TSTP Solution File: SET880+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET880+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 12:35:27 EDT 2023
% Result : Theorem 0.18s 0.57s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 5 unt; 0 def)
% Number of atoms : 63 ( 40 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 71 ( 27 ~; 26 |; 13 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 (; 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
! [A,B] :
( ( B != singleton(A)
| ! [C] :
( ( ~ in(C,B)
| C = A )
& ( in(C,B)
| C != A ) ) )
& ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f12,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f13,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ( ( ~ in(sk0_0(B,A),B)
| sk0_0(B,A) != A )
& ( in(sk0_0(B,A),B)
| sk0_0(B,A) = A ) ) ) ),
inference(skolemization,[status(esa)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f19,plain,
! [A,B] :
( ( set_difference(singleton(A),B) != empty_set
| in(A,B) )
& ( set_difference(singleton(A),B) = empty_set
| ~ in(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f20,plain,
( ! [A,B] :
( set_difference(singleton(A),B) != empty_set
| in(A,B) )
& ! [A,B] :
( set_difference(singleton(A),B) = empty_set
| ~ in(A,B) ) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( set_difference(singleton(X0),X1) != empty_set
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f27,plain,
? [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
& A != B ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f28,plain,
( set_difference(singleton(sk0_3),singleton(sk0_4)) = empty_set
& sk0_3 != sk0_4 ),
inference(skolemization,[status(esa)],[f27]) ).
fof(f29,plain,
set_difference(singleton(sk0_3),singleton(sk0_4)) = empty_set,
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
sk0_3 != sk0_4,
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f31,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f14]) ).
fof(f33,plain,
in(sk0_3,singleton(sk0_4)),
inference(resolution,[status(thm)],[f21,f29]) ).
fof(f44,plain,
sk0_3 = sk0_4,
inference(resolution,[status(thm)],[f33,f31]) ).
fof(f45,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f44,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET880+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n009.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 : Tue May 30 10:11:01 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.18/0.57 % Refutation found
% 0.18/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.57 % Elapsed time: 0.018071 seconds
% 0.18/0.57 % CPU time: 0.028011 seconds
% 0.18/0.57 % Memory used: 14.224 MB
%------------------------------------------------------------------------------