%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU140+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 02:19:21 PM UTC 2026
% Result : Theorem 0.20s 0.79s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 73 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 64 ( 25 ~; 19 |; 15 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 50 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,conjecture,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
~ ! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f63,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f64,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f65,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)],[f64]) ).
fof(f68,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f108,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f109,plain,
( ! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ! [A,B] :
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f151,plain,
! [A,B,C] :
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f152,plain,
! [A,B] :
( ! [C] : subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f162,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f193,plain,
? [A,B,C] :
( ~ disjoint(A,C)
& disjoint(B,C)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f194,plain,
? [A,C] :
( ~ disjoint(A,C)
& ? [B] :
( disjoint(B,C)
& subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f193]) ).
fof(f195,plain,
( ~ disjoint(sK10_skl,sK11_skl)
& disjoint(sK12_skl,sK11_skl)
& subset(sK10_skl,sK12_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(A,sK10_skl),skolemize(C,sK11_skl),skolemize(B,sK12_skl)],[f194]) ).
fof(f196,plain,
subset(sK10_skl,sK12_skl),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f197,plain,
disjoint(sK12_skl,sK11_skl),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f198,plain,
~ disjoint(sK10_skl,sK11_skl),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f242,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f162,f68]) ).
fof(f260,plain,
set_intersection2(sK10_skl,sK11_skl) != empty_set,
inference(resolution,[status(thm)],[f111,f198]) ).
fof(f345,plain,
! [X0,X1] :
( set_intersection2(X1,X0) = empty_set
| ~ disjoint(X0,X1) ),
inference(paramodulation,[status(thm)],[f63,f110]) ).
fof(f407,plain,
set_intersection2(sK11_skl,sK12_skl) = empty_set,
inference(resolution,[status(thm)],[f345,f197]) ).
fof(f410,plain,
set_intersection2(sK12_skl,sK11_skl) = empty_set,
inference(paramodulation,[status(thm)],[f63,f407]) ).
fof(f1706,plain,
! [X0] : subset(set_intersection2(sK10_skl,X0),set_intersection2(sK12_skl,X0)),
inference(resolution,[status(thm)],[f153,f196]) ).
fof(f2286,plain,
subset(set_intersection2(sK10_skl,sK11_skl),empty_set),
inference(paramodulation,[status(thm)],[f410,f1706]) ).
fof(f3123,plain,
set_intersection2(sK10_skl,sK11_skl) = empty_set,
inference(resolution,[status(thm)],[f2286,f242]) ).
fof(f3138,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3123,f260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU140+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.47 % Computer : n003.cluster.edu
% 0.16/0.47 % Model : x86_64 x86_64
% 0.16/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.47 % Memory : 8046.5625MB
% 0.16/0.47 % OS : Linux 6.8.0-71-generic
% 0.16/0.47 % CPULimit : 300
% 0.16/0.47 % WCLimit : 300
% 0.16/0.47 % DateTime : Mon Sep 21 05:53:45 UTC 2026
% 0.16/0.47 % CPUTime :
% 0.16/0.49 % Drodi V4.1.1
% 0.20/0.79 % Refutation found
% 0.20/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.84 % Elapsed time: 0.344675 seconds
% 0.20/0.84 % CPU time: 2.348094 seconds
% 0.20/0.84 % Total memory used: 123.028 MB
% 0.20/0.84 % Net memory used: 119.469 MB
%------------------------------------------------------------------------------