TSTP Solution File: SEU317+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 7 unt; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 213 ( 87 ~; 88 |; 21 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 92 (; 87 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( in(C,the_carrier(A))
=> ( in(C,topstr_closure(A,B))
<=> ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( ( closed_subset(D,A)
& subset(B,D) )
=> in(C,D) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(B,topstr_closure(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(B,topstr_closure(A,B)) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f101,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f17]) ).
fof(f102,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)],[f101]) ).
fof(f103,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)],[f102]) ).
fof(f104,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)],[f103]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f107,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f145,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f36]) ).
fof(f146,plain,
( ! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) )
& ! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f148,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f149,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| ! [C] :
( ~ in(C,the_carrier(A))
| ( in(C,topstr_closure(A,B))
<=> ! [D] :
( ~ element(D,powerset(the_carrier(A)))
| ~ closed_subset(D,A)
| ~ subset(B,D)
| in(C,D) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f150,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| ! [C] :
( ~ in(C,the_carrier(A))
| ( ( ~ in(C,topstr_closure(A,B))
| ! [D] :
( ~ element(D,powerset(the_carrier(A)))
| ~ closed_subset(D,A)
| ~ subset(B,D)
| in(C,D) ) )
& ( in(C,topstr_closure(A,B))
| ? [D] :
( element(D,powerset(the_carrier(A)))
& closed_subset(D,A)
& subset(B,D)
& ~ in(C,D) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f149]) ).
fof(f151,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(the_carrier(A)))
| ! [C] :
( ~ in(C,the_carrier(A))
| ( ( ~ in(C,topstr_closure(A,B))
| ! [D] :
( ~ element(D,powerset(the_carrier(A)))
| ~ closed_subset(D,A)
| ~ subset(B,D)
| in(C,D) ) )
& ( in(C,topstr_closure(A,B))
| ( element(sk0_7(C,B,A),powerset(the_carrier(A)))
& closed_subset(sk0_7(C,B,A),A)
& subset(B,sk0_7(C,B,A))
& ~ in(C,sk0_7(C,B,A)) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f150]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| in(X2,topstr_closure(X0,X1))
| subset(X1,sk0_7(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f156,plain,
! [X0,X1,X2] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| in(X2,topstr_closure(X0,X1))
| ~ in(X2,sk0_7(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f157,plain,
? [A] :
( top_str(A)
& ? [B] :
( element(B,powerset(the_carrier(A)))
& ~ subset(B,topstr_closure(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f39]) ).
fof(f158,plain,
( top_str(sk0_8)
& element(sk0_9,powerset(the_carrier(sk0_8)))
& ~ subset(sk0_9,topstr_closure(sk0_8,sk0_9)) ),
inference(skolemization,[status(esa)],[f157]) ).
fof(f159,plain,
top_str(sk0_8),
inference(cnf_transformation,[status(esa)],[f158]) ).
fof(f160,plain,
element(sk0_9,powerset(the_carrier(sk0_8))),
inference(cnf_transformation,[status(esa)],[f158]) ).
fof(f161,plain,
~ subset(sk0_9,topstr_closure(sk0_8,sk0_9)),
inference(cnf_transformation,[status(esa)],[f158]) ).
fof(f176,plain,
subset(sk0_9,the_carrier(sk0_8)),
inference(resolution,[status(thm)],[f147,f160]) ).
fof(f182,plain,
( spl0_0
<=> top_str(sk0_8) ),
introduced(split_symbol_definition) ).
fof(f184,plain,
( ~ top_str(sk0_8)
| spl0_0 ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f191,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f159]) ).
fof(f192,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f191]) ).
fof(f536,plain,
! [X0,X1,X2,X3] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| in(X2,topstr_closure(X0,X1))
| ~ in(X3,X1)
| in(X3,sk0_7(X2,X1,X0)) ),
inference(resolution,[status(thm)],[f155,f105]) ).
fof(f539,plain,
! [X0,X1,X2] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| in(X2,topstr_closure(X0,X1))
| ~ in(X2,X1)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| in(X2,topstr_closure(X0,X1)) ),
inference(resolution,[status(thm)],[f536,f156]) ).
fof(f540,plain,
! [X0,X1,X2] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| in(X2,topstr_closure(X0,X1))
| ~ in(X2,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f539]) ).
fof(f559,plain,
! [X0,X1,X2] :
( ~ top_str(X0)
| ~ in(X1,the_carrier(X0))
| in(X1,topstr_closure(X0,X2))
| ~ in(X1,X2)
| ~ subset(X2,the_carrier(X0)) ),
inference(resolution,[status(thm)],[f540,f148]) ).
fof(f560,plain,
! [X0,X1,X2] :
( ~ top_str(X0)
| in(X1,topstr_closure(X0,X2))
| ~ in(X1,X2)
| ~ subset(X2,the_carrier(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f105]) ).
fof(f572,plain,
( spl0_26
<=> subset(sk0_9,the_carrier(sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f574,plain,
( ~ subset(sk0_9,the_carrier(sk0_8))
| spl0_26 ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f584,plain,
( $false
| spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f176]) ).
fof(f585,plain,
spl0_26,
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f586,plain,
! [X0,X1,X2] :
( ~ top_str(X0)
| ~ in(sk0_0(topstr_closure(X0,X1),X2),X1)
| ~ subset(X1,the_carrier(X0))
| subset(X2,topstr_closure(X0,X1)) ),
inference(resolution,[status(thm)],[f560,f107]) ).
fof(f640,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ subset(X1,the_carrier(X0))
| subset(X1,topstr_closure(X0,X1))
| subset(X1,topstr_closure(X0,X1)) ),
inference(resolution,[status(thm)],[f586,f106]) ).
fof(f641,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ subset(X1,the_carrier(X0))
| subset(X1,topstr_closure(X0,X1)) ),
inference(duplicate_literals_removal,[status(esa)],[f640]) ).
fof(f646,plain,
( ~ top_str(sk0_8)
| ~ subset(sk0_9,the_carrier(sk0_8)) ),
inference(resolution,[status(thm)],[f641,f161]) ).
fof(f647,plain,
( ~ spl0_0
| ~ spl0_26 ),
inference(split_clause,[status(thm)],[f646,f182,f572]) ).
fof(f650,plain,
$false,
inference(sat_refutation,[status(thm)],[f192,f585,f647]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:07:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.19/0.44 % Refutation found
% 0.19/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.45 % Elapsed time: 0.103894 seconds
% 0.19/0.45 % CPU time: 0.695932 seconds
% 0.19/0.45 % Memory used: 54.028 MB
%------------------------------------------------------------------------------