TSTP Solution File: SEU120+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU120+1 : TPTP v8.1.2. Released v3.3.0.
% 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 12:35:51 EDT 2023
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 3 unt; 0 def)
% Number of atoms : 101 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 111 ( 51 ~; 36 |; 18 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 64 (; 49 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,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(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ~ ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ~ ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f17,plain,
! [A] :
( ( A != empty_set
| ! [B] : ~ in(B,A) )
& ( A = empty_set
| ? [B] : in(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f18,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| ? [B] : in(B,A) ) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f19,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| in(sk0_0(A),A) ) ),
inference(skolemization,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
! [X0] :
( X0 = empty_set
| in(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f22,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)],[f4]) ).
fof(f23,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)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f35,plain,
? [A,B] :
( ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
| ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f36,plain,
! [A,B] :
( pd0_0(B,A)
=> ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) ) ),
introduced(predicate_definition,[f35]) ).
fof(f37,plain,
? [A,B] :
( pd0_0(B,A)
| ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
inference(formula_renaming,[status(thm)],[f35,f36]) ).
fof(f38,plain,
( ? [A,B] : pd0_0(B,A)
| ? [A,B] :
( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
inference(miniscoping,[status(esa)],[f37]) ).
fof(f39,plain,
( pd0_0(sk0_4,sk0_3)
| ( in(sk0_7,set_intersection2(sk0_5,sk0_6))
& disjoint(sk0_5,sk0_6) ) ),
inference(skolemization,[status(esa)],[f38]) ).
fof(f40,plain,
( pd0_0(sk0_4,sk0_3)
| in(sk0_7,set_intersection2(sk0_5,sk0_6)) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
( pd0_0(sk0_4,sk0_3)
| disjoint(sk0_5,sk0_6) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f42,plain,
! [A,B] :
( ~ pd0_0(B,A)
| ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f36]) ).
fof(f43,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| ~ disjoint(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1)
| ~ in(X2,set_intersection2(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
( spl0_0
<=> pd0_0(sk0_4,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( pd0_0(sk0_4,sk0_3)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( spl0_1
<=> in(sk0_7,set_intersection2(sk0_5,sk0_6)) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( in(sk0_7,set_intersection2(sk0_5,sk0_6))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f40,f45,f48]) ).
fof(f52,plain,
( spl0_2
<=> disjoint(sk0_5,sk0_6) ),
introduced(split_symbol_definition) ).
fof(f53,plain,
( disjoint(sk0_5,sk0_6)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f41,f45,f52]) ).
fof(f63,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ pd0_0(X1,X0) ),
inference(resolution,[status(thm)],[f21,f44]) ).
fof(f75,plain,
! [X0,X1] :
( disjoint(X0,X1)
| ~ pd0_0(X1,X0) ),
inference(resolution,[status(thm)],[f25,f63]) ).
fof(f76,plain,
! [X0,X1] : ~ pd0_0(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f75,f43]) ).
fof(f82,plain,
( $false
| ~ spl0_0 ),
inference(backward_subsumption_resolution,[status(thm)],[f46,f76]) ).
fof(f83,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f82]) ).
fof(f93,plain,
( set_intersection2(sk0_5,sk0_6) != empty_set
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f49,f20]) ).
fof(f96,plain,
( ~ disjoint(sk0_5,sk0_6)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f93,f24]) ).
fof(f97,plain,
( $false
| ~ spl0_2
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f53]) ).
fof(f98,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f99,plain,
$false,
inference(sat_refutation,[status(thm)],[f51,f55,f83,f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU120+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 09:29:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.024670 seconds
% 0.13/0.38 % CPU time: 0.036234 seconds
% 0.13/0.38 % Memory used: 14.315 MB
%------------------------------------------------------------------------------