TSTP Solution File: SET076+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET076+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 : Tue Apr 30 20:39:00 EDT 2024
% Result : Theorem 0.16s 0.41s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 7 unt; 0 def)
% Number of atoms : 115 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 112 ( 39 ~; 43 |; 19 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 47 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( U = X
| U = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [X,Y,Z] :
( ( member(X,Z)
& member(Y,Z) )
=> subclass(unordered_pair(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X,Y,Z] :
( ( member(X,Z)
& member(Y,Z) )
=> subclass(unordered_pair(X,Y),Z) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( ~ member(U,X)
| member(U,Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f47,plain,
! [X,Y] :
( ( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ( member(sk0_0(Y,X),X)
& ~ member(sk0_0(Y,X),Y) ) ) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f59,plain,
! [U,X,Y] :
( ( ~ member(U,unordered_pair(X,Y))
| ( member(U,universal_class)
& ( U = X
| U = Y ) ) )
& ( member(U,unordered_pair(X,Y))
| ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f60,plain,
( ! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( member(U,universal_class)
& ( U = X
| U = Y ) ) )
& ! [U,X,Y] :
( member(U,unordered_pair(X,Y))
| ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(miniscoping,[status(esa)],[f59]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f191,plain,
? [X,Y,Z] :
( member(X,Z)
& member(Y,Z)
& ~ subclass(unordered_pair(X,Y),Z) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f192,plain,
( member(sk0_7,sk0_9)
& member(sk0_8,sk0_9)
& ~ subclass(unordered_pair(sk0_7,sk0_8),sk0_9) ),
inference(skolemization,[status(esa)],[f191]) ).
fof(f193,plain,
member(sk0_7,sk0_9),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f194,plain,
member(sk0_8,sk0_9),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f195,plain,
~ subclass(unordered_pair(sk0_7,sk0_8),sk0_9),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f249,plain,
! [X0,X1,X2] :
( subclass(unordered_pair(X0,X1),X2)
| sk0_0(X2,unordered_pair(X0,X1)) = X0
| sk0_0(X2,unordered_pair(X0,X1)) = X1 ),
inference(resolution,[status(thm)],[f51,f62]) ).
fof(f1164,plain,
( spl0_18
<=> sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_7 ),
introduced(split_symbol_definition) ).
fof(f1165,plain,
( sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_7
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f1164]) ).
fof(f1167,plain,
( spl0_19
<=> sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_8 ),
introduced(split_symbol_definition) ).
fof(f1168,plain,
( sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_8
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f1167]) ).
fof(f1170,plain,
( sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_7
| sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_8 ),
inference(resolution,[status(thm)],[f249,f195]) ).
fof(f1171,plain,
( spl0_18
| spl0_19 ),
inference(split_clause,[status(thm)],[f1170,f1164,f1167]) ).
fof(f1412,plain,
( spl0_22
<=> subclass(unordered_pair(sk0_7,sk0_8),sk0_9) ),
introduced(split_symbol_definition) ).
fof(f1413,plain,
( subclass(unordered_pair(sk0_7,sk0_8),sk0_9)
| ~ spl0_22 ),
inference(component_clause,[status(thm)],[f1412]) ).
fof(f1420,plain,
( spl0_24
<=> member(sk0_7,sk0_9) ),
introduced(split_symbol_definition) ).
fof(f1422,plain,
( ~ member(sk0_7,sk0_9)
| spl0_24 ),
inference(component_clause,[status(thm)],[f1420]) ).
fof(f1423,plain,
( subclass(unordered_pair(sk0_7,sk0_8),sk0_9)
| ~ member(sk0_7,sk0_9)
| ~ spl0_18 ),
inference(paramodulation,[status(thm)],[f1165,f52]) ).
fof(f1424,plain,
( spl0_22
| ~ spl0_24
| ~ spl0_18 ),
inference(split_clause,[status(thm)],[f1423,f1412,f1420,f1164]) ).
fof(f1430,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f1413,f195]) ).
fof(f1431,plain,
~ spl0_22,
inference(contradiction_clause,[status(thm)],[f1430]) ).
fof(f1437,plain,
( spl0_27
<=> member(sk0_8,sk0_9) ),
introduced(split_symbol_definition) ).
fof(f1439,plain,
( ~ member(sk0_8,sk0_9)
| spl0_27 ),
inference(component_clause,[status(thm)],[f1437]) ).
fof(f1440,plain,
( subclass(unordered_pair(sk0_7,sk0_8),sk0_9)
| ~ member(sk0_8,sk0_9)
| ~ spl0_19 ),
inference(paramodulation,[status(thm)],[f1168,f52]) ).
fof(f1441,plain,
( spl0_22
| ~ spl0_27
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f1440,f1412,f1437,f1167]) ).
fof(f1447,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f1439,f194]) ).
fof(f1448,plain,
spl0_27,
inference(contradiction_clause,[status(thm)],[f1447]) ).
fof(f1449,plain,
( $false
| spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f1422,f193]) ).
fof(f1450,plain,
spl0_24,
inference(contradiction_clause,[status(thm)],[f1449]) ).
fof(f1451,plain,
$false,
inference(sat_refutation,[status(thm)],[f1171,f1424,f1431,f1441,f1448,f1450]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET076+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.05/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34 % Computer : n004.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Apr 29 21:43:18 EDT 2024
% 0.10/0.34 % CPUTime :
% 0.10/0.35 % Drodi V3.6.0
% 0.16/0.41 % Refutation found
% 0.16/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.42 % Elapsed time: 0.076674 seconds
% 0.16/0.42 % CPU time: 0.478939 seconds
% 0.16/0.42 % Total memory used: 68.795 MB
% 0.16/0.42 % Net memory used: 68.099 MB
%------------------------------------------------------------------------------