TSTP Solution File: SET867+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% 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 12:35:26 EDT 2023
% Result : Theorem 0.25s 0.57s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 73 ( 21 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 89 ( 33 ~; 34 |; 19 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 49 (; 40 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
union(empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
union(empty_set) != empty_set,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
! [A] :
( ( A != empty_set
| ! [B] : ~ in(B,A) )
& ( A = empty_set
| ? [B] : in(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f12,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| ? [B] : in(B,A) ) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f13,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| in(sk0_0(A),A) ) ),
inference(skolemization,[status(esa)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f16,plain,
! [A,B] :
( ( B != union(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) )
& ( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) )
& ( in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f17,plain,
( ! [A,B] :
( B != union(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) )
& ! [C] :
( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ! [A,B] :
( B = union(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) )
& ( in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f18,plain,
( ! [A,B] :
( B != union(A)
| ( ! [C] :
( ~ in(C,B)
| ( in(C,sk0_1(C,B,A))
& in(sk0_1(C,B,A),A) ) )
& ! [C] :
( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ! [A,B] :
( B = union(A)
| ( ( ~ in(sk0_2(B,A),B)
| ! [D] :
( ~ in(sk0_2(B,A),D)
| ~ in(D,A) ) )
& ( in(sk0_2(B,A),B)
| ( in(sk0_2(B,A),sk0_3(B,A))
& in(sk0_3(B,A),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f17]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = union(X1)
| in(sk0_2(X0,X1),X0)
| in(sk0_3(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f30,plain,
union(empty_set) != empty_set,
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f31,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(esa)],[f14]) ).
fof(f72,plain,
! [X0] :
( empty_set = union(X0)
| in(sk0_3(empty_set,X0),X0) ),
inference(resolution,[status(thm)],[f24,f31]) ).
fof(f80,plain,
empty_set = union(empty_set),
inference(resolution,[status(thm)],[f72,f31]) ).
fof(f81,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f80,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n002.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 : Tue May 30 10:34:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.25/0.57 % Refutation found
% 0.25/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.25/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.57 % Elapsed time: 0.015928 seconds
% 0.25/0.57 % CPU time: 0.055727 seconds
% 0.25/0.57 % Memory used: 11.582 MB
%------------------------------------------------------------------------------