TSTP Solution File: SET877+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET877+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 20:40:37 EDT 2024
% Result : Theorem 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 61 ( 40 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 65 ( 25 ~; 24 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( set_intersection2(A,singleton(B)) = singleton(B)
=> in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B] :
( set_intersection2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B] :
( set_intersection2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f13,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(f14,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)],[f13]) ).
fof(f15,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)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f22,plain,
! [A,B] :
( set_intersection2(A,singleton(B)) != singleton(B)
| in(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f23,plain,
! [X0,X1] :
( set_intersection2(X0,singleton(X1)) != singleton(X1)
| in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f28,plain,
? [A,B] :
( set_intersection2(singleton(A),singleton(B)) = singleton(A)
& A != B ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f29,plain,
( set_intersection2(singleton(sk0_3),singleton(sk0_4)) = singleton(sk0_3)
& sk0_3 != sk0_4 ),
inference(skolemization,[status(esa)],[f28]) ).
fof(f30,plain,
set_intersection2(singleton(sk0_3),singleton(sk0_4)) = singleton(sk0_3),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
sk0_3 != sk0_4,
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f16]) ).
fof(f43,plain,
! [X0,X1] :
( set_intersection2(singleton(X0),X1) != singleton(X0)
| in(X0,X1) ),
inference(paramodulation,[status(thm)],[f12,f23]) ).
fof(f47,plain,
in(sk0_3,singleton(sk0_4)),
inference(resolution,[status(thm)],[f43,f30]) ).
fof(f65,plain,
sk0_3 = sk0_4,
inference(resolution,[status(thm)],[f32,f47]) ).
fof(f66,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f65,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET877+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34 % Computer : n013.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Mon Apr 29 21:37:04 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.11/0.35 % Drodi V3.6.0
% 0.11/0.36 % Refutation found
% 0.11/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.37 % Elapsed time: 0.020129 seconds
% 0.11/0.37 % CPU time: 0.017435 seconds
% 0.11/0.37 % Total memory used: 7.241 MB
% 0.11/0.37 % Net memory used: 7.181 MB
%------------------------------------------------------------------------------