%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN317+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 : n004.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 03:15:43 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 3 unt; 6 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 41 ~; 40 |; 9 &)
% ( 8 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 35 ( 19 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X] :
( big_f(X)
=> big_g(X) )
<=> ? [X,Y] :
( big_f(X)
=> big_g(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X] :
( big_f(X)
=> big_g(X) )
<=> ? [X,Y] :
( big_f(X)
=> big_g(Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X] :
( big_g(X)
| ~ big_f(X) )
<~> ? [X,Y] :
( big_g(Y)
| ~ big_f(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ! [X,Y] :
( ~ big_g(Y)
& big_f(X) )
| ! [X] :
( ~ big_g(X)
& big_f(X) ) )
& ( ? [X,Y] :
( big_g(Y)
| ~ big_f(X) )
| ? [X] :
( big_g(X)
| ~ big_f(X) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ( ( ! [Y] : ~ big_g(Y)
& ! [X] : big_f(X) )
| ( ! [X] : ~ big_g(X)
& ! [X] : big_f(X) ) )
& ( ? [Y] : big_g(Y)
| ? [X] : ~ big_f(X)
| ? [X] : big_g(X)
| ? [X] : ~ big_f(X) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ( ( ! [Y] : ~ big_g(Y)
& ! [X] : big_f(X) )
| ( ! [X] : ~ big_g(X)
& ! [X] : big_f(X) ) )
& ( big_g(sK3_skl)
| ~ big_f(sK2_skl)
| big_g(sK1_skl)
| ~ big_f(sK0_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f5]) ).
fof(f7,plain,
( big_g(sK3_skl)
| ~ big_f(sK2_skl)
| big_g(sK1_skl)
| ~ big_f(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_f(X1)
| big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
! [X0,X1] :
( ~ big_g(X1)
| ~ big_g(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f12,definition,
( sQ0_spl
<=> big_f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f14,plain,
( sQ0_spl
| ~ big_f(sK0_skl) ),
inference(component_clause,[status(thm)],[f12]) ).
fof(f15,definition,
( sQ1_spl
<=> big_g(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f16,plain,
( ~ sQ1_spl
| big_g(sK1_skl) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,definition,
( sQ2_spl
<=> big_f(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f20,plain,
( sQ2_spl
| ~ big_f(sK2_skl) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,definition,
( sQ3_spl
<=> big_g(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( ~ sQ3_spl
| big_g(sK3_skl) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( sQ3_spl
| ~ sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f12,f15,f18,f21]) ).
fof(f25,definition,
! [X0] :
( sQ4_spl
<=> big_f(X0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f26,plain,
! [X0] :
( ~ sQ4_spl
| big_f(X0) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
sQ4_spl,
inference(split_clause,[status(thm)],[f8,f25]) ).
fof(f29,definition,
! [X1] :
( sQ5_spl
<=> ~ big_g(X1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f30,plain,
! [X0] :
( ~ sQ5_spl
| ~ big_g(X0) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f34,plain,
sQ5_spl,
inference(split_clause,[status(thm)],[f11,f29]) ).
fof(f35,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f30]) ).
fof(f36,plain,
( ~ sQ3_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f35]) ).
fof(f37,plain,
( sQ2_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20,f26]) ).
fof(f38,plain,
( sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f37]) ).
fof(f39,plain,
( sQ0_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14,f26]) ).
fof(f40,plain,
( sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f39]) ).
fof(f41,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16,f30]) ).
fof(f42,plain,
( ~ sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f43,plain,
$false,
inference(sat_refutation,[status(thm)],[f24,f28,f34,f36,f38,f40,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN317+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 10:49:04 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.50 % Elapsed time: 0.062185 seconds
% 0.17/0.50 % CPU time: 0.150364 seconds
% 0.17/0.50 % Total memory used: 16.521 MB
% 0.17/0.50 % Net memory used: 15.933 MB
%------------------------------------------------------------------------------