TSTP Solution File: SET679+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET679+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 05:28:02 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 20 ( 9 unt; 6 nHn; 20 RR)
% Number of literals : 40 ( 0 equ; 19 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ empty(skc2),
file('SET679+3.p',unknown),
[] ).
cnf(6,axiom,
ilf_type(u,set_type),
file('SET679+3.p',unknown),
[] ).
cnf(11,axiom,
~ not_equal(identity_relation_of(skc2),empty_set),
file('SET679+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ ilf_type(u,set_type)
| ~ member(u,empty_set) ),
file('SET679+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ ilf_type(u,set_type)
| empty(u)
| ilf_type(skf15(u),member_type(u)) ),
file('SET679+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| equal(u,v)
| not_equal(u,v) ),
file('SET679+3.p',unknown),
[] ).
cnf(32,axiom,
( ~ member(u,v)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| member(ordered_pair(u,u),identity_relation_of(v)) ),
file('SET679+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ ilf_type(u,member_type(v))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(u,v)
| empty(v) ),
file('SET679+3.p',unknown),
[] ).
cnf(51,plain,
~ member(u,empty_set),
inference(mrr,[status(thm)],[14,6]),
[iquote('0:MRR:14.0,6.0')] ).
cnf(58,plain,
( empty(u)
| ilf_type(skf15(u),member_type(u)) ),
inference(mrr,[status(thm)],[24,6]),
[iquote('0:MRR:24.0,6.0')] ).
cnf(59,plain,
( not_equal(u,v)
| equal(u,v) ),
inference(mrr,[status(thm)],[27,6]),
[iquote('0:MRR:27.0,27.1,6.0,6.0')] ).
cnf(65,plain,
( ~ ilf_type(u,member_type(v))
| empty(v)
| member(u,v) ),
inference(mrr,[status(thm)],[37,6]),
[iquote('0:MRR:37.1,37.2,6.0,6.0')] ).
cnf(70,plain,
( ~ member(u,v)
| member(ordered_pair(u,u),identity_relation_of(v)) ),
inference(mrr,[status(thm)],[32,6]),
[iquote('0:MRR:32.1,32.2,6.0,6.0')] ).
cnf(80,plain,
ilf_type(skf15(skc2),member_type(skc2)),
inference(res,[status(thm),theory(equality)],[58,2]),
[iquote('0:Res:58.0,2.0')] ).
cnf(82,plain,
( ~ ilf_type(u,member_type(skc2))
| member(u,skc2) ),
inference(res,[status(thm),theory(equality)],[65,2]),
[iquote('0:Res:65.2,2.0')] ).
cnf(83,plain,
equal(identity_relation_of(skc2),empty_set),
inference(res,[status(thm),theory(equality)],[59,11]),
[iquote('0:Res:59.1,11.0')] ).
cnf(98,plain,
member(skf15(skc2),skc2),
inference(res,[status(thm),theory(equality)],[80,82]),
[iquote('0:Res:80.0,82.0')] ).
cnf(113,plain,
( ~ member(u,skc2)
| member(ordered_pair(u,u),empty_set) ),
inference(spr,[status(thm),theory(equality)],[83,70]),
[iquote('0:SpR:83.0,70.1')] ).
cnf(115,plain,
~ member(u,skc2),
inference(mrr,[status(thm)],[113,51]),
[iquote('0:MRR:113.1,51.0')] ).
cnf(116,plain,
$false,
inference(unc,[status(thm)],[115,98]),
[iquote('0:UnC:115.0,98.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET679+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.12 % 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 16:14:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 33 clauses, backtracked 0 clauses, performed 0 splits and kept 56 clauses.
% 0.19/0.44 SPASS allocated 97779 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.44 0:00:00.03 for the input.
% 0.19/0.44 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.00 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 2, length 20 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : prove_relset_1_46 p22 p2 p21 p7 p1 p20
% 0.19/0.44
%------------------------------------------------------------------------------