TSTP Solution File: SET009-1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET009-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 12:33:29 EDT 2023
% Result : Unsatisfiable 0.09s 0.30s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 11 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 96 ( 45 ~; 49 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 60 (; 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Element,Subset,Superset] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f7,axiom,
! [Set1,Set2,Difference,Element] :
( ~ difference(Set1,Set2,Difference)
| ~ member(Element,Difference)
| member(Element,Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Element,Set1,Set2,A_set] :
( ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ difference(A_set,Set1,Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Element,Set1,Set2,Difference] :
( ~ member(Element,Set1)
| ~ difference(Set1,Set2,Difference)
| member(Element,Difference)
| member(Element,Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
subset(d,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
difference(b,a,bDa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
difference(b,d,bDd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ subset(bDa,bDd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [Element,Superset] :
( ! [Subset] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset) )
| member(Element,Superset) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
! [Set1,Element] :
( ! [Difference] :
( ! [Set2] : ~ difference(Set1,Set2,Difference)
| ~ member(Element,Difference) )
| member(Element,Set1) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ difference(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [Set1,Set2] :
( ! [Element] :
( ~ member(Element,Set1)
| ~ member(Element,Set2) )
| ! [A_set] : ~ difference(A_set,Set1,Set2) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ difference(X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [Element,Set2] :
( ! [Difference] :
( ! [Set1] :
( ~ member(Element,Set1)
| ~ difference(Set1,Set2,Difference) )
| member(Element,Difference) )
| member(Element,Set2) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ difference(X1,X2,X3)
| member(X0,X3)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f33,plain,
subset(d,a),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f34,plain,
difference(b,a,bDa),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f35,plain,
difference(b,d,bDd),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f36,plain,
~ subset(bDa,bDd),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f37,plain,
! [X0] :
( ~ member(X0,d)
| member(X0,a) ),
inference(resolution,[status(thm)],[f33,f18]) ).
fof(f59,plain,
! [X0] :
( ~ member(X0,bDa)
| member(X0,b) ),
inference(resolution,[status(thm)],[f25,f34]) ).
fof(f61,plain,
! [X0] :
( member(member_of_1_not_of_2(bDa,X0),b)
| subset(bDa,X0) ),
inference(resolution,[status(thm)],[f59,f19]) ).
fof(f68,plain,
! [X0] :
( ~ member(X0,a)
| ~ member(X0,bDa) ),
inference(resolution,[status(thm)],[f27,f34]) ).
fof(f70,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(bDa,X0),a)
| subset(bDa,X0) ),
inference(resolution,[status(thm)],[f68,f19]) ).
fof(f76,plain,
! [X0] :
( ~ member(X0,b)
| member(X0,bDd)
| member(X0,d) ),
inference(resolution,[status(thm)],[f29,f35]) ).
fof(f78,plain,
! [X0] :
( member(member_of_1_not_of_2(bDa,X0),bDd)
| member(member_of_1_not_of_2(bDa,X0),d)
| subset(bDa,X0) ),
inference(resolution,[status(thm)],[f76,f61]) ).
fof(f93,plain,
( spl0_5
<=> member(member_of_1_not_of_2(bDa,bDd),d) ),
introduced(split_symbol_definition) ).
fof(f94,plain,
( member(member_of_1_not_of_2(bDa,bDd),d)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( spl0_6
<=> subset(bDa,bDd) ),
introduced(split_symbol_definition) ).
fof(f97,plain,
( subset(bDa,bDd)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( member(member_of_1_not_of_2(bDa,bDd),d)
| subset(bDa,bDd)
| subset(bDa,bDd) ),
inference(resolution,[status(thm)],[f78,f20]) ).
fof(f100,plain,
( spl0_5
| spl0_6 ),
inference(split_clause,[status(thm)],[f99,f93,f96]) ).
fof(f173,plain,
( member(member_of_1_not_of_2(bDa,bDd),a)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f94,f37]) ).
fof(f174,plain,
( subset(bDa,bDd)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f173,f70]) ).
fof(f175,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f36]) ).
fof(f176,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f177,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f36]) ).
fof(f178,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f179,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f176,f178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n009.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue May 30 10:11:46 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.09/0.30 % Refutation found
% 0.09/0.30 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.56 % Elapsed time: 0.047705 seconds
% 0.13/0.56 % CPU time: 0.016822 seconds
% 0.13/0.56 % Memory used: 660.496 KB
%------------------------------------------------------------------------------