TSTP Solution File: SET880+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 5 unt; 0 nHn; 8 RR)
% Number of literals : 12 ( 0 equ; 7 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ equal(skc5,skc4),
file('SET880+1.p',unknown),
[] ).
cnf(5,axiom,
equal(set_difference(singleton(skc4),singleton(skc5)),empty_set),
file('SET880+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(set_difference(singleton(u),v),empty_set)
| in(u,v) ),
file('SET880+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET880+1.p',unknown),
[] ).
cnf(14,plain,
( ~ equal(u,singleton(skc5))
| ~ in(skc4,u) ),
inference(res,[status(thm),theory(equality)],[10,4]),
[iquote('0:Res:10.2,4.0')] ).
cnf(15,plain,
in(skc4,singleton(skc5)),
inference(res,[status(thm),theory(equality)],[5,7]),
[iquote('0:Res:5.0,7.0')] ).
cnf(24,plain,
~ equal(singleton(skc5),singleton(skc5)),
inference(res,[status(thm),theory(equality)],[15,14]),
[iquote('0:Res:15.0,14.1')] ).
cnf(25,plain,
$false,
inference(obv,[status(thm),theory(equality)],[24]),
[iquote('0:Obv:24.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 04:05:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 10 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.19/0.43 SPASS allocated 85192 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.43 0:00:00.03 for the input.
% 0.19/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.00 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 2, length 8 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : t21_zfmisc_1 l36_zfmisc_1 d1_tarski antisymmetry_r2_hidden
% 0.19/0.43
%------------------------------------------------------------------------------