%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN951+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 03:18:33 PM UTC 2026
% Result : Theorem 0.10s 0.50s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 3 unt; 6 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 86 ( 30 ~; 27 |; 17 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 10 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 14 ( 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X] : p(X)
=> ( ( a
=> ( ( q
=> q )
& ( ~ b
| b ) ) )
& ? [X] : p(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X] : p(X)
=> ( ( a
=> ( ( q
=> q )
& ( ~ b
| b ) ) )
& ? [X] : p(X) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ( ( ( ~ q
& q )
| ( b
& ~ b ) )
& a )
| ! [X] : ~ p(X) )
& ? [X] : p(X) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( b
& ~ b ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ( ( ( ( ~ q
& q )
| sP0_prd )
& a )
| ! [X] : ~ p(X) )
& ? [X] : p(X) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ( ( ( ~ q
& q )
| sP0_prd )
& a )
| ! [X] : ~ p(X) )
& p(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f5]) ).
fof(f7,plain,
p(sK0_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] :
( a
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0] :
( q
| sP0_prd
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0] :
( ~ q
| sP0_prd
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
( ( ~ b
| b
| sP0_prd )
& ( ( b
& ~ b )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
( ~ b
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
( b
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,definition,
! [X0] :
( sQ0_spl
<=> ~ p(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f16,plain,
! [X0] :
( ~ sQ0_spl
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,definition,
( sQ1_spl
<=> a ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f21,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f15,f18]) ).
fof(f22,definition,
( sQ2_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f25,definition,
( sQ3_spl
<=> q ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f28,plain,
( sQ3_spl
| sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f15,f22,f25]) ).
fof(f29,plain,
( ~ sQ3_spl
| sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f15,f22,f25]) ).
fof(f30,definition,
( sQ4_spl
<=> b ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f12,f22,f30]) ).
fof(f34,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13,f22,f30]) ).
fof(f36,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7,f16]) ).
fof(f37,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f36]) ).
fof(f38,plain,
$false,
inference(sat_refutation,[status(thm)],[f21,f28,f29,f33,f34,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN951+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.47 % Computer : n006.cluster.edu
% 0.10/0.47 % Model : x86_64 x86_64
% 0.10/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.47 % Memory : 8046.5625MB
% 0.10/0.47 % OS : Linux 6.8.0-71-generic
% 0.10/0.47 % CPULimit : 300
% 0.10/0.47 % WCLimit : 300
% 0.10/0.47 % DateTime : Mon Sep 21 11:30:42 UTC 2026
% 0.10/0.47 % CPUTime :
% 0.10/0.48 % Drodi V4.1.1
% 0.10/0.50 % Refutation found
% 0.10/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.52 % Elapsed time: 0.040163 seconds
% 0.10/0.52 % CPU time: 0.102769 seconds
% 0.10/0.52 % Total memory used: 16.524 MB
% 0.10/0.52 % Net memory used: 15.969 MB
%------------------------------------------------------------------------------