TSTP Solution File: SEU117+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU117+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 128 ( 9 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 142 ( 53 ~; 51 |; 27 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 58 (; 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( ~ empty(finite_subsets(A))
& cup_closed(finite_subsets(A))
& diff_closed(finite_subsets(A))
& preboolean(finite_subsets(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,conjecture,
! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ ! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f40,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f55,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f61,plain,
( ! [A] : ~ empty(finite_subsets(A))
& ! [A] : cup_closed(finite_subsets(A))
& ! [A] : diff_closed(finite_subsets(A))
& ! [A] : preboolean(finite_subsets(A)) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f62,plain,
! [X0] : ~ empty(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f118,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f28]) ).
fof(f119,plain,
( ! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) )
& ! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f118]) ).
fof(f121,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f128,plain,
? [A,B] :
( element(B,finite_subsets(A))
& ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f32]) ).
fof(f129,plain,
( element(sk0_11,finite_subsets(sk0_10))
& ~ element(sk0_11,powerset(sk0_10)) ),
inference(skolemization,[status(esa)],[f128]) ).
fof(f130,plain,
element(sk0_11,finite_subsets(sk0_10)),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f131,plain,
~ element(sk0_11,powerset(sk0_10)),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f132,plain,
! [A,B] :
( ~ preboolean(B)
| ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f133,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)],[f132]) ).
fof(f134,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)],[f133]) ).
fof(f135,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_12(A,B),B)
| ~ subset(sk0_12(A,B),A)
| ~ finite(sk0_12(A,B)) )
& ( in(sk0_12(A,B),B)
| ( subset(sk0_12(A,B),A)
& finite(sk0_12(A,B)) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ preboolean(X0)
| X0 != finite_subsets(X1)
| ~ in(X2,X0)
| subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f135]) ).
fof(f142,plain,
! [X0,X1] :
( ~ preboolean(finite_subsets(X0))
| ~ in(X1,finite_subsets(X0))
| subset(X1,X0) ),
inference(destructive_equality_resolution,[status(esa)],[f136]) ).
fof(f161,plain,
( spl0_2
<=> empty(finite_subsets(sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f162,plain,
( empty(finite_subsets(sk0_10))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( spl0_3
<=> in(sk0_11,finite_subsets(sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f165,plain,
( in(sk0_11,finite_subsets(sk0_10))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( empty(finite_subsets(sk0_10))
| in(sk0_11,finite_subsets(sk0_10)) ),
inference(resolution,[status(thm)],[f40,f130]) ).
fof(f168,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f167,f161,f164]) ).
fof(f169,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f62]) ).
fof(f170,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f241,plain,
~ subset(sk0_11,sk0_10),
inference(resolution,[status(thm)],[f121,f131]) ).
fof(f283,plain,
! [X0,X1] :
( ~ in(X0,finite_subsets(X1))
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f55]) ).
fof(f286,plain,
( subset(sk0_11,sk0_10)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f283,f165]) ).
fof(f287,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f286,f241]) ).
fof(f288,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f289,plain,
$false,
inference(sat_refutation,[status(thm)],[f168,f170,f288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU117+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 : n027.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
% 0.12/0.34 % DateTime : Tue May 30 09:28:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.58 % Elapsed time: 0.015556 seconds
% 0.24/0.58 % CPU time: 0.047024 seconds
% 0.24/0.58 % Memory used: 12.015 MB
%------------------------------------------------------------------------------