TSTP Solution File: SEU114+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 1.99s 0.61s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 8 unt; 0 def)
% Number of atoms : 180 ( 22 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 207 ( 78 ~; 82 |; 32 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 106 (; 101 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] : subset(finite_subsets(A),powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,plain,
! [A] :
( ~ finite(A)
| ! [B] :
( ~ element(B,powerset(A))
| finite(B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f46,plain,
! [X0,X1] :
( ~ finite(X0)
| ~ element(X1,powerset(X0))
| finite(X1) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f52,plain,
! [A,B] :
( ( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f53,plain,
( ! [A,B] :
( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f58,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)],[f57]) ).
fof(f59,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)],[f58]) ).
fof(f60,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)],[f59]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f64,plain,
! [A,B] :
( ~ preboolean(B)
| ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f65,plain,
! [A,B] :
( ~ preboolean(B)
| ( ( B != finite_subsets(A)
| ! [C] :
( ( ~ in(C,B)
| ( subset(C,A)
& finite(C) ) )
& ( in(C,B)
| ~ subset(C,A)
| ~ finite(C) ) ) )
& ( B = finite_subsets(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A)
| ~ finite(C) )
& ( in(C,B)
| ( subset(C,A)
& finite(C) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [B] :
( ~ preboolean(B)
| ( ! [A] :
( B != finite_subsets(A)
| ( ! [C] :
( ~ in(C,B)
| ( subset(C,A)
& finite(C) ) )
& ! [C] :
( in(C,B)
| ~ subset(C,A)
| ~ finite(C) ) ) )
& ! [A] :
( B = finite_subsets(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A)
| ~ finite(C) )
& ( in(C,B)
| ( subset(C,A)
& finite(C) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f65]) ).
fof(f67,plain,
! [B] :
( ~ preboolean(B)
| ( ! [A] :
( B != finite_subsets(A)
| ( ! [C] :
( ~ in(C,B)
| ( subset(C,A)
& finite(C) ) )
& ! [C] :
( in(C,B)
| ~ subset(C,A)
| ~ finite(C) ) ) )
& ! [A] :
( B = finite_subsets(A)
| ( ( ~ in(sk0_1(A,B),B)
| ~ subset(sk0_1(A,B),A)
| ~ finite(sk0_1(A,B)) )
& ( in(sk0_1(A,B),B)
| ( subset(sk0_1(A,B),A)
& finite(sk0_1(A,B)) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f66]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ preboolean(X0)
| X0 != finite_subsets(X1)
| in(X2,X0)
| ~ subset(X2,X1)
| ~ finite(X2) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f74,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f135,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f136,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f135]) ).
fof(f137,plain,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f138,plain,
? [A] :
( finite(A)
& finite_subsets(A) != powerset(A) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f139,plain,
( finite(sk0_12)
& finite_subsets(sk0_12) != powerset(sk0_12) ),
inference(skolemization,[status(esa)],[f138]) ).
fof(f140,plain,
finite(sk0_12),
inference(cnf_transformation,[status(esa)],[f139]) ).
fof(f141,plain,
finite_subsets(sk0_12) != powerset(sk0_12),
inference(cnf_transformation,[status(esa)],[f139]) ).
fof(f144,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f32]) ).
fof(f145,plain,
( ! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) )
& ! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f166,plain,
! [X0,X1] :
( ~ preboolean(finite_subsets(X0))
| in(X1,finite_subsets(X0))
| ~ subset(X1,X0)
| ~ finite(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f70]) ).
fof(f177,plain,
! [X0] :
( powerset(X0) = finite_subsets(X0)
| ~ subset(powerset(X0),finite_subsets(X0)) ),
inference(resolution,[status(thm)],[f56,f137]) ).
fof(f319,plain,
! [X0,X1] :
( in(X0,finite_subsets(X1))
| ~ subset(X0,X1)
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f74]) ).
fof(f320,plain,
! [X0,X1] :
( ~ subset(sk0_0(finite_subsets(X0),X1),X0)
| ~ finite(sk0_0(finite_subsets(X0),X1))
| subset(X1,finite_subsets(X0)) ),
inference(resolution,[status(thm)],[f319,f63]) ).
fof(f378,plain,
! [X0,X1] :
( element(sk0_0(X0,X1),X1)
| subset(X1,X0) ),
inference(resolution,[status(thm)],[f136,f62]) ).
fof(f1496,plain,
! [X0,X1] :
( subset(powerset(X0),X1)
| ~ finite(X0)
| finite(sk0_0(X1,powerset(X0))) ),
inference(resolution,[status(thm)],[f378,f46]) ).
fof(f1498,plain,
! [X0,X1] :
( subset(powerset(X0),X1)
| subset(sk0_0(X1,powerset(X0)),X0) ),
inference(resolution,[status(thm)],[f378,f146]) ).
fof(f1860,plain,
! [X0] :
( subset(powerset(X0),finite_subsets(X0))
| ~ finite(sk0_0(finite_subsets(X0),powerset(X0)))
| subset(powerset(X0),finite_subsets(X0)) ),
inference(resolution,[status(thm)],[f1498,f320]) ).
fof(f1861,plain,
! [X0] :
( subset(powerset(X0),finite_subsets(X0))
| ~ finite(sk0_0(finite_subsets(X0),powerset(X0))) ),
inference(duplicate_literals_removal,[status(esa)],[f1860]) ).
fof(f1875,plain,
! [X0] :
( subset(powerset(X0),finite_subsets(X0))
| subset(powerset(X0),finite_subsets(X0))
| ~ finite(X0) ),
inference(resolution,[status(thm)],[f1861,f1496]) ).
fof(f1876,plain,
! [X0] :
( subset(powerset(X0),finite_subsets(X0))
| ~ finite(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f1875]) ).
fof(f1879,plain,
! [X0] :
( ~ finite(X0)
| powerset(X0) = finite_subsets(X0) ),
inference(resolution,[status(thm)],[f1876,f177]) ).
fof(f1890,plain,
~ finite(sk0_12),
inference(resolution,[status(thm)],[f1879,f141]) ).
fof(f1891,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1890,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 09:31:17 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 1.99/0.61 % Refutation found
% 1.99/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.99/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.20/0.63 % Elapsed time: 0.293075 seconds
% 2.20/0.63 % CPU time: 2.197899 seconds
% 2.20/0.63 % Memory used: 72.415 MB
%------------------------------------------------------------------------------