TSTP Solution File: SET027+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET027+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 05:22:49 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 7 unt; 1 nHn; 13 RR)
% Number of literals : 20 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc5,skc3),
file('SET027+3.p',unknown),
[] ).
cnf(2,axiom,
subset(skc3,skc4),
file('SET027+3.p',unknown),
[] ).
cnf(4,axiom,
~ subset(skc5,skc4),
file('SET027+3.p',unknown),
[] ).
cnf(5,axiom,
( subset(u,v)
| member(skf1(v,u),u) ),
file('SET027+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(skf1(u,v),u)
| subset(w,u) ),
file('SET027+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET027+3.p',unknown),
[] ).
cnf(8,plain,
( ~ member(u,skc3)
| member(u,skc4) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.0,7.0')] ).
cnf(9,plain,
( ~ member(u,skc5)
| member(u,skc3) ),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.0,7.0')] ).
cnf(10,plain,
member(skf1(skc4,skc5),skc5),
inference(res,[status(thm),theory(equality)],[5,4]),
[iquote('0:Res:5.1,4.0')] ).
cnf(11,plain,
~ member(skf1(skc4,u),skc4),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.1,4.0')] ).
cnf(14,plain,
( ~ member(u,skc5)
| member(u,skc4) ),
inference(res,[status(thm),theory(equality)],[9,8]),
[iquote('0:Res:9.1,8.0')] ).
cnf(19,plain,
~ member(skf1(skc4,u),skc5),
inference(res,[status(thm),theory(equality)],[14,11]),
[iquote('0:Res:14.1,11.0')] ).
cnf(20,plain,
$false,
inference(unc,[status(thm)],[19,10]),
[iquote('0:UnC:19.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 : Sun Jul 10 04:57:47 EDT 2022
% 0.13/0.34 % 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/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 11 clauses, backtracked 0 clauses, performed 0 splits and kept 16 clauses.
% 0.19/0.43 SPASS allocated 85154 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 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 13 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : prove_transitivity_of_subset subset_defn
% 0.19/0.43
%------------------------------------------------------------------------------