TSTP Solution File: SET002-1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 12:33:27 EDT 2023
% Result : Unsatisfiable 0.11s 0.35s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 72 ( 31 ~; 38 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 41 (; 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Subset,Superset] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Set1,Set2] :
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Set1,Set2,Union,Element] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Union)
| member(Element,Set1)
| member(Element,Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Set1,Set2,Union,Element] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Set1)
| member(Element,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
union(a,a,aUa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ equal_sets(aUa,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f18,plain,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f21,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_sets(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f22,plain,
! [Set2,Element] :
( ! [Set1] :
( ! [Union] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Union) )
| member(Element,Set1) )
| member(Element,Set2) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ~ union(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [Union,Element] :
( ! [Set1] :
( ! [Set2] : ~ union(Set1,Set2,Union)
| ~ member(Element,Set1) )
| member(Element,Union) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ union(X0,X1,X2)
| ~ member(X3,X0)
| member(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f31,plain,
union(a,a,aUa),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f32,plain,
~ equal_sets(aUa,a),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f39,plain,
! [X0] :
( ~ member(X0,a)
| member(X0,aUa) ),
inference(resolution,[status(thm)],[f25,f31]) ).
fof(f40,plain,
! [X0] :
( member(member_of_1_not_of_2(a,X0),aUa)
| subset(a,X0) ),
inference(resolution,[status(thm)],[f39,f17]) ).
fof(f41,plain,
( spl0_0
<=> subset(a,aUa) ),
introduced(split_symbol_definition) ).
fof(f44,plain,
( subset(a,aUa)
| subset(a,aUa) ),
inference(resolution,[status(thm)],[f40,f18]) ).
fof(f45,plain,
spl0_0,
inference(split_clause,[status(thm)],[f44,f41]) ).
fof(f47,plain,
! [X0] :
( ~ member(X0,aUa)
| member(X0,a)
| member(X0,a) ),
inference(resolution,[status(thm)],[f23,f31]) ).
fof(f48,plain,
! [X0] :
( ~ member(X0,aUa)
| member(X0,a) ),
inference(duplicate_literals_removal,[status(esa)],[f47]) ).
fof(f50,plain,
! [X0] :
( member(member_of_1_not_of_2(aUa,X0),a)
| subset(aUa,X0) ),
inference(resolution,[status(thm)],[f48,f17]) ).
fof(f51,plain,
( spl0_1
<=> subset(aUa,a) ),
introduced(split_symbol_definition) ).
fof(f52,plain,
( subset(aUa,a)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( subset(aUa,a)
| subset(aUa,a) ),
inference(resolution,[status(thm)],[f50,f18]) ).
fof(f55,plain,
spl0_1,
inference(split_clause,[status(thm)],[f54,f51]) ).
fof(f215,plain,
( spl0_19
<=> equal_sets(aUa,a) ),
introduced(split_symbol_definition) ).
fof(f216,plain,
( equal_sets(aUa,a)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( ~ subset(a,aUa)
| equal_sets(aUa,a)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f52,f21]) ).
fof(f219,plain,
( ~ spl0_0
| spl0_19
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f218,f41,f215,f51]) ).
fof(f220,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f32]) ).
fof(f221,plain,
~ spl0_19,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f222,plain,
$false,
inference(sat_refutation,[status(thm)],[f45,f55,f219,f221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34 % Computer : n023.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Tue May 30 10:40:23 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.11/0.35 % Drodi V3.5.1
% 0.11/0.35 % Refutation found
% 0.11/0.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.58 % Elapsed time: 0.020626 seconds
% 0.17/0.58 % CPU time: 0.017866 seconds
% 0.17/0.58 % Memory used: 597.332 KB
%------------------------------------------------------------------------------