TSTP Solution File: SET008+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:22:22 EDT 2022
% Result : Theorem 0.82s 1.05s
% Output : Refutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 9 unt; 5 nHn; 22 RR)
% Number of literals : 36 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ member(u,empty_set),
file('SET008+3.p',unknown),
[] ).
cnf(3,axiom,
( empty(u)
| member(skf4(u),u) ),
file('SET008+3.p',unknown),
[] ).
cnf(6,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET008+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ empty(u)
| ~ member(v,u) ),
file('SET008+3.p',unknown),
[] ).
cnf(8,axiom,
~ equal(intersection(difference(skc3,skc2),skc2),empty_set),
file('SET008+3.p',unknown),
[] ).
cnf(9,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET008+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET008+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET008+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| ~ member(u,difference(w,v)) ),
file('SET008+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET008+3.p',unknown),
[] ).
cnf(23,plain,
~ equal(intersection(skc2,difference(skc3,skc2)),empty_set),
inference(rew,[status(thm),theory(equality)],[6,8]),
[iquote('0:Rew:6.0,8.0')] ).
cnf(24,plain,
( ~ subset(empty_set,intersection(skc2,difference(skc3,skc2)))
| ~ subset(intersection(skc2,difference(skc3,skc2)),empty_set) ),
inference(res,[status(thm),theory(equality)],[15,23]),
[iquote('0:Res:15.2,23.0')] ).
cnf(36,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.1,2.0')] ).
cnf(37,plain,
( ~ empty(u)
| subset(u,v) ),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.1,7.1')] ).
cnf(38,plain,
~ subset(intersection(skc2,difference(skc3,skc2)),empty_set),
inference(mrr,[status(thm)],[24,36]),
[iquote('0:MRR:24.0,36.0')] ).
cnf(42,plain,
~ empty(intersection(skc2,difference(skc3,skc2))),
inference(res,[status(thm),theory(equality)],[37,38]),
[iquote('0:Res:37.1,38.0')] ).
cnf(47,plain,
( empty(intersection(u,v))
| member(skf4(intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.1,11.0')] ).
cnf(51,plain,
( empty(intersection(u,v))
| member(skf4(intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[3,10]),
[iquote('0:Res:3.1,10.0')] ).
cnf(101,plain,
( ~ member(skf4(intersection(u,difference(v,w))),w)
| empty(intersection(u,difference(v,w))) ),
inference(res,[status(thm),theory(equality)],[47,14]),
[iquote('0:Res:47.1,14.1')] ).
cnf(6745,plain,
( empty(intersection(u,difference(v,u)))
| empty(intersection(u,difference(v,u))) ),
inference(res,[status(thm),theory(equality)],[51,101]),
[iquote('0:Res:51.1,101.0')] ).
cnf(6756,plain,
empty(intersection(u,difference(v,u))),
inference(obv,[status(thm),theory(equality)],[6745]),
[iquote('0:Obv:6745.0')] ).
cnf(6757,plain,
$false,
inference(unc,[status(thm)],[6756,42]),
[iquote('0:UnC:6756.0,42.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n016.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 : Mon Jul 11 02:14:57 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.82/1.05
% 0.82/1.05 SPASS V 3.9
% 0.82/1.05 SPASS beiseite: Proof found.
% 0.82/1.05 % SZS status Theorem
% 0.82/1.05 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.82/1.05 SPASS derived 4613 clauses, backtracked 0 clauses, performed 0 splits and kept 781 clauses.
% 0.82/1.05 SPASS allocated 101432 KBytes.
% 0.82/1.05 SPASS spent 0:00:00.66 on the problem.
% 0.82/1.05 0:00:00.03 for the input.
% 0.82/1.05 0:00:00.03 for the FLOTTER CNF translation.
% 0.82/1.05 0:00:00.06 for inferences.
% 0.82/1.05 0:00:00.00 for the backtracking.
% 0.82/1.05 0:00:00.51 for the reduction.
% 0.82/1.05
% 0.82/1.05
% 0.82/1.05 Here is a proof with depth 3, length 22 :
% 0.82/1.05 % SZS output start Refutation
% See solution above
% 0.82/1.05 Formulae used in the proof : empty_set_defn empty_defn commutativity_of_intersection prove_intersection_difference_empty_set subset_defn intersection_defn difference_defn equal_defn
% 0.82/1.05
%------------------------------------------------------------------------------