%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 05:24:30 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 10 unt; 3 nHn; 18 RR)
% Number of literals : 27 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ member(u,empty_set),
file('SET146+3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(intersection(skc1,empty_set),empty_set),
file('SET146+3.p',unknown),
[] ).
cnf(4,axiom,
( empty(u)
| member(skf4(u),u) ),
file('SET146+3.p',unknown),
[] ).
cnf(7,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET146+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ empty(u)
| ~ member(v,u) ),
file('SET146+3.p',unknown),
[] ).
cnf(9,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET146+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET146+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET146+3.p',unknown),
[] ).
cnf(20,plain,
~ equal(intersection(empty_set,skc1),empty_set),
inference(rew,[status(thm),theory(equality)],[7,3]),
[iquote('0:Rew:7.0,3.0')] ).
cnf(21,plain,
( ~ subset(empty_set,intersection(empty_set,skc1))
| ~ subset(intersection(empty_set,skc1),empty_set) ),
inference(res,[status(thm),theory(equality)],[13,20]),
[iquote('0:Res:13.2,20.0')] ).
cnf(33,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.1,2.0')] ).
cnf(34,plain,
( ~ empty(u)
| subset(u,v) ),
inference(res,[status(thm),theory(equality)],[9,8]),
[iquote('0:Res:9.1,8.1')] ).
cnf(35,plain,
~ subset(intersection(empty_set,skc1),empty_set),
inference(mrr,[status(thm)],[21,33]),
[iquote('0:MRR:21.0,33.0')] ).
cnf(39,plain,
~ empty(intersection(empty_set,skc1)),
inference(res,[status(thm),theory(equality)],[34,35]),
[iquote('0:Res:34.1,35.0')] ).
cnf(42,plain,
( empty(intersection(u,v))
| member(skf4(intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[4,11]),
[iquote('0:Res:4.1,11.0')] ).
cnf(50,plain,
empty(intersection(u,empty_set)),
inference(res,[status(thm),theory(equality)],[42,2]),
[iquote('0:Res:42.1,2.0')] ).
cnf(54,plain,
empty(intersection(empty_set,u)),
inference(spr,[status(thm),theory(equality)],[7,50]),
[iquote('0:SpR:7.0,50.0')] ).
cnf(56,plain,
$false,
inference(unc,[status(thm)],[54,39]),
[iquote('0:UnC:54.0,39.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 00:47:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 31 clauses, backtracked 0 clauses, performed 0 splits and kept 35 clauses.
% 0.19/0.43 SPASS allocated 97826 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.43 0:00:00.03 for the input.
% 0.19/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.00 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 3, length 18 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : empty_set_defn prove_th61 empty_defn commutativity_of_intersection subset_defn intersection_defn equal_defn
% 0.19/0.43
%------------------------------------------------------------------------------