TSTP Solution File: SET083+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 05:23:45 EDT 2022
% Result : Theorem 0.47s 0.68s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 17 unt; 3 nHn; 36 RR)
% Number of literals : 62 ( 0 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
member(skc4,universal_class),
file('SET083+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(skc5,skc4),
file('SET083+1.p',unknown),
[] ).
cnf(10,axiom,
equal(singleton(skc5),singleton(skc4)),
file('SET083+1.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET083+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ member(ordered_pair(u,v),element_relation)
| member(v,universal_class) ),
file('SET083+1.p',unknown),
[] ).
cnf(58,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('SET083+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET083+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ member(u,universal_class)
| equal(u,null_class)
| member(apply(skc13,u),u) ),
file('SET083+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ equal(u,v)
| ~ member(u,universal_class)
| member(u,unordered_pair(v,w)) ),
file('SET083+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ member(u,v)
| ~ member(v,universal_class)
| member(ordered_pair(u,v),element_relation) ),
file('SET083+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ member(u,universal_class)
| ~ member(v,universal_class)
| equal(second(ordered_pair(v,u)),u) ),
file('SET083+1.p',unknown),
[] ).
cnf(97,plain,
( ~ equal(skc4,u)
| member(skc4,unordered_pair(u,v)) ),
inference(res,[status(thm),theory(equality)],[3,72]),
[iquote('0:Res:3.0,72.1')] ).
cnf(101,plain,
( equal(skc4,null_class)
| member(apply(skc13,skc4),skc4) ),
inference(res,[status(thm),theory(equality)],[3,71]),
[iquote('0:Res:3.0,71.0')] ).
cnf(107,plain,
( ~ member(u,universal_class)
| equal(second(ordered_pair(u,skc4)),skc4) ),
inference(res,[status(thm),theory(equality)],[3,80]),
[iquote('0:Res:3.0,80.1')] ).
cnf(108,plain,
( ~ member(u,skc4)
| member(ordered_pair(u,skc4),element_relation) ),
inference(res,[status(thm),theory(equality)],[3,75]),
[iquote('0:Res:3.0,75.1')] ).
cnf(129,plain,
( ~ member(skc4,unordered_pair(u,skc5))
| equal(skc4,u) ),
inference(res,[status(thm),theory(equality)],[64,6]),
[iquote('0:Res:64.2,6.0')] ).
cnf(152,plain,
~ member(skc4,unordered_pair(skc5,skc5)),
inference(res,[status(thm),theory(equality)],[129,6]),
[iquote('0:Res:129.1,6.0')] ).
cnf(156,plain,
~ member(skc4,singleton(skc4)),
inference(rew,[status(thm),theory(equality)],[10,152,14]),
[iquote('0:Rew:10.0,152.0,14.0,152.0')] ).
cnf(158,plain,
equal(skc4,null_class),
inference(spt,[spt(split,[position(s1)])],[101]),
[iquote('1:Spt:101.0')] ).
cnf(172,plain,
( ~ equal(null_class,u)
| member(skc4,unordered_pair(u,v)) ),
inference(rew,[status(thm),theory(equality)],[158,97]),
[iquote('1:Rew:158.0,97.0')] ).
cnf(193,plain,
~ member(null_class,singleton(null_class)),
inference(rew,[status(thm),theory(equality)],[158,156]),
[iquote('1:Rew:158.0,156.0')] ).
cnf(210,plain,
( ~ equal(null_class,u)
| member(null_class,unordered_pair(u,v)) ),
inference(rew,[status(thm),theory(equality)],[158,172]),
[iquote('1:Rew:158.0,172.1')] ).
cnf(358,plain,
( ~ equal(null_class,u)
| member(null_class,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[14,210]),
[iquote('1:SpR:14.0,210.1')] ).
cnf(365,plain,
~ equal(null_class,null_class),
inference(res,[status(thm),theory(equality)],[358,193]),
[iquote('1:Res:358.1,193.0')] ).
cnf(368,plain,
$false,
inference(obv,[status(thm),theory(equality)],[365]),
[iquote('1:Obv:365.0')] ).
cnf(369,plain,
~ equal(skc4,null_class),
inference(spt,[spt(split,[position(sa)])],[368,158]),
[iquote('1:Spt:368.0,101.0,158.0')] ).
cnf(370,plain,
member(apply(skc13,skc4),skc4),
inference(spt,[spt(split,[position(s2)])],[101]),
[iquote('1:Spt:368.0,101.1')] ).
cnf(517,plain,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(skc4))),ordered_pair(u,skc5)),
inference(spr,[status(thm),theory(equality)],[10,58]),
[iquote('0:SpR:10.0,58.0')] ).
cnf(521,plain,
equal(ordered_pair(u,skc5),ordered_pair(u,skc4)),
inference(rew,[status(thm),theory(equality)],[58,517]),
[iquote('0:Rew:58.0,517.0')] ).
cnf(530,plain,
( ~ member(ordered_pair(u,skc4),element_relation)
| member(skc5,universal_class) ),
inference(spl,[status(thm),theory(equality)],[521,40]),
[iquote('0:SpL:521.0,40.0')] ).
cnf(769,plain,
( ~ member(u,skc4)
| member(skc5,universal_class) ),
inference(res,[status(thm),theory(equality)],[108,530]),
[iquote('0:Res:108.1,530.0')] ).
cnf(782,plain,
member(skc5,universal_class),
inference(res,[status(thm),theory(equality)],[370,769]),
[iquote('1:Res:370.0,769.0')] ).
cnf(1505,plain,
( ~ member(skc5,universal_class)
| ~ member(u,universal_class)
| equal(second(ordered_pair(u,skc4)),skc5) ),
inference(spr,[status(thm),theory(equality)],[521,80]),
[iquote('0:SpR:521.0,80.2')] ).
cnf(1518,plain,
( ~ member(skc5,universal_class)
| ~ member(u,universal_class)
| equal(skc5,skc4) ),
inference(rew,[status(thm),theory(equality)],[107,1505]),
[iquote('0:Rew:107.1,1505.2')] ).
cnf(1519,plain,
( ~ member(skc5,universal_class)
| equal(skc5,skc4) ),
inference(con,[status(thm)],[1518]),
[iquote('0:Con:1518.1')] ).
cnf(1520,plain,
$false,
inference(mrr,[status(thm)],[1519,782,6]),
[iquote('1:MRR:1519.0,1519.1,782.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jul 9 19:59:46 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.47/0.68
% 0.47/0.68 SPASS V 3.9
% 0.47/0.68 SPASS beiseite: Proof found.
% 0.47/0.68 % SZS status Theorem
% 0.47/0.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.68 SPASS derived 1294 clauses, backtracked 117 clauses, performed 2 splits and kept 982 clauses.
% 0.47/0.68 SPASS allocated 98714 KBytes.
% 0.47/0.68 SPASS spent 0:00:00.30 on the problem.
% 0.47/0.68 0:00:00.03 for the input.
% 0.47/0.68 0:00:00.06 for the FLOTTER CNF translation.
% 0.47/0.68 0:00:00.01 for inferences.
% 0.47/0.68 0:00:00.00 for the backtracking.
% 0.47/0.68 0:00:00.15 for the reduction.
% 0.47/0.68
% 0.47/0.68
% 0.47/0.68 Here is a proof with depth 4, length 36 :
% 0.47/0.68 % SZS output start Refutation
% See solution above
% 0.47/0.68 Formulae used in the proof : singleton_identified_by_element1 singleton_set_defn element_relation_defn ordered_pair_defn unordered_pair_defn choice first_second
% 0.47/0.68
%------------------------------------------------------------------------------