TSTP Solution File: SEU217+3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU217+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 12:36:19 EDT 2023
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 10 unt; 0 def)
% Number of atoms : 121 ( 33 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 130 ( 54 ~; 48 |; 17 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 58 (; 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( B = identity_relation(A)
<=> ( relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f54,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f72,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f73,plain,
( ! [A] : relation(identity_relation(A))
& ! [A] : function(identity_relation(A)) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f75,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f73]) ).
fof(f99,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f100,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f99]) ).
fof(f101,plain,
! [A,B] :
( ~ in(A,B)
| ~ empty(B) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f102,plain,
! [B] :
( ! [A] : ~ in(A,B)
| ~ empty(B) ),
inference(miniscoping,[status(esa)],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[status(esa)],[f102]) ).
fof(f104,plain,
? [A,B] :
( in(B,A)
& apply(identity_relation(A),B) != B ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f105,plain,
( in(sk0_10,sk0_9)
& apply(identity_relation(sk0_9),sk0_10) != sk0_10 ),
inference(skolemization,[status(esa)],[f104]) ).
fof(f106,plain,
in(sk0_10,sk0_9),
inference(cnf_transformation,[status(esa)],[f105]) ).
fof(f107,plain,
apply(identity_relation(sk0_9),sk0_10) != sk0_10,
inference(cnf_transformation,[status(esa)],[f105]) ).
fof(f108,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ( B = identity_relation(A)
<=> ( relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = C ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f32]) ).
fof(f109,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ( ( B != identity_relation(A)
| ( relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = C ) ) )
& ( B = identity_relation(A)
| relation_dom(B) != A
| ? [C] :
( in(C,A)
& apply(B,C) != C ) ) ) ),
inference(NNF_transformation,[status(esa)],[f108]) ).
fof(f110,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ( ! [A] :
( B != identity_relation(A)
| ( relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = C ) ) )
& ! [A] :
( B = identity_relation(A)
| relation_dom(B) != A
| ? [C] :
( in(C,A)
& apply(B,C) != C ) ) ) ),
inference(miniscoping,[status(esa)],[f109]) ).
fof(f111,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ( ! [A] :
( B != identity_relation(A)
| ( relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = C ) ) )
& ! [A] :
( B = identity_relation(A)
| relation_dom(B) != A
| ( in(sk0_11(A,B),A)
& apply(B,sk0_11(A,B)) != sk0_11(A,B) ) ) ) ),
inference(skolemization,[status(esa)],[f110]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| X0 != identity_relation(X1)
| ~ in(X2,X1)
| apply(X0,X2) = X2 ),
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f117,plain,
! [X0,X1] :
( ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f113]) ).
fof(f120,plain,
~ empty(sk0_9),
inference(resolution,[status(thm)],[f103,f106]) ).
fof(f122,plain,
element(sk0_10,sk0_9),
inference(resolution,[status(thm)],[f100,f106]) ).
fof(f123,plain,
( spl0_0
<=> empty(sk0_9) ),
introduced(split_symbol_definition) ).
fof(f124,plain,
( empty(sk0_9)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( spl0_1
<=> in(sk0_10,sk0_9) ),
introduced(split_symbol_definition) ).
fof(f129,plain,
( empty(sk0_9)
| in(sk0_10,sk0_9) ),
inference(resolution,[status(thm)],[f54,f122]) ).
fof(f130,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f129,f123,f126]) ).
fof(f131,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f120]) ).
fof(f132,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ~ function(identity_relation(X0))
| ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f72]) ).
fof(f134,plain,
( spl0_2
<=> function(identity_relation(sk0_9)) ),
introduced(split_symbol_definition) ).
fof(f136,plain,
( ~ function(identity_relation(sk0_9))
| spl0_2 ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( ~ function(identity_relation(sk0_9))
| ~ in(sk0_10,sk0_9) ),
inference(resolution,[status(thm)],[f133,f107]) ).
fof(f138,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f137,f134,f126]) ).
fof(f148,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f75]) ).
fof(f149,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f150,plain,
$false,
inference(sat_refutation,[status(thm)],[f130,f132,f138,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU217+3 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:10:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.57 % Elapsed time: 0.015091 seconds
% 0.19/0.57 % CPU time: 0.031227 seconds
% 0.19/0.57 % Memory used: 11.718 MB
%------------------------------------------------------------------------------