%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN398+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 : n013.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 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 1 unt; 6 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 37 ~; 40 |; 18 &)
% ( 8 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 8 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 20 ( 17 !; 3 ?)
% 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,
( ! [X] :
( f(X)
& p )
<~> ( ! [Y] : f(Y)
& p ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( ! [Y] : f(Y)
& p ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ! [X] :
( f(X)
& p )
<~> sP0_prd ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ~ sP0_prd
| ? [X] :
( ~ f(X)
| ~ p ) )
& ( sP0_prd
| ! [X] :
( f(X)
& p ) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ~ sP0_prd
| ? [X] : ~ f(X)
| ~ p )
& ( sP0_prd
| ( ! [X] : f(X)
& p ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ( ~ sP0_prd
| ~ f(sK0_skl)
| ~ p )
& ( sP0_prd
| ( ! [X] : f(X)
& p ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f7]) ).
fof(f9,plain,
( sP0_prd
| p ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0] :
( sP0_prd
| f(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
( ~ sP0_prd
| ~ f(sK0_skl)
| ~ p ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f12,plain,
( ( ? [Y] : ~ f(Y)
| ~ p
| sP0_prd )
& ( ( ! [Y] : f(Y)
& p )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( ( ~ f(sK1_skl)
| ~ p
| sP0_prd )
& ( ( ! [Y] : f(Y)
& p )
| ~ sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl)],[f12]) ).
fof(f14,plain,
( p
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] :
( f(X0)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
( ~ f(sK1_skl)
| ~ p
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,definition,
( sQ0_spl
<=> p ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f20,definition,
( sQ1_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f23,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f17,f20]) ).
fof(f24,definition,
! [X0] :
( sQ2_spl
<=> f(X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f25,plain,
! [X0] :
( ~ sQ2_spl
| f(X0) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f10,f24,f20]) ).
fof(f28,definition,
( sQ3_spl
<=> f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( sQ3_spl
| ~ f(sK0_skl) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f17,f28,f20]) ).
fof(f32,plain,
( sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f14,f20,f17]) ).
fof(f33,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f15,f20,f24]) ).
fof(f34,definition,
( sQ4_spl
<=> f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( sQ4_spl
| ~ f(sK1_skl) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f16,f20,f17,f34]) ).
fof(f38,plain,
( sQ4_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f36,f25]) ).
fof(f39,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f38]) ).
fof(f40,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f25]) ).
fof(f41,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f40]) ).
fof(f42,plain,
$false,
inference(sat_refutation,[status(thm)],[f23,f27,f31,f32,f33,f37,f39,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN398+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 10:52:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.043754 seconds
% 0.13/0.42 % CPU time: 0.114244 seconds
% 0.13/0.42 % Total memory used: 16.525 MB
% 0.13/0.42 % Net memory used: 15.934 MB
%------------------------------------------------------------------------------