TSTP Solution File: SET879+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET879+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 3 unt; 0 def)
% Number of atoms : 113 ( 59 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 126 ( 52 ~; 52 |; 13 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 43 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f10,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(f11,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)],[f10]) ).
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)
| ( ( ~ 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)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| in(X2,X0)
| X2 != X1 ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f17,plain,
! [A,B] :
( ( set_difference(singleton(A),B) != singleton(A)
| ~ in(A,B) )
& ( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f18,plain,
( ! [A,B] :
( set_difference(singleton(A),B) != singleton(A)
| ~ in(A,B) )
& ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( set_difference(singleton(X0),X1) != singleton(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f25,plain,
? [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<~> A != B ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
? [A,B] :
( ( set_difference(singleton(A),singleton(B)) = singleton(A)
| A != B )
& ( set_difference(singleton(A),singleton(B)) != singleton(A)
| A = B ) ),
inference(NNF_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
( ( set_difference(singleton(sk0_3),singleton(sk0_4)) = singleton(sk0_3)
| sk0_3 != sk0_4 )
& ( set_difference(singleton(sk0_3),singleton(sk0_4)) != singleton(sk0_3)
| sk0_3 = sk0_4 ) ),
inference(skolemization,[status(esa)],[f26]) ).
fof(f28,plain,
( set_difference(singleton(sk0_3),singleton(sk0_4)) = singleton(sk0_3)
| sk0_3 != sk0_4 ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
( set_difference(singleton(sk0_3),singleton(sk0_4)) != singleton(sk0_3)
| sk0_3 = sk0_4 ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f30,plain,
( spl0_0
<=> set_difference(singleton(sk0_3),singleton(sk0_4)) = singleton(sk0_3) ),
introduced(split_symbol_definition) ).
fof(f31,plain,
( set_difference(singleton(sk0_3),singleton(sk0_4)) = singleton(sk0_3)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f32,plain,
( set_difference(singleton(sk0_3),singleton(sk0_4)) != singleton(sk0_3)
| spl0_0 ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,plain,
( spl0_1
<=> sk0_3 = sk0_4 ),
introduced(split_symbol_definition) ).
fof(f34,plain,
( sk0_3 = sk0_4
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f28,f30,f33]) ).
fof(f37,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f29,f30,f33]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f13]) ).
fof(f39,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f14]) ).
fof(f40,plain,
( in(sk0_3,singleton(sk0_4))
| spl0_0 ),
inference(resolution,[status(thm)],[f20,f32]) ).
fof(f41,plain,
( spl0_2
<=> singleton(sk0_3) = singleton(sk0_3) ),
introduced(split_symbol_definition) ).
fof(f43,plain,
( singleton(sk0_3) != singleton(sk0_3)
| spl0_2 ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f49,plain,
( set_difference(singleton(sk0_3),singleton(sk0_3)) = singleton(sk0_3)
| ~ spl0_1
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f34,f31]) ).
fof(f50,plain,
( ~ in(sk0_3,singleton(sk0_3))
| ~ spl0_1
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f49,f19]) ).
fof(f60,plain,
( $false
| ~ spl0_1
| ~ spl0_0 ),
inference(backward_subsumption_resolution,[status(thm)],[f50,f39]) ).
fof(f61,plain,
( ~ spl0_1
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f43]) ).
fof(f63,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f69,plain,
( sk0_3 = sk0_4
| spl0_0 ),
inference(resolution,[status(thm)],[f38,f40]) ).
fof(f70,plain,
( spl0_1
| spl0_0 ),
inference(split_clause,[status(thm)],[f69,f33,f30]) ).
fof(f71,plain,
$false,
inference(sat_refutation,[status(thm)],[f36,f37,f61,f63,f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SET879+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.16 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.38 % Computer : n014.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Mon Apr 29 21:33:49 EDT 2024
% 0.14/0.38 % CPUTime :
% 0.14/0.39 % Drodi V3.6.0
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.023209 seconds
% 0.14/0.41 % CPU time: 0.032690 seconds
% 0.14/0.41 % Total memory used: 11.141 MB
% 0.14/0.41 % Net memory used: 11.112 MB
%------------------------------------------------------------------------------