%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM471+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 : n009.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 01:40:38 PM UTC 2026
% Result : Theorem 0.13s 5.93s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 40
% Syntax : Number of formulae : 157 ( 25 unt; 25 def)
% Number of atoms : 512 ( 94 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 602 ( 247 ~; 249 |; 63 &)
% ( 28 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 23 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 119 ( 109 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& W1 != W2
& W0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,hypothesis,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
( sdtlseqdt0(xp,xq)
| ? [W0] :
( sdtpldt0(xp,W0) = xq
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ( sdtlseqdt0(xp,xq)
| ? [W0] :
( sdtpldt0(xp,W0) = xq
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f44,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f47,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f56,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f82,plain,
! [W0,W1] :
( ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f83,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ( sdtpldt0(W0,sK0_skl(W1,W0)) = W1
& aNaturalNumber0(sK0_skl(W1,W0)) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f83]) ).
fof(f87,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f94,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f95,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f97,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f99,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f102,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f108,plain,
! [W0,W1,W2] :
( ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ sdtlseqdt0(W1,W2)
| W1 = W2
| W0 = sz00
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f110,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| X0 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f122,plain,
! [W0,W1] :
( ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f123,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( W1 = sdtasdt0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f123]) ).
fof(f127,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f128,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f129,plain,
! [W0,W1] :
( ! [W2] :
( ( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [W0,W1] :
( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ! [W2] :
( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f129]) ).
fof(f132,plain,
! [X0,X1,X2] :
( X1 = sdtasdt0(X0,X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f138,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f139,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f140,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f141,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& sdtpldt0(xm,xn) = sdtasdt0(xl,sK3_skl)
& aNaturalNumber0(sK3_skl)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK2_skl)
& aNaturalNumber0(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W0,sK2_skl),skolemize(W0,sK3_skl)],[f35]) ).
fof(f145,plain,
aNaturalNumber0(sK3_skl),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f148,plain,
xl != sz00,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f149,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f150,plain,
xm = sdtasdt0(xl,xp),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f151,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f152,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f154,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f155,plain,
( ~ sdtlseqdt0(xp,xq)
& ! [W0] :
( sdtpldt0(xp,W0) != xq
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f156,plain,
! [X0] :
( sdtpldt0(xp,X0) != xq
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f157,plain,
~ sdtlseqdt0(xp,xq),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f162,plain,
( aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f150,f50]) ).
fof(f163,definition,
( sQ0_spl
<=> aNaturalNumber0(xl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( sQ0_spl
| ~ aNaturalNumber0(xl) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f169,definition,
( sQ2_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( sQ2_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f177,definition,
( sQ4_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f162,f163,f169,f177]) ).
fof(f181,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f149]) ).
fof(f182,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f215,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f138]) ).
fof(f216,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f215]) ).
fof(f220,definition,
( sQ10_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ10_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f230,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xq)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f99,f157]) ).
fof(f234,definition,
! [X0] :
( sQ12_spl
<=> ( ~ sdtlseqdt0(X0,xq)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f235,plain,
! [X0] :
( ~ sQ12_spl
| ~ sdtlseqdt0(X0,xq)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,definition,
( sQ13_spl
<=> aNaturalNumber0(xq) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ13_spl
| ~ aNaturalNumber0(xq) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( ~ sQ13_spl
| sQ12_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f230,f169,f234,f237]) ).
fof(f248,definition,
( sQ14_spl
<=> sdtlseqdt0(xq,xp) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f239,f152]) ).
fof(f254,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f270,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f222]) ).
fof(f271,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f293,definition,
( sQ21_spl
<=> xl = sz00 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( ~ sQ21_spl
| xl = sz00 ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f305,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f294,f148]) ).
fof(f306,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f305]) ).
fof(f343,definition,
( sQ29_spl
<=> xp = xq ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f347,plain,
! [X0] :
( ~ sQ12_spl
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xq)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f235,f102]) ).
fof(f350,definition,
! [X0] :
( sQ30_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xq)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f351,plain,
! [X0] :
( ~ sQ30_spl
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xq)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( ~ sQ12_spl
| ~ sQ2_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f347,f350,f169,f234]) ).
fof(f359,plain,
! [X0] :
( ~ sQ30_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,xq)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f351]) ).
fof(f533,plain,
( ~ aNaturalNumber0(xn)
| sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f153,f87]) ).
fof(f540,definition,
( sQ55_spl
<=> aNaturalNumber0(sdtasdt0(xl,xq)) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( sQ55_spl
| ~ aNaturalNumber0(sdtasdt0(xl,xq)) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f543,definition,
( sQ56_spl
<=> sdtlseqdt0(xm,sdtasdt0(xl,xq)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( ~ sQ56_spl
| sdtlseqdt0(xm,sdtasdt0(xl,xq)) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f546,definition,
( sQ57_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( sQ57_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f549,plain,
( ~ sQ57_spl
| sQ56_spl
| ~ sQ55_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f533,f177,f540,f543,f546]) ).
fof(f568,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f140]) ).
fof(f569,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f570,plain,
( sQ55_spl
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_demodulation,[status(thm)],[f153,f542]) ).
fof(f653,plain,
! [X0] :
( sdtlseqdt0(sdtasdt0(xl,X0),xm)
| ~ sdtlseqdt0(X0,xp)
| X0 = xp
| xl = sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f150,f110]) ).
fof(f671,definition,
! [X0] :
( sQ69_spl
<=> ( sdtlseqdt0(sdtasdt0(xl,X0),xm)
| ~ sdtlseqdt0(X0,xp)
| X0 = xp
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f672,plain,
! [X0] :
( ~ sQ69_spl
| sdtlseqdt0(sdtasdt0(xl,X0),xm)
| ~ sdtlseqdt0(X0,xp)
| X0 = xp
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f674,plain,
( sQ21_spl
| ~ sQ2_spl
| sQ69_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f653,f163,f671,f169,f293]) ).
fof(f821,plain,
( sQ55_spl
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f48,f570]) ).
fof(f822,plain,
( sQ55_spl
| ~ sQ57_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f821,f177,f546,f540]) ).
fof(f841,plain,
( ~ aNaturalNumber0(xp)
| doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f127,f150]) ).
fof(f861,definition,
( sQ92_spl
<=> doDivides0(xl,xm) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f864,plain,
( ~ sQ2_spl
| sQ92_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f841,f163,f177,f861,f169]) ).
fof(f868,definition,
! [X0] :
( sQ94_spl
<=> ( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f869,plain,
! [X0] :
( ~ sQ94_spl
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f868]) ).
fof(f928,definition,
( sQ101_spl
<=> aNaturalNumber0(sdtpldt0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f930,plain,
( sQ101_spl
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(component_clause,[status(thm)],[f928]) ).
fof(f1090,plain,
! [X0] :
( xm = sdtasdt0(xl,X0)
| X0 != xp
| ~ doDivides0(xl,xm)
| xl = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f151,f132]) ).
fof(f1104,definition,
! [X0] :
( sQ130_spl
<=> ( xm = sdtasdt0(xl,X0)
| X0 != xp ) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1105,plain,
! [X0] :
( ~ sQ130_spl
| xm = sdtasdt0(xl,X0)
| X0 != xp ),
inference(component_clause,[status(thm)],[f1104]) ).
fof(f1107,plain,
( sQ130_spl
| ~ sQ92_spl
| sQ21_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1090,f163,f177,f293,f861,f1104]) ).
fof(f1231,plain,
! [X0] :
( ~ sQ94_spl
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f869]) ).
fof(f1260,definition,
( sQ148_spl
<=> aNaturalNumber0(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1262,plain,
( sQ148_spl
| ~ aNaturalNumber0(sK3_skl) ),
inference(component_clause,[status(thm)],[f1260]) ).
fof(f1316,plain,
( sQ148_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1262,f145]) ).
fof(f1317,plain,
sQ148_spl,
inference(contradiction_clause,[status(thm)],[f1316]) ).
fof(f1319,plain,
( sQ101_spl
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f930,f48]) ).
fof(f1321,plain,
( sQ101_spl
| ~ sQ57_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1319,f177,f546,f928]) ).
fof(f1354,plain,
( ~ sQ94_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f152,f1231]) ).
fof(f1366,plain,
~ sQ94_spl,
inference(contradiction_clause,[status(thm)],[f1354]) ).
fof(f1567,plain,
( ~ sQ30_spl
| ~ aNaturalNumber0(xq)
| sdtlseqdt0(xq,xp)
| ~ aNaturalNumber0(xq) ),
inference(resolution,[status(thm)],[f359,f95]) ).
fof(f1576,plain,
( ~ sQ30_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1567,f237,f248,f350]) ).
fof(f1577,plain,
( ~ sQ56_spl
| sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(forward_demodulation,[status(thm)],[f153,f544]) ).
fof(f1677,plain,
( ~ sQ130_spl
| xm = sdtpldt0(xm,xn)
| xq != xp ),
inference(paramodulation,[status(thm)],[f153,f1105]) ).
fof(f1690,definition,
( sQ189_spl
<=> xm = sdtpldt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1691,plain,
( ~ sQ189_spl
| xm = sdtpldt0(xm,xn) ),
inference(component_clause,[status(thm)],[f1690]) ).
fof(f1693,plain,
( ~ sQ130_spl
| sQ189_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1677,f343,f1690,f1104]) ).
fof(f1705,plain,
( ~ sQ189_spl
| xq = sdtsldt0(xm,xl) ),
inference(backward_demodulation,[status(thm)],[f1691,f154]) ).
fof(f1715,plain,
( ~ sQ189_spl
| xq = xp ),
inference(forward_demodulation,[status(thm)],[f151,f1705]) ).
fof(f1824,plain,
! [X0] :
( ~ sQ189_spl
| sdtpldt0(xp,X0) != xp
| ~ aNaturalNumber0(X0) ),
inference(backward_demodulation,[status(thm)],[f1715,f156]) ).
fof(f1890,plain,
( ~ sQ189_spl
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1824,f56]) ).
fof(f1898,plain,
( ~ sQ189_spl
| ~ sQ2_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1890,f220,f169,f1690]) ).
fof(f4337,plain,
( ~ sQ56_spl
| sdtpldt0(xm,xn) = xm
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[status(thm)],[f1577,f97]) ).
fof(f4359,definition,
( sQ421_spl
<=> sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f4362,plain,
( ~ sQ56_spl
| sQ189_spl
| ~ sQ421_spl
| ~ sQ4_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f4337,f928,f177,f4359,f1690,f543]) ).
fof(f4988,definition,
( sQ490_spl
<=> aNaturalNumber0(sdtasdt0(xl,xp)) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f4990,plain,
( sQ490_spl
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(component_clause,[status(thm)],[f4988]) ).
fof(f4992,plain,
( sQ490_spl
| ~ aNaturalNumber0(xm) ),
inference(forward_demodulation,[status(thm)],[f150,f4990]) ).
fof(f4993,plain,
( sQ490_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4992,f139]) ).
fof(f4994,plain,
sQ490_spl,
inference(contradiction_clause,[status(thm)],[f4993]) ).
fof(f5277,plain,
( ~ sQ69_spl
| sdtlseqdt0(sdtpldt0(xm,xn),xm)
| ~ sdtlseqdt0(xq,xp)
| xq = xp
| ~ aNaturalNumber0(xq) ),
inference(paramodulation,[status(thm)],[f153,f672]) ).
fof(f5307,plain,
( ~ sQ69_spl
| sQ421_spl
| ~ sQ14_spl
| sQ29_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f5277,f237,f343,f248,f4359,f671]) ).
fof(f5312,plain,
$false,
inference(sat_refutation,[status(thm)],[f180,f182,f216,f240,f254,f271,f306,f353,f549,f569,f674,f822,f864,f1107,f1317,f1321,f1366,f1576,f1693,f1898,f4362,f4994,f5307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM471+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.35 % Computer : n009.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 02:33:03 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 0.13/5.93 % Refutation found
% 0.13/5.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.95 % Elapsed time: 0.580840 seconds
% 0.13/5.95 % CPU time: 4.338288 seconds
% 0.13/5.95 % Total memory used: 147.126 MB
% 0.13/5.95 % Net memory used: 142.442 MB
%------------------------------------------------------------------------------