TSTP Solution File: SET879+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 05:29:32 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 11 unt; 1 nHn; 21 RR)
% Number of literals : 33 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( in(u,v)
| equal(set_difference(singleton(u),v),singleton(u)) ),
file('SET879+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(skc5,skc4)
| equal(set_difference(singleton(skc4),singleton(skc5)),singleton(skc4)) ),
file('SET879+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(set_difference(singleton(skc4),singleton(skc5)),singleton(skc4))
| equal(skc5,skc4) ),
file('SET879+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET879+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SET879+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(u,v)
| ~ equal(set_difference(singleton(u),v),singleton(u)) ),
file('SET879+1.p',unknown),
[] ).
cnf(13,plain,
~ equal(skc5,skc4),
inference(spt,[spt(split,[position(s1)])],[5]),
[iquote('1:Spt:5.0')] ).
cnf(14,plain,
~ equal(set_difference(singleton(skc4),singleton(skc5)),singleton(skc4)),
inference(mrr,[status(thm)],[6,13]),
[iquote('1:MRR:6.1,13.0')] ).
cnf(15,plain,
( ~ equal(singleton(skc4),singleton(skc4))
| in(skc4,singleton(skc5)) ),
inference(spl,[status(thm),theory(equality)],[4,14]),
[iquote('1:SpL:4.1,14.0')] ).
cnf(16,plain,
in(skc4,singleton(skc5)),
inference(obv,[status(thm),theory(equality)],[15]),
[iquote('1:Obv:15.0')] ).
cnf(19,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[9]),
[iquote('0:EqR:9.1')] ).
cnf(24,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[8]),
[iquote('0:EqR:8.1')] ).
cnf(25,plain,
equal(skc5,skc4),
inference(res,[status(thm),theory(equality)],[16,24]),
[iquote('1:Res:16.0,24.0')] ).
cnf(27,plain,
$false,
inference(mrr,[status(thm)],[25,13]),
[iquote('1:MRR:25.0,13.0')] ).
cnf(28,plain,
equal(skc5,skc4),
inference(spt,[spt(split,[position(sa)])],[27,13]),
[iquote('1:Spt:27.0,5.0,13.0')] ).
cnf(29,plain,
equal(set_difference(singleton(skc4),singleton(skc5)),singleton(skc4)),
inference(spt,[spt(split,[position(s2)])],[5]),
[iquote('1:Spt:27.0,5.1')] ).
cnf(30,plain,
equal(set_difference(singleton(skc4),singleton(skc4)),singleton(skc4)),
inference(rew,[status(thm),theory(equality)],[28,29]),
[iquote('1:Rew:28.0,29.0')] ).
cnf(34,plain,
( ~ in(skc4,singleton(skc4))
| ~ equal(singleton(skc4),singleton(skc4)) ),
inference(spl,[status(thm),theory(equality)],[30,10]),
[iquote('1:SpL:30.0,10.1')] ).
cnf(35,plain,
~ in(skc4,singleton(skc4)),
inference(obv,[status(thm),theory(equality)],[34]),
[iquote('1:Obv:34.1')] ).
cnf(39,plain,
~ equal(skc4,skc4),
inference(res,[status(thm),theory(equality)],[19,35]),
[iquote('1:Res:19.1,35.0')] ).
cnf(40,plain,
$false,
inference(obv,[status(thm),theory(equality)],[39]),
[iquote('1:Obv:39.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.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 : Sun Jul 10 17:38:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 22 clauses, backtracked 3 clauses, performed 1 splits and kept 28 clauses.
% 0.19/0.44 SPASS allocated 85149 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.04 for the input.
% 0.19/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.00 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 3, length 21 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : l34_zfmisc_1 t20_zfmisc_1 d1_tarski antisymmetry_r2_hidden
% 0.19/0.44
%------------------------------------------------------------------------------