TSTP Solution File: SET945+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET945+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:35:35 EDT 2023
% Result : Theorem 0.21s 0.42s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 4 unt; 0 def)
% Number of atoms : 184 ( 19 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 233 ( 94 ~; 90 |; 40 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 136 (; 122 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f4,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [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(f10,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> disjoint(C,B) )
=> disjoint(union(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> disjoint(C,B) )
=> disjoint(union(A),B) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,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)],[f3]) ).
fof(f16,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)],[f15]) ).
fof(f17,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_0(C,B,A),C)
| ~ in(sk0_0(C,B,A),A)
| ~ in(sk0_0(C,B,A),B) )
& ( in(sk0_0(C,B,A),C)
| ( in(sk0_0(C,B,A),A)
& in(sk0_0(C,B,A),B) ) ) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f24,plain,
! [A,B] :
( ( B != union(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) )
& ( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) )
& ( in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f25,plain,
( ! [A,B] :
( B != union(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) )
& ! [C] :
( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ! [A,B] :
( B = union(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) )
& ( in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f24]) ).
fof(f26,plain,
( ! [A,B] :
( B != union(A)
| ( ! [C] :
( ~ in(C,B)
| ( in(C,sk0_1(C,B,A))
& in(sk0_1(C,B,A),A) ) )
& ! [C] :
( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ! [A,B] :
( B = union(A)
| ( ( ~ in(sk0_2(B,A),B)
| ! [D] :
( ~ in(sk0_2(B,A),D)
| ~ in(D,A) ) )
& ( in(sk0_2(B,A),B)
| ( in(sk0_2(B,A),sk0_3(B,A))
& in(sk0_3(B,A),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( X0 != union(X1)
| ~ in(X2,X0)
| in(X2,sk0_1(X2,X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( X0 != union(X1)
| ~ in(X2,X0)
| in(sk0_1(X2,X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f41,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)],[f9]) ).
fof(f42,plain,
( ! [A,B] :
( disjoint(A,B)
| ? [C] : in(C,set_intersection2(A,B)) )
& ! [A,B] :
( ! [C] : ~ in(C,set_intersection2(A,B))
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f43,plain,
( ! [A,B] :
( disjoint(A,B)
| in(sk0_6(B,A),set_intersection2(A,B)) )
& ! [A,B] :
( ! [C] : ~ in(C,set_intersection2(A,B))
| ~ disjoint(A,B) ) ),
inference(skolemization,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sk0_6(X1,X0),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f46,plain,
? [A,B] :
( ! [C] :
( ~ in(C,A)
| disjoint(C,B) )
& ~ disjoint(union(A),B) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f47,plain,
( ! [C] :
( ~ in(C,sk0_7)
| disjoint(C,sk0_8) )
& ~ disjoint(union(sk0_7),sk0_8) ),
inference(skolemization,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0] :
( ~ in(X0,sk0_7)
| disjoint(X0,sk0_8) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
~ disjoint(union(sk0_7),sk0_8),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f18]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f19]) ).
fof(f52,plain,
! [X0,X1,X2] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X1)
| ~ in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f20]) ).
fof(f53,plain,
! [X0,X1] :
( ~ in(X0,union(X1))
| in(X0,sk0_1(X0,union(X1),X1)) ),
inference(destructive_equality_resolution,[status(esa)],[f27]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in(X0,union(X1))
| in(sk0_1(X0,union(X1),X1),X1) ),
inference(destructive_equality_resolution,[status(esa)],[f28]) ).
fof(f87,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sk0_6(X1,X0),X1) ),
inference(resolution,[status(thm)],[f44,f51]) ).
fof(f88,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sk0_6(X1,X0),X0) ),
inference(resolution,[status(thm)],[f44,f50]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(resolution,[status(thm)],[f52,f45]) ).
fof(f352,plain,
! [X0] :
( ~ in(X0,union(sk0_7))
| disjoint(sk0_1(X0,union(sk0_7),sk0_7),sk0_8) ),
inference(resolution,[status(thm)],[f54,f48]) ).
fof(f435,plain,
! [X0,X1] :
( ~ in(X0,union(sk0_7))
| ~ in(X1,sk0_1(X0,union(sk0_7),sk0_7))
| ~ in(X1,sk0_8) ),
inference(resolution,[status(thm)],[f352,f125]) ).
fof(f445,plain,
! [X0] :
( ~ in(X0,union(sk0_7))
| ~ in(X0,sk0_8)
| ~ in(X0,union(sk0_7)) ),
inference(resolution,[status(thm)],[f435,f53]) ).
fof(f446,plain,
! [X0] :
( ~ in(X0,union(sk0_7))
| ~ in(X0,sk0_8) ),
inference(duplicate_literals_removal,[status(esa)],[f445]) ).
fof(f451,plain,
! [X0] :
( ~ in(sk0_6(X0,union(sk0_7)),sk0_8)
| disjoint(union(sk0_7),X0) ),
inference(resolution,[status(thm)],[f446,f88]) ).
fof(f462,plain,
( spl0_0
<=> disjoint(union(sk0_7),sk0_8) ),
introduced(split_symbol_definition) ).
fof(f463,plain,
( disjoint(union(sk0_7),sk0_8)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( disjoint(union(sk0_7),sk0_8)
| disjoint(union(sk0_7),sk0_8) ),
inference(resolution,[status(thm)],[f451,f87]) ).
fof(f466,plain,
spl0_0,
inference(split_clause,[status(thm)],[f465,f462]) ).
fof(f467,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f49]) ).
fof(f468,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f469,plain,
$false,
inference(sat_refutation,[status(thm)],[f466,f468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET945+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n007.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
% 0.12/0.35 % DateTime : Tue May 30 10:00:47 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.5.1
% 0.21/0.42 % Refutation found
% 0.21/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.36/0.66 % Elapsed time: 0.098574 seconds
% 0.36/0.66 % CPU time: 0.279933 seconds
% 0.36/0.66 % Memory used: 31.547 MB
%------------------------------------------------------------------------------