TSTP Solution File: SET941+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET941+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 : Wed May 31 12:35:35 EDT 2023
% Result : Theorem 0.21s 0.37s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 4 unt; 0 def)
% Number of atoms : 125 ( 9 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 147 ( 56 ~; 57 |; 24 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 86 (; 75 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,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(f7,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> subset(C,B) )
=> subset(union(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> subset(C,B) )
=> subset(union(A),B) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f12,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f11]) ).
fof(f13,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f14,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_0(B,A),A)
& ~ in(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f18,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)],[f3]) ).
fof(f19,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)],[f18]) ).
fof(f20,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)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( X0 != union(X1)
| ~ in(X2,X0)
| in(X2,sk0_1(X2,X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( X0 != union(X1)
| ~ in(X2,X0)
| in(sk0_1(X2,X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f33,plain,
? [A,B] :
( ! [C] :
( ~ in(C,A)
| subset(C,B) )
& ~ subset(union(A),B) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f34,plain,
( ! [C] :
( ~ in(C,sk0_6)
| subset(C,sk0_7) )
& ~ subset(union(sk0_6),sk0_7) ),
inference(skolemization,[status(esa)],[f33]) ).
fof(f35,plain,
! [X0] :
( ~ in(X0,sk0_6)
| subset(X0,sk0_7) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
~ subset(union(sk0_6),sk0_7),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( ~ in(X0,union(X1))
| in(X0,sk0_1(X0,union(X1),X1)) ),
inference(destructive_equality_resolution,[status(esa)],[f21]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X0,union(X1))
| in(sk0_1(X0,union(X1),X1),X1) ),
inference(destructive_equality_resolution,[status(esa)],[f22]) ).
fof(f86,plain,
! [X0] :
( ~ in(X0,union(sk0_6))
| subset(sk0_1(X0,union(sk0_6),sk0_6),sk0_7) ),
inference(resolution,[status(thm)],[f38,f35]) ).
fof(f106,plain,
! [X0,X1] :
( ~ in(X0,union(sk0_6))
| ~ in(X1,sk0_1(X0,union(sk0_6),sk0_6))
| in(X1,sk0_7) ),
inference(resolution,[status(thm)],[f86,f15]) ).
fof(f111,plain,
! [X0] :
( ~ in(X0,union(sk0_6))
| in(X0,sk0_7)
| ~ in(X0,union(sk0_6)) ),
inference(resolution,[status(thm)],[f106,f37]) ).
fof(f112,plain,
! [X0] :
( ~ in(X0,union(sk0_6))
| in(X0,sk0_7) ),
inference(duplicate_literals_removal,[status(esa)],[f111]) ).
fof(f115,plain,
! [X0] :
( in(sk0_0(X0,union(sk0_6)),sk0_7)
| subset(union(sk0_6),X0) ),
inference(resolution,[status(thm)],[f112,f16]) ).
fof(f122,plain,
( spl0_0
<=> subset(union(sk0_6),sk0_7) ),
introduced(split_symbol_definition) ).
fof(f123,plain,
( subset(union(sk0_6),sk0_7)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( subset(union(sk0_6),sk0_7)
| subset(union(sk0_6),sk0_7) ),
inference(resolution,[status(thm)],[f115,f17]) ).
fof(f126,plain,
spl0_0,
inference(split_clause,[status(thm)],[f125,f122]) ).
fof(f128,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f36]) ).
fof(f129,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f128]) ).
fof(f130,plain,
$false,
inference(sat_refutation,[status(thm)],[f126,f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET941+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n014.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 10:08:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.35 % Drodi V3.5.1
% 0.21/0.37 % Refutation found
% 0.21/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.32/0.59 % Elapsed time: 0.025248 seconds
% 0.32/0.59 % CPU time: 0.074170 seconds
% 0.32/0.59 % Memory used: 11.884 MB
%------------------------------------------------------------------------------