TSTP Solution File: SET004-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 05:22:20 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 6 unt; 1 nHn; 10 RR)
% Number of literals : 15 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
union(a,b,aUb),
file('SET004-1.p',unknown),
[] ).
cnf(2,axiom,
~ subset(a,aUb),
file('SET004-1.p',unknown),
[] ).
cnf(4,axiom,
( subset(u,v)
| member(member_of_1_not_of_2(u,v),u) ),
file('SET004-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(member_of_1_not_of_2(u,v),v)
| subset(u,v) ),
file('SET004-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,v)
| ~ union(v,w,x)
| member(u,x) ),
file('SET004-1.p',unknown),
[] ).
cnf(16,plain,
~ member(member_of_1_not_of_2(a,aUb),aUb),
inference(res,[status(thm),theory(equality)],[5,2]),
[iquote('0:Res:5.1,2.0')] ).
cnf(17,plain,
member(member_of_1_not_of_2(a,aUb),a),
inference(res,[status(thm),theory(equality)],[4,2]),
[iquote('0:Res:4.0,2.0')] ).
cnf(27,plain,
( ~ member(u,a)
| member(u,aUb) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.1')] ).
cnf(29,plain,
member(member_of_1_not_of_2(a,aUb),aUb),
inference(res,[status(thm),theory(equality)],[17,27]),
[iquote('0:Res:17.0,27.0')] ).
cnf(31,plain,
$false,
inference(mrr,[status(thm)],[29,16]),
[iquote('0:MRR:29.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 09:22:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.20/0.42 SPASS allocated 63102 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.42 0:00:00.04 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.00 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 2, length 10 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : a_union_b_is_aUb prove_a_is_a_subset_of_aUb subsets_axiom1 subsets_axiom2 member_of_set1_is_member_of_union
% 0.20/0.42
%------------------------------------------------------------------------------