%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM042-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 : Mon Jul 18 14:23:50 EDT 2022
% Result : Unsatisfiable 44.75s 44.92s
% Output : Refutation 44.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 7 unt; 3 nHn; 16 RR)
% Number of literals : 26 ( 0 equ; 8 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 : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subclass(x__dfg,complement(identity_relation)),
file('NUM042-1.p',unknown),
[] ).
cnf(2,axiom,
~ irreflexive(x__dfg,domain_of(symmetrization_of(x__dfg))),
file('NUM042-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('NUM042-1.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('NUM042-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('NUM042-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('NUM042-1.p',unknown),
[] ).
cnf(31,axiom,
equal(intersection(cross_product(u,v),w),restrict(w,u,v)),
file('NUM042-1.p',unknown),
[] ).
cnf(117,axiom,
( ~ subclass(restrict(u,v,v),complement(identity_relation))
| irreflexive(u,v) ),
file('NUM042-1.p',unknown),
[] ).
cnf(164,plain,
( ~ member(u,x__dfg)
| member(u,complement(identity_relation)) ),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.0')] ).
cnf(287,plain,
( ~ member(not_subclass_element(u,complement(identity_relation)),x__dfg)
| subclass(u,complement(identity_relation)) ),
inference(res,[status(thm),theory(equality)],[164,5]),
[iquote('0:Res:164.1,5.0')] ).
cnf(372,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[4,24]),
[iquote('0:Res:4.1,24.0')] ).
cnf(82944,plain,
( subclass(intersection(u,x__dfg),complement(identity_relation))
| subclass(intersection(u,x__dfg),complement(identity_relation)) ),
inference(res,[status(thm),theory(equality)],[372,287]),
[iquote('0:Res:372.1,287.0')] ).
cnf(82950,plain,
subclass(intersection(u,x__dfg),complement(identity_relation)),
inference(obv,[status(thm),theory(equality)],[82944]),
[iquote('0:Obv:82944.0')] ).
cnf(82956,plain,
subclass(restrict(x__dfg,u,v),complement(identity_relation)),
inference(spr,[status(thm),theory(equality)],[31,82950]),
[iquote('0:SpR:31.0,82950.0')] ).
cnf(82991,plain,
irreflexive(x__dfg,u),
inference(res,[status(thm),theory(equality)],[82956,117]),
[iquote('0:Res:82956.0,117.0')] ).
cnf(82992,plain,
$false,
inference(unc,[status(thm)],[82991,2]),
[iquote('0:UnC:82991.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM042-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 10:25:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 44.75/44.92
% 44.75/44.92 SPASS V 3.9
% 44.75/44.92 SPASS beiseite: Proof found.
% 44.75/44.92 % SZS status Theorem
% 44.75/44.92 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.75/44.92 SPASS derived 69041 clauses, backtracked 11256 clauses, performed 53 splits and kept 34684 clauses.
% 44.75/44.92 SPASS allocated 130792 KBytes.
% 44.75/44.92 SPASS spent 0:0:43.49 on the problem.
% 44.75/44.92 0:00:00.04 for the input.
% 44.75/44.92 0:00:00.00 for the FLOTTER CNF translation.
% 44.75/44.92 0:00:00.92 for inferences.
% 44.75/44.92 0:00:04.49 for the backtracking.
% 44.75/44.92 0:0:37.13 for the reduction.
% 44.75/44.92
% 44.75/44.92
% 44.75/44.92 Here is a proof with depth 5, length 16 :
% 44.75/44.92 % SZS output start Refutation
% See solution above
% 44.75/44.92 Formulae used in the proof : prove_irreflexive_class_property4_1 prove_irreflexive_class_property4_2 subclass_members not_subclass_members1 not_subclass_members2 intersection2 restriction2 irreflexive2
% 44.75/44.92
%------------------------------------------------------------------------------