TSTP Solution File: SET012-2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET012-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 12:33:30 EDT 2023
% Result : Unsatisfiable 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 55 ( 16 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 86 ( 40 ~; 43 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 49 (; 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [Element,Subset,Superset] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Subset,Superset] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Xs] :
( member(X,Xs)
| member(X,complement(Xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Xs] :
( ~ member(X,Xs)
| ~ member(X,complement(Xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Subset,Superset] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Set1,Set2] :
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Xs,Ys] :
( ~ equal_sets(Xs,Ys)
| equal_sets(Ys,Xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
equal_sets(complement(a),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
equal_sets(complement(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ equal_sets(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [Element,Superset] :
( ! [Subset] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset) )
| member(Element,Superset) ),
inference(miniscoping,[status(esa)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f30,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f31,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f43,plain,
! [X0,X1] :
( ~ equal_sets(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f45,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_sets(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f47,plain,
! [X0,X1] :
( ~ equal_sets(X0,X1)
| equal_sets(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f54,plain,
equal_sets(complement(a),b),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f55,plain,
equal_sets(complement(b),c),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f56,plain,
~ equal_sets(a,c),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f59,plain,
equal_sets(b,complement(a)),
inference(resolution,[status(thm)],[f54,f47]) ).
fof(f61,plain,
equal_sets(c,complement(b)),
inference(resolution,[status(thm)],[f55,f47]) ).
fof(f136,plain,
subset(c,complement(b)),
inference(resolution,[status(thm)],[f43,f61]) ).
fof(f137,plain,
subset(b,complement(a)),
inference(resolution,[status(thm)],[f43,f59]) ).
fof(f138,plain,
subset(complement(b),c),
inference(resolution,[status(thm)],[f43,f55]) ).
fof(f140,plain,
subset(complement(a),b),
inference(resolution,[status(thm)],[f43,f54]) ).
fof(f185,plain,
! [X0] :
( ~ member(X0,complement(a))
| member(X0,b) ),
inference(resolution,[status(thm)],[f27,f140]) ).
fof(f186,plain,
! [X0] :
( ~ member(X0,complement(b))
| member(X0,c) ),
inference(resolution,[status(thm)],[f27,f138]) ).
fof(f187,plain,
! [X0] :
( ~ member(X0,b)
| member(X0,complement(a)) ),
inference(resolution,[status(thm)],[f27,f137]) ).
fof(f188,plain,
! [X0] :
( ~ member(X0,c)
| member(X0,complement(b)) ),
inference(resolution,[status(thm)],[f27,f136]) ).
fof(f209,plain,
! [X0] :
( member(X0,b)
| member(X0,a) ),
inference(resolution,[status(thm)],[f185,f30]) ).
fof(f212,plain,
! [X0] :
( member(X0,c)
| member(X0,b) ),
inference(resolution,[status(thm)],[f186,f30]) ).
fof(f214,plain,
! [X0] :
( ~ member(X0,b)
| ~ member(X0,a) ),
inference(resolution,[status(thm)],[f187,f31]) ).
fof(f215,plain,
! [X0] :
( member(member_of_1_not_of_2(X0,c),b)
| subset(X0,c) ),
inference(resolution,[status(thm)],[f212,f29]) ).
fof(f218,plain,
! [X0] :
( ~ member(X0,c)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[f188,f31]) ).
fof(f219,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(c,X0),b)
| subset(c,X0) ),
inference(resolution,[status(thm)],[f218,f28]) ).
fof(f244,plain,
! [X0] :
( subset(X0,c)
| ~ member(member_of_1_not_of_2(X0,c),a) ),
inference(resolution,[status(thm)],[f215,f214]) ).
fof(f255,plain,
! [X0] :
( subset(c,X0)
| member(member_of_1_not_of_2(c,X0),a) ),
inference(resolution,[status(thm)],[f219,f209]) ).
fof(f256,plain,
( spl0_20
<=> subset(a,c) ),
introduced(split_symbol_definition) ).
fof(f257,plain,
( subset(a,c)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,plain,
( subset(a,c)
| subset(a,c) ),
inference(resolution,[status(thm)],[f244,f28]) ).
fof(f260,plain,
spl0_20,
inference(split_clause,[status(thm)],[f259,f256]) ).
fof(f262,plain,
( spl0_21
<=> subset(c,a) ),
introduced(split_symbol_definition) ).
fof(f265,plain,
( spl0_22
<=> equal_sets(a,c) ),
introduced(split_symbol_definition) ).
fof(f266,plain,
( equal_sets(a,c)
| ~ spl0_22 ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( ~ subset(c,a)
| equal_sets(a,c)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f257,f45]) ).
fof(f269,plain,
( ~ spl0_21
| spl0_22
| ~ spl0_20 ),
inference(split_clause,[status(thm)],[f268,f262,f265,f256]) ).
fof(f284,plain,
( subset(c,a)
| subset(c,a) ),
inference(resolution,[status(thm)],[f255,f29]) ).
fof(f285,plain,
spl0_21,
inference(split_clause,[status(thm)],[f284,f262]) ).
fof(f287,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f56]) ).
fof(f288,plain,
~ spl0_22,
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f289,plain,
$false,
inference(sat_refutation,[status(thm)],[f260,f269,f285,f288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET012-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 10:20:12 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Drodi V3.5.1
% 0.16/0.51 % Refutation found
% 0.16/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.52 % Elapsed time: 0.196895 seconds
% 0.16/0.52 % CPU time: 0.911327 seconds
% 0.16/0.52 % Memory used: 11.612 MB
%------------------------------------------------------------------------------