%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET627+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 05:27:38 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 1 nHn; 9 RR)
% Number of literals : 12 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ disjoint(skc1,empty_set),
file('SET627+3.p',unknown),
[] ).
cnf(2,axiom,
~ member(u,empty_set),
file('SET627+3.p',unknown),
[] ).
cnf(3,axiom,
( disjoint(u,v)
| intersect(u,v) ),
file('SET627+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ intersect(u,v)
| intersect(v,u) ),
file('SET627+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ intersect(u,v)
| member(skf2(v,u),u) ),
file('SET627+3.p',unknown),
[] ).
cnf(11,plain,
intersect(skc1,empty_set),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.1,1.0')] ).
cnf(15,plain,
intersect(empty_set,skc1),
inference(res,[status(thm),theory(equality)],[11,5]),
[iquote('0:Res:11.0,5.0')] ).
cnf(23,plain,
~ intersect(empty_set,u),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.1,2.0')] ).
cnf(25,plain,
$false,
inference(unc,[status(thm)],[23,15]),
[iquote('0:UnC:23.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET627+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 14:58:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 18 clauses.
% 0.18/0.43 SPASS allocated 97651 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 2, length 9 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : prove_th104 empty_set_defn disjoint_defn symmetry_of_intersect intersect_defn
% 0.18/0.43
%------------------------------------------------------------------------------