%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU129+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 : n011.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 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 11 unt; 2 def)
% Number of atoms : 60 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 22 ~; 17 |; 5 &)
% ( 2 <=>; 4 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 39 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f42,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f103,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f104,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f105,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f108,plain,
! [A,C] :
( subset(A,C)
| ! [B] :
( ~ subset(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
? [A,B,C] :
( ~ subset(set_intersection2(A,C),set_intersection2(B,C))
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f111,plain,
? [A,B] :
( ? [C] : ~ subset(set_intersection2(A,C),set_intersection2(B,C))
& subset(A,B) ),
inference(miniscoping,[status(thm)],[f110]) ).
fof(f112,plain,
( ~ subset(set_intersection2(sK6_skl,sK8_skl),set_intersection2(sK7_skl,sK8_skl))
& subset(sK6_skl,sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl),skolemize(C,sK8_skl)],[f111]) ).
fof(f113,plain,
subset(sK6_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
~ subset(set_intersection2(sK6_skl,sK8_skl),set_intersection2(sK7_skl,sK8_skl)),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f159,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X1),
inference(paramodulation,[status(thm)],[f42,f103]) ).
fof(f255,plain,
! [X0] :
( subset(X0,sK7_skl)
| ~ subset(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f109,f113]) ).
fof(f277,plain,
( ~ subset(set_intersection2(sK6_skl,sK8_skl),sK8_skl)
| ~ subset(set_intersection2(sK6_skl,sK8_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f105,f114]) ).
fof(f294,definition,
( sQ4_spl
<=> subset(set_intersection2(sK6_skl,sK8_skl),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ4_spl
| ~ subset(set_intersection2(sK6_skl,sK8_skl),sK7_skl) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,definition,
( sQ5_spl
<=> subset(set_intersection2(sK6_skl,sK8_skl),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( sQ5_spl
| ~ subset(set_intersection2(sK6_skl,sK8_skl),sK8_skl) ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f277,f294,f297]) ).
fof(f378,plain,
! [X0] : subset(set_intersection2(sK6_skl,X0),sK7_skl),
inference(resolution,[status(thm)],[f255,f103]) ).
fof(f392,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f378]) ).
fof(f393,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f394,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f299,f159]) ).
fof(f395,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f396,plain,
$false,
inference(sat_refutation,[status(thm)],[f300,f393,f395]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU129+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n011.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 05:51:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.058104 seconds
% 0.14/0.41 % CPU time: 0.096080 seconds
% 0.14/0.41 % Total memory used: 23.054 MB
% 0.14/0.41 % Net memory used: 22.980 MB
%------------------------------------------------------------------------------