%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM525+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 01:40:51 PM UTC 2026
% Result : Theorem 53.58s 7.15s
% Output : CNFRefutation 53.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 122 ( 34 unt; 12 def)
% Number of atoms : 339 ( 110 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 369 ( 152 ~; 153 |; 41 &)
% ( 14 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 79 ( 78 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ! [W1] :
( ( doDivides0(W1,W0)
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f52,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f56,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f65,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f68,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f70,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0] :
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f107,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f109,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f135,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(f136,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)],[f135]) ).
fof(f137,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)],[f136]) ).
fof(f138,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,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)],[f137]) ).
fof(f151,plain,
! [W0] :
( ( isPrime0(W0)
<=> ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 ) )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f152,plain,
! [W0] :
( ( ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
! [W0] :
( ( ( ( sK2_skl(W0) != W0
& sK2_skl(W0) != sz10
& doDivides0(sK2_skl(W0),W0)
& aNaturalNumber0(sK2_skl(W0)) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W1,sK2_skl(W0))],[f152]) ).
fof(f155,plain,
! [X0] :
( X0 != sz10
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f168,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f169,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f170,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f173,plain,
xp != sz00,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f176,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f177,plain,
isPrime0(xp),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f179,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f180,plain,
xq = sdtsldt0(xn,xp),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f181,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f189,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f138]) ).
fof(f190,plain,
! [X0,X1] :
( X1 = sdtasdt0(X0,sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f139]) ).
fof(f193,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(destructive_equality_resolution,[status(thm)],[f155]) ).
fof(f203,plain,
! [X0,X1] :
( sdtasdt0(sdtasdt0(X0,xp),X1) = sdtasdt0(X0,sdtasdt0(xp,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f170,f68]) ).
fof(f204,plain,
! [X0] :
( aNaturalNumber0(sdtasdt0(X0,xp))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f170,f57]) ).
fof(f205,plain,
! [X0] :
( sdtasdt0(X0,xp) = sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f170,f66]) ).
fof(f206,plain,
sdtasdt0(xn,xn) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(backward_demodulation,[status(thm)],[f176,f181]) ).
fof(f216,plain,
! [X0,X1] :
( sdtasdt0(sdtasdt0(X0,sz10),X1) = sdtasdt0(X0,sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f52,f68]) ).
fof(f229,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[f70,f170]) ).
fof(f260,plain,
xn = sdtasdt0(sz10,xn),
inference(resolution,[status(thm)],[f168,f71]) ).
fof(f267,plain,
! [X0,X1] :
( sdtasdt0(sdtasdt0(X0,xn),X1) = sdtasdt0(X0,sdtasdt0(xn,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f168,f68]) ).
fof(f300,plain,
sdtasdt0(xn,xp) = sdtasdt0(xp,xn),
inference(resolution,[status(thm)],[f205,f168]) ).
fof(f335,plain,
! [X0] :
( sdtasdt0(sdtasdt0(X0,sz10),xn) = sdtasdt0(X0,sdtasdt0(sz10,xn))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f216,f168]) ).
fof(f465,definition,
( sQ13_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( sQ13_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f477,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f170]) ).
fof(f478,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f477]) ).
fof(f726,definition,
( sQ52_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f727,plain,
( ~ sQ52_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f764,plain,
( ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f727,f173]) ).
fof(f765,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f764]) ).
fof(f999,plain,
sdtasdt0(sdtasdt0(xp,sz10),xn) = sdtasdt0(xp,sdtasdt0(sz10,xn)),
inference(resolution,[status(thm)],[f335,f170]) ).
fof(f1002,plain,
sdtasdt0(xp,xn) = sdtasdt0(xp,sdtasdt0(sz10,xn)),
inference(forward_demodulation,[status(thm)],[f229,f999]) ).
fof(f1003,plain,
sdtasdt0(xn,xp) = sdtasdt0(xp,sdtasdt0(sz10,xn)),
inference(forward_demodulation,[status(thm)],[f300,f1002]) ).
fof(f1070,plain,
! [X0] :
( sdtlseqdt0(xp,X0)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f109,f170]) ).
fof(f1071,plain,
! [X0] :
( sdtlseqdt0(xm,X0)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f109,f169]) ).
fof(f1282,definition,
( sQ103_spl
<=> aNaturalNumber0(sdtasdt0(xn,xp)) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1284,plain,
( sQ103_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xp)) ),
inference(component_clause,[status(thm)],[f1282]) ).
fof(f1296,definition,
( sQ106_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1298,plain,
( sQ106_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f1296]) ).
fof(f1311,plain,
( sQ106_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1298,f168]) ).
fof(f1312,plain,
sQ106_spl,
inference(contradiction_clause,[status(thm)],[f1311]) ).
fof(f1384,definition,
( sQ118_spl
<=> xp = sz10 ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1385,plain,
( ~ sQ118_spl
| xp = sz10 ),
inference(component_clause,[status(thm)],[f1384]) ).
fof(f1758,plain,
~ isPrime0(sz10),
inference(forward_subsumption_resolution,[status(thm)],[f193,f52]) ).
fof(f2009,definition,
( sQ207_spl
<=> isPrime0(xp) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2011,plain,
( sQ207_spl
| ~ isPrime0(xp) ),
inference(component_clause,[status(thm)],[f2009]) ).
fof(f2046,plain,
( sQ207_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2011,f177]) ).
fof(f2047,plain,
sQ207_spl,
inference(contradiction_clause,[status(thm)],[f2046]) ).
fof(f2355,plain,
( xn = sdtasdt0(xp,sdtsldt0(xn,xp))
| xp = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f179,f190]) ).
fof(f2356,plain,
( aNaturalNumber0(sdtsldt0(xn,xp))
| xp = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f179,f189]) ).
fof(f2380,definition,
( sQ269_spl
<=> xn = sdtasdt0(xp,sdtsldt0(xn,xp)) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f2381,plain,
( ~ sQ269_spl
| xn = sdtasdt0(xp,sdtsldt0(xn,xp)) ),
inference(component_clause,[status(thm)],[f2380]) ).
fof(f2383,plain,
( sQ269_spl
| sQ52_spl
| ~ sQ106_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2355,f465,f1296,f726,f2380]) ).
fof(f2384,definition,
( sQ270_spl
<=> aNaturalNumber0(sdtsldt0(xn,xp)) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2385,plain,
( ~ sQ270_spl
| aNaturalNumber0(sdtsldt0(xn,xp)) ),
inference(component_clause,[status(thm)],[f2384]) ).
fof(f2387,plain,
( sQ270_spl
| sQ52_spl
| ~ sQ106_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2356,f465,f1296,f726,f2384]) ).
fof(f2397,plain,
( ~ sQ269_spl
| xn = sdtasdt0(xp,xq) ),
inference(forward_demodulation,[status(thm)],[f180,f2381]) ).
fof(f2398,plain,
( ~ sQ270_spl
| aNaturalNumber0(xq) ),
inference(forward_demodulation,[status(thm)],[f180,f2385]) ).
fof(f2417,plain,
( sdtlseqdt0(xp,xp)
| sdtlseqdt0(xp,xp) ),
inference(resolution,[status(thm)],[f1070,f170]) ).
fof(f2434,definition,
( sQ280_spl
<=> sdtlseqdt0(xp,xp) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f2437,plain,
sQ280_spl,
inference(split_clause,[status(thm)],[f2417,f2434]) ).
fof(f2520,plain,
! [X0] :
( ~ sQ270_spl
| sdtasdt0(sdtasdt0(X0,xn),xq) = sdtasdt0(X0,sdtasdt0(xn,xq))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2398,f267]) ).
fof(f2558,plain,
! [X0] :
( ~ sQ270_spl
| sdtasdt0(sdtasdt0(X0,xp),xq) = sdtasdt0(X0,sdtasdt0(xp,xq))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2398,f203]) ).
fof(f2574,plain,
! [X0] :
( ~ sQ270_spl
| sdtasdt0(sdtasdt0(X0,xq),xq) = sdtasdt0(X0,sdtasdt0(xq,xq))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f2398,f68]) ).
fof(f2700,plain,
! [X0] :
( ~ sQ270_spl
| ~ sQ269_spl
| sdtasdt0(sdtasdt0(X0,xp),xq) = sdtasdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f2397,f2558]) ).
fof(f2719,plain,
( sdtlseqdt0(xm,xm)
| sdtlseqdt0(xm,xm) ),
inference(resolution,[status(thm)],[f1071,f169]) ).
fof(f2746,definition,
( sQ323_spl
<=> sdtlseqdt0(xm,xm) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f2749,plain,
sQ323_spl,
inference(split_clause,[status(thm)],[f2719,f2746]) ).
fof(f3116,plain,
( ~ sQ118_spl
| isPrime0(sz10) ),
inference(backward_demodulation,[status(thm)],[f1385,f177]) ).
fof(f3196,plain,
( ~ sQ118_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3116,f1758]) ).
fof(f3197,plain,
~ sQ118_spl,
inference(contradiction_clause,[status(thm)],[f3196]) ).
fof(f3315,plain,
( ~ sQ270_spl
| sdtasdt0(sdtasdt0(xp,xn),xq) = sdtasdt0(xp,sdtasdt0(xn,xq)) ),
inference(resolution,[status(thm)],[f170,f2520]) ).
fof(f3441,plain,
( ~ sQ270_spl
| ~ sQ269_spl
| sdtasdt0(sdtasdt0(xn,xp),xq) = sdtasdt0(xn,xn) ),
inference(resolution,[status(thm)],[f2700,f168]) ).
fof(f3499,plain,
( ~ sQ270_spl
| sdtasdt0(sdtasdt0(xp,xq),xq) = sdtasdt0(xp,sdtasdt0(xq,xq)) ),
inference(resolution,[status(thm)],[f2574,f170]) ).
fof(f3793,plain,
sdtasdt0(xn,xp) = sdtasdt0(xp,xn),
inference(forward_demodulation,[status(thm)],[f260,f1003]) ).
fof(f4335,plain,
( ~ sQ270_spl
| sdtasdt0(sdtasdt0(xn,xp),xq) = sdtasdt0(xp,sdtasdt0(xn,xq)) ),
inference(forward_demodulation,[status(thm)],[f3793,f3315]) ).
fof(f5700,plain,
aNaturalNumber0(sdtasdt0(xn,xp)),
inference(resolution,[status(thm)],[f204,f168]) ).
fof(f5704,plain,
( sQ103_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5700,f1284]) ).
fof(f5705,plain,
sQ103_spl,
inference(contradiction_clause,[status(thm)],[f5704]) ).
fof(f5762,plain,
( ~ sQ270_spl
| ~ sQ269_spl
| sdtasdt0(xp,sdtasdt0(xn,xq)) = sdtasdt0(xn,xn) ),
inference(forward_demodulation,[status(thm)],[f4335,f3441]) ).
fof(f5910,plain,
( ~ sQ270_spl
| ~ sQ269_spl
| sdtasdt0(xn,xn) != sdtasdt0(xp,sdtasdt0(xn,xq)) ),
inference(backward_demodulation,[status(thm)],[f5911,f206]) ).
fof(f5911,plain,
( ~ sQ270_spl
| ~ sQ269_spl
| sdtasdt0(xn,xq) = sdtasdt0(xp,sdtasdt0(xq,xq)) ),
inference(forward_demodulation,[status(thm)],[f2397,f3499]) ).
fof(f5912,plain,
( ~ sQ270_spl
| ~ sQ269_spl
| sdtasdt0(xn,xn) != sdtasdt0(xn,xn) ),
inference(forward_demodulation,[status(thm)],[f5762,f5910]) ).
fof(f5913,plain,
( ~ sQ270_spl
| ~ sQ269_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5912]) ).
fof(f5914,plain,
( ~ sQ270_spl
| ~ sQ269_spl ),
inference(contradiction_clause,[status(thm)],[f5913]) ).
fof(f5915,plain,
$false,
inference(sat_refutation,[status(thm)],[f478,f765,f1312,f2047,f2383,f2387,f2437,f2749,f3197,f5705,f5914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM525+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 02:37:22 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Drodi V4.1.1
% 53.58/7.15 % Refutation found
% 53.58/7.15 % SZS status Theorem for theBenchmark: Theorem is valid
% 53.58/7.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 27.48/7.19 % Elapsed time: 6.875316 seconds
% 27.48/7.19 % CPU time: 54.447164 seconds
% 27.48/7.19 % Total memory used: 390.998 MB
% 27.48/7.19 % Net memory used: 358.130 MB
%------------------------------------------------------------------------------