TSTP Solution File: SET696+4 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 12:35:03 EDT 2023
% Result : Theorem 0.15s 0.37s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 6 unt; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 52 ~; 47 |; 23 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 78 (; 74 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,E] :
( subset(A,E)
=> equal_set(intersection(difference(E,A),A),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,E] :
( subset(A,E)
=> equal_set(intersection(difference(E,A),A),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(f32,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
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(f41,plain,
! [B,A,E] :
( ( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) )
& ( member(B,difference(E,A))
| ~ member(B,E)
| member(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f42,plain,
( ! [B,A,E] :
( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) )
& ! [B,A,E] :
( member(B,difference(E,A))
| ~ member(B,E)
| member(B,A) ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f68,plain,
? [A,E] :
( subset(A,E)
& ~ equal_set(intersection(difference(E,A),A),empty_set) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
( subset(sk0_3,sk0_4)
& ~ equal_set(intersection(difference(sk0_4,sk0_3),sk0_3),empty_set) ),
inference(skolemization,[status(esa)],[f68]) ).
fof(f71,plain,
~ equal_set(intersection(difference(sk0_4,sk0_3),sk0_3),empty_set),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f80,plain,
! [X0,X1] :
( member(sk0_0(X0,X1),X1)
| equal_set(X0,X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f19,f25]) ).
fof(f89,plain,
! [X0,X1] :
( member(sk0_0(X0,X1),X1)
| equal_set(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(resolution,[status(thm)],[f80,f19]) ).
fof(f90,plain,
( spl0_4
<=> member(sk0_0(intersection(difference(sk0_4,sk0_3),sk0_3),empty_set),empty_set) ),
introduced(split_symbol_definition) ).
fof(f91,plain,
( member(sk0_0(intersection(difference(sk0_4,sk0_3),sk0_3),empty_set),empty_set)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( spl0_5
<=> member(sk0_0(empty_set,intersection(difference(sk0_4,sk0_3),sk0_3)),intersection(difference(sk0_4,sk0_3),sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f94,plain,
( member(sk0_0(empty_set,intersection(difference(sk0_4,sk0_3),sk0_3)),intersection(difference(sk0_4,sk0_3),sk0_3))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( member(sk0_0(intersection(difference(sk0_4,sk0_3),sk0_3),empty_set),empty_set)
| member(sk0_0(empty_set,intersection(difference(sk0_4,sk0_3),sk0_3)),intersection(difference(sk0_4,sk0_3),sk0_3)) ),
inference(resolution,[status(thm)],[f89,f71]) ).
fof(f97,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f96,f90,f93]) ).
fof(f100,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f40]) ).
fof(f101,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f100]) ).
fof(f154,plain,
( member(sk0_0(empty_set,intersection(difference(sk0_4,sk0_3),sk0_3)),sk0_3)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f94,f33]) ).
fof(f155,plain,
( member(sk0_0(empty_set,intersection(difference(sk0_4,sk0_3),sk0_3)),difference(sk0_4,sk0_3))
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f94,f32]) ).
fof(f179,plain,
( ~ member(sk0_0(empty_set,intersection(difference(sk0_4,sk0_3),sk0_3)),sk0_3)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f155,f44]) ).
fof(f180,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f154]) ).
fof(f181,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f180]) ).
fof(f182,plain,
$false,
inference(sat_refutation,[status(thm)],[f97,f101,f181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.10 % Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n031.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue May 30 10:36:22 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.5.1
% 0.15/0.37 % Refutation found
% 0.15/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.31/0.61 % Elapsed time: 0.080464 seconds
% 0.31/0.61 % CPU time: 0.140663 seconds
% 0.31/0.61 % Memory used: 11.614 MB
%------------------------------------------------------------------------------