TSTP Solution File: TOP001-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 48 ( 6 unt; 22 nHn; 33 RR)
% Number of literals : 104 ( 0 equ; 35 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 81 ( 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(union_of_members_3,axiom,
( element_of_set(U,union_of_members(Vf))
| ~ element_of_set(U,Uu1)
| ~ element_of_collection(Uu1,Vf) ) ).
cnf(basis_for_topology_28,axiom,
( ~ basis(X,Vf)
| equal_sets(union_of_members(Vf),X) ) ).
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(set_theory_2,axiom,
( ~ subset_sets(X,Y)
| ~ element_of_set(U,X)
| element_of_set(U,Y) ) ).
cnf(set_theory_3,axiom,
( ~ equal_sets(X,Y)
| subset_sets(X,Y) ) ).
cnf(set_theory_4,axiom,
( subset_sets(X,Y)
| element_of_set(in_1st_set(X,Y),X) ) ).
cnf(set_theory_5,axiom,
( subset_sets(X,Y)
| ~ element_of_set(in_1st_set(X,Y),Y) ) ).
cnf(lemma_1a_1,negated_conjecture,
basis(cx,f) ).
cnf(lemma_1a_2,negated_conjecture,
~ subset_sets(union_of_members(top_of_basis(f)),cx) ).
cnf(refute_0_0,plain,
( ~ element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),cx)
| subset_sets(union_of_members(top_of_basis(f)),cx) ),
inference(subst,[],[set_theory_5:[bind(X,$fot(union_of_members(top_of_basis(f)))),bind(Y,$fot(cx))]]) ).
cnf(refute_0_1,plain,
( ~ equal_sets(union_of_members(f),cx)
| subset_sets(union_of_members(f),cx) ),
inference(subst,[],[set_theory_3:[bind(X,$fot(union_of_members(f))),bind(Y,$fot(cx))]]) ).
cnf(refute_0_2,plain,
( ~ basis(cx,f)
| equal_sets(union_of_members(f),cx) ),
inference(subst,[],[basis_for_topology_28:[bind(Vf,$fot(f)),bind(X,$fot(cx))]]) ).
cnf(refute_0_3,plain,
equal_sets(union_of_members(f),cx),
inference(resolve,[$cnf( basis(cx,f) )],[lemma_1a_1,refute_0_2]) ).
cnf(refute_0_4,plain,
subset_sets(union_of_members(f),cx),
inference(resolve,[$cnf( equal_sets(union_of_members(f),cx) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
( ~ element_of_set(X_17,union_of_members(f))
| ~ subset_sets(union_of_members(f),cx)
| element_of_set(X_17,cx) ),
inference(subst,[],[set_theory_2:[bind(U,$fot(X_17)),bind(X,$fot(union_of_members(f))),bind(Y,$fot(cx))]]) ).
cnf(refute_0_6,plain,
( ~ element_of_set(X_17,union_of_members(f))
| element_of_set(X_17,cx) ),
inference(resolve,[$cnf( subset_sets(union_of_members(f),cx) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ element_of_set(in_1st_set(union_of_members(top_of_basis(f)),X_95),union_of_members(f))
| element_of_set(in_1st_set(union_of_members(top_of_basis(f)),X_95),cx) ),
inference(subst,[],[refute_0_6:[bind(X_17,$fot(in_1st_set(union_of_members(top_of_basis(f)),X_95)))]]) ).
cnf(refute_0_8,plain,
( element_of_set(in_1st_set(union_of_members(X_10),Y),union_of_members(X_10))
| subset_sets(union_of_members(X_10),Y) ),
inference(subst,[],[set_theory_4:[bind(X,$fot(union_of_members(X_10)))]]) ).
cnf(refute_0_9,plain,
( ~ element_of_set(in_1st_set(union_of_members(X_10),Y),union_of_members(X_10))
| element_of_set(in_1st_set(union_of_members(X_10),Y),f1(X_10,in_1st_set(union_of_members(X_10),Y))) ),
inference(subst,[],[union_of_members_1:[bind(U,$fot(in_1st_set(union_of_members(X_10),Y))),bind(Vf,$fot(X_10))]]) ).
cnf(refute_0_10,plain,
( element_of_set(in_1st_set(union_of_members(X_10),Y),f1(X_10,in_1st_set(union_of_members(X_10),Y)))
| subset_sets(union_of_members(X_10),Y) ),
inference(resolve,[$cnf( element_of_set(in_1st_set(union_of_members(X_10),Y),union_of_members(X_10)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( element_of_set(in_1st_set(union_of_members(top_of_basis(X_76)),X_75),f1(top_of_basis(X_76),in_1st_set(union_of_members(top_of_basis(X_76)),X_75)))
| subset_sets(union_of_members(top_of_basis(X_76)),X_75) ),
inference(subst,[],[refute_0_10:[bind(Y,$fot(X_75)),bind(X_10,$fot(top_of_basis(X_76)))]]) ).
cnf(refute_0_12,plain,
( element_of_set(in_1st_set(union_of_members(X_12),Y),union_of_members(X_12))
| subset_sets(union_of_members(X_12),Y) ),
inference(subst,[],[set_theory_4:[bind(X,$fot(union_of_members(X_12)))]]) ).
cnf(refute_0_13,plain,
( ~ element_of_set(in_1st_set(union_of_members(X_12),Y),union_of_members(X_12))
| element_of_collection(f1(X_12,in_1st_set(union_of_members(X_12),Y)),X_12) ),
inference(subst,[],[union_of_members_2:[bind(U,$fot(in_1st_set(union_of_members(X_12),Y))),bind(Vf,$fot(X_12))]]) ).
cnf(refute_0_14,plain,
( element_of_collection(f1(X_12,in_1st_set(union_of_members(X_12),Y)),X_12)
| subset_sets(union_of_members(X_12),Y) ),
inference(resolve,[$cnf( element_of_set(in_1st_set(union_of_members(X_12),Y),union_of_members(X_12)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( element_of_collection(f1(top_of_basis(X_28),in_1st_set(union_of_members(top_of_basis(X_28)),Y)),top_of_basis(X_28))
| subset_sets(union_of_members(top_of_basis(X_28)),Y) ),
inference(subst,[],[refute_0_14:[bind(X_12,$fot(top_of_basis(X_28)))]]) ).
cnf(refute_0_16,plain,
( ~ element_of_collection(f1(top_of_basis(X_28),in_1st_set(union_of_members(top_of_basis(X_28)),Y)),top_of_basis(X_28))
| ~ element_of_set(X_29,f1(top_of_basis(X_28),in_1st_set(union_of_members(top_of_basis(X_28)),Y)))
| element_of_set(X_29,f10(X_28,f1(top_of_basis(X_28),in_1st_set(union_of_members(top_of_basis(X_28)),Y)),X_29)) ),
inference(subst,[],[topology_generated_37:[bind(U,$fot(f1(top_of_basis(X_28),in_1st_set(union_of_members(top_of_basis(X_28)),Y)))),bind(Vf,$fot(X_28)),bind(X,$fot(X_29))]]) ).
cnf(refute_0_17,plain,
( ~ element_of_set(X_29,f1(top_of_basis(X_28),in_1st_set(union_of_members(top_of_basis(X_28)),Y)))
| element_of_set(X_29,f10(X_28,f1(top_of_basis(X_28),in_1st_set(union_of_members(top_of_basis(X_28)),Y)),X_29))
| subset_sets(union_of_members(top_of_basis(X_28)),Y) ),
inference(resolve,[$cnf( element_of_collection(f1(top_of_basis(X_28),in_1st_set(union_of_members(top_of_basis(X_28)),Y)),top_of_basis(X_28)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ element_of_set(in_1st_set(union_of_members(top_of_basis(X_76)),X_75),f1(top_of_basis(X_76),in_1st_set(union_of_members(top_of_basis(X_76)),X_75)))
| element_of_set(in_1st_set(union_of_members(top_of_basis(X_76)),X_75),f10(X_76,f1(top_of_basis(X_76),in_1st_set(union_of_members(top_of_basis(X_76)),X_75)),in_1st_set(union_of_members(top_of_basis(X_76)),X_75)))
| subset_sets(union_of_members(top_of_basis(X_76)),X_75) ),
inference(subst,[],[refute_0_17:[bind(Y,$fot(X_75)),bind(X_28,$fot(X_76)),bind(X_29,$fot(in_1st_set(union_of_members(top_of_basis(X_76)),X_75)))]]) ).
cnf(refute_0_19,plain,
( element_of_set(in_1st_set(union_of_members(top_of_basis(X_76)),X_75),f10(X_76,f1(top_of_basis(X_76),in_1st_set(union_of_members(top_of_basis(X_76)),X_75)),in_1st_set(union_of_members(top_of_basis(X_76)),X_75)))
| subset_sets(union_of_members(top_of_basis(X_76)),X_75) ),
inference(resolve,[$cnf( element_of_set(in_1st_set(union_of_members(top_of_basis(X_76)),X_75),f1(top_of_basis(X_76),in_1st_set(union_of_members(top_of_basis(X_76)),X_75))) )],[refute_0_11,refute_0_18]) ).
cnf(refute_0_20,plain,
( element_of_set(in_1st_set(union_of_members(top_of_basis(X_94)),X_93),f10(X_94,f1(top_of_basis(X_94),in_1st_set(union_of_members(top_of_basis(X_94)),X_93)),in_1st_set(union_of_members(top_of_basis(X_94)),X_93)))
| subset_sets(union_of_members(top_of_basis(X_94)),X_93) ),
inference(subst,[],[refute_0_19:[bind(X_75,$fot(X_93)),bind(X_76,$fot(X_94))]]) ).
cnf(refute_0_21,plain,
( ~ element_of_collection(f10(X_74,f1(top_of_basis(X_74),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)),X_74)
| ~ element_of_set(U,f10(X_74,f1(top_of_basis(X_74),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)))
| element_of_set(U,union_of_members(X_74)) ),
inference(subst,[],[union_of_members_3:[bind(Uu1,$fot(f10(X_74,f1(top_of_basis(X_74),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)))),bind(Vf,$fot(X_74))]]) ).
cnf(refute_0_22,plain,
( element_of_collection(f1(top_of_basis(X_72),in_1st_set(union_of_members(top_of_basis(X_72)),X_70)),top_of_basis(X_72))
| subset_sets(union_of_members(top_of_basis(X_72)),X_70) ),
inference(subst,[],[refute_0_14:[bind(Y,$fot(X_70)),bind(X_12,$fot(top_of_basis(X_72)))]]) ).
cnf(refute_0_23,plain,
( ~ element_of_collection(f1(X_10,in_1st_set(union_of_members(X_10),Y)),top_of_basis(X_31))
| ~ element_of_set(in_1st_set(union_of_members(X_10),Y),f1(X_10,in_1st_set(union_of_members(X_10),Y)))
| element_of_collection(f10(X_31,f1(X_10,in_1st_set(union_of_members(X_10),Y)),in_1st_set(union_of_members(X_10),Y)),X_31) ),
inference(subst,[],[topology_generated_38:[bind(U,$fot(f1(X_10,in_1st_set(union_of_members(X_10),Y)))),bind(Vf,$fot(X_31)),bind(X,$fot(in_1st_set(union_of_members(X_10),Y)))]]) ).
cnf(refute_0_24,plain,
( ~ element_of_collection(f1(X_10,in_1st_set(union_of_members(X_10),Y)),top_of_basis(X_31))
| element_of_collection(f10(X_31,f1(X_10,in_1st_set(union_of_members(X_10),Y)),in_1st_set(union_of_members(X_10),Y)),X_31)
| subset_sets(union_of_members(X_10),Y) ),
inference(resolve,[$cnf( element_of_set(in_1st_set(union_of_members(X_10),Y),f1(X_10,in_1st_set(union_of_members(X_10),Y))) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ element_of_collection(f1(top_of_basis(X_72),in_1st_set(union_of_members(top_of_basis(X_72)),X_70)),top_of_basis(X_72))
| element_of_collection(f10(X_72,f1(top_of_basis(X_72),in_1st_set(union_of_members(top_of_basis(X_72)),X_70)),in_1st_set(union_of_members(top_of_basis(X_72)),X_70)),X_72)
| subset_sets(union_of_members(top_of_basis(X_72)),X_70) ),
inference(subst,[],[refute_0_24:[bind(Y,$fot(X_70)),bind(X_10,$fot(top_of_basis(X_72))),bind(X_31,$fot(X_72))]]) ).
cnf(refute_0_26,plain,
( element_of_collection(f10(X_72,f1(top_of_basis(X_72),in_1st_set(union_of_members(top_of_basis(X_72)),X_70)),in_1st_set(union_of_members(top_of_basis(X_72)),X_70)),X_72)
| subset_sets(union_of_members(top_of_basis(X_72)),X_70) ),
inference(resolve,[$cnf( element_of_collection(f1(top_of_basis(X_72),in_1st_set(union_of_members(top_of_basis(X_72)),X_70)),top_of_basis(X_72)) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
( element_of_collection(f10(X_74,f1(top_of_basis(X_74),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)),X_74)
| subset_sets(union_of_members(top_of_basis(X_74)),X_73) ),
inference(subst,[],[refute_0_26:[bind(X_70,$fot(X_73)),bind(X_72,$fot(X_74))]]) ).
cnf(refute_0_28,plain,
( ~ element_of_set(U,f10(X_74,f1(top_of_basis(X_74),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)))
| element_of_set(U,union_of_members(X_74))
| subset_sets(union_of_members(top_of_basis(X_74)),X_73) ),
inference(resolve,[$cnf( element_of_collection(f10(X_74,f1(top_of_basis(X_74),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)),in_1st_set(union_of_members(top_of_basis(X_74)),X_73)),X_74) )],[refute_0_27,refute_0_21]) ).
cnf(refute_0_29,plain,
( ~ element_of_set(in_1st_set(union_of_members(top_of_basis(X_94)),X_93),f10(X_94,f1(top_of_basis(X_94),in_1st_set(union_of_members(top_of_basis(X_94)),X_93)),in_1st_set(union_of_members(top_of_basis(X_94)),X_93)))
| element_of_set(in_1st_set(union_of_members(top_of_basis(X_94)),X_93),union_of_members(X_94))
| subset_sets(union_of_members(top_of_basis(X_94)),X_93) ),
inference(subst,[],[refute_0_28:[bind(U,$fot(in_1st_set(union_of_members(top_of_basis(X_94)),X_93))),bind(X_73,$fot(X_93)),bind(X_74,$fot(X_94))]]) ).
cnf(refute_0_30,plain,
( element_of_set(in_1st_set(union_of_members(top_of_basis(X_94)),X_93),union_of_members(X_94))
| subset_sets(union_of_members(top_of_basis(X_94)),X_93) ),
inference(resolve,[$cnf( element_of_set(in_1st_set(union_of_members(top_of_basis(X_94)),X_93),f10(X_94,f1(top_of_basis(X_94),in_1st_set(union_of_members(top_of_basis(X_94)),X_93)),in_1st_set(union_of_members(top_of_basis(X_94)),X_93))) )],[refute_0_20,refute_0_29]) ).
cnf(refute_0_31,plain,
( element_of_set(in_1st_set(union_of_members(top_of_basis(f)),X_95),union_of_members(f))
| subset_sets(union_of_members(top_of_basis(f)),X_95) ),
inference(subst,[],[refute_0_30:[bind(X_93,$fot(X_95)),bind(X_94,$fot(f))]]) ).
cnf(refute_0_32,plain,
( element_of_set(in_1st_set(union_of_members(top_of_basis(f)),X_95),cx)
| subset_sets(union_of_members(top_of_basis(f)),X_95) ),
inference(resolve,[$cnf( element_of_set(in_1st_set(union_of_members(top_of_basis(f)),X_95),union_of_members(f)) )],[refute_0_31,refute_0_7]) ).
cnf(refute_0_33,plain,
( element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),cx)
| subset_sets(union_of_members(top_of_basis(f)),cx) ),
inference(subst,[],[refute_0_32:[bind(X_95,$fot(cx))]]) ).
cnf(refute_0_34,plain,
subset_sets(union_of_members(top_of_basis(f)),cx),
inference(resolve,[$cnf( element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),cx) )],[refute_0_33,refute_0_0]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( subset_sets(union_of_members(top_of_basis(f)),cx) )],[refute_0_34,lemma_1a_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.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 May 29 14:19:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------