%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU130+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:18 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 9 unt; 2 def)
% Number of atoms : 64 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 24 ~; 20 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 31 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f44,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f104,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f105,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f106,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f114,plain,
? [A,B] :
( set_intersection2(A,B) != A
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f115,plain,
( set_intersection2(sK6_skl,sK7_skl) != sK6_skl
& subset(sK6_skl,sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl)],[f114]) ).
fof(f116,plain,
subset(sK6_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
set_intersection2(sK6_skl,sK7_skl) != sK6_skl,
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f144,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f245,plain,
! [X0] :
( subset(sK6_skl,set_intersection2(X0,sK7_skl))
| ~ subset(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f106,f116]) ).
fof(f290,plain,
subset(sK6_skl,set_intersection2(sK6_skl,sK7_skl)),
inference(resolution,[status(thm)],[f245,f144]) ).
fof(f294,plain,
( ~ subset(set_intersection2(sK6_skl,sK7_skl),sK6_skl)
| set_intersection2(sK6_skl,sK7_skl) = sK6_skl ),
inference(resolution,[status(thm)],[f290,f48]) ).
fof(f297,definition,
( sQ2_spl
<=> set_intersection2(sK6_skl,sK7_skl) = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( ~ sQ2_spl
| set_intersection2(sK6_skl,sK7_skl) = sK6_skl ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,definition,
( sQ3_spl
<=> subset(set_intersection2(sK6_skl,sK7_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( sQ3_spl
| ~ subset(set_intersection2(sK6_skl,sK7_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f303,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f294,f297,f300]) ).
fof(f304,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f117]) ).
fof(f305,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f302,f104]) ).
fof(f307,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f308,plain,
$false,
inference(sat_refutation,[status(thm)],[f303,f305,f307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU130+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:49:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.057083 seconds
% 0.14/0.43 % CPU time: 0.177844 seconds
% 0.14/0.43 % Total memory used: 103.473 MB
% 0.14/0.43 % Net memory used: 103.337 MB
%------------------------------------------------------------------------------