TSTP Solution File: SEU153+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU153+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 12:36:01 EDT 2023
% Result : Theorem 0.15s 0.33s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 135 ( 45 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 164 ( 62 ~; 62 |; 34 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 89 (; 81 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] :
~ ( disjoint(singleton(A),B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] :
~ ( disjoint(singleton(A),B)
& in(A,B) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f20,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)],[f3]) ).
fof(f21,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)],[f20]) ).
fof(f22,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)],[f21]) ).
fof(f24,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| in(X2,X0)
| X2 != X1 ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f27,plain,
! [A] :
( ( A != empty_set
| ! [B] : ~ in(B,A) )
& ( A = empty_set
| ? [B] : in(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f28,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| ? [B] : in(B,A) ) ),
inference(miniscoping,[status(esa)],[f27]) ).
fof(f29,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| in(sk0_1(A),A) ) ),
inference(skolemization,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f32,plain,
! [A,B,C] :
( ( C != set_intersection2(A,B)
| ! [D] :
( ( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ~ in(D,A)
| ~ in(D,B) )
& ( in(D,C)
| ( in(D,A)
& in(D,B) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f33,plain,
( ! [A,B,C] :
( C != set_intersection2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ! [D] :
( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ! [A,B,C] :
( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ~ in(D,A)
| ~ in(D,B) )
& ( in(D,C)
| ( in(D,A)
& in(D,B) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f32]) ).
fof(f34,plain,
( ! [A,B,C] :
( C != set_intersection2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ! [D] :
( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ! [A,B,C] :
( C = set_intersection2(A,B)
| ( ( ~ in(sk0_2(C,B,A),C)
| ~ in(sk0_2(C,B,A),A)
| ~ in(sk0_2(C,B,A),B) )
& ( in(sk0_2(C,B,A),C)
| ( in(sk0_2(C,B,A),A)
& in(sk0_2(C,B,A),B) ) ) ) ) ),
inference(skolemization,[status(esa)],[f33]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f41,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set )
& ( disjoint(A,B)
| set_intersection2(A,B) != empty_set ) ),
inference(NNF_transformation,[status(esa)],[f6]) ).
fof(f42,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set )
& ! [A,B] :
( disjoint(A,B)
| set_intersection2(A,B) != empty_set ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f48,plain,
? [A,B] :
( disjoint(singleton(A),B)
& in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f49,plain,
( disjoint(singleton(sk0_3),sk0_4)
& in(sk0_3,sk0_4) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
disjoint(singleton(sk0_3),sk0_4),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
in(sk0_3,sk0_4),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f59,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f24]) ).
fof(f60,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(esa)],[f30]) ).
fof(f63,plain,
! [X0,X1,X2] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X1)
| ~ in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f37]) ).
fof(f66,plain,
set_intersection2(singleton(sk0_3),sk0_4) = empty_set,
inference(resolution,[status(thm)],[f43,f50]) ).
fof(f130,plain,
! [X0] :
( in(sk0_3,set_intersection2(X0,sk0_4))
| ~ in(sk0_3,X0) ),
inference(resolution,[status(thm)],[f63,f51]) ).
fof(f140,plain,
in(sk0_3,set_intersection2(singleton(sk0_3),sk0_4)),
inference(resolution,[status(thm)],[f130,f59]) ).
fof(f141,plain,
in(sk0_3,empty_set),
inference(forward_demodulation,[status(thm)],[f66,f140]) ).
fof(f142,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f141,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU153+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n019.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 09:10:10 EDT 2023
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % Drodi V3.5.1
% 0.15/0.33 % Refutation found
% 0.15/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.55 % Elapsed time: 0.011754 seconds
% 0.15/0.55 % CPU time: 0.012978 seconds
% 0.15/0.55 % Memory used: 3.666 MB
%------------------------------------------------------------------------------