TSTP Solution File: SET014-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 05:22:29 EDT 2022
% Result : Unsatisfiable 2.04s 2.19s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 6 unt; 6 nHn; 17 RR)
% Number of literals : 32 ( 0 equ; 8 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(1,axiom,
subset(as,cs),
file('SET014-2.p',unknown),
[] ).
cnf(2,axiom,
subset(bs,cs),
file('SET014-2.p',unknown),
[] ).
cnf(3,axiom,
~ subset(union(as,bs),cs),
file('SET014-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ subset(u,v)
| ~ member(w,u)
| member(w,v) ),
file('SET014-2.p',unknown),
[] ).
cnf(6,axiom,
( subset(u,v)
| member(member_of_1_not_of_2(u,v),u) ),
file('SET014-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(member_of_1_not_of_2(u,v),v)
| subset(u,v) ),
file('SET014-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,union(v,w))
| member(u,w)
| member(u,v) ),
file('SET014-2.p',unknown),
[] ).
cnf(43,plain,
( ~ member(u,bs)
| member(u,cs) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.0,5.0')] ).
cnf(44,plain,
( ~ member(u,as)
| member(u,cs) ),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.0,5.0')] ).
cnf(48,plain,
( ~ member(member_of_1_not_of_2(u,cs),bs)
| subset(u,cs) ),
inference(res,[status(thm),theory(equality)],[43,7]),
[iquote('0:Res:43.1,7.0')] ).
cnf(85,plain,
( subset(union(u,v),w)
| member(member_of_1_not_of_2(union(u,v),w),v)
| member(member_of_1_not_of_2(union(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[6,12]),
[iquote('0:Res:6.1,12.0')] ).
cnf(320,plain,
( subset(union(u,bs),cs)
| member(member_of_1_not_of_2(union(u,bs),cs),u)
| subset(union(u,bs),cs) ),
inference(res,[status(thm),theory(equality)],[85,48]),
[iquote('0:Res:85.1,48.0')] ).
cnf(339,plain,
( member(member_of_1_not_of_2(union(u,bs),cs),u)
| subset(union(u,bs),cs) ),
inference(obv,[status(thm),theory(equality)],[320]),
[iquote('0:Obv:320.0')] ).
cnf(6735,plain,
( subset(union(as,bs),cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs) ),
inference(res,[status(thm),theory(equality)],[339,44]),
[iquote('0:Res:339.0,44.0')] ).
cnf(6740,plain,
member(member_of_1_not_of_2(union(as,bs),cs),cs),
inference(mrr,[status(thm)],[6735,3]),
[iquote('0:MRR:6735.0,3.0')] ).
cnf(6753,plain,
subset(union(as,bs),cs),
inference(res,[status(thm),theory(equality)],[6740,7]),
[iquote('0:Res:6740.0,7.0')] ).
cnf(6754,plain,
$false,
inference(mrr,[status(thm)],[6753,3]),
[iquote('0:MRR:6753.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Mon Jul 11 09:38:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.04/2.19
% 2.04/2.19 SPASS V 3.9
% 2.04/2.19 SPASS beiseite: Proof found.
% 2.04/2.19 % SZS status Theorem
% 2.04/2.19 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.04/2.19 SPASS derived 5275 clauses, backtracked 0 clauses, performed 0 splits and kept 4193 clauses.
% 2.04/2.19 SPASS allocated 71838 KBytes.
% 2.04/2.19 SPASS spent 0:00:01.75 on the problem.
% 2.04/2.19 0:00:00.04 for the input.
% 2.04/2.19 0:00:00.00 for the FLOTTER CNF translation.
% 2.04/2.19 0:00:00.08 for inferences.
% 2.04/2.19 0:00:00.00 for the backtracking.
% 2.04/2.19 0:00:01.56 for the reduction.
% 2.04/2.19
% 2.04/2.19
% 2.04/2.19 Here is a proof with depth 5, length 17 :
% 2.04/2.19 % SZS output start Refutation
% See solution above
% 2.04/2.19 Formulae used in the proof : a_subset_of_c b_subset_of_c prove_a_union_b_subset_of_c membership_in_subsets subsets_axiom1 subsets_axiom2 member_of_union_is_member_of_one_set
% 2.04/2.19
%------------------------------------------------------------------------------