TSTP Solution File: TOP005-2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : TOP005-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %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 : 300s
% DateTime : Wed May 31 12:49:54 EDT 2023
% Result : Unsatisfiable 0.16s 0.33s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 56 ( 11 unt; 0 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 141 ( 69 ~; 68 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 68 (; 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U,Vf] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,Vf] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U,Vf,X] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_set(X,f10(Vf,U,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,Vf,X] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_collection(f10(Vf,U,X),Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U,Vf,X] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| subset_sets(f10(Vf,U,X),U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U,Vf] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U,Vf,Uu11] :
( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11)
| ~ element_of_collection(Uu11,Vf)
| ~ subset_sets(Uu11,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( ~ subset_sets(X,Y)
| ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,U] :
( ~ subset_collections(X,Y)
| ~ element_of_collection(U,X)
| element_of_collection(U,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
subset_collections(g,top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] :
( ~ element_of_set(X0,union_of_members(X1))
| element_of_set(X0,f1(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( ~ element_of_set(X0,union_of_members(X1))
| element_of_collection(f1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(X2,X0)
| element_of_set(X2,f10(X1,X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(X2,X0)
| element_of_collection(f10(X1,X0,X2),X1) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(X2,X0)
| subset_sets(f10(X1,X0,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( element_of_collection(X0,top_of_basis(X1))
| element_of_set(f11(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f19,plain,
! [U,Uu11] :
( ! [Vf] :
( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11)
| ~ element_of_collection(Uu11,Vf) )
| ~ subset_sets(Uu11,U) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2] :
( element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(f11(X1,X0),X2)
| ~ element_of_collection(X2,X1)
| ~ subset_sets(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f23,plain,
! [X,Z] :
( ! [Y] :
( ~ subset_sets(X,Y)
| ~ element_of_collection(Y,Z) )
| subset_sets(X,union_of_members(Z)) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ subset_sets(X0,X1)
| ~ element_of_collection(X1,X2)
| subset_sets(X0,union_of_members(X2)) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
! [Y,U] :
( ! [X] :
( ~ subset_collections(X,Y)
| ~ element_of_collection(U,X) )
| element_of_collection(U,Y) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ subset_collections(X0,X1)
| ~ element_of_collection(X2,X0)
| element_of_collection(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
subset_collections(g,top_of_basis(f)),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f28,plain,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f29,plain,
! [X0] :
( ~ element_of_collection(X0,g)
| element_of_collection(X0,top_of_basis(f)) ),
inference(resolution,[status(thm)],[f26,f27]) ).
fof(f31,plain,
! [X0,X1] :
( ~ element_of_set(X0,X1)
| element_of_set(X0,f10(f,X1,X0))
| ~ element_of_collection(X1,g) ),
inference(resolution,[status(thm)],[f15,f29]) ).
fof(f32,plain,
! [X0,X1] :
( ~ element_of_set(X0,X1)
| element_of_collection(f10(f,X1,X0),f)
| ~ element_of_collection(X1,g) ),
inference(resolution,[status(thm)],[f16,f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ element_of_set(X0,X1)
| subset_sets(f10(f,X1,X0),X1)
| ~ element_of_collection(X1,g) ),
inference(resolution,[status(thm)],[f17,f29]) ).
fof(f34,plain,
! [X0] :
( ~ element_of_set(f11(f,union_of_members(g)),X0)
| ~ element_of_collection(X0,f)
| ~ subset_sets(X0,union_of_members(g)) ),
inference(resolution,[status(thm)],[f20,f28]) ).
fof(f38,plain,
element_of_set(f11(f,union_of_members(g)),union_of_members(g)),
inference(resolution,[status(thm)],[f18,f28]) ).
fof(f50,plain,
element_of_collection(f1(g,f11(f,union_of_members(g))),g),
inference(resolution,[status(thm)],[f38,f14]) ).
fof(f51,plain,
element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))),
inference(resolution,[status(thm)],[f38,f13]) ).
fof(f52,plain,
! [X0] :
( ~ element_of_set(X0,f1(g,f11(f,union_of_members(g))))
| subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),X0),f1(g,f11(f,union_of_members(g)))) ),
inference(resolution,[status(thm)],[f50,f33]) ).
fof(f53,plain,
! [X0] :
( ~ element_of_set(X0,f1(g,f11(f,union_of_members(g))))
| element_of_set(X0,f10(f,f1(g,f11(f,union_of_members(g))),X0)) ),
inference(resolution,[status(thm)],[f50,f31]) ).
fof(f62,plain,
element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))),
inference(resolution,[status(thm)],[f53,f51]) ).
fof(f63,plain,
( spl0_4
<=> element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ),
introduced(split_symbol_definition) ).
fof(f65,plain,
( ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
| spl0_4 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( spl0_5
<=> subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)) ),
introduced(split_symbol_definition) ).
fof(f68,plain,
( ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| spl0_5 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)) ),
inference(resolution,[status(thm)],[f62,f34]) ).
fof(f70,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f69,f63,f66]) ).
fof(f71,plain,
( spl0_6
<=> element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))) ),
introduced(split_symbol_definition) ).
fof(f73,plain,
( ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| spl0_6 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( spl0_7
<=> element_of_collection(f1(g,f11(f,union_of_members(g))),g) ),
introduced(split_symbol_definition) ).
fof(f76,plain,
( ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| spl0_7 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| spl0_4 ),
inference(resolution,[status(thm)],[f65,f32]) ).
fof(f78,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_4 ),
inference(split_clause,[status(thm)],[f77,f71,f74,f63]) ).
fof(f79,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f50]) ).
fof(f80,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f81,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f73,f51]) ).
fof(f82,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0] :
( ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),X0)
| ~ element_of_collection(X0,g)
| spl0_5 ),
inference(resolution,[status(thm)],[f68,f24]) ).
fof(f112,plain,
( ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| spl0_5 ),
inference(resolution,[status(thm)],[f52,f83]) ).
fof(f113,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_5 ),
inference(split_clause,[status(thm)],[f112,f71,f74,f66]) ).
fof(f114,plain,
$false,
inference(sat_refutation,[status(thm)],[f70,f78,f80,f82,f113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : TOP005-2 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n019.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 10:34:10 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.31 % Drodi V3.5.1
% 0.16/0.33 % Refutation found
% 0.16/0.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.37 % Elapsed time: 0.064451 seconds
% 0.16/0.37 % CPU time: 0.059800 seconds
% 0.16/0.37 % Memory used: 1.548 MB
%------------------------------------------------------------------------------