%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN399+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 03:15:59 PM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 1 unt; 4 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 82 ( 31 ~; 29 |; 10 &)
% ( 9 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 23 ( 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( f(X)
<=> p )
=> ( ! [Y] : f(Y)
<=> p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( f(X)
<=> p )
=> ( ! [Y] : f(Y)
<=> p ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ! [Y] : f(Y)
<~> p )
& ! [X] :
( f(X)
<=> p ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ~ p
| ? [Y] : ~ f(Y) )
& ( p
| ! [Y] : f(Y) )
& ! [X] :
( ( ~ p
| f(X) )
& ( p
| ~ f(X) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ( ~ p
| ? [Y] : ~ f(Y) )
& ( p
| ! [Y] : f(Y) )
& ( ~ p
| ! [X] : f(X) )
& ( p
| ! [X] : ~ f(X) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ( ~ p
| ~ f(sK0_skl) )
& ( p
| ! [Y] : f(Y) )
& ( ~ p
| ! [X] : f(X) )
& ( p
| ! [X] : ~ f(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl)],[f5]) ).
fof(f7,plain,
! [X0] :
( p
| ~ f(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ p
| f(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0] :
( p
| f(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
( ~ p
| ~ f(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,definition,
! [X0] :
( sQ0_spl
<=> ~ f(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f12,plain,
! [X0] :
( ~ sQ0_spl
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,definition,
( sQ1_spl
<=> p ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f17,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f11,f14]) ).
fof(f18,definition,
! [X0] :
( sQ2_spl
<=> f(X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f19,plain,
! [X0] :
( ~ sQ2_spl
| f(X0) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f8,f18,f14]) ).
fof(f22,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f9,f18,f14]) ).
fof(f23,definition,
( sQ3_spl
<=> f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f25,plain,
( sQ3_spl
| ~ f(sK0_skl) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( ~ sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f10,f23,f14]) ).
fof(f27,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12,f19]) ).
fof(f28,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f27]) ).
fof(f29,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f19]) ).
fof(f30,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f29]) ).
fof(f31,plain,
$false,
inference(sat_refutation,[status(thm)],[f17,f21,f22,f26,f28,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN399+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n026.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 10:55:52 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Drodi V4.1.1
% 0.19/0.48 % Refutation found
% 0.19/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.51 % Elapsed time: 0.058440 seconds
% 0.24/0.51 % CPU time: 0.147455 seconds
% 0.24/0.51 % Total memory used: 16.455 MB
% 0.24/0.51 % Net memory used: 15.851 MB
%------------------------------------------------------------------------------