TSTP Solution File: SET591+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 05:27:12 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 8 unt; 1 nHn; 14 RR)
% Number of literals : 22 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 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(2,axiom,
~ equal(skc2,empty_set),
file('SET591+3.p',unknown),
[] ).
cnf(3,axiom,
~ member(u,empty_set),
file('SET591+3.p',unknown),
[] ).
cnf(4,axiom,
subset(skc2,difference(skc3,skc2)),
file('SET591+3.p',unknown),
[] ).
cnf(9,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET591+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,v)
| ~ member(u,difference(w,v)) ),
file('SET591+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET591+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET591+3.p',unknown),
[] ).
cnf(16,plain,
( ~ subset(empty_set,skc2)
| ~ subset(skc2,empty_set) ),
inference(res,[status(thm),theory(equality)],[14,2]),
[iquote('0:Res:14.2,2.0')] ).
cnf(19,plain,
( ~ member(u,skc2)
| member(u,difference(skc3,skc2)) ),
inference(res,[status(thm),theory(equality)],[4,13]),
[iquote('0:Res:4.0,13.0')] ).
cnf(21,plain,
~ member(u,skc2),
inference(mrr,[status(thm)],[19,12]),
[iquote('0:MRR:19.1,12.1')] ).
cnf(26,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.1,3.0')] ).
cnf(27,plain,
subset(skc2,u),
inference(res,[status(thm),theory(equality)],[9,21]),
[iquote('0:Res:9.1,21.0')] ).
cnf(29,plain,
~ subset(skc2,empty_set),
inference(mrr,[status(thm)],[16,26]),
[iquote('0:MRR:16.0,26.0')] ).
cnf(30,plain,
$false,
inference(mrr,[status(thm)],[29,27]),
[iquote('0:MRR:29.0,27.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 12:39:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 23 clauses.
% 0.20/0.45 SPASS allocated 97705 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.00 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 2, length 14 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : prove_th50 empty_set_defn subset_defn difference_defn equal_defn
% 0.20/0.45
%------------------------------------------------------------------------------