TSTP Solution File: SET072-7 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET072-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 20:38:59 EDT 2024
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 94 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 36 ~; 38 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 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(f9,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,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(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,axiom,
! [X,Y,U,V] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(X,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f108,axiom,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f117,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f126,plain,
! [U,Y] :
( ! [X] :
( ~ member(U,unordered_pair(X,Y))
| U = X )
| U = Y ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f126]) ).
fof(f128,plain,
! [X] :
( ~ member(X,universal_class)
| ! [Y] : member(X,unordered_pair(X,Y)) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f129,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f128]) ).
fof(f133,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f137,plain,
! [V,Y] :
( ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f223,plain,
! [X,Y] :
( ! [U,V] : ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(X,unordered_pair(X,Y)) ),
inference(miniscoping,[status(esa)],[f92]) ).
fof(f224,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f223]) ).
fof(f244,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f255,plain,
unordered_pair(x,z) = unordered_pair(y,z),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f256,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f116]) ).
fof(f257,plain,
x != y,
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f262,plain,
unordered_pair(x,z) = unordered_pair(z,y),
inference(paramodulation,[status(thm)],[f255,f244]) ).
fof(f281,plain,
( spl0_2
<=> member(y,universal_class) ),
introduced(split_symbol_definition) ).
fof(f283,plain,
( ~ member(y,universal_class)
| spl0_2 ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( spl0_3
<=> member(y,unordered_pair(x,z)) ),
introduced(split_symbol_definition) ).
fof(f285,plain,
( member(y,unordered_pair(x,z))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f287,plain,
( ~ member(y,universal_class)
| member(y,unordered_pair(x,z)) ),
inference(paramodulation,[status(thm)],[f255,f129]) ).
fof(f288,plain,
( ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f287,f281,f284]) ).
fof(f298,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f138,f256]) ).
fof(f311,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f133,f127]) ).
fof(f312,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f311]) ).
fof(f329,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f298]) ).
fof(f330,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f329]) ).
fof(f331,plain,
( spl0_6
<=> y = x ),
introduced(split_symbol_definition) ).
fof(f332,plain,
( y = x
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,plain,
( spl0_7
<=> y = z ),
introduced(split_symbol_definition) ).
fof(f335,plain,
( y = z
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( y = x
| y = z
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f285,f127]) ).
fof(f338,plain,
( spl0_6
| spl0_7
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f337,f331,f334,f284]) ).
fof(f340,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f257]) ).
fof(f341,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f346,plain,
( unordered_pair(x,z) = unordered_pair(z,z)
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f335,f262]) ).
fof(f347,plain,
( unordered_pair(x,z) = singleton(z)
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f133,f346]) ).
fof(f348,plain,
( member(ordered_pair(x,z),cross_product(universal_class,universal_class))
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f335,f256]) ).
fof(f351,plain,
( x != z
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f335,f257]) ).
fof(f388,plain,
( member(x,unordered_pair(x,z))
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f224,f348]) ).
fof(f389,plain,
( member(x,singleton(z))
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f347,f388]) ).
fof(f390,plain,
( x = z
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f389,f312]) ).
fof(f391,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f351]) ).
fof(f392,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f393,plain,
$false,
inference(sat_refutation,[status(thm)],[f288,f330,f338,f341,f392]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET072-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n011.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 21:45:46 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % 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: 0.024636 seconds
% 0.12/0.37 % CPU time: 0.040572 seconds
% 0.12/0.37 % Total memory used: 13.728 MB
% 0.12/0.37 % Net memory used: 13.712 MB
%------------------------------------------------------------------------------