TSTP Solution File: SET014+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:22:30 EDT 2022
% Result : Theorem 1.38s 1.58s
% Output : Refutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 7 unt; 7 nHn; 18 RR)
% Number of literals : 34 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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(1,axiom,
subset(skc5,skc3),
file('SET014+3.p',unknown),
[] ).
cnf(2,axiom,
subset(skc4,skc3),
file('SET014+3.p',unknown),
[] ).
cnf(4,axiom,
~ subset(union(skc5,skc4),skc3),
file('SET014+3.p',unknown),
[] ).
cnf(5,axiom,
equal(union(u,v),union(v,u)),
file('SET014+3.p',unknown),
[] ).
cnf(6,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET014+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET014+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET014+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET014+3.p',unknown),
[] ).
cnf(16,plain,
~ subset(union(skc4,skc5),skc3),
inference(rew,[status(thm),theory(equality)],[5,4]),
[iquote('0:Rew:5.0,4.0')] ).
cnf(17,plain,
( ~ member(u,skc4)
| member(u,skc3) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.0')] ).
cnf(18,plain,
( ~ member(u,skc5)
| member(u,skc3) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(62,plain,
( subset(union(u,v),w)
| member(skf2(w,union(u,v)),u)
| member(skf2(w,union(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[6,13]),
[iquote('0:Res:6.1,13.0')] ).
cnf(867,plain,
( subset(union(u,skc5),v)
| member(skf2(v,union(u,skc5)),u)
| member(skf2(v,union(u,skc5)),skc3) ),
inference(res,[status(thm),theory(equality)],[62,18]),
[iquote('0:Res:62.2,18.0')] ).
cnf(2491,plain,
( subset(union(skc4,skc5),u)
| member(skf2(u,union(skc4,skc5)),skc3)
| member(skf2(u,union(skc4,skc5)),skc3) ),
inference(res,[status(thm),theory(equality)],[867,17]),
[iquote('0:Res:867.1,17.0')] ).
cnf(2506,plain,
( subset(union(skc4,skc5),u)
| member(skf2(u,union(skc4,skc5)),skc3) ),
inference(obv,[status(thm),theory(equality)],[2491]),
[iquote('0:Obv:2491.1')] ).
cnf(4394,plain,
( subset(union(skc4,skc5),skc3)
| subset(u,skc3) ),
inference(res,[status(thm),theory(equality)],[2506,9]),
[iquote('0:Res:2506.1,9.0')] ).
cnf(4405,plain,
subset(union(skc4,skc5),skc3),
inference(con,[status(thm)],[4394]),
[iquote('0:Con:4394.1')] ).
cnf(4406,plain,
$false,
inference(mrr,[status(thm)],[4405,16]),
[iquote('0:MRR:4405.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.13 % Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 13:28:32 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.38/1.58
% 1.38/1.58 SPASS V 3.9
% 1.38/1.58 SPASS beiseite: Proof found.
% 1.38/1.58 % SZS status Theorem
% 1.38/1.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.38/1.58 SPASS derived 3681 clauses, backtracked 220 clauses, performed 4 splits and kept 1873 clauses.
% 1.38/1.58 SPASS allocated 88549 KBytes.
% 1.38/1.58 SPASS spent 0:00:01.20 on the problem.
% 1.38/1.58 0:00:00.04 for the input.
% 1.38/1.58 0:00:00.03 for the FLOTTER CNF translation.
% 1.38/1.58 0:00:00.05 for inferences.
% 1.38/1.58 0:00:00.00 for the backtracking.
% 1.38/1.58 0:00:01.05 for the reduction.
% 1.38/1.58
% 1.38/1.58
% 1.38/1.58 Here is a proof with depth 4, length 18 :
% 1.38/1.58 % SZS output start Refutation
% See solution above
% 1.38/1.58 Formulae used in the proof : prove_union_subset commutativity_of_union subset_defn union_defn
% 1.38/1.58
%------------------------------------------------------------------------------