%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN409+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 03:16:01 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 2 unt; 4 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 69 ( 26 ~; 27 |; 9 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 28 ( 22 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] : f(X)
<=> ! [Y,Z] :
( f(Z)
& f(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] : f(X)
<=> ! [Y,Z] :
( f(Z)
& f(Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X] : f(X)
<~> ! [Y,Z] :
( f(Z)
& f(Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ? [Y,Z] :
( ~ f(Z)
| ~ f(Y) )
| ? [X] : ~ f(X) )
& ( ! [Y,Z] :
( f(Z)
& f(Y) )
| ! [X] : f(X) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ( ? [Z] : ~ f(Z)
| ? [Y] : ~ f(Y)
| ? [X] : ~ f(X) )
& ( ( ! [Z] : f(Z)
& ! [Y] : f(Y) )
| ! [X] : f(X) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ( ~ f(sK2_skl)
| ~ f(sK1_skl)
| ~ f(sK0_skl) )
& ( ( ! [Z] : f(Z)
& ! [Y] : f(Y) )
| ! [X] : f(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( f(X1)
| f(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
( ~ f(sK2_skl)
| ~ f(sK1_skl)
| ~ f(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,definition,
! [X0] :
( sQ0_spl
<=> f(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f11,plain,
! [X0] :
( ~ sQ0_spl
| f(X0) ),
inference(component_clause,[status(thm)],[f10]) ).
fof(f13,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f7,f10]) ).
fof(f15,definition,
( sQ1_spl
<=> f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f17,plain,
( sQ1_spl
| ~ f(sK0_skl) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,definition,
( sQ2_spl
<=> f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f20,plain,
( sQ2_spl
| ~ f(sK1_skl) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,definition,
( sQ3_spl
<=> f(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f23,plain,
( sQ3_spl
| ~ f(sK2_skl) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f9,f15,f18,f21]) ).
fof(f25,plain,
( sQ3_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23,f11]) ).
fof(f26,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f25]) ).
fof(f27,plain,
( sQ1_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f11]) ).
fof(f28,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f27]) ).
fof(f29,plain,
( sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20,f11]) ).
fof(f30,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f29]) ).
fof(f31,plain,
$false,
inference(sat_refutation,[status(thm)],[f13,f24,f26,f28,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN409+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 10:48:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.039349 seconds
% 0.13/0.42 % CPU time: 0.109524 seconds
% 0.13/0.42 % Total memory used: 16.493 MB
% 0.13/0.42 % Net memory used: 15.850 MB
%------------------------------------------------------------------------------