%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM410+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 01:40:27 PM UTC 2026
% Result : Theorem 0.07s 0.39s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 11 unt; 3 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 128 ( 52 ~; 49 |; 14 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 27 ( 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f66,plain,
! [A] :
( ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f67,plain,
! [A] :
( ( ( ~ ordinal(relation_dom(A))
| transfinite_sequence(A) )
& ( ordinal(relation_dom(A))
| ~ transfinite_sequence(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f69,plain,
! [X0] :
( ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
! [A,B] :
( ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f71,plain,
! [A,B] :
( ( ( ~ subset(relation_rng(B),A)
| transfinite_sequence_of(B,A) )
& ( subset(relation_rng(B),A)
| ~ transfinite_sequence_of(B,A) ) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [B] :
( ( ! [A] :
( ~ subset(relation_rng(B),A)
| transfinite_sequence_of(B,A) )
& ! [A] :
( subset(relation_rng(B),A)
| ~ transfinite_sequence_of(B,A) ) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f71]) ).
fof(f74,plain,
! [X0,X1] :
( ~ subset(relation_rng(X0),X1)
| transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f163,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f164,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f173,plain,
? [A] :
( ~ transfinite_sequence_of(A,relation_rng(A))
& ordinal(relation_dom(A))
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f174,plain,
( ~ transfinite_sequence_of(sK16_skl,relation_rng(sK16_skl))
& ordinal(relation_dom(sK16_skl))
& function(sK16_skl)
& relation(sK16_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(A,sK16_skl)],[f173]) ).
fof(f175,plain,
relation(sK16_skl),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
function(sK16_skl),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f177,plain,
ordinal(relation_dom(sK16_skl)),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f178,plain,
~ transfinite_sequence_of(sK16_skl,relation_rng(sK16_skl)),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f195,plain,
! [X0,X1] :
( ~ ordinal(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_rng(X0),X1)
| transfinite_sequence_of(X0,X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f74,f69]) ).
fof(f196,plain,
! [X0,X1] :
( ~ ordinal(relation_dom(X0))
| ~ subset(relation_rng(X0),X1)
| transfinite_sequence_of(X0,X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f195]) ).
fof(f293,plain,
! [X0] :
( ~ ordinal(relation_dom(X0))
| transfinite_sequence_of(X0,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f164,f196]) ).
fof(f294,plain,
( transfinite_sequence_of(sK16_skl,relation_rng(sK16_skl))
| ~ function(sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f293,f177]) ).
fof(f298,definition,
( sQ18_spl
<=> relation(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( sQ18_spl
| ~ relation(sK16_skl) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,definition,
( sQ19_spl
<=> function(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ19_spl
| ~ function(sK16_skl) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,definition,
( sQ20_spl
<=> transfinite_sequence_of(sK16_skl,relation_rng(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( ~ sQ20_spl
| transfinite_sequence_of(sK16_skl,relation_rng(sK16_skl)) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,plain,
( sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f294,f298,f301,f304]) ).
fof(f309,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f178]) ).
fof(f310,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f311,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f176]) ).
fof(f312,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f175]) ).
fof(f314,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f315,plain,
$false,
inference(sat_refutation,[status(thm)],[f307,f310,f312,f314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM410+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 02:28:17 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.07/0.39 % Refutation found
% 0.07/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.064230 seconds
% 0.13/0.43 % CPU time: 0.166783 seconds
% 0.13/0.43 % Total memory used: 82.514 MB
% 0.13/0.43 % Net memory used: 82.488 MB
%------------------------------------------------------------------------------