%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN376+1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 03:15:55 PM UTC 2026
% Result : Theorem 0.13s 5.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 5 unt; 3 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 25 ~; 16 |; 11 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 29 ( 18 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X] :
! [Y] :
( big_p(Y)
<=> big_p(X) )
=> ( ! [X] : ~ big_p(X)
| ! [X] : big_p(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X] :
! [Y] :
( big_p(Y)
<=> big_p(X) )
=> ( ! [X] : ~ big_p(X)
| ! [X] : big_p(X) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X] : big_p(X)
& ? [X] : ~ big_p(X)
& ? [X] :
! [Y] :
( big_p(Y)
<=> big_p(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ? [X] : big_p(X)
& ? [X] : ~ big_p(X)
& ? [X] :
! [Y] :
( ( ~ big_p(X)
| big_p(Y) )
& ( big_p(X)
| ~ big_p(Y) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ? [X] : big_p(X)
& ? [X] : ~ big_p(X)
& ? [X] :
( ( ~ big_p(X)
| ! [Y] : big_p(Y) )
& ( big_p(X)
| ! [Y] : ~ big_p(Y) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( big_p(sK2_skl)
& ~ big_p(sK1_skl)
& ( ~ big_p(sK0_skl)
| ! [Y] : big_p(Y) )
& ( big_p(sK0_skl)
| ! [Y] : ~ big_p(Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(X,sK2_skl)],[f5]) ).
fof(f7,plain,
! [X0] :
( big_p(sK0_skl)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ big_p(sK0_skl)
| big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
~ big_p(sK1_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
big_p(sK2_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,definition,
! [X0] :
( sQ0_spl
<=> ~ big_p(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f12,plain,
! [X0] :
( ~ sQ0_spl
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,definition,
( sQ1_spl
<=> big_p(sK0_skl) ),
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
<=> big_p(X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f19,plain,
! [X0] :
( ~ sQ2_spl
| big_p(X0) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f8,f18,f14]) ).
fof(f24,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10,f12]) ).
fof(f25,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f24]) ).
fof(f26,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9,f19]) ).
fof(f27,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f26]) ).
fof(f28,plain,
$false,
inference(sat_refutation,[status(thm)],[f17,f21,f25,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN376+1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n016.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Mon Sep 21 10:57:00 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 0.13/5.40 % Refutation found
% 0.13/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.43 % Elapsed time: 0.045907 seconds
% 0.13/5.43 % CPU time: 0.138209 seconds
% 0.13/5.43 % Total memory used: 55.269 MB
% 0.13/5.43 % Net memory used: 54.612 MB
%------------------------------------------------------------------------------