TSTP Solution File: TOP005-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 : Thu Jul 21 21:32:21 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 52 ( 4 unt; 26 nHn; 35 RR)
% Number of literals : 124 ( 0 equ; 47 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 77 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(union_of_members_1,axiom,
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ) ).
cnf(union_of_members_2,axiom,
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ) ).
cnf(topology_generated_37,axiom,
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_set(X,f10(Vf,U,X)) ) ).
cnf(topology_generated_38,axiom,
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_collection(f10(Vf,U,X),Vf) ) ).
cnf(topology_generated_39,axiom,
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| subset_sets(f10(Vf,U,X),U) ) ).
cnf(topology_generated_40,axiom,
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ) ).
cnf(topology_generated_41,axiom,
( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11)
| ~ element_of_collection(Uu11,Vf)
| ~ subset_sets(Uu11,U) ) ).
cnf(set_theory_20,axiom,
( ~ subset_sets(X,Y)
| ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z)) ) ).
cnf(set_theory_21,axiom,
( ~ subset_collections(X,Y)
| ~ element_of_collection(U,X)
| element_of_collection(U,Y) ) ).
cnf(lemma_1e_2,negated_conjecture,
subset_collections(g,top_of_basis(f)) ).
cnf(lemma_1e_3,negated_conjecture,
~ element_of_collection(union_of_members(g),top_of_basis(f)) ).
cnf(refute_0_0,plain,
( ~ element_of_set(f11(X_5,union_of_members(Vf)),union_of_members(Vf))
| element_of_set(f11(X_5,union_of_members(Vf)),f1(Vf,f11(X_5,union_of_members(Vf)))) ),
inference(subst,[],[union_of_members_1:[bind(U,$fot(f11(X_5,union_of_members(Vf))))]]) ).
cnf(refute_0_1,plain,
( element_of_collection(union_of_members(Vf),top_of_basis(X_5))
| element_of_set(f11(X_5,union_of_members(Vf)),union_of_members(Vf)) ),
inference(subst,[],[topology_generated_40:[bind(U,$fot(union_of_members(Vf))),bind(Vf,$fot(X_5))]]) ).
cnf(refute_0_2,plain,
( element_of_collection(union_of_members(Vf),top_of_basis(X_5))
| element_of_set(f11(X_5,union_of_members(Vf)),f1(Vf,f11(X_5,union_of_members(Vf)))) ),
inference(resolve,[$cnf( element_of_set(f11(X_5,union_of_members(Vf)),union_of_members(Vf)) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( element_of_collection(union_of_members(g),top_of_basis(X_71))
| element_of_set(f11(X_71,union_of_members(g)),f1(g,f11(X_71,union_of_members(g)))) ),
inference(subst,[],[refute_0_2:[bind(Vf,$fot(g)),bind(X_5,$fot(X_71))]]) ).
cnf(refute_0_4,plain,
( ~ element_of_set(f11(X_5,union_of_members(Vf)),union_of_members(Vf))
| element_of_collection(f1(Vf,f11(X_5,union_of_members(Vf))),Vf) ),
inference(subst,[],[union_of_members_2:[bind(U,$fot(f11(X_5,union_of_members(Vf))))]]) ).
cnf(refute_0_5,plain,
( element_of_collection(f1(Vf,f11(X_5,union_of_members(Vf))),Vf)
| element_of_collection(union_of_members(Vf),top_of_basis(X_5)) ),
inference(resolve,[$cnf( element_of_set(f11(X_5,union_of_members(Vf)),union_of_members(Vf)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
( element_of_collection(f1(g,f11(X_5,union_of_members(g))),g)
| element_of_collection(union_of_members(g),top_of_basis(X_5)) ),
inference(subst,[],[refute_0_5:[bind(Vf,$fot(g))]]) ).
cnf(refute_0_7,plain,
( ~ element_of_collection(X_14,g)
| ~ subset_collections(g,top_of_basis(f))
| element_of_collection(X_14,top_of_basis(f)) ),
inference(subst,[],[set_theory_21:[bind(U,$fot(X_14)),bind(X,$fot(g)),bind(Y,$fot(top_of_basis(f)))]]) ).
cnf(refute_0_8,plain,
( ~ element_of_collection(X_14,g)
| element_of_collection(X_14,top_of_basis(f)) ),
inference(resolve,[$cnf( subset_collections(g,top_of_basis(f)) )],[lemma_1e_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ element_of_collection(f1(g,f11(X_5,union_of_members(g))),g)
| element_of_collection(f1(g,f11(X_5,union_of_members(g))),top_of_basis(f)) ),
inference(subst,[],[refute_0_8:[bind(X_14,$fot(f1(g,f11(X_5,union_of_members(g)))))]]) ).
cnf(refute_0_10,plain,
( element_of_collection(f1(g,f11(X_5,union_of_members(g))),top_of_basis(f))
| element_of_collection(union_of_members(g),top_of_basis(X_5)) ),
inference(resolve,[$cnf( element_of_collection(f1(g,f11(X_5,union_of_members(g))),g) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ element_of_collection(f1(g,f11(X_5,union_of_members(g))),top_of_basis(f))
| ~ element_of_set(X_29,f1(g,f11(X_5,union_of_members(g))))
| element_of_collection(f10(f,f1(g,f11(X_5,union_of_members(g))),X_29),f) ),
inference(subst,[],[topology_generated_38:[bind(U,$fot(f1(g,f11(X_5,union_of_members(g))))),bind(Vf,$fot(f)),bind(X,$fot(X_29))]]) ).
cnf(refute_0_12,plain,
( ~ element_of_set(X_29,f1(g,f11(X_5,union_of_members(g))))
| element_of_collection(f10(f,f1(g,f11(X_5,union_of_members(g))),X_29),f)
| element_of_collection(union_of_members(g),top_of_basis(X_5)) ),
inference(resolve,[$cnf( element_of_collection(f1(g,f11(X_5,union_of_members(g))),top_of_basis(f)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ element_of_set(f11(X_71,union_of_members(g)),f1(g,f11(X_71,union_of_members(g))))
| element_of_collection(f10(f,f1(g,f11(X_71,union_of_members(g))),f11(X_71,union_of_members(g))),f)
| element_of_collection(union_of_members(g),top_of_basis(X_71)) ),
inference(subst,[],[refute_0_12:[bind(X_29,$fot(f11(X_71,union_of_members(g)))),bind(X_5,$fot(X_71))]]) ).
cnf(refute_0_14,plain,
( element_of_collection(f10(f,f1(g,f11(X_71,union_of_members(g))),f11(X_71,union_of_members(g))),f)
| element_of_collection(union_of_members(g),top_of_basis(X_71)) ),
inference(resolve,[$cnf( element_of_set(f11(X_71,union_of_members(g)),f1(g,f11(X_71,union_of_members(g)))) )],[refute_0_3,refute_0_13]) ).
cnf(refute_0_15,plain,
( element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
| element_of_collection(union_of_members(g),top_of_basis(f)) ),
inference(subst,[],[refute_0_14:[bind(X_71,$fot(f))]]) ).
cnf(refute_0_16,plain,
( element_of_collection(f1(X_10,f11(X_5,union_of_members(X_10))),X_10)
| element_of_collection(union_of_members(X_10),top_of_basis(X_5)) ),
inference(subst,[],[refute_0_5:[bind(Vf,$fot(X_10))]]) ).
cnf(refute_0_17,plain,
( ~ element_of_collection(f1(X_10,f11(X_5,union_of_members(X_10))),X_10)
| ~ subset_sets(X_8,f1(X_10,f11(X_5,union_of_members(X_10))))
| subset_sets(X_8,union_of_members(X_10)) ),
inference(subst,[],[set_theory_20:[bind(X,$fot(X_8)),bind(Y,$fot(f1(X_10,f11(X_5,union_of_members(X_10))))),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_18,plain,
( ~ subset_sets(X_8,f1(X_10,f11(X_5,union_of_members(X_10))))
| element_of_collection(union_of_members(X_10),top_of_basis(X_5))
| subset_sets(X_8,union_of_members(X_10)) ),
inference(resolve,[$cnf( element_of_collection(f1(X_10,f11(X_5,union_of_members(X_10))),X_10) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ subset_sets(f10(f,f1(g,f11(X_83,union_of_members(g))),f11(X_83,union_of_members(g))),f1(g,f11(X_83,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X_83))
| subset_sets(f10(f,f1(g,f11(X_83,union_of_members(g))),f11(X_83,union_of_members(g))),union_of_members(g)) ),
inference(subst,[],[refute_0_18:[bind(X_10,$fot(g)),bind(X_5,$fot(X_83)),bind(X_8,$fot(f10(f,f1(g,f11(X_83,union_of_members(g))),f11(X_83,union_of_members(g)))))]]) ).
cnf(refute_0_20,plain,
( element_of_collection(union_of_members(g),top_of_basis(X_82))
| element_of_set(f11(X_82,union_of_members(g)),f1(g,f11(X_82,union_of_members(g)))) ),
inference(subst,[],[refute_0_2:[bind(Vf,$fot(g)),bind(X_5,$fot(X_82))]]) ).
cnf(refute_0_21,plain,
( ~ element_of_collection(f1(g,f11(X_5,union_of_members(g))),top_of_basis(f))
| ~ element_of_set(X_32,f1(g,f11(X_5,union_of_members(g))))
| subset_sets(f10(f,f1(g,f11(X_5,union_of_members(g))),X_32),f1(g,f11(X_5,union_of_members(g)))) ),
inference(subst,[],[topology_generated_39:[bind(U,$fot(f1(g,f11(X_5,union_of_members(g))))),bind(Vf,$fot(f)),bind(X,$fot(X_32))]]) ).
cnf(refute_0_22,plain,
( ~ element_of_set(X_32,f1(g,f11(X_5,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X_5))
| subset_sets(f10(f,f1(g,f11(X_5,union_of_members(g))),X_32),f1(g,f11(X_5,union_of_members(g)))) ),
inference(resolve,[$cnf( element_of_collection(f1(g,f11(X_5,union_of_members(g))),top_of_basis(f)) )],[refute_0_10,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ element_of_set(f11(X_82,union_of_members(g)),f1(g,f11(X_82,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X_82))
| subset_sets(f10(f,f1(g,f11(X_82,union_of_members(g))),f11(X_82,union_of_members(g))),f1(g,f11(X_82,union_of_members(g)))) ),
inference(subst,[],[refute_0_22:[bind(X_32,$fot(f11(X_82,union_of_members(g)))),bind(X_5,$fot(X_82))]]) ).
cnf(refute_0_24,plain,
( element_of_collection(union_of_members(g),top_of_basis(X_82))
| subset_sets(f10(f,f1(g,f11(X_82,union_of_members(g))),f11(X_82,union_of_members(g))),f1(g,f11(X_82,union_of_members(g)))) ),
inference(resolve,[$cnf( element_of_set(f11(X_82,union_of_members(g)),f1(g,f11(X_82,union_of_members(g)))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( element_of_collection(union_of_members(g),top_of_basis(X_83))
| subset_sets(f10(f,f1(g,f11(X_83,union_of_members(g))),f11(X_83,union_of_members(g))),f1(g,f11(X_83,union_of_members(g)))) ),
inference(subst,[],[refute_0_24:[bind(X_82,$fot(X_83))]]) ).
cnf(refute_0_26,plain,
( element_of_collection(union_of_members(g),top_of_basis(X_83))
| subset_sets(f10(f,f1(g,f11(X_83,union_of_members(g))),f11(X_83,union_of_members(g))),union_of_members(g)) ),
inference(resolve,[$cnf( subset_sets(f10(f,f1(g,f11(X_83,union_of_members(g))),f11(X_83,union_of_members(g))),f1(g,f11(X_83,union_of_members(g)))) )],[refute_0_25,refute_0_19]) ).
cnf(refute_0_27,plain,
( element_of_collection(union_of_members(g),top_of_basis(X_107))
| subset_sets(f10(f,f1(g,f11(X_107,union_of_members(g))),f11(X_107,union_of_members(g))),union_of_members(g)) ),
inference(subst,[],[refute_0_26:[bind(X_83,$fot(X_107))]]) ).
cnf(refute_0_28,plain,
( ~ element_of_collection(f10(f,f1(g,f11(X_77,union_of_members(g))),f11(X_77,union_of_members(g))),X_77)
| ~ element_of_set(f11(X_77,union_of_members(g)),f10(f,f1(g,f11(X_77,union_of_members(g))),f11(X_77,union_of_members(g))))
| ~ subset_sets(f10(f,f1(g,f11(X_77,union_of_members(g))),f11(X_77,union_of_members(g))),union_of_members(g))
| element_of_collection(union_of_members(g),top_of_basis(X_77)) ),
inference(subst,[],[topology_generated_41:[bind(U,$fot(union_of_members(g))),bind(Uu11,$fot(f10(f,f1(g,f11(X_77,union_of_members(g))),f11(X_77,union_of_members(g))))),bind(Vf,$fot(X_77))]]) ).
cnf(refute_0_29,plain,
( element_of_collection(union_of_members(g),top_of_basis(X_76))
| element_of_set(f11(X_76,union_of_members(g)),f1(g,f11(X_76,union_of_members(g)))) ),
inference(subst,[],[refute_0_2:[bind(Vf,$fot(g)),bind(X_5,$fot(X_76))]]) ).
cnf(refute_0_30,plain,
( ~ element_of_collection(f1(g,f11(X_5,union_of_members(g))),top_of_basis(f))
| ~ element_of_set(X_26,f1(g,f11(X_5,union_of_members(g))))
| element_of_set(X_26,f10(f,f1(g,f11(X_5,union_of_members(g))),X_26)) ),
inference(subst,[],[topology_generated_37:[bind(U,$fot(f1(g,f11(X_5,union_of_members(g))))),bind(Vf,$fot(f)),bind(X,$fot(X_26))]]) ).
cnf(refute_0_31,plain,
( ~ element_of_set(X_26,f1(g,f11(X_5,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X_5))
| element_of_set(X_26,f10(f,f1(g,f11(X_5,union_of_members(g))),X_26)) ),
inference(resolve,[$cnf( element_of_collection(f1(g,f11(X_5,union_of_members(g))),top_of_basis(f)) )],[refute_0_10,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ element_of_set(f11(X_76,union_of_members(g)),f1(g,f11(X_76,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X_76))
| element_of_set(f11(X_76,union_of_members(g)),f10(f,f1(g,f11(X_76,union_of_members(g))),f11(X_76,union_of_members(g)))) ),
inference(subst,[],[refute_0_31:[bind(X_26,$fot(f11(X_76,union_of_members(g)))),bind(X_5,$fot(X_76))]]) ).
cnf(refute_0_33,plain,
( element_of_collection(union_of_members(g),top_of_basis(X_76))
| element_of_set(f11(X_76,union_of_members(g)),f10(f,f1(g,f11(X_76,union_of_members(g))),f11(X_76,union_of_members(g)))) ),
inference(resolve,[$cnf( element_of_set(f11(X_76,union_of_members(g)),f1(g,f11(X_76,union_of_members(g)))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( element_of_collection(union_of_members(g),top_of_basis(X_77))
| element_of_set(f11(X_77,union_of_members(g)),f10(f,f1(g,f11(X_77,union_of_members(g))),f11(X_77,union_of_members(g)))) ),
inference(subst,[],[refute_0_33:[bind(X_76,$fot(X_77))]]) ).
cnf(refute_0_35,plain,
( ~ element_of_collection(f10(f,f1(g,f11(X_77,union_of_members(g))),f11(X_77,union_of_members(g))),X_77)
| ~ subset_sets(f10(f,f1(g,f11(X_77,union_of_members(g))),f11(X_77,union_of_members(g))),union_of_members(g))
| element_of_collection(union_of_members(g),top_of_basis(X_77)) ),
inference(resolve,[$cnf( element_of_set(f11(X_77,union_of_members(g)),f10(f,f1(g,f11(X_77,union_of_members(g))),f11(X_77,union_of_members(g)))) )],[refute_0_34,refute_0_28]) ).
cnf(refute_0_36,plain,
( ~ element_of_collection(f10(f,f1(g,f11(X_107,union_of_members(g))),f11(X_107,union_of_members(g))),X_107)
| ~ subset_sets(f10(f,f1(g,f11(X_107,union_of_members(g))),f11(X_107,union_of_members(g))),union_of_members(g))
| element_of_collection(union_of_members(g),top_of_basis(X_107)) ),
inference(subst,[],[refute_0_35:[bind(X_77,$fot(X_107))]]) ).
cnf(refute_0_37,plain,
( ~ element_of_collection(f10(f,f1(g,f11(X_107,union_of_members(g))),f11(X_107,union_of_members(g))),X_107)
| element_of_collection(union_of_members(g),top_of_basis(X_107)) ),
inference(resolve,[$cnf( subset_sets(f10(f,f1(g,f11(X_107,union_of_members(g))),f11(X_107,union_of_members(g))),union_of_members(g)) )],[refute_0_27,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
| element_of_collection(union_of_members(g),top_of_basis(f)) ),
inference(subst,[],[refute_0_37:[bind(X_107,$fot(f))]]) ).
cnf(refute_0_39,plain,
element_of_collection(union_of_members(g),top_of_basis(f)),
inference(resolve,[$cnf( element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) )],[refute_0_15,refute_0_38]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( element_of_collection(union_of_members(g),top_of_basis(f)) )],[refute_0_39,lemma_1e_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n019.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 May 29 12:28:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.40
% 0.20/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.41
%------------------------------------------------------------------------------