TSTP Solution File: SET090+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET090+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 20:39:04 EDT 2024
% Result : Theorem 0.21s 0.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 73 ( 11 unt; 0 def)
% Number of atoms : 172 ( 58 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 168 ( 69 ~; 72 |; 13 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(f5,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [Y] :
( member(Y,universal_class)
=> member(member_of(singleton(Y)),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [Y] :
( member(Y,universal_class)
=> singleton(member_of(singleton(Y))) = singleton(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( singleton(member_of(X)) = X
| member_of(X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
! [X,U] :
( ( member(U,universal_class)
& X = singleton(U) )
=> member_of(X) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ! [X,U] :
( ( member(U,universal_class)
& X = singleton(U) )
=> member_of(X) = U ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f63,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(f64,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)],[f63]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f67,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f69,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f70,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f195,plain,
! [Y] :
( ~ member(Y,universal_class)
| member(member_of(singleton(Y)),universal_class) ),
inference(pre_NNF_transformation,[status(esa)],[f44]) ).
fof(f196,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(member_of(singleton(X0)),universal_class) ),
inference(cnf_transformation,[status(esa)],[f195]) ).
fof(f197,plain,
! [Y] :
( ~ member(Y,universal_class)
| singleton(member_of(singleton(Y))) = singleton(Y) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f198,plain,
! [X0] :
( ~ member(X0,universal_class)
| singleton(member_of(singleton(X0))) = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f197]) ).
fof(f200,plain,
! [X0] :
( singleton(member_of(X0)) = X0
| member_of(X0) = X0 ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f201,plain,
? [X,U] :
( member(U,universal_class)
& X = singleton(U)
& member_of(X) != U ),
inference(pre_NNF_transformation,[status(esa)],[f49]) ).
fof(f202,plain,
( member(sk0_8,universal_class)
& sk0_7 = singleton(sk0_8)
& member_of(sk0_7) != sk0_8 ),
inference(skolemization,[status(esa)],[f201]) ).
fof(f203,plain,
member(sk0_8,universal_class),
inference(cnf_transformation,[status(esa)],[f202]) ).
fof(f204,plain,
sk0_7 = singleton(sk0_8),
inference(cnf_transformation,[status(esa)],[f202]) ).
fof(f205,plain,
member_of(sk0_7) != sk0_8,
inference(cnf_transformation,[status(esa)],[f202]) ).
fof(f208,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(destructive_equality_resolution,[status(esa)],[f67]) ).
fof(f212,plain,
( spl0_0
<=> member(sk0_8,universal_class) ),
introduced(split_symbol_definition) ).
fof(f214,plain,
( ~ member(sk0_8,universal_class)
| spl0_0 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( spl0_1
<=> member(member_of(sk0_7),universal_class) ),
introduced(split_symbol_definition) ).
fof(f216,plain,
( member(member_of(sk0_7),universal_class)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( ~ member(sk0_8,universal_class)
| member(member_of(sk0_7),universal_class) ),
inference(paramodulation,[status(thm)],[f204,f196]) ).
fof(f219,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f218,f212,f215]) ).
fof(f220,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f203]) ).
fof(f221,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( spl0_2
<=> singleton(member_of(sk0_7)) = singleton(sk0_8) ),
introduced(split_symbol_definition) ).
fof(f223,plain,
( singleton(member_of(sk0_7)) = singleton(sk0_8)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( ~ member(sk0_8,universal_class)
| singleton(member_of(sk0_7)) = singleton(sk0_8) ),
inference(paramodulation,[status(thm)],[f204,f198]) ).
fof(f226,plain,
( ~ spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f225,f212,f222]) ).
fof(f227,plain,
( singleton(member_of(sk0_7)) = sk0_7
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f204,f223]) ).
fof(f231,plain,
( spl0_4
<=> member_of(sk0_7) = sk0_7 ),
introduced(split_symbol_definition) ).
fof(f232,plain,
( member_of(sk0_7) = sk0_7
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f245,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f70,f69]) ).
fof(f247,plain,
! [X0] :
( member(X0,universal_class)
| member_of(X0) = X0 ),
inference(paramodulation,[status(thm)],[f200,f245]) ).
fof(f255,plain,
( spl0_7
<=> member(sk0_7,universal_class) ),
introduced(split_symbol_definition) ).
fof(f260,plain,
( member(sk0_7,universal_class)
| member(sk0_7,universal_class)
| ~ spl0_1 ),
inference(paramodulation,[status(thm)],[f247,f216]) ).
fof(f261,plain,
( spl0_7
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f260,f255,f215]) ).
fof(f262,plain,
( spl0_8
<=> sk0_7 = sk0_8 ),
introduced(split_symbol_definition) ).
fof(f278,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f70,f66]) ).
fof(f279,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f278]) ).
fof(f283,plain,
! [X0,X1] :
( ~ member(X0,X1)
| X0 = member_of(X1)
| member_of(X1) = X1 ),
inference(paramodulation,[status(thm)],[f200,f279]) ).
fof(f305,plain,
( spl0_13
<=> member(sk0_8,sk0_7) ),
introduced(split_symbol_definition) ).
fof(f306,plain,
( member(sk0_8,sk0_7)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f403,plain,
( singleton(sk0_7) = sk0_7
| ~ spl0_4
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f232,f227]) ).
fof(f455,plain,
( spl0_34
<=> member_of(sk0_7) = sk0_8 ),
introduced(split_symbol_definition) ).
fof(f456,plain,
( member_of(sk0_7) = sk0_8
| ~ spl0_34 ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f492,plain,
( spl0_37
<=> singleton(member_of(sk0_7)) = singleton(sk0_7) ),
introduced(split_symbol_definition) ).
fof(f493,plain,
( singleton(member_of(sk0_7)) = singleton(sk0_7)
| ~ spl0_37 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( ~ member(sk0_7,universal_class)
| singleton(member_of(sk0_7)) = singleton(sk0_7)
| ~ spl0_4
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f403,f198]) ).
fof(f496,plain,
( ~ spl0_7
| spl0_37
| ~ spl0_4
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f495,f255,f492,f231,f222]) ).
fof(f523,plain,
( sk0_7 = singleton(sk0_7)
| ~ spl0_2
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f227,f493]) ).
fof(f524,plain,
! [X0] :
( ~ member(X0,sk0_7)
| X0 = sk0_7
| ~ spl0_2
| ~ spl0_37 ),
inference(paramodulation,[status(thm)],[f523,f279]) ).
fof(f754,plain,
( sk0_7 != sk0_8
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f232,f205]) ).
fof(f792,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f754,f262,f231]) ).
fof(f954,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f70,f208]) ).
fof(f963,plain,
( member(sk0_8,sk0_7)
| ~ member(sk0_8,universal_class) ),
inference(paramodulation,[status(thm)],[f204,f954]) ).
fof(f964,plain,
( spl0_13
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f963,f305,f212]) ).
fof(f970,plain,
( sk0_8 = member_of(sk0_7)
| member_of(sk0_7) = sk0_7
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f306,f283]) ).
fof(f971,plain,
( spl0_34
| spl0_4
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f970,f455,f231,f305]) ).
fof(f1028,plain,
( sk0_8 = sk0_7
| ~ spl0_2
| ~ spl0_37
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f524,f306]) ).
fof(f1029,plain,
( spl0_8
| ~ spl0_2
| ~ spl0_37
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f1028,f262,f222,f492,f305]) ).
fof(f1055,plain,
( sk0_8 != sk0_8
| ~ spl0_34 ),
inference(forward_demodulation,[status(thm)],[f456,f205]) ).
fof(f1056,plain,
( $false
| ~ spl0_34 ),
inference(trivial_equality_resolution,[status(esa)],[f1055]) ).
fof(f1057,plain,
~ spl0_34,
inference(contradiction_clause,[status(thm)],[f1056]) ).
fof(f1058,plain,
$false,
inference(sat_refutation,[status(thm)],[f219,f221,f226,f261,f496,f792,f964,f971,f1029,f1057]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET090+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 21:56:02 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.37 % Drodi V3.6.0
% 0.21/0.50 % Refutation found
% 0.21/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.52 % Elapsed time: 0.148797 seconds
% 0.21/0.52 % CPU time: 1.000514 seconds
% 0.21/0.52 % Total memory used: 80.251 MB
% 0.21/0.52 % Net memory used: 78.484 MB
%------------------------------------------------------------------------------