TSTP Solution File: SEU160+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 12:36:03 EDT 2023
% Result : Theorem 0.09s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 4 unt; 0 def)
% Number of atoms : 110 ( 42 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 43 ~; 51 |; 13 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 31 (; 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ),
inference(negated_conjecture,[status(cth)],[f70]) ).
fof(f99,plain,
! [A,B] :
( ( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f6]) ).
fof(f100,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)],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( X0 != X1
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f226,plain,
! [A,B] :
( ( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) )
& ( subset(A,singleton(B))
| ( A != empty_set
& A != singleton(B) ) ) ),
inference(NNF_transformation,[status(esa)],[f44]) ).
fof(f227,plain,
( ! [A,B] :
( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) )
& ! [A,B] :
( subset(A,singleton(B))
| ( A != empty_set
& A != singleton(B) ) ) ),
inference(miniscoping,[status(esa)],[f226]) ).
fof(f228,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| X0 = empty_set
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(esa)],[f227]) ).
fof(f270,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f292,plain,
? [A,B] :
( subset(A,singleton(B))
<~> ( A = empty_set
| A = singleton(B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f71]) ).
fof(f293,plain,
? [A,B] :
( ( subset(A,singleton(B))
| A = empty_set
| A = singleton(B) )
& ( ~ subset(A,singleton(B))
| ( A != empty_set
& A != singleton(B) ) ) ),
inference(NNF_transformation,[status(esa)],[f292]) ).
fof(f294,plain,
( ( subset(sk0_19,singleton(sk0_20))
| sk0_19 = empty_set
| sk0_19 = singleton(sk0_20) )
& ( ~ subset(sk0_19,singleton(sk0_20))
| ( sk0_19 != empty_set
& sk0_19 != singleton(sk0_20) ) ) ),
inference(skolemization,[status(esa)],[f293]) ).
fof(f295,plain,
( subset(sk0_19,singleton(sk0_20))
| sk0_19 = empty_set
| sk0_19 = singleton(sk0_20) ),
inference(cnf_transformation,[status(esa)],[f294]) ).
fof(f296,plain,
( ~ subset(sk0_19,singleton(sk0_20))
| sk0_19 != empty_set ),
inference(cnf_transformation,[status(esa)],[f294]) ).
fof(f297,plain,
( ~ subset(sk0_19,singleton(sk0_20))
| sk0_19 != singleton(sk0_20) ),
inference(cnf_transformation,[status(esa)],[f294]) ).
fof(f352,plain,
( spl0_0
<=> subset(sk0_19,singleton(sk0_20)) ),
introduced(split_symbol_definition) ).
fof(f353,plain,
( subset(sk0_19,singleton(sk0_20))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( ~ subset(sk0_19,singleton(sk0_20))
| spl0_0 ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( spl0_1
<=> sk0_19 = empty_set ),
introduced(split_symbol_definition) ).
fof(f356,plain,
( sk0_19 = empty_set
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f358,plain,
( spl0_2
<=> sk0_19 = singleton(sk0_20) ),
introduced(split_symbol_definition) ).
fof(f359,plain,
( sk0_19 = singleton(sk0_20)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,plain,
( spl0_0
| spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f295,f352,f355,f358]) ).
fof(f362,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f296,f352,f355]) ).
fof(f363,plain,
( ~ spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f297,f352,f358]) ).
fof(f364,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f101]) ).
fof(f422,plain,
( ~ subset(empty_set,singleton(sk0_20))
| ~ spl0_1
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f356,f354]) ).
fof(f423,plain,
( $false
| ~ spl0_1
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f422,f270]) ).
fof(f424,plain,
( ~ spl0_1
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f425,plain,
( sk0_19 = empty_set
| sk0_19 = singleton(sk0_20)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f353,f228]) ).
fof(f426,plain,
( spl0_1
| spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f425,f355,f358,f352]) ).
fof(f433,plain,
( ~ subset(sk0_19,sk0_19)
| ~ spl0_2
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f359,f354]) ).
fof(f434,plain,
( $false
| ~ spl0_2
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f433,f364]) ).
fof(f435,plain,
( ~ spl0_2
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f434]) ).
fof(f436,plain,
$false,
inference(sat_refutation,[status(thm)],[f361,f362,f363,f424,f426,f435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n016.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 09:37:44 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.09/0.31 % Refutation found
% 0.09/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.015656 seconds
% 0.14/0.53 % CPU time: 0.015516 seconds
% 0.14/0.53 % Memory used: 3.939 MB
%------------------------------------------------------------------------------