%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG093+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:04:56 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 10 unt; 14 def)
% Number of atoms : 339 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 405 ( 151 ~; 137 |; 81 &)
% ( 19 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 114 ( 96 !; 18 ?)
% 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(f26,hypothesis,
( aIdeal0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) )
& ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
<=> ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) ) )
& aSet0(sdtasasdt0(xI,xJ)) )
=> ( aIdeal0(sdtasasdt0(xI,xJ))
| ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),sdtasasdt0(xI,xJ)) )
& ! [W1] :
( aElementOf0(W1,sdtasasdt0(xI,xJ))
=> aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
<=> ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) ) )
& aSet0(sdtasasdt0(xI,xJ)) )
=> ( aIdeal0(sdtasasdt0(xI,xJ))
| ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),sdtasasdt0(xI,xJ)) )
& ! [W1] :
( aElementOf0(W1,sdtasasdt0(xI,xJ))
=> aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f102,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(f103,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)],[f102]) ).
fof(f104,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)],[f103]) ).
fof(f105,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))],[f104]) ).
fof(f107,plain,
! [X0,X1,X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f116,plain,
( aIdeal0(xJ)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xJ)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xJ)
| ~ aElementOf0(W1,xJ) ) )
| ~ aElementOf0(W0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f119,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f120,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f123,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f124,plain,
aIdeal0(xJ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f125,plain,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),sdtasasdt0(xI,xJ))
& aElement0(W1) )
| ? [W1] :
( ~ aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ))
& aElementOf0(W1,sdtasasdt0(xI,xJ)) ) )
& aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
<=> ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) ) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f126,definition,
! [W0,W1] :
( sP2_prd(W1,W0)
<=> ( ~ aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ))
& aElementOf0(W1,sdtasasdt0(xI,xJ)) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f127,plain,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),sdtasasdt0(xI,xJ))
& aElement0(W1) )
| ? [W1] : sP2_prd(W1,W0) )
& aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
<=> ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) ) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(formula_renaming,[status(thm)],[f125,f126]) ).
fof(f128,plain,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),sdtasasdt0(xI,xJ))
& aElement0(W1) )
| ? [W1] : sP2_prd(W1,W0) )
& aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xJ)
| ~ aElementOf0(W0,xI)
| aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& ( ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) )
| ~ aElementOf0(W0,sdtasasdt0(xI,xJ)) ) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(NNF_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),sdtasasdt0(xI,xJ))
& aElement0(W1) )
| ? [W1] : sP2_prd(W1,W0) )
& aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& ! [W0] :
( ~ aElementOf0(W0,xJ)
| ~ aElementOf0(W0,xI)
| aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& ! [W0] :
( ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) )
| ~ aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(miniscoping,[status(thm)],[f128]) ).
fof(f130,plain,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ( ( ~ aElementOf0(sdtasdt0(sK13_skl,sK11_skl),sdtasasdt0(xI,xJ))
& aElement0(sK13_skl) )
| sP2_prd(sK12_skl,sK11_skl) )
& aElementOf0(sK11_skl,sdtasasdt0(xI,xJ))
& ! [W0] :
( ~ aElementOf0(W0,xJ)
| ~ aElementOf0(W0,xI)
| aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& ! [W0] :
( ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) )
| ~ aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(W0,sK11_skl),skolemize(W1,sK12_skl),skolemize(W1,sK13_skl)],[f129]) ).
fof(f132,plain,
! [X0] :
( aElementOf0(X0,xI)
| ~ aElementOf0(X0,sdtasasdt0(xI,xJ)) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f133,plain,
! [X0] :
( aElementOf0(X0,xJ)
| ~ aElementOf0(X0,sdtasasdt0(xI,xJ)) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f134,plain,
! [X0] :
( ~ aElementOf0(X0,xJ)
| ~ aElementOf0(X0,xI)
| aElementOf0(X0,sdtasasdt0(xI,xJ)) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f135,plain,
aElementOf0(sK11_skl,sdtasasdt0(xI,xJ)),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f136,plain,
( aElement0(sK13_skl)
| sP2_prd(sK12_skl,sK11_skl) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f137,plain,
( ~ aElementOf0(sdtasdt0(sK13_skl,sK11_skl),sdtasasdt0(xI,xJ))
| sP2_prd(sK12_skl,sK11_skl) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f150,plain,
! [W0,W1] :
( ( aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ))
| ~ aElementOf0(W1,sdtasasdt0(xI,xJ))
| sP2_prd(W1,W0) )
& ( ( ~ aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ))
& aElementOf0(W1,sdtasasdt0(xI,xJ)) )
| ~ sP2_prd(W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f126]) ).
fof(f151,plain,
( ! [W0,W1] :
( aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ))
| ~ aElementOf0(W1,sdtasasdt0(xI,xJ))
| sP2_prd(W1,W0) )
& ! [W0,W1] :
( ( ~ aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ))
& aElementOf0(W1,sdtasasdt0(xI,xJ)) )
| ~ sP2_prd(W1,W0) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f152,plain,
! [X0,X1] :
( aElementOf0(X0,sdtasasdt0(xI,xJ))
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ~ aElementOf0(sdtpldt0(X1,X0),sdtasasdt0(xI,xJ))
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f155,definition,
( sQ0_spl
<=> sP2_prd(sK12_skl,sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ0_spl
| sP2_prd(sK12_skl,sK11_skl) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,definition,
( sQ1_spl
<=> aElement0(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f136,f155,f158]) ).
fof(f162,definition,
( sQ2_spl
<=> aElementOf0(sdtasdt0(sK13_skl,sK11_skl),sdtasasdt0(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ2_spl
| ~ aElementOf0(sdtasdt0(sK13_skl,sK11_skl),sdtasasdt0(xI,xJ)) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f137,f155,f162]) ).
fof(f174,plain,
aElementOf0(sK11_skl,xI),
inference(resolution,[status(thm)],[f132,f135]) ).
fof(f175,plain,
! [X0,X1] :
( ~ sP2_prd(X0,X1)
| aElementOf0(X0,xI) ),
inference(resolution,[status(thm)],[f132,f152]) ).
fof(f176,plain,
aElementOf0(sK11_skl,xJ),
inference(resolution,[status(thm)],[f133,f135]) ).
fof(f177,plain,
! [X0,X1] :
( ~ sP2_prd(X0,X1)
| aElementOf0(X0,xJ) ),
inference(resolution,[status(thm)],[f133,f152]) ).
fof(f218,plain,
! [X0,X1] :
( ~ sP2_prd(X1,X0)
| ~ aElementOf0(sdtpldt0(X0,X1),xJ)
| ~ aElementOf0(sdtpldt0(X0,X1),xI) ),
inference(resolution,[status(thm)],[f134,f153]) ).
fof(f219,plain,
( sQ2_spl
| ~ aElementOf0(sdtasdt0(sK13_skl,sK11_skl),xJ)
| ~ aElementOf0(sdtasdt0(sK13_skl,sK11_skl),xI) ),
inference(resolution,[status(thm)],[f134,f164]) ).
fof(f223,definition,
( sQ9_spl
<=> aElementOf0(sdtasdt0(sK13_skl,sK11_skl),xI) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ9_spl
| ~ aElementOf0(sdtasdt0(sK13_skl,sK11_skl),xI) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
( sQ10_spl
<=> aElementOf0(sdtasdt0(sK13_skl,sK11_skl),xJ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( sQ10_spl
| ~ aElementOf0(sdtasdt0(sK13_skl,sK11_skl),xJ) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( sQ2_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f219,f223,f226,f162]) ).
fof(f257,definition,
( sQ14_spl
<=> aElementOf0(sK11_skl,xI) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ14_spl
| ~ aElementOf0(sK11_skl,xI) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f261,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f174]) ).
fof(f262,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f281,definition,
( sQ15_spl
<=> aIdeal0(xJ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ15_spl
| ~ aIdeal0(xJ) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f351,plain,
( sQ9_spl
| ~ aElement0(sK13_skl)
| ~ aElementOf0(sK11_skl,xI) ),
inference(resolution,[status(thm)],[f119,f225]) ).
fof(f353,plain,
( sQ9_spl
| ~ sQ1_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f351,f257,f158,f223]) ).
fof(f358,plain,
( sQ10_spl
| ~ aElement0(sK13_skl)
| ~ aElementOf0(sK11_skl,xJ) ),
inference(resolution,[status(thm)],[f123,f228]) ).
fof(f361,definition,
( sQ27_spl
<=> aElementOf0(sK11_skl,xJ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ27_spl
| ~ aElementOf0(sK11_skl,xJ) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( sQ10_spl
| ~ sQ1_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f358,f361,f158,f226]) ).
fof(f369,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f363,f176]) ).
fof(f370,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f369]) ).
fof(f465,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f124]) ).
fof(f466,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f572,plain,
! [X0,X1] :
( ~ sP2_prd(X1,X0)
| ~ aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xJ)
| ~ aIdeal0(xJ) ),
inference(resolution,[status(thm)],[f107,f218]) ).
fof(f583,definition,
! [X0,X1] :
( sQ58_spl
<=> ( ~ sP2_prd(X1,X0)
| ~ aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xJ) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f584,plain,
! [X0,X1] :
( ~ sQ58_spl
| ~ sP2_prd(X1,X0)
| ~ aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xJ) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( sQ58_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f572,f281,f583]) ).
fof(f616,plain,
! [X0,X1] :
( ~ sQ58_spl
| ~ sP2_prd(X1,X0)
| ~ aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X0,xJ) ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f177]) ).
fof(f619,plain,
! [X0,X1] :
( ~ sQ58_spl
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI)
| ~ aIdeal0(xI)
| ~ sP2_prd(X1,X0)
| ~ aElementOf0(X0,xJ) ),
inference(resolution,[status(thm)],[f616,f107]) ).
fof(f620,definition,
! [X0,X1] :
( sQ66_spl
<=> ( ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI)
| ~ sP2_prd(X1,X0)
| ~ aElementOf0(X0,xJ) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f621,plain,
! [X0,X1] :
( ~ sQ66_spl
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI)
| ~ sP2_prd(X1,X0)
| ~ aElementOf0(X0,xJ) ),
inference(component_clause,[status(thm)],[f620]) ).
fof(f623,definition,
( sQ67_spl
<=> aIdeal0(xI) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( sQ67_spl
| ~ aIdeal0(xI) ),
inference(component_clause,[status(thm)],[f623]) ).
fof(f626,plain,
( ~ sQ58_spl
| ~ sQ67_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f619,f620,f623,f583]) ).
fof(f627,plain,
! [X0,X1] :
( ~ sQ66_spl
| ~ aElementOf0(X0,xI)
| ~ sP2_prd(X1,X0)
| ~ aElementOf0(X0,xJ) ),
inference(forward_subsumption_resolution,[status(thm)],[f621,f175]) ).
fof(f628,plain,
( sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f625,f120]) ).
fof(f629,plain,
sQ67_spl,
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f639,plain,
! [X0] :
( ~ sQ66_spl
| ~ aElementOf0(sK11_skl,xI)
| ~ sP2_prd(X0,sK11_skl) ),
inference(resolution,[status(thm)],[f627,f176]) ).
fof(f666,definition,
! [X0] :
( sQ74_spl
<=> ~ sP2_prd(X0,sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f667,plain,
! [X0] :
( ~ sQ74_spl
| ~ sP2_prd(X0,sK11_skl) ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f669,plain,
( ~ sQ66_spl
| ~ sQ14_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f639,f666,f257,f620]) ).
fof(f677,plain,
( ~ sQ0_spl
| ~ sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f156,f667]) ).
fof(f678,plain,
( ~ sQ0_spl
| ~ sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f677]) ).
fof(f679,plain,
$false,
inference(sat_refutation,[status(thm)],[f161,f165,f229,f262,f353,f364,f370,f466,f586,f626,f629,f669,f678]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG093+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 04:19:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46 % Elapsed time: 0.068942 seconds
% 0.15/0.46 % CPU time: 0.286028 seconds
% 0.15/0.46 % Total memory used: 78.515 MB
% 0.15/0.46 % Net memory used: 78.239 MB
%------------------------------------------------------------------------------