TSTP Solution File: SET900+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET900+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 05:29:40 EDT 2022
% Result : Theorem 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 6 unt; 3 nHn; 11 RR)
% Number of literals : 18 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 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(skc4,empty_set),
file('SET900+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(singleton(skc5),skc4),
file('SET900+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ in(u,skc4)
| equal(u,skc5) ),
file('SET900+1.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,empty_set)
| equal(u,singleton(v))
| in(skf1(v,u),u) ),
file('SET900+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(skf1(u,v),u)
| equal(w,singleton(u))
| equal(w,empty_set) ),
file('SET900+1.p',unknown),
[] ).
cnf(12,plain,
( in(skf1(skc5,skc4),skc4)
| equal(skc4,empty_set) ),
inference(res,[status(thm),theory(equality)],[8,5]),
[iquote('0:Res:8.1,5.0')] ).
cnf(13,plain,
( ~ equal(skf1(skc5,u),skc5)
| equal(skc4,empty_set) ),
inference(res,[status(thm),theory(equality)],[9,5]),
[iquote('0:Res:9.1,5.0')] ).
cnf(14,plain,
in(skf1(skc5,skc4),skc4),
inference(mrr,[status(thm)],[12,4]),
[iquote('0:MRR:12.1,4.0')] ).
cnf(15,plain,
~ equal(skf1(skc5,u),skc5),
inference(mrr,[status(thm)],[13,4]),
[iquote('0:MRR:13.1,4.0')] ).
cnf(22,plain,
equal(skf1(skc5,skc4),skc5),
inference(res,[status(thm),theory(equality)],[14,6]),
[iquote('0:Res:14.0,6.0')] ).
cnf(23,plain,
$false,
inference(mrr,[status(thm)],[22,15]),
[iquote('0:MRR:22.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET900+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.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 00:57:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 11 clauses, backtracked 0 clauses, performed 0 splits and kept 16 clauses.
% 0.18/0.42 SPASS allocated 85079 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.00 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 2, length 11 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : t41_zfmisc_1 l45_zfmisc_1
% 0.18/0.42
%------------------------------------------------------------------------------