%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG125+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 : n016.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 02:05:03 PM UTC 2026
% Result : Theorem 0.14s 10.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 84 ( 17 unt; 13 def)
% Number of atoms : 282 ( 28 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 312 ( 114 ~; 110 |; 61 &)
% ( 18 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 11 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 87 ( 73 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
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(f34,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( doDivides0(W1,W0)
& aElement0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
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(f46,hypothesis,
~ ( aDivisorOf0(xu,xb)
& aDivisorOf0(xu,xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
~ ~ doDivides0(xu,xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
~ ~ doDivides0(xu,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f96,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f125,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(f126,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)],[f125]) ).
fof(f127,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)],[f126]) ).
fof(f128,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))],[f127]) ).
fof(f129,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f171,plain,
! [W0] :
( ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( doDivides0(W1,W0)
& aElement0(W1) ) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f172,plain,
! [W0] :
( ! [W1] :
( ( ~ doDivides0(W1,W0)
| ~ aElement0(W1)
| aDivisorOf0(W1,W0) )
& ( ( doDivides0(W1,W0)
& aElement0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
! [W0] :
( ( ! [W1] :
( ~ doDivides0(W1,W0)
| ~ aElement0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( doDivides0(W1,W0)
& aElement0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aElement0(W0) ),
inference(miniscoping,[status(thm)],[f172]) ).
fof(f176,plain,
! [X0,X1] :
( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f191,plain,
! [W0] :
( ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f192,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ( ( ! [W2] :
( ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f191]) ).
fof(f193,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(miniscoping,[status(thm)],[f192]) ).
fof(f194,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( sdtasdt0(W0,sK19_skl(W1,W0)) = sK18_skl(W1,W0)
& aElement0(sK19_skl(W1,W0)) )
| aElementOf0(sK18_skl(W1,W0),W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != sK18_skl(W1,W0)
| ~ aElement0(W3) )
| ~ aElementOf0(sK18_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtasdt0(W0,sK17_skl(W2,W1,W0)) = W2
& aElement0(sK17_skl(W2,W1,W0)) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(W3,sK17_skl(W2,W1,W0)),skolemize(W2,sK18_skl(W1,W0)),skolemize(W3,sK19_skl(W1,W0))],[f193]) ).
fof(f195,plain,
! [X0,X1] :
( aSet0(X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f202,plain,
! [W0] :
( aIdeal0(slsdtgt0(W0))
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f203,plain,
! [X0] :
( aIdeal0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f205,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f208,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f211,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f213,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f217,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(f218,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f221,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f222,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f227,plain,
doDivides0(xu,xa),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f228,plain,
doDivides0(xu,xb),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f253,definition,
( sQ2_spl
<=> aDivisorOf0(xu,xa) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f256,definition,
( sQ3_spl
<=> aDivisorOf0(xu,xb) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f222,f253,f256]) ).
fof(f268,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f195]) ).
fof(f273,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f129,f208]) ).
fof(f275,plain,
( aElement0(xb)
| ~ aSet0(slsdtgt0(xb)) ),
inference(resolution,[status(thm)],[f96,f213]) ).
fof(f276,plain,
( aElement0(xa)
| ~ aSet0(slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[f96,f211]) ).
fof(f279,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f96,f218]) ).
fof(f280,definition,
( sQ4_spl
<=> aSet0(slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( sQ4_spl
| ~ aSet0(slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,definition,
( sQ5_spl
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f275,f280,f283]) ).
fof(f287,definition,
( sQ6_spl
<=> aSet0(slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( sQ6_spl
| ~ aSet0(slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,definition,
( sQ7_spl
<=> aElement0(xa) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f276,f287,f290]) ).
fof(f299,definition,
( sQ9_spl
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( sQ9_spl
| ~ aSet0(xI) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,definition,
( sQ10_spl
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f279,f299,f302]) ).
fof(f306,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f301,f273]) ).
fof(f307,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f308,plain,
( sQ6_spl
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f289,f268]) ).
fof(f309,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f204]) ).
fof(f310,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f311,plain,
( sQ4_spl
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f282,f268]) ).
fof(f312,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f311,f205]) ).
fof(f313,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f312]) ).
fof(f320,definition,
( sQ11_spl
<=> aIdeal0(slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ11_spl
| ~ aIdeal0(slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,definition,
( sQ12_spl
<=> aIdeal0(slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( sQ12_spl
| ~ aIdeal0(slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f333,plain,
( sQ12_spl
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f325,f203]) ).
fof(f334,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f205]) ).
fof(f335,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f336,plain,
( sQ11_spl
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f322,f203]) ).
fof(f337,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f336,f204]) ).
fof(f338,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f343,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xb)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f176,f228]) ).
fof(f344,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xa)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f176,f227]) ).
fof(f345,plain,
( ~ sQ10_spl
| sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f343,f283,f256,f302]) ).
fof(f346,plain,
( ~ sQ10_spl
| sQ2_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f344,f290,f253,f302]) ).
fof(f347,plain,
$false,
inference(sat_refutation,[status(thm)],[f259,f286,f293,f305,f307,f310,f313,f335,f338,f345,f346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG125+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/10.41 % Computer : n016.cluster.edu
% 0.14/10.41 % Model : x86_64 x86_64
% 0.14/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.41 % Memory : 8046.5625MB
% 0.14/10.41 % OS : Linux 6.8.0-71-generic
% 0.14/10.41 % CPULimit : 300
% 0.14/10.41 % WCLimit : 300
% 0.14/10.42 % DateTime : Mon Sep 21 04:26:47 UTC 2026
% 0.14/10.42 % CPUTime :
% 0.14/10.44 % Drodi V4.1.1
% 0.14/10.47 % Refutation found
% 0.14/10.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/10.57 % Elapsed time: 0.145109 seconds
% 0.21/10.57 % CPU time: 0.122332 seconds
% 0.21/10.57 % Total memory used: 13.415 MB
% 0.21/10.57 % Net memory used: 13.394 MB
%------------------------------------------------------------------------------