TSTP Solution File: SET063+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET063+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 20:38:55 EDT 2024
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 39 ~; 37 |; 16 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A] : equal_set(intersection(A,empty_set),empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] : equal_set(intersection(A,empty_set),empty_set),
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(f21,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f30,plain,
! [X,A,B] :
( ( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) )
& ( member(X,intersection(A,B))
| ~ member(X,A)
| ~ member(X,B) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f31,plain,
( ! [X,A,B] :
( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) )
& ! [X,A,B] :
( member(X,intersection(A,B))
| ~ member(X,A)
| ~ member(X,B) ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f68,plain,
? [A] : ~ equal_set(intersection(A,empty_set),empty_set),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ equal_set(intersection(sk0_3,empty_set),empty_set),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ equal_set(intersection(sk0_3,empty_set),empty_set),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f74,plain,
! [X0,X1] :
( member(sk0_0(X0,X1),X1)
| equal_set(X0,X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f19,f25]) ).
fof(f75,plain,
! [X0,X1] :
( member(sk0_0(X0,X1),X1)
| equal_set(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(resolution,[status(thm)],[f74,f19]) ).
fof(f76,plain,
( spl0_0
<=> member(sk0_0(intersection(sk0_3,empty_set),empty_set),empty_set) ),
introduced(split_symbol_definition) ).
fof(f77,plain,
( member(sk0_0(intersection(sk0_3,empty_set),empty_set),empty_set)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( spl0_1
<=> member(sk0_0(empty_set,intersection(sk0_3,empty_set)),intersection(sk0_3,empty_set)) ),
introduced(split_symbol_definition) ).
fof(f80,plain,
( member(sk0_0(empty_set,intersection(sk0_3,empty_set)),intersection(sk0_3,empty_set))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( member(sk0_0(intersection(sk0_3,empty_set),empty_set),empty_set)
| member(sk0_0(empty_set,intersection(sk0_3,empty_set)),intersection(sk0_3,empty_set)) ),
inference(resolution,[status(thm)],[f75,f70]) ).
fof(f83,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f82,f76,f79]) ).
fof(f86,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f40]) ).
fof(f87,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f88,plain,
( member(sk0_0(empty_set,intersection(sk0_3,empty_set)),empty_set)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f80,f33]) ).
fof(f89,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f40]) ).
fof(f90,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f91,plain,
$false,
inference(sat_refutation,[status(thm)],[f83,f87,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET063+4 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n017.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 21:07:48 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 Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37 % Elapsed time: 0.022383 seconds
% 0.12/0.37 % CPU time: 0.052627 seconds
% 0.12/0.37 % Total memory used: 12.882 MB
% 0.12/0.37 % Net memory used: 12.810 MB
%------------------------------------------------------------------------------