%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 02:19:12 PM UTC 2026
% Result : Theorem 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 10 unt; 4 def)
% Number of atoms : 70 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 22 ~; 19 |; 11 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 24 ( 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(cartesian_product2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f102,plain,
! [X0,X1,X2] : cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f108,plain,
! [A,B] :
( finite(cartesian_product2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f109,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f245,plain,
? [A,B,C] :
( ~ finite(cartesian_product3(A,B,C))
& finite(C)
& finite(B)
& finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f246,plain,
( ~ finite(cartesian_product3(sK26_skl,sK27_skl,sK28_skl))
& finite(sK28_skl)
& finite(sK27_skl)
& finite(sK26_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl,sK28_skl]),skolemize(A,sK26_skl),skolemize(B,sK27_skl),skolemize(C,sK28_skl)],[f245]) ).
fof(f247,plain,
finite(sK26_skl),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f248,plain,
finite(sK27_skl),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f249,plain,
finite(sK28_skl),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f250,plain,
~ finite(cartesian_product3(sK26_skl,sK27_skl,sK28_skl)),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f583,plain,
! [X0,X1,X2] :
( finite(cartesian_product3(X0,X1,X2))
| ~ finite(X2)
| ~ finite(cartesian_product2(X0,X1)) ),
inference(paramodulation,[status(thm)],[f102,f109]) ).
fof(f584,plain,
( ~ finite(sK28_skl)
| ~ finite(cartesian_product2(sK26_skl,sK27_skl)) ),
inference(resolution,[status(thm)],[f583,f250]) ).
fof(f585,definition,
( sQ52_spl
<=> finite(cartesian_product2(sK26_skl,sK27_skl)) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f587,plain,
( sQ52_spl
| ~ finite(cartesian_product2(sK26_skl,sK27_skl)) ),
inference(component_clause,[status(thm)],[f585]) ).
fof(f588,definition,
( sQ53_spl
<=> finite(sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( sQ53_spl
| ~ finite(sK28_skl) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,plain,
( ~ sQ53_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f584,f585,f588]) ).
fof(f592,plain,
( sQ52_spl
| ~ finite(sK27_skl)
| ~ finite(sK26_skl) ),
inference(resolution,[status(thm)],[f587,f109]) ).
fof(f593,definition,
( sQ54_spl
<=> finite(sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f595,plain,
( sQ54_spl
| ~ finite(sK26_skl) ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f596,definition,
( sQ55_spl
<=> finite(sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( sQ55_spl
| ~ finite(sK27_skl) ),
inference(component_clause,[status(thm)],[f596]) ).
fof(f599,plain,
( sQ52_spl
| ~ sQ55_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f592,f593,f596,f585]) ).
fof(f600,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f249]) ).
fof(f601,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f600]) ).
fof(f602,plain,
( sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f247]) ).
fof(f603,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f604,plain,
( sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f598,f248]) ).
fof(f605,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f604]) ).
fof(f606,plain,
$false,
inference(sat_refutation,[status(thm)],[f591,f599,f601,f603,f605]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 % Computer : n016.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 05:54:07 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.52 % Drodi V4.1.1
% 0.18/0.52 % Refutation found
% 0.18/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.61 % Elapsed time: 0.115473 seconds
% 0.22/0.61 % CPU time: 0.114355 seconds
% 0.22/0.61 % Total memory used: 13.393 MB
% 0.22/0.61 % Net memory used: 13.384 MB
%------------------------------------------------------------------------------