TSTP Solution File: SET095+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 20:39:06 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 4 unt; 0 def)
% Number of atoms : 59 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 23 ~; 21 |; 10 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 43 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,X] :
( member(X,A)
=> subset(singleton(X),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,X] :
( member(X,A)
=> subset(singleton(X),A) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f46,plain,
! [X,A] :
( ( ~ member(X,singleton(A))
| X = A )
& ( member(X,singleton(A))
| X != A ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f47,plain,
( ! [X,A] :
( ~ member(X,singleton(A))
| X = A )
& ! [X,A] :
( member(X,singleton(A))
| X != A ) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f68,plain,
? [A,X] :
( member(X,A)
& ~ subset(singleton(X),A) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
( member(sk0_4,sk0_3)
& ~ subset(singleton(sk0_4),sk0_3) ),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
member(sk0_4,sk0_3),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f71,plain,
~ subset(singleton(sk0_4),sk0_3),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f81,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| sk0_0(X1,singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f19,f48]) ).
fof(f93,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ member(X0,X1)
| subset(singleton(X0),X1) ),
inference(paramodulation,[status(thm)],[f81,f20]) ).
fof(f94,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f93]) ).
fof(f104,plain,
~ member(sk0_4,sk0_3),
inference(resolution,[status(thm)],[f94,f71]) ).
fof(f105,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f104,f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n012.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 : Mon Apr 29 21:37:57 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.032832 seconds
% 0.13/0.40 % CPU time: 0.078946 seconds
% 0.13/0.40 % Total memory used: 14.683 MB
% 0.13/0.40 % Net memory used: 14.635 MB
%------------------------------------------------------------------------------