TSTP Solution File: SET095+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET095+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 05:23:56 EDT 2022
% Result : Theorem 36.74s 36.91s
% Output : Refutation 36.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 34 ( 9 unt; 11 nHn; 34 RR)
% Number of literals : 69 ( 0 equ; 31 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 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,
member(skc4,skc5),
file('SET095+1.p',unknown),
[] ).
cnf(4,axiom,
subclass(u,universal_class),
file('SET095+1.p',unknown),
[] ).
cnf(9,axiom,
~ subclass(singleton(skc4),skc5),
file('SET095+1.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET095+1.p',unknown),
[] ).
cnf(23,axiom,
( subclass(u,v)
| member(skf5(v,u),u) ),
file('SET095+1.p',unknown),
[] ).
cnf(35,axiom,
( disjoint(u,v)
| member(skf8(v,u),u) ),
file('SET095+1.p',unknown),
[] ).
cnf(36,axiom,
( disjoint(u,v)
| member(skf8(v,w),v) ),
file('SET095+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ member(skf5(u,v),u)
| subclass(w,u) ),
file('SET095+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET095+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET095+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ member(u,v)
| ~ member(u,w)
| ~ disjoint(w,v) ),
file('SET095+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ equal(u,v)
| ~ member(u,universal_class)
| member(u,unordered_pair(w,v)) ),
file('SET095+1.p',unknown),
[] ).
cnf(93,plain,
( ~ member(skc4,u)
| ~ disjoint(skc5,u) ),
inference(res,[status(thm),theory(equality)],[3,69]),
[iquote('0:Res:3.0,69.1')] ).
cnf(94,plain,
( ~ subclass(skc5,u)
| member(skc4,u) ),
inference(res,[status(thm),theory(equality)],[3,55]),
[iquote('0:Res:3.0,55.1')] ).
cnf(108,plain,
~ member(skf5(skc5,u),skc5),
inference(res,[status(thm),theory(equality)],[37,9]),
[iquote('0:Res:37.1,9.0')] ).
cnf(119,plain,
member(skc4,universal_class),
inference(res,[status(thm),theory(equality)],[4,94]),
[iquote('0:Res:4.0,94.0')] ).
cnf(797,plain,
( ~ member(skf8(u,v),w)
| ~ disjoint(w,v)
| disjoint(v,u) ),
inference(res,[status(thm),theory(equality)],[35,69]),
[iquote('0:Res:35.1,69.0')] ).
cnf(838,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(853,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[838]),
[iquote('0:Obv:838.1')] ).
cnf(960,plain,
( disjoint(singleton(u),v)
| equal(skf8(v,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[35,853]),
[iquote('0:Res:35.1,853.0')] ).
cnf(961,plain,
( subclass(singleton(u),v)
| equal(skf5(v,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[23,853]),
[iquote('0:Res:23.1,853.0')] ).
cnf(998,plain,
( ~ equal(u,v)
| ~ member(u,universal_class)
| member(u,singleton(v)) ),
inference(spr,[status(thm),theory(equality)],[13,72]),
[iquote('0:SpR:13.0,72.2')] ).
cnf(6729,plain,
( ~ disjoint(u,v)
| disjoint(w,u)
| disjoint(v,u) ),
inference(res,[status(thm),theory(equality)],[36,797]),
[iquote('0:Res:36.1,797.0')] ).
cnf(6743,plain,
( ~ disjoint(u,v)
| disjoint(v,u) ),
inference(con,[status(thm)],[6729]),
[iquote('0:Con:6729.1')] ).
cnf(31541,plain,
( disjoint(singleton(u),v)
| disjoint(w,v)
| member(u,v) ),
inference(spr,[status(thm),theory(equality)],[960,36]),
[iquote('0:SpR:960.1,36.1')] ).
cnf(31692,plain,
( disjoint(singleton(u),v)
| member(u,v) ),
inference(con,[status(thm)],[31541]),
[iquote('0:Con:31541.1')] ).
cnf(31771,plain,
( member(u,v)
| disjoint(v,singleton(u)) ),
inference(res,[status(thm),theory(equality)],[31692,6743]),
[iquote('0:Res:31692.0,6743.0')] ).
cnf(33331,plain,
( ~ equal(skc4,u)
| ~ member(skc4,universal_class)
| ~ disjoint(skc5,singleton(u)) ),
inference(res,[status(thm),theory(equality)],[998,93]),
[iquote('0:Res:998.2,93.0')] ).
cnf(33360,plain,
( ~ equal(skc4,u)
| ~ disjoint(skc5,singleton(u)) ),
inference(mrr,[status(thm)],[33331,119]),
[iquote('0:MRR:33331.1,119.0')] ).
cnf(35173,plain,
( ~ equal(skc4,u)
| member(u,skc5) ),
inference(res,[status(thm),theory(equality)],[31771,33360]),
[iquote('0:Res:31771.1,33360.1')] ).
cnf(35200,plain,
~ equal(skf5(skc5,u),skc4),
inference(res,[status(thm),theory(equality)],[35173,108]),
[iquote('0:Res:35173.1,108.0')] ).
cnf(35236,plain,
( ~ equal(u,skc4)
| subclass(singleton(u),skc5) ),
inference(spl,[status(thm),theory(equality)],[961,35200]),
[iquote('0:SpL:961.1,35200.0')] ).
cnf(39864,plain,
~ equal(skc4,skc4),
inference(res,[status(thm),theory(equality)],[35236,9]),
[iquote('0:Res:35236.1,9.0')] ).
cnf(39865,plain,
$false,
inference(obv,[status(thm),theory(equality)],[39864]),
[iquote('0:Obv:39864.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET095+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 13:12:41 EDT 2022
% 0.14/0.35 % CPUTime :
% 36.74/36.91
% 36.74/36.91 SPASS V 3.9
% 36.74/36.91 SPASS beiseite: Proof found.
% 36.74/36.91 % SZS status Theorem
% 36.74/36.91 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.74/36.91 SPASS derived 34555 clauses, backtracked 6804 clauses, performed 8 splits and kept 18175 clauses.
% 36.74/36.91 SPASS allocated 123819 KBytes.
% 36.74/36.91 SPASS spent 0:0:36.20 on the problem.
% 36.74/36.91 0:00:00.04 for the input.
% 36.74/36.91 0:00:00.06 for the FLOTTER CNF translation.
% 36.74/36.91 0:00:00.43 for inferences.
% 36.74/36.91 0:00:00.93 for the backtracking.
% 36.74/36.91 0:0:34.22 for the reduction.
% 36.74/36.91
% 36.74/36.91
% 36.74/36.91 Here is a proof with depth 8, length 34 :
% 36.74/36.91 % SZS output start Refutation
% See solution above
% 36.74/36.91 Formulae used in the proof : property_of_singletons2 class_elements_are_sets singleton_set_defn subclass_defn disjoint_defn unordered_pair_defn
% 36.74/36.91
%------------------------------------------------------------------------------