TSTP Solution File: SEU320+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 12:36:41 EDT 2023
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 12 unt; 0 def)
% Number of atoms : 132 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 123 ( 46 ~; 49 |; 9 &)
% ( 10 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 36 (; 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,plain,
! [A,B] :
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f24,plain,
! [A] : element(sk0_2(A),A),
inference(skolemization,[status(esa)],[f9]) ).
fof(f25,plain,
! [X0] : element(sk0_2(X0),X0),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,subset_complement(A,B)) = B ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f27,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset_complement(X1,subset_complement(X1,X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f30,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f31,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| ( ( ~ closed_subset(B,A)
| open_subset(subset_complement(the_carrier(A),B),A) )
& ( closed_subset(B,A)
| ~ open_subset(subset_complement(the_carrier(A),B),A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
? [A] :
( top_str(A)
& ? [B] :
( element(B,powerset(the_carrier(A)))
& ( open_subset(B,A)
<~> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f35,plain,
? [A] :
( top_str(A)
& ? [B] :
( element(B,powerset(the_carrier(A)))
& ( open_subset(B,A)
| closed_subset(subset_complement(the_carrier(A),B),A) )
& ( ~ open_subset(B,A)
| ~ closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(NNF_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
( top_str(sk0_3)
& element(sk0_4,powerset(the_carrier(sk0_3)))
& ( open_subset(sk0_4,sk0_3)
| closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) )
& ( ~ open_subset(sk0_4,sk0_3)
| ~ closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) ) ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
top_str(sk0_3),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
element(sk0_4,powerset(the_carrier(sk0_3))),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
( open_subset(sk0_4,sk0_3)
| closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f40,plain,
( ~ open_subset(sk0_4,sk0_3)
| ~ closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f45,plain,
( spl0_0
<=> open_subset(sk0_4,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f47,plain,
( ~ open_subset(sk0_4,sk0_3)
| spl0_0 ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( spl0_1
<=> closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f39,f45,f48]) ).
fof(f52,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f40,f45,f48]) ).
fof(f53,plain,
subset_complement(the_carrier(sk0_3),subset_complement(the_carrier(sk0_3),sk0_4)) = sk0_4,
inference(resolution,[status(thm)],[f27,f38]) ).
fof(f54,plain,
element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3))),
inference(resolution,[status(thm)],[f17,f38]) ).
fof(f58,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sk0_3)))
| closed_subset(X0,sk0_3)
| ~ open_subset(subset_complement(the_carrier(sk0_3),X0),sk0_3) ),
inference(resolution,[status(thm)],[f33,f37]) ).
fof(f59,plain,
( spl0_2
<=> element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f61,plain,
( ~ element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3)))
| spl0_2 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3)))
| closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3)
| ~ open_subset(sk0_4,sk0_3) ),
inference(paramodulation,[status(thm)],[f53,f58]) ).
fof(f63,plain,
( ~ spl0_2
| spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f62,f59,f48,f45]) ).
fof(f64,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f54]) ).
fof(f65,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f64]) ).
fof(f67,plain,
! [X0] : element(subset_complement(X0,sk0_2(powerset(X0))),powerset(X0)),
inference(resolution,[status(thm)],[f25,f17]) ).
fof(f82,plain,
( spl0_6
<=> element(subset_complement(the_carrier(sk0_3),sk0_2(powerset(the_carrier(sk0_3)))),powerset(the_carrier(sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f84,plain,
( ~ element(subset_complement(the_carrier(sk0_3),sk0_2(powerset(the_carrier(sk0_3)))),powerset(the_carrier(sk0_3)))
| spl0_6 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f93,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f67]) ).
fof(f94,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f93]) ).
fof(f146,plain,
( spl0_15
<=> top_str(sk0_3) ),
introduced(split_symbol_definition) ).
fof(f148,plain,
( ~ top_str(sk0_3)
| spl0_15 ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( spl0_16
<=> open_subset(subset_complement(the_carrier(sk0_3),subset_complement(the_carrier(sk0_3),sk0_4)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f150,plain,
( open_subset(subset_complement(the_carrier(sk0_3),subset_complement(the_carrier(sk0_3),sk0_4)),sk0_3)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( ~ top_str(sk0_3)
| ~ element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3)))
| open_subset(subset_complement(the_carrier(sk0_3),subset_complement(the_carrier(sk0_3),sk0_4)),sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f49,f32]) ).
fof(f153,plain,
( ~ spl0_15
| ~ spl0_2
| spl0_16
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f152,f146,f59,f149,f48]) ).
fof(f154,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f37]) ).
fof(f155,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f156,plain,
( open_subset(sk0_4,sk0_3)
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f53,f150]) ).
fof(f157,plain,
( $false
| spl0_0
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f47]) ).
fof(f158,plain,
( spl0_0
| ~ spl0_16 ),
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f159,plain,
$false,
inference(sat_refutation,[status(thm)],[f51,f52,f63,f65,f94,f153,f155,f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n026.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 09:34:13 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.12/0.35 % Refutation found
% 0.12/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.36 % Elapsed time: 0.020710 seconds
% 0.12/0.36 % CPU time: 0.033284 seconds
% 0.12/0.36 % Memory used: 11.545 MB
%------------------------------------------------------------------------------