%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN935+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 03:18:21 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 3 unt; 4 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 79 ( 29 ~; 30 |; 9 &)
% ( 6 <=>; 4 =>; 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 20 ( 12 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X] :
( p(X)
=> c )
<=> ( ! [X] : p(X)
=> c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X] :
( p(X)
=> c )
<=> ( ! [X] : p(X)
=> c ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X] :
( c
| ~ p(X) )
<~> ( c
| ? [X] : ~ p(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ( ~ c
& ! [X] : p(X) )
| ! [X] :
( ~ c
& p(X) ) )
& ( c
| ? [X] : ~ p(X)
| ? [X] :
( c
| ~ p(X) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ( ( ~ c
& ! [X] : p(X) )
| ( ~ c
& ! [X] : p(X) ) )
& ( c
| ? [X] : ~ p(X)
| c
| ? [X] : ~ p(X) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ( ( ~ c
& ! [X] : p(X) )
| ( ~ c
& ! [X] : p(X) ) )
& ( c
| ~ p(sK1_skl)
| c
| ~ p(sK0_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl)],[f5]) ).
fof(f7,plain,
( c
| ~ p(sK1_skl)
| c
| ~ p(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( p(X1)
| p(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
( ~ c
| ~ c ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f12,definition,
( sQ0_spl
<=> p(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f14,plain,
( sQ0_spl
| ~ p(sK0_skl) ),
inference(component_clause,[status(thm)],[f12]) ).
fof(f15,definition,
( sQ1_spl
<=> c ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f18,definition,
( sQ2_spl
<=> p(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f20,plain,
( sQ2_spl
| ~ p(sK1_skl) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,plain,
( ~ sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f12,f15,f18]) ).
fof(f22,definition,
! [X0] :
( sQ3_spl
<=> p(X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f23,plain,
! [X0] :
( ~ sQ3_spl
| p(X0) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,plain,
sQ3_spl,
inference(split_clause,[status(thm)],[f8,f22]) ).
fof(f28,plain,
~ sQ1_spl,
inference(split_clause,[status(thm)],[f11,f15]) ).
fof(f29,plain,
( sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14,f23]) ).
fof(f30,plain,
( sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f29]) ).
fof(f31,plain,
( sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20,f23]) ).
fof(f32,plain,
( sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f31]) ).
fof(f33,plain,
$false,
inference(sat_refutation,[status(thm)],[f21,f25,f28,f30,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN935+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 11:32:01 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.029506 seconds
% 0.13/0.39 % CPU time: 0.074672 seconds
% 0.13/0.39 % Total memory used: 7.727 MB
% 0.13/0.39 % Net memory used: 7.447 MB
%------------------------------------------------------------------------------