%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG099+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 : 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 02:04:57 PM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 91 ( 21 unt; 15 def)
% Number of atoms : 251 ( 3 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 259 ( 99 ~; 100 |; 35 &)
% ( 17 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 63 ( 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f27,definition,
! [W0,W1,W2] :
( ( aIdeal0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
( aElement0(xy)
& aElement0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,hypothesis,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
? [W0] :
( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& aElement0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ? [W0] :
( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f44,plain,
! [W0,W1] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f80,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f81,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f110,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(f111,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)],[f110]) ).
fof(f112,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)],[f111]) ).
fof(f113,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))],[f112]) ).
fof(f114,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f126,plain,
! [W0,W1,W2] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f127,plain,
! [W0,W1,W2] :
( ( ( ~ aElementOf0(sdtpldt0(W0,smndt0(W1)),W2)
| sdteqdtlpzmzozddtrp0(W0,W1,W2) )
& ( aElementOf0(sdtpldt0(W0,smndt0(W1)),W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f126]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(X1)),X2)
| sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aIdeal0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f131,plain,
aIdeal0(xJ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f134,plain,
aElement0(xx),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f135,plain,
aElement0(xy),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f136,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f137,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f139,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f140,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f141,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f142,plain,
! [W0] :
( ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f143,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| ~ sdteqdtlpzmzozddtrp0(X0,xx,xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f172,plain,
aSet0(xJ),
inference(resolution,[status(thm)],[f114,f131]) ).
fof(f173,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f114,f130]) ).
fof(f175,definition,
( sQ2_spl
<=> aElement0(xa) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f178,definition,
( sQ3_spl
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( aElement0(xb)
| ~ aSet0(xJ) ),
inference(resolution,[status(thm)],[f81,f137]) ).
fof(f186,plain,
( aElement0(xa)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f81,f136]) ).
fof(f189,definition,
( sQ5_spl
<=> aSet0(xJ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ5_spl
| ~ aSet0(xJ) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f185,f189,f178]) ).
fof(f193,definition,
( sQ6_spl
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ6_spl
| ~ aSet0(xI) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ2_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f186,f193,f175]) ).
fof(f205,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f173]) ).
fof(f206,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f207,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f172]) ).
fof(f208,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f234,plain,
( sdteqdtlpzmzozddtrp0(xw,xx,xI)
| ~ aIdeal0(xI)
| ~ aElement0(xx)
| ~ aElement0(xw) ),
inference(resolution,[status(thm)],[f140,f129]) ).
fof(f236,definition,
( sQ12_spl
<=> aElement0(xw) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f239,definition,
( sQ13_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ13_spl
| ~ aElement0(xx) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ14_spl
<=> aIdeal0(xI) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( sQ14_spl
| ~ aIdeal0(xI) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ15_spl
<=> sdteqdtlpzmzozddtrp0(xw,xx,xI) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ15_spl
| sdteqdtlpzmzozddtrp0(xw,xx,xI) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f234,f236,f239,f242,f245]) ).
fof(f253,plain,
( ~ sQ15_spl
| ~ sdteqdtlpzmzozddtrp0(xw,xy,xJ)
| ~ aElement0(xw) ),
inference(resolution,[status(thm)],[f246,f143]) ).
fof(f254,definition,
( sQ17_spl
<=> sdteqdtlpzmzozddtrp0(xw,xy,xJ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( ~ sQ15_spl
| ~ sQ17_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f253,f236,f254,f245]) ).
fof(f258,plain,
( sdteqdtlpzmzozddtrp0(xw,xy,xJ)
| ~ aIdeal0(xJ)
| ~ aElement0(xy)
| ~ aElement0(xw) ),
inference(resolution,[status(thm)],[f141,f129]) ).
fof(f260,definition,
( sQ18_spl
<=> aElement0(xy) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ18_spl
| ~ aElement0(xy) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,definition,
( sQ19_spl
<=> aIdeal0(xJ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ19_spl
| ~ aIdeal0(xJ) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( sQ17_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f258,f236,f260,f263,f254]) ).
fof(f274,plain,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(paramodulation,[status(thm)],[f139,f45]) ).
fof(f275,definition,
( sQ21_spl
<=> aElement0(sdtasdt0(xy,xa)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( sQ21_spl
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,definition,
( sQ22_spl
<=> aElement0(sdtasdt0(xx,xb)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ22_spl
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f285,plain,
( sQ12_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f274,f275,f278,f236]) ).
fof(f286,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f131]) ).
fof(f287,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f288,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f135]) ).
fof(f289,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f290,plain,
( sQ21_spl
| ~ aElement0(xa)
| ~ aElement0(xy) ),
inference(resolution,[status(thm)],[f277,f47]) ).
fof(f291,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f290,f260,f175,f275]) ).
fof(f292,plain,
( sQ22_spl
| ~ aElement0(xb)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f280,f47]) ).
fof(f293,plain,
( sQ22_spl
| ~ sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f292,f239,f178,f278]) ).
fof(f294,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f241,f134]) ).
fof(f295,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f296,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f130]) ).
fof(f297,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f298,plain,
$false,
inference(sat_refutation,[status(thm)],[f192,f196,f206,f208,f248,f257,f266,f285,f287,f289,f291,f293,f295,f297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG099+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n003.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 04:21:16 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 0.18/0.50 % Refutation found
% 0.18/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.60 % Elapsed time: 0.127981 seconds
% 0.23/0.60 % CPU time: 0.130078 seconds
% 0.23/0.60 % Total memory used: 13.368 MB
% 0.23/0.60 % Net memory used: 13.346 MB
%------------------------------------------------------------------------------