inference(res,[status(thm),theory(equality)],[21,779]),
[iquote('0:Res:21.1,779.0')] ).
cnf(1783,plain,
( equal(singleton(u),null_class)
| member(u,sum_class(universal_class)) ),
inference(rew,[status(thm),theory(equality)],[1207,1773]),
[iquote('0:Rew:1207.1,1773.1')] ).
cnf(1804,plain,
equal(singleton(skc4),null_class),
inference(res,[status(thm),theory(equality)],[1783,115]),
[iquote('0:Res:1783.1,115.0')] ).
cnf(1840,plain,
equal(unordered_pair(singleton(u),unordered_pair(u,null_class)),ordered_pair(u,skc4)),
inference(spr,[status(thm),theory(equality)],[1804,57]),
[iquote('0:SpR:1804.0,57.0')] ).
cnf(1853,plain,
$false,
inference(unc,[status(thm)],[1840,54]),
[iquote('0:UnC:1840.0,54.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET103+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 16:53:30 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.50/0.71
% 0.50/0.71 SPASS V 3.9
% 0.50/0.71 SPASS beiseite: Proof found.
% 0.50/0.71 % SZS status Theorem
% 0.50/0.71 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.50/0.71 SPASS derived 1549 clauses, backtracked 4 clauses, performed 1 splits and kept 1037 clauses.
% 0.50/0.71 SPASS allocated 99191 KBytes.
% 0.50/0.71 SPASS spent 0:00:00.34 on the problem.
% 0.50/0.71 0:00:00.04 for the input.
% 0.50/0.71 0:00:00.05 for the FLOTTER CNF translation.
% 0.50/0.71 0:00:00.02 for inferences.
% 0.50/0.71 0:00:00.00 for the backtracking.
% 0.50/0.71 0:00:00.19 for the reduction.
% 0.50/0.71
% 0.50/0.71
% 0.50/0.71 Here is a proof with depth 5, length 22 :
% 0.50/0.71 % SZS output start Refutation
% See solution above
% 0.50/0.71 Formulae used in the proof : class_elements_are_sets property_1_of_ordered_pair unordered_pair singleton_set_defn regularity infinity subclass_defn ordered_pair_defn unordered_pair_defn sum_class_defn
% 0.50/0.71
%------------------------------------------------------------------------------