TSTP Solution File: SET027+4 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET027+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 12:33:39 EDT 2023
% Result : Theorem 0.10s 0.49s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 6 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 27 ~; 23 |; 14 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 47 (; 39 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
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(f18,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
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(f68,plain,
? [A,B,C] :
( subset(A,B)
& subset(B,C)
& ~ subset(A,C) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
? [A,C] :
( ? [B] :
( subset(A,B)
& subset(B,C) )
& ~ subset(A,C) ),
inference(miniscoping,[status(esa)],[f68]) ).
fof(f70,plain,
( subset(sk0_3,sk0_5)
& subset(sk0_5,sk0_4)
& ~ subset(sk0_3,sk0_4) ),
inference(skolemization,[status(esa)],[f69]) ).
fof(f71,plain,
subset(sk0_3,sk0_5),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
subset(sk0_5,sk0_4),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
~ subset(sk0_3,sk0_4),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f86,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X2,X1)
| ~ member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f123,plain,
! [X0] :
( subset(X0,sk0_4)
| ~ member(sk0_0(sk0_4,X0),sk0_5) ),
inference(resolution,[status(thm)],[f86,f72]) ).
fof(f132,plain,
! [X0,X1] :
( subset(X0,sk0_4)
| ~ subset(X1,sk0_5)
| ~ member(sk0_0(sk0_4,X0),X1) ),
inference(resolution,[status(thm)],[f123,f18]) ).
fof(f140,plain,
! [X0] :
( subset(X0,sk0_4)
| ~ member(sk0_0(sk0_4,X0),sk0_3) ),
inference(resolution,[status(thm)],[f132,f71]) ).
fof(f142,plain,
( spl0_2
<=> subset(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f143,plain,
( subset(sk0_3,sk0_4)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( subset(sk0_3,sk0_4)
| subset(sk0_3,sk0_4) ),
inference(resolution,[status(thm)],[f140,f19]) ).
fof(f146,plain,
spl0_2,
inference(split_clause,[status(thm)],[f145,f142]) ).
fof(f148,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f73]) ).
fof(f149,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f150,plain,
$false,
inference(sat_refutation,[status(thm)],[f146,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET027+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.26 % Computer : n002.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue May 30 10:30:42 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.06/0.26 % Drodi V3.5.1
% 0.10/0.49 % Refutation found
% 0.10/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.49 % Elapsed time: 0.012195 seconds
% 0.10/0.49 % CPU time: 0.014294 seconds
% 0.10/0.49 % Memory used: 2.943 MB
%------------------------------------------------------------------------------