%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU275+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 : n002.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 02:20:00 PM UTC 2026
% Result : Theorem 19.87s 3.04s
% Output : CNFRefutation 19.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 19 unt; 8 def)
% Number of atoms : 149 ( 3 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 132 ( 47 ~; 47 |; 23 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 21 ( 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [A] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f132,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f262,lemma,
! [A] : reflexive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f285,lemma,
! [A] : transitive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f305,lemma,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f317,lemma,
! [A] : antisymmetric(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f318,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f328,lemma,
! [A] :
( ordinal(A)
=> well_founded_relation(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f337,conjecture,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f338,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
inference(negated_conjecture,[status(cth)],[f337]) ).
fof(f704,plain,
! [A] :
( ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f705,plain,
! [A] :
( ( ( ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A)
| well_ordering(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f704]) ).
fof(f711,plain,
! [X0] :
( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f705]) ).
fof(f842,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f910,plain,
function(empty_set),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f1351,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f262]) ).
fof(f1427,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f285]) ).
fof(f1478,plain,
! [A] :
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f305]) ).
fof(f1479,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f1478]) ).
fof(f1528,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f317]) ).
fof(f1529,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f1560,plain,
! [A] :
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f328]) ).
fof(f1561,plain,
! [X0] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f1560]) ).
fof(f1590,plain,
? [A] :
( ~ well_ordering(inclusion_relation(A))
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f338]) ).
fof(f1591,plain,
( ~ well_ordering(inclusion_relation(sK143_skl))
& ordinal(sK143_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143_skl]),skolemize(A,sK143_skl)],[f1590]) ).
fof(f1592,plain,
ordinal(sK143_skl),
inference(cnf_transformation,[status(thm)],[f1591]) ).
fof(f1593,plain,
~ well_ordering(inclusion_relation(sK143_skl)),
inference(cnf_transformation,[status(thm)],[f1591]) ).
fof(f1824,definition,
( sQ2_spl
<=> ordinal(sK143_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1826,plain,
( sQ2_spl
| ~ ordinal(sK143_skl) ),
inference(component_clause,[status(thm)],[f1824]) ).
fof(f1878,definition,
( sQ11_spl
<=> relation(inclusion_relation(sK143_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1880,plain,
( sQ11_spl
| ~ relation(inclusion_relation(sK143_skl)) ),
inference(component_clause,[status(thm)],[f1878]) ).
fof(f1904,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1880,f842]) ).
fof(f1905,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f1904]) ).
fof(f4565,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1826,f1592]) ).
fof(f4566,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f4565]) ).
fof(f16169,plain,
( ~ well_founded_relation(inclusion_relation(sK143_skl))
| ~ connected(inclusion_relation(sK143_skl))
| ~ antisymmetric(inclusion_relation(sK143_skl))
| ~ transitive(inclusion_relation(sK143_skl))
| ~ reflexive(inclusion_relation(sK143_skl))
| ~ relation(inclusion_relation(sK143_skl)) ),
inference(resolution,[status(thm)],[f711,f1593]) ).
fof(f16247,definition,
( sQ1223_spl
<=> reflexive(inclusion_relation(sK143_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1223_spl])],[split_symbol_definition]) ).
fof(f16249,plain,
( sQ1223_spl
| ~ reflexive(inclusion_relation(sK143_skl)) ),
inference(component_clause,[status(thm)],[f16247]) ).
fof(f16250,definition,
( sQ1224_spl
<=> transitive(inclusion_relation(sK143_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1224_spl])],[split_symbol_definition]) ).
fof(f16252,plain,
( sQ1224_spl
| ~ transitive(inclusion_relation(sK143_skl)) ),
inference(component_clause,[status(thm)],[f16250]) ).
fof(f16253,definition,
( sQ1225_spl
<=> antisymmetric(inclusion_relation(sK143_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1225_spl])],[split_symbol_definition]) ).
fof(f16255,plain,
( sQ1225_spl
| ~ antisymmetric(inclusion_relation(sK143_skl)) ),
inference(component_clause,[status(thm)],[f16253]) ).
fof(f16256,definition,
( sQ1226_spl
<=> connected(inclusion_relation(sK143_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1226_spl])],[split_symbol_definition]) ).
fof(f16258,plain,
( sQ1226_spl
| ~ connected(inclusion_relation(sK143_skl)) ),
inference(component_clause,[status(thm)],[f16256]) ).
fof(f16259,definition,
( sQ1227_spl
<=> well_founded_relation(inclusion_relation(sK143_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1227_spl])],[split_symbol_definition]) ).
fof(f16261,plain,
( sQ1227_spl
| ~ well_founded_relation(inclusion_relation(sK143_skl)) ),
inference(component_clause,[status(thm)],[f16259]) ).
fof(f16262,plain,
( ~ sQ1227_spl
| ~ sQ1226_spl
| ~ sQ1225_spl
| ~ sQ1224_spl
| ~ sQ1223_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f16169,f1878,f16247,f16250,f16253,f16256,f16259]) ).
fof(f16330,plain,
( sQ1225_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16255,f1528]) ).
fof(f16331,plain,
sQ1225_spl,
inference(contradiction_clause,[status(thm)],[f16330]) ).
fof(f16332,plain,
( sQ1224_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16252,f1427]) ).
fof(f16333,plain,
sQ1224_spl,
inference(contradiction_clause,[status(thm)],[f16332]) ).
fof(f16334,plain,
( sQ1223_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16249,f1351]) ).
fof(f16335,plain,
sQ1223_spl,
inference(contradiction_clause,[status(thm)],[f16334]) ).
fof(f16523,definition,
( sQ1233_spl
<=> function(relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ1233_spl])],[split_symbol_definition]) ).
fof(f16525,plain,
( sQ1233_spl
| ~ function(relation_dom(empty_set)) ),
inference(component_clause,[status(thm)],[f16523]) ).
fof(f16527,plain,
( sQ1233_spl
| ~ function(empty_set) ),
inference(forward_demodulation,[status(thm)],[f1529,f16525]) ).
fof(f16528,plain,
( sQ1233_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16527,f910]) ).
fof(f16529,plain,
sQ1233_spl,
inference(contradiction_clause,[status(thm)],[f16528]) ).
fof(f16653,plain,
( sQ1227_spl
| ~ ordinal(sK143_skl) ),
inference(resolution,[status(thm)],[f16261,f1561]) ).
fof(f16658,plain,
( sQ1227_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f16653,f1824,f16259]) ).
fof(f16666,plain,
( sQ1226_spl
| ~ ordinal(sK143_skl) ),
inference(resolution,[status(thm)],[f16258,f1479]) ).
fof(f16673,plain,
( sQ1226_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f16666,f1824,f16256]) ).
fof(f16682,plain,
$false,
inference(sat_refutation,[status(thm)],[f1905,f4566,f16262,f16331,f16333,f16335,f16529,f16658,f16673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU275+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % Computer : n002.cluster.edu
% 0.17/0.47 % Model : x86_64 x86_64
% 0.17/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.47 % Memory : 8046.5625MB
% 0.17/0.47 % OS : Linux 6.8.0-71-generic
% 0.17/0.47 % CPULimit : 300
% 0.17/0.47 % WCLimit : 300
% 0.17/0.47 % DateTime : Mon Sep 21 06:09:20 UTC 2026
% 0.17/0.47 % CPUTime :
% 0.17/0.51 % Drodi V4.1.1
% 19.87/3.04 % Refutation found
% 19.87/3.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.87/3.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.87/3.09 % Elapsed time: 2.609781 seconds
% 19.87/3.09 % CPU time: 20.233142 seconds
% 19.87/3.09 % Total memory used: 238.892 MB
% 19.87/3.09 % Net memory used: 221.577 MB
%------------------------------------------------------------------------------