TSTP Solution File: SEU118+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU118+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 0.05s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 138 ( 9 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 153 ( 58 ~; 56 |; 23 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 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] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,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(f8,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,plain,
! [A] :
( ~ finite(A)
| ! [B] :
( ~ element(B,powerset(A))
| finite(B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( ~ finite(X0)
| ~ element(X1,powerset(X0))
| finite(X1) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f49,plain,
! [A,B] :
( ~ preboolean(B)
| ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f50,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)],[f49]) ).
fof(f51,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)],[f50]) ).
fof(f52,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_0(A,B),B)
| ~ subset(sk0_0(A,B),A)
| ~ finite(sk0_0(A,B)) )
& ( in(sk0_0(A,B),B)
| ( subset(sk0_0(A,B),A)
& finite(sk0_0(A,B)) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f51]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ preboolean(X0)
| X0 != finite_subsets(X1)
| in(X2,X0)
| ~ subset(X2,X1)
| ~ finite(X2) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f59,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f120,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f121,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f124,plain,
? [A,B] :
( element(B,powerset(A))
& finite(A)
& ~ element(B,finite_subsets(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f125,plain,
( element(sk0_12,powerset(sk0_11))
& finite(sk0_11)
& ~ element(sk0_12,finite_subsets(sk0_11)) ),
inference(skolemization,[status(esa)],[f124]) ).
fof(f126,plain,
element(sk0_12,powerset(sk0_11)),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f127,plain,
finite(sk0_11),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f128,plain,
~ element(sk0_12,finite_subsets(sk0_11)),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f129,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f29]) ).
fof(f130,plain,
( ! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) )
& ! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f130]) ).
fof(f149,plain,
! [X0,X1] :
( ~ preboolean(finite_subsets(X0))
| in(X1,finite_subsets(X0))
| ~ subset(X1,X0)
| ~ finite(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f55]) ).
fof(f150,plain,
( spl0_0
<=> finite(sk0_11) ),
introduced(split_symbol_definition) ).
fof(f152,plain,
( ~ finite(sk0_11)
| spl0_0 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( spl0_1
<=> finite(sk0_12) ),
introduced(split_symbol_definition) ).
fof(f156,plain,
( ~ finite(sk0_11)
| finite(sk0_12) ),
inference(resolution,[status(thm)],[f43,f126]) ).
fof(f157,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f156,f150,f153]) ).
fof(f158,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f127]) ).
fof(f159,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f174,plain,
! [X0,X1] :
( in(X0,finite_subsets(X1))
| ~ subset(X0,X1)
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f59]) ).
fof(f236,plain,
~ in(sk0_12,finite_subsets(sk0_11)),
inference(resolution,[status(thm)],[f121,f128]) ).
fof(f248,plain,
subset(sk0_12,sk0_11),
inference(resolution,[status(thm)],[f131,f126]) ).
fof(f259,plain,
( spl0_7
<=> in(sk0_12,finite_subsets(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f260,plain,
( in(sk0_12,finite_subsets(sk0_11))
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( in(sk0_12,finite_subsets(sk0_11))
| ~ finite(sk0_12) ),
inference(resolution,[status(thm)],[f248,f174]) ).
fof(f263,plain,
( spl0_7
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f262,f259,f153]) ).
fof(f264,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f236]) ).
fof(f265,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f264]) ).
fof(f266,plain,
$false,
inference(sat_refutation,[status(thm)],[f157,f159,f263,f265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU118+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.05/0.25 % Computer : n025.cluster.edu
% 0.05/0.25 % Model : x86_64 x86_64
% 0.05/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.25 % Memory : 8042.1875MB
% 0.05/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.05/0.25 % CPULimit : 300
% 0.05/0.25 % WCLimit : 300
% 0.05/0.25 % DateTime : Tue May 30 09:20:12 EDT 2023
% 0.05/0.25 % CPUTime :
% 0.05/0.26 % Drodi V3.5.1
% 0.05/0.26 % Refutation found
% 0.05/0.26 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.05/0.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.48 % Elapsed time: 0.015877 seconds
% 0.09/0.48 % CPU time: 0.020894 seconds
% 0.09/0.48 % Memory used: 3.026 MB
%------------------------------------------------------------------------------