TSTP Solution File: SET017-6 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET017-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 20:38:40 EDT 2024
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 55 ( 14 unt; 0 def)
% Number of atoms : 108 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 96 ( 43 ~; 47 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| U = X
| U = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,plain,
! [U,Y] :
( ! [X] :
( ~ member(U,unordered_pair(X,Y))
| U = X )
| U = Y ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f107,plain,
! [Y] :
( ~ member(Y,universal_class)
| ! [X] : member(Y,unordered_pair(X,Y)) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f108,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f112,plain,
! [U,X] :
( ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f112]) ).
fof(f114,plain,
! [V,Y] :
( ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f200,plain,
unordered_pair(x,y) = unordered_pair(x,z),
inference(cnf_transformation,[status(esa)],[f92]) ).
fof(f201,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f93]) ).
fof(f202,plain,
y != z,
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f208,plain,
! [X0] :
( ~ member(X0,unordered_pair(x,y))
| X0 = x
| X0 = z ),
inference(paramodulation,[status(thm)],[f200,f104]) ).
fof(f209,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f110,f104]) ).
fof(f210,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f209]) ).
fof(f220,plain,
( spl0_2
<=> member(z,universal_class) ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( ~ member(z,universal_class)
| spl0_2 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,plain,
( spl0_3
<=> member(z,unordered_pair(x,y)) ),
introduced(split_symbol_definition) ).
fof(f224,plain,
( member(z,unordered_pair(x,y))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( ~ member(z,universal_class)
| member(z,unordered_pair(x,y)) ),
inference(paramodulation,[status(thm)],[f200,f108]) ).
fof(f227,plain,
( ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f226,f220,f223]) ).
fof(f229,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f113,f201]) ).
fof(f230,plain,
member(z,universal_class),
inference(resolution,[status(thm)],[f115,f201]) ).
fof(f249,plain,
( spl0_6
<=> y = x ),
introduced(split_symbol_definition) ).
fof(f250,plain,
( y = x
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,plain,
( spl0_7
<=> y = z ),
introduced(split_symbol_definition) ).
fof(f253,plain,
( y = z
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,plain,
( spl0_8
<=> member(y,universal_class) ),
introduced(split_symbol_definition) ).
fof(f257,plain,
( ~ member(y,universal_class)
| spl0_8 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( y = x
| y = z
| ~ member(y,universal_class) ),
inference(resolution,[status(thm)],[f208,f108]) ).
fof(f259,plain,
( spl0_6
| spl0_7
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f258,f249,f252,f255]) ).
fof(f263,plain,
( spl0_10
<=> x = z ),
introduced(split_symbol_definition) ).
fof(f264,plain,
( x = z
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f268,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f229]) ).
fof(f269,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f306,plain,
( x != z
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f250,f202]) ).
fof(f307,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f230]) ).
fof(f308,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f309,plain,
( member(z,unordered_pair(x,x))
| ~ spl0_6
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f250,f224]) ).
fof(f310,plain,
( member(z,singleton(x))
| ~ spl0_6
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f110,f309]) ).
fof(f343,plain,
( $false
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f306]) ).
fof(f344,plain,
( ~ spl0_6
| ~ spl0_10 ),
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f359,plain,
( z = x
| ~ spl0_6
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f210,f310]) ).
fof(f360,plain,
( spl0_10
| ~ spl0_6
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f359,f263,f249,f223]) ).
fof(f442,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f202]) ).
fof(f443,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f442]) ).
fof(f444,plain,
$false,
inference(sat_refutation,[status(thm)],[f227,f259,f269,f308,f344,f360,f443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET017-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 21:56:03 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % Drodi V3.6.0
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37 % Elapsed time: 0.025661 seconds
% 0.12/0.37 % CPU time: 0.049352 seconds
% 0.12/0.37 % Total memory used: 15.768 MB
% 0.12/0.37 % Net memory used: 15.737 MB
%------------------------------------------------------------------------------