%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG089+1 : TPTP v9.3.1. Released v4.0.0.
% 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 02:04:55 PM UTC 2026
% Result : Theorem 0.10s 5.74s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 11 unt; 8 def)
% Number of atoms : 143 ( 1 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 148 ( 53 ~; 54 |; 29 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 31 ( 25 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f105,plain,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f106,plain,
! [W0] :
( ( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(NNF_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
( ! [W0] :
( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
( ! [W0] :
( ( ( ( ~ aElementOf0(sdtasdt0(sK10_skl(W0),sK8_skl(W0)),W0)
& aElement0(sK10_skl(W0)) )
| ( ~ aElementOf0(sdtpldt0(sK8_skl(W0),sK9_skl(W0)),W0)
& aElementOf0(sK9_skl(W0),W0) ) )
& aElementOf0(sK8_skl(W0),W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(W1,sK8_skl(W0)),skolemize(W2,sK9_skl(W0)),skolemize(W2,sK10_skl(W0))],[f107]) ).
fof(f111,plain,
! [X0,X1,X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f117,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f118,plain,
aIdeal0(xJ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f121,plain,
aElement0(xz),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f122,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f123,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f130,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f131,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f143,definition,
( sQ0_spl
<=> aElementOf0(sdtasdt0(xz,xk),xI) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( sQ0_spl
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ1_spl
<=> aElementOf0(sdtasdt0(xz,xl),xJ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( sQ1_spl
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f131,f143,f146]) ).
fof(f298,plain,
( sQ0_spl
| ~ aElement0(xz)
| ~ aElementOf0(xk,xI)
| ~ aIdeal0(xI) ),
inference(resolution,[status(thm)],[f111,f145]) ).
fof(f300,definition,
( sQ20_spl
<=> aIdeal0(xI) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( sQ20_spl
| ~ aIdeal0(xI) ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f303,definition,
( sQ21_spl
<=> aElementOf0(xk,xI) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( sQ21_spl
| ~ aElementOf0(xk,xI) ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,definition,
( sQ22_spl
<=> aElement0(xz) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ22_spl
| ~ aElement0(xz) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( sQ0_spl
| ~ sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f298,f300,f303,f306,f143]) ).
fof(f311,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f121]) ).
fof(f312,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f122]) ).
fof(f314,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f315,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f302,f117]) ).
fof(f316,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f315]) ).
fof(f317,plain,
( sQ1_spl
| ~ aElement0(xz)
| ~ aElementOf0(xl,xJ)
| ~ aIdeal0(xJ) ),
inference(resolution,[status(thm)],[f148,f111]) ).
fof(f318,definition,
( sQ23_spl
<=> aIdeal0(xJ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ23_spl
| ~ aIdeal0(xJ) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,definition,
( sQ24_spl
<=> aElementOf0(xl,xJ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( sQ24_spl
| ~ aElementOf0(xl,xJ) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,plain,
( sQ1_spl
| ~ sQ22_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f317,f318,f321,f306,f146]) ).
fof(f325,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f320,f118]) ).
fof(f326,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f325]) ).
fof(f327,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f123]) ).
fof(f328,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f327]) ).
fof(f329,plain,
$false,
inference(sat_refutation,[status(thm)],[f149,f309,f312,f314,f316,f324,f326,f328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.71 % Computer : n004.cluster.edu
% 0.10/5.71 % Model : x86_64 x86_64
% 0.10/5.71 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.71 % Memory : 8046.5625MB
% 0.10/5.71 % OS : Linux 6.8.0-71-generic
% 0.10/5.71 % CPULimit : 300
% 0.10/5.71 % WCLimit : 300
% 0.10/5.71 % DateTime : Mon Sep 21 04:19:14 UTC 2026
% 0.10/5.71 % CPUTime :
% 0.10/5.72 % Drodi V4.1.1
% 0.10/5.74 % Refutation found
% 0.10/5.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/5.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/5.77 % Elapsed time: 0.050204 seconds
% 0.10/5.77 % CPU time: 0.157541 seconds
% 0.10/5.77 % Total memory used: 104.534 MB
% 0.10/5.77 % Net memory used: 104.407 MB
%------------------------------------------------------------------------------