%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG121+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 : 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 02:05:02 PM UTC 2026
% Result : Theorem 141.53s 23.37s
% Output : CNFRefutation 89.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 99 ( 21 unt; 13 def)
% Number of atoms : 341 ( 39 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 385 ( 143 ~; 145 |; 67 &)
% ( 19 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-5 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-4 aty)
% Number of variables : 161 ( 139 !; 22 ?)
% 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(f9,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
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(f22,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
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(f38,axiom,
! [W0] :
( aElement0(W0)
=> aIdeal0(slsdtgt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( ! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
aElementOf0(xb,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ aElementOf0(xb,xI),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f62,plain,
! [W0,W1] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f65,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f70,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f72,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f98,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f99,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f106,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f107,definition,
! [W0,W1,W3,W4,W5] :
( sP1_prd(W5,W4,W3,W1,W0)
<=> ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f108,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(formula_renaming,[status(thm)],[f106,f107]) ).
fof(f109,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ( ( ! [W3] :
( ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f111,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( sP1_prd(sK6_skl(W2,W1,W0),sK5_skl(W2,W1,W0),sK4_skl(W2,W1,W0),W1,W0)
| aElementOf0(sK4_skl(W2,W1,W0),W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,sK4_skl(W2,W1,W0),W1,W0)
| ~ aElementOf0(sK4_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP1_prd(sK3_skl(W3,W2,W1,W0),sK2_skl(W3,W2,W1,W0),W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(W4,sK2_skl(W3,W2,W1,W0)),skolemize(W5,sK3_skl(W3,W2,W1,W0)),skolemize(W3,sK4_skl(W2,W1,W0)),skolemize(W4,sK5_skl(W2,W1,W0)),skolemize(W5,sK6_skl(W2,W1,W0))],[f110]) ).
fof(f114,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP1_prd(X4,X5,X3,X1,X0)
| aElementOf0(X3,X2)
| X2 != sdtpldt1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f128,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(f129,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)],[f128]) ).
fof(f130,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)],[f129]) ).
fof(f131,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))],[f130]) ).
fof(f132,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f205,plain,
! [W0] :
( aIdeal0(slsdtgt0(W0))
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f206,plain,
! [X0] :
( aIdeal0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f207,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f208,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f211,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f212,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f213,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f216,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f220,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ~ aElementOf0(W0,xI) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f221,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f232,plain,
aElement0(xq),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f233,plain,
aElement0(xr),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f234,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f238,plain,
~ aElementOf0(xb,xI),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f244,plain,
! [W0,W1,W3,W4,W5] :
( ( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0)
| sP1_prd(W5,W4,W3,W1,W0) )
& ( ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ sP1_prd(W5,W4,W3,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f107]) ).
fof(f245,plain,
( ! [W0,W1,W3,W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0)
| sP1_prd(W5,W4,W3,W1,W0) )
& ! [W0,W1,W3,W4,W5] :
( ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ sP1_prd(W5,W4,W3,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f244]) ).
fof(f249,plain,
! [X0,X1,X2,X3,X4] :
( sdtpldt0(X1,X0) != X2
| ~ aElementOf0(X0,X3)
| ~ aElementOf0(X1,X4)
| sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f279,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f132,f211]) ).
fof(f280,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f206,f132]) ).
fof(f306,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f99,f221]) ).
fof(f307,definition,
( sQ11_spl
<=> aSet0(slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ11_spl
| ~ aSet0(slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,definition,
( sQ12_spl
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f315,definition,
( sQ13_spl
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( sQ13_spl
| ~ aSet0(xI) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,definition,
( sQ14_spl
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f306,f315,f318]) ).
fof(f322,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f317,f279]) ).
fof(f323,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f325,definition,
( sQ15_spl
<=> aSet0(slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( sQ15_spl
| ~ aSet0(slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f334,plain,
( sQ15_spl
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f280,f327]) ).
fof(f335,plain,
( sQ11_spl
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f280,f309]) ).
fof(f336,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f207]) ).
fof(f337,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f336]) ).
fof(f338,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f208]) ).
fof(f339,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f338]) ).
fof(f427,plain,
( aElement0(xb)
| ~ aElement0(xr)
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(paramodulation,[status(thm)],[f234,f63]) ).
fof(f428,definition,
( sQ21_spl
<=> aElement0(sdtasdt0(xq,xu)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( sQ21_spl
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,definition,
( sQ22_spl
<=> aElement0(xr) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( sQ22_spl
| ~ aElement0(xr) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f443,plain,
( sQ12_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f427,f428,f431,f310]) ).
fof(f444,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f433,f233]) ).
fof(f445,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f444]) ).
fof(f446,plain,
( sQ21_spl
| ~ aElement0(xu)
| ~ aElement0(xq) ),
inference(resolution,[status(thm)],[f430,f65]) ).
fof(f447,definition,
( sQ25_spl
<=> aElement0(xq) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ25_spl
| ~ aElement0(xq) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f446,f447,f318,f428]) ).
fof(f451,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f449,f232]) ).
fof(f452,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f451]) ).
fof(f786,plain,
! [X0,X1,X2,X3,X4,X5] :
( aElementOf0(X4,X5)
| X5 != sdtpldt1(X1,X3)
| ~ aSet0(X3)
| ~ aSet0(X1)
| sdtpldt0(X0,X2) != X4
| ~ aElementOf0(X2,X3)
| ~ aElementOf0(X0,X1) ),
inference(resolution,[status(thm)],[f249,f114]) ).
fof(f8338,definition,
( sQ465_spl
<=> aElementOf0(xb,xI) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f8339,plain,
( ~ sQ465_spl
| aElementOf0(xb,xI) ),
inference(component_clause,[status(thm)],[f8338]) ).
fof(f8709,plain,
! [X0,X1,X2] :
( aElementOf0(X2,xI)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| sdtpldt0(X0,X1) != X2
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[f786,f212]) ).
fof(f8717,definition,
! [X0,X1,X2] :
( sQ490_spl
<=> ( aElementOf0(X2,xI)
| sdtpldt0(X0,X1) != X2
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f8718,plain,
! [X0,X1,X2] :
( ~ sQ490_spl
| aElementOf0(X2,xI)
| sdtpldt0(X0,X1) != X2
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f8717]) ).
fof(f8720,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| sQ490_spl ),
inference(split_clause,[status(thm)],[f8709,f8717,f325,f307]) ).
fof(f8798,plain,
! [X0,X1] :
( ~ sQ490_spl
| aElementOf0(X1,xI)
| sdtpldt0(X0,xb) != X1
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[f8718,f216]) ).
fof(f13898,plain,
! [X0] :
( ~ sQ490_spl
| aElementOf0(X0,xI)
| sdtpldt0(sz00,xb) != X0 ),
inference(resolution,[status(thm)],[f8798,f213]) ).
fof(f15024,plain,
( ~ sQ490_spl
| ~ aElement0(xb)
| aElementOf0(xb,xI) ),
inference(resolution,[status(thm)],[f13898,f72]) ).
fof(f15058,plain,
( ~ sQ490_spl
| ~ sQ12_spl
| sQ465_spl ),
inference(split_clause,[status(thm)],[f15024,f8338,f310,f8717]) ).
fof(f15060,plain,
( ~ sQ465_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8339,f238]) ).
fof(f15061,plain,
~ sQ465_spl,
inference(contradiction_clause,[status(thm)],[f15060]) ).
fof(f15062,plain,
$false,
inference(sat_refutation,[status(thm)],[f321,f323,f337,f339,f443,f445,f450,f452,f8720,f15058,f15061]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG121+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n019.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 04:21:40 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 141.53/23.37 % Refutation found
% 141.53/23.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 141.53/23.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 89.37/23.47 % Elapsed time: 18.097104 seconds
% 89.37/23.47 % CPU time: 142.577946 seconds
% 89.37/23.47 % Total memory used: 492.047 MB
% 89.37/23.47 % Net memory used: 446.830 MB
%------------------------------------------------------------------------------