%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU090+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 : n013.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 0.14s 10.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 12 unt; 5 def)
% Number of atoms : 96 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 86 ( 31 ~; 29 |; 17 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 39 ( 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [A,B,C,D] : cartesian_product4(A,B,C,D) = cartesian_product2(cartesian_product3(A,B,C),D),
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(f18,axiom,
! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,conjecture,
! [A,B,C,D] :
( ( finite(D)
& finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product4(A,B,C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
~ ! [A,B,C,D] :
( ( finite(D)
& finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product4(A,B,C,D)) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f105,plain,
! [X0,X1,X2,X3] : cartesian_product4(X0,X1,X2,X3) = cartesian_product2(cartesian_product3(X0,X1,X2),X3),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f111,plain,
! [A,B] :
( finite(cartesian_product2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f112,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [A,B,C] :
( finite(cartesian_product3(A,B,C))
| ~ finite(C)
| ~ finite(B)
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f114,plain,
! [X0,X1,X2] :
( finite(cartesian_product3(X0,X1,X2))
| ~ finite(X2)
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f254,plain,
? [A,B,C,D] :
( ~ finite(cartesian_product4(A,B,C,D))
& finite(D)
& finite(C)
& finite(B)
& finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f255,plain,
( ~ finite(cartesian_product4(sK26_skl,sK27_skl,sK28_skl,sK29_skl))
& finite(sK29_skl)
& finite(sK28_skl)
& finite(sK27_skl)
& finite(sK26_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl,sK28_skl,sK29_skl]),skolemize(A,sK26_skl),skolemize(B,sK27_skl),skolemize(C,sK28_skl),skolemize(D,sK29_skl)],[f254]) ).
fof(f256,plain,
finite(sK26_skl),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
finite(sK27_skl),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f258,plain,
finite(sK28_skl),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f259,plain,
finite(sK29_skl),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f260,plain,
~ finite(cartesian_product4(sK26_skl,sK27_skl,sK28_skl,sK29_skl)),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f590,plain,
! [X0,X1,X2,X3] :
( finite(cartesian_product4(X0,X1,X2,X3))
| ~ finite(X3)
| ~ finite(cartesian_product3(X0,X1,X2)) ),
inference(paramodulation,[status(thm)],[f105,f112]) ).
fof(f591,plain,
( ~ finite(sK29_skl)
| ~ finite(cartesian_product3(sK26_skl,sK27_skl,sK28_skl)) ),
inference(resolution,[status(thm)],[f590,f260]) ).
fof(f592,definition,
( sQ52_spl
<=> finite(cartesian_product3(sK26_skl,sK27_skl,sK28_skl)) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( sQ52_spl
| ~ finite(cartesian_product3(sK26_skl,sK27_skl,sK28_skl)) ),
inference(component_clause,[status(thm)],[f592]) ).
fof(f595,definition,
( sQ53_spl
<=> finite(sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ53_spl
| ~ finite(sK29_skl) ),
inference(component_clause,[status(thm)],[f595]) ).
fof(f598,plain,
( ~ sQ53_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f591,f592,f595]) ).
fof(f599,plain,
( sQ52_spl
| ~ finite(sK28_skl)
| ~ finite(sK27_skl)
| ~ finite(sK26_skl) ),
inference(resolution,[status(thm)],[f114,f594]) ).
fof(f600,definition,
( sQ54_spl
<=> finite(sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( sQ54_spl
| ~ finite(sK26_skl) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,definition,
( sQ55_spl
<=> finite(sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f605,plain,
( sQ55_spl
| ~ finite(sK27_skl) ),
inference(component_clause,[status(thm)],[f603]) ).
fof(f606,definition,
( sQ56_spl
<=> finite(sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( sQ56_spl
| ~ finite(sK28_skl) ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f609,plain,
( sQ52_spl
| ~ sQ56_spl
| ~ sQ55_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f599,f600,f603,f606,f592]) ).
fof(f610,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f597,f259]) ).
fof(f611,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f610]) ).
fof(f612,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f608,f258]) ).
fof(f613,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f612]) ).
fof(f614,plain,
( sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f602,f256]) ).
fof(f615,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f614]) ).
fof(f616,plain,
( sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f605,f257]) ).
fof(f617,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f616]) ).
fof(f618,plain,
$false,
inference(sat_refutation,[status(thm)],[f598,f609,f611,f613,f615,f617]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU090+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.38 % Computer : n013.cluster.edu
% 0.08/10.38 % Model : x86_64 x86_64
% 0.08/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.38 % Memory : 8046.5625MB
% 0.08/10.38 % OS : Linux 6.8.0-71-generic
% 0.08/10.38 % CPULimit : 300
% 0.08/10.38 % WCLimit : 300
% 0.08/10.38 % DateTime : Mon Sep 21 05:49:47 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.08/10.39 % Drodi V4.1.1
% 0.14/10.41 % Refutation found
% 0.14/10.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.43 % Elapsed time: 0.045981 seconds
% 0.14/10.43 % CPU time: 0.159842 seconds
% 0.14/10.43 % Total memory used: 106.083 MB
% 0.14/10.43 % Net memory used: 106.030 MB
%------------------------------------------------------------------------------