%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM395+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 01:40:26 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 13 unt; 2 def)
% Number of atoms : 52 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 15 ~; 12 |; 6 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 7 ( 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
ordinal(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ordinal(empty_set),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f30,axiom,
( epsilon_connected(empty_set)
& epsilon_transitive(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f57,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f65,plain,
( function(sK3_skl)
& empty(sK3_skl)
& relation(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f14]) ).
fof(f67,plain,
empty(sK3_skl),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f100,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f101,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
~ ordinal(empty_set),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f108,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f109,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f111,plain,
sK3_skl = empty_set,
inference(resolution,[status(thm)],[f67,f101]) ).
fof(f116,plain,
~ ordinal(sK3_skl),
inference(backward_demodulation,[status(thm)],[f111,f102]) ).
fof(f126,plain,
epsilon_transitive(sK3_skl),
inference(forward_demodulation,[status(thm)],[f111,f108]) ).
fof(f133,plain,
epsilon_connected(sK3_skl),
inference(forward_demodulation,[status(thm)],[f111,f109]) ).
fof(f134,plain,
( ~ epsilon_connected(sK3_skl)
| ~ epsilon_transitive(sK3_skl) ),
inference(resolution,[status(thm)],[f57,f116]) ).
fof(f135,definition,
( sQ0_spl
<=> epsilon_transitive(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( sQ0_spl
| ~ epsilon_transitive(sK3_skl) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,definition,
( sQ1_spl
<=> epsilon_connected(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ1_spl
| ~ epsilon_connected(sK3_skl) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f134,f135,f138]) ).
fof(f142,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f126]) ).
fof(f143,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f144,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f133]) ).
fof(f145,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f146,plain,
$false,
inference(sat_refutation,[status(thm)],[f141,f143,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM395+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 21 02:27:47 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.41 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.043585 seconds
% 0.13/0.45 % CPU time: 0.065965 seconds
% 0.13/0.45 % Total memory used: 7.606 MB
% 0.13/0.45 % Net memory used: 7.603 MB
%------------------------------------------------------------------------------