%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM505+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 : n014.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 01:40:46 PM UTC 2026
% Result : Theorem 6.40s 1.35s
% Output : CNFRefutation 6.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 70 ( 14 unt; 11 def)
% Number of atoms : 220 ( 56 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 248 ( 98 ~; 93 |; 35 &)
% ( 13 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 40 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,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(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,conjecture,
( ~ sdtlseqdt0(xp,xk)
=> ( sdtlseqdt0(xk,xp)
& xk != xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
~ ( ~ sdtlseqdt0(xp,xk)
=> ( sdtlseqdt0(xk,xp)
& xk != xp ) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f60,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f61,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f105,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f106,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f111,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f113,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f139,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(f140,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)],[f139]) ).
fof(f141,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)],[f140]) ).
fof(f142,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f155,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(f156,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)],[f155]) ).
fof(f157,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))],[f156]) ).
fof(f158,plain,
! [X0] :
( X0 != sz00
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f170,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f171,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f172,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f175,plain,
isPrime0(xp),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f176,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f183,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f194,plain,
( ( ~ sdtlseqdt0(xk,xp)
| xk = xp )
& ~ sdtlseqdt0(xp,xk) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f195,plain,
~ sdtlseqdt0(xp,xk),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f196,plain,
( ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f197,definition,
( sQ0_spl
<=> xk = xp ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ0_spl
| xk = xp ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,definition,
( sQ1_spl
<=> sdtlseqdt0(xk,xp) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f196,f197,f200]) ).
fof(f206,plain,
( ~ sQ0_spl
| ~ sdtlseqdt0(xp,xp) ),
inference(forward_demodulation,[status(thm)],[f198,f195]) ).
fof(f208,plain,
( ~ sQ0_spl
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f106,f206]) ).
fof(f209,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f172]) ).
fof(f210,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f218,definition,
( sQ2_spl
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f224,definition,
( sQ4_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ4_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f230,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f172]) ).
fof(f231,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f237,plain,
( sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f113,f195]) ).
fof(f241,plain,
( sQ1_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f237,f218,f224,f200]) ).
fof(f341,definition,
( sQ15_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ15_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f356,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f170]) ).
fof(f357,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f361,definition,
( sQ19_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ19_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f376,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f363,f171]) ).
fof(f377,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f823,plain,
( xp != sz00
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f158,f175]) ).
fof(f831,definition,
( sQ75_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f834,plain,
( ~ sQ75_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f823,f224,f831]) ).
fof(f4308,definition,
( sQ391_spl
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f4310,plain,
( sQ391_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f4308]) ).
fof(f4410,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f183,f142]) ).
fof(f4416,definition,
( sQ402_spl
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f4418,plain,
( sQ402_spl
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f4416]) ).
fof(f4419,plain,
( sQ2_spl
| ~ sQ402_spl
| sQ75_spl
| ~ sQ391_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4410,f224,f4308,f831,f4416,f218]) ).
fof(f4598,plain,
( sQ391_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f4310,f61]) ).
fof(f4599,plain,
( sQ391_spl
| ~ sQ19_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4598,f341,f361,f4308]) ).
fof(f4600,plain,
( sQ402_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4418,f176]) ).
fof(f4601,plain,
sQ402_spl,
inference(contradiction_clause,[status(thm)],[f4600]) ).
fof(f4602,plain,
$false,
inference(sat_refutation,[status(thm)],[f203,f210,f231,f241,f357,f377,f834,f4419,f4599,f4601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM505+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n014.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 02:35:50 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 6.40/1.35 % Refutation found
% 6.40/1.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.40/1.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.40/1.40 % Elapsed time: 0.933609 seconds
% 6.40/1.40 % CPU time: 6.789035 seconds
% 6.40/1.40 % Total memory used: 137.042 MB
% 6.40/1.40 % Net memory used: 132.583 MB
%------------------------------------------------------------------------------