%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN053+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 : n019.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 03:15:02 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 2 unt; 4 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 77 ( 27 ~; 34 |; 9 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 20 ( 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( big_f(X)
| p )
<=> ( ! [X1] : big_f(X1)
| p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( big_f(X)
| p )
<=> ( ! [X1] : big_f(X1)
| p ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X] :
( big_f(X)
| p )
<~> ( ! [X1] : big_f(X1)
| p ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ( ? [X1] : ~ big_f(X1)
& ~ p )
| ? [X] :
( ~ big_f(X)
& ~ p ) )
& ( ! [X1] : big_f(X1)
| p
| ! [X] :
( big_f(X)
| p ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ( ( ? [X1] : ~ big_f(X1)
& ~ p )
| ( ? [X] : ~ big_f(X)
& ~ p ) )
& ( ! [X1] : big_f(X1)
| p
| ! [X] : big_f(X)
| p ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ( ( ~ big_f(sK1_skl)
& ~ p )
| ( ~ big_f(sK0_skl)
& ~ p ) )
& ( ! [X1] : big_f(X1)
| p
| ! [X] : big_f(X)
| p ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X1,sK1_skl)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( big_f(X1)
| p
| big_f(X0)
| p ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
( ~ p
| ~ p ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
( ~ big_f(sK1_skl)
| ~ big_f(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f12,definition,
( sQ0_spl
<=> p ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f15,definition,
! [X0] :
( sQ1_spl
<=> big_f(X0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f16,plain,
! [X0] :
( ~ sQ1_spl
| big_f(X0) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f12,f15]) ).
fof(f19,plain,
~ sQ0_spl,
inference(split_clause,[status(thm)],[f8,f12]) ).
fof(f20,definition,
( sQ2_spl
<=> big_f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( sQ2_spl
| ~ big_f(sK1_skl) ),
inference(component_clause,[status(thm)],[f20]) ).
fof(f24,definition,
( sQ3_spl
<=> big_f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f26,plain,
( sQ3_spl
| ~ big_f(sK0_skl) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f28,plain,
( ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f11,f24,f20]) ).
fof(f29,plain,
( sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26,f16]) ).
fof(f30,plain,
( sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f29]) ).
fof(f31,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f16]) ).
fof(f32,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f31]) ).
fof(f33,plain,
$false,
inference(sat_refutation,[status(thm)],[f18,f19,f28,f30,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN053+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 10:40:49 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.50 % Elapsed time: 0.044543 seconds
% 0.18/0.50 % CPU time: 0.109084 seconds
% 0.18/0.50 % Total memory used: 9.272 MB
% 0.18/0.50 % Net memory used: 8.945 MB
%------------------------------------------------------------------------------