TSTP Solution File: SET602+4 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET602+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 20:39:56 EDT 2024
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 106 ( 44 ~; 39 |; 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 : 60 ( 57 !; 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(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [E] : equal_set(difference(E,E),empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [E] : equal_set(difference(E,E),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(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(f43,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f68,plain,
? [E] : ~ equal_set(difference(E,E),empty_set),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ equal_set(difference(sk0_3,sk0_3),empty_set),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ equal_set(difference(sk0_3,sk0_3),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(difference(sk0_3,sk0_3),empty_set),empty_set) ),
introduced(split_symbol_definition) ).
fof(f77,plain,
( member(sk0_0(difference(sk0_3,sk0_3),empty_set),empty_set)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( spl0_1
<=> member(sk0_0(empty_set,difference(sk0_3,sk0_3)),difference(sk0_3,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f80,plain,
( member(sk0_0(empty_set,difference(sk0_3,sk0_3)),difference(sk0_3,sk0_3))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( member(sk0_0(difference(sk0_3,sk0_3),empty_set),empty_set)
| member(sk0_0(empty_set,difference(sk0_3,sk0_3)),difference(sk0_3,sk0_3)) ),
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,difference(sk0_3,sk0_3)),sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f80,f44]) ).
fof(f89,plain,
( member(sk0_0(empty_set,difference(sk0_3,sk0_3)),sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f80,f43]) ).
fof(f91,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f88]) ).
fof(f92,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f91]) ).
fof(f93,plain,
$false,
inference(sat_refutation,[status(thm)],[f83,f87,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET602+4 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 21:19:17 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 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
% 0.13/0.38 % Elapsed time: 0.022556 seconds
% 0.13/0.38 % CPU time: 0.051833 seconds
% 0.13/0.38 % Total memory used: 12.974 MB
% 0.13/0.38 % Net memory used: 12.939 MB
%------------------------------------------------------------------------------