%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM504+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 : n018.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 0.14s 0.54s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 79 ( 20 unt; 12 def)
% Number of atoms : 240 ( 63 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 266 ( 105 ~; 106 |; 34 &)
% ( 14 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 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 : 40 ( 39 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
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(f21,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> 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(f51,hypothesis,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f62,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f109,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f110,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f141,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(f142,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)],[f141]) ).
fof(f143,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)],[f142]) ).
fof(f145,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)],[f143]) ).
fof(f157,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(f158,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)],[f157]) ).
fof(f159,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))],[f158]) ).
fof(f160,plain,
! [X0] :
( X0 != sz00
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f172,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f173,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f174,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f177,plain,
isPrime0(xp),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f178,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f185,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f197,plain,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f198,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f200,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f209,plain,
! [X0,X1] :
( X1 = sdtasdt0(X0,sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f145]) ).
fof(f211,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(destructive_equality_resolution,[status(thm)],[f160]) ).
fof(f337,plain,
~ isPrime0(sz00),
inference(forward_subsumption_resolution,[status(thm)],[f211,f57]) ).
fof(f346,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f185,f209]) ).
fof(f347,definition,
( sQ15_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f349,plain,
( sQ15_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,definition,
( sQ16_spl
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( sQ16_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,definition,
( sQ17_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( ~ sQ17_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
( sQ18_spl
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f358,plain,
( sQ18_spl
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,definition,
( sQ19_spl
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( ~ sQ19_spl
| sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,plain,
( sQ19_spl
| ~ sQ18_spl
| sQ17_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f346,f347,f350,f353,f356,f359]) ).
fof(f416,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f174]) ).
fof(f417,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f429,plain,
( ~ sQ17_spl
| isPrime0(sz00) ),
inference(backward_demodulation,[status(thm)],[f354,f177]) ).
fof(f430,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f429,f337]) ).
fof(f431,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f430]) ).
fof(f447,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f358]) ).
fof(f448,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f447]) ).
fof(f458,definition,
( sQ32_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( sQ32_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f468,definition,
( sQ35_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( sQ35_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f501,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f173]) ).
fof(f502,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f505,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f172]) ).
fof(f506,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f691,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[f198,f110]) ).
fof(f695,definition,
( sQ68_spl
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f697,plain,
( sQ68_spl
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(component_clause,[status(thm)],[f695]) ).
fof(f699,definition,
( sQ69_spl
<=> sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f701,plain,
( sQ69_spl
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f699]) ).
fof(f702,definition,
( sQ70_spl
<=> sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f703,plain,
( ~ sQ70_spl
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f702]) ).
fof(f705,plain,
( sQ70_spl
| ~ sQ69_spl
| ~ sQ16_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f691,f695,f350,f699,f702]) ).
fof(f706,plain,
( sQ68_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f697,f63]) ).
fof(f707,plain,
( sQ68_spl
| ~ sQ35_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f706,f347,f468,f695]) ).
fof(f708,plain,
( sQ16_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f352,f63]) ).
fof(f709,plain,
( sQ16_spl
| ~ sQ35_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f708,f458,f468,f350]) ).
fof(f776,plain,
( ~ sQ19_spl
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(forward_demodulation,[status(thm)],[f360,f200]) ).
fof(f777,plain,
( ~ sQ19_spl
| sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f776,f701]) ).
fof(f778,plain,
( ~ sQ19_spl
| sQ69_spl ),
inference(contradiction_clause,[status(thm)],[f777]) ).
fof(f779,plain,
( ~ sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f703,f197]) ).
fof(f780,plain,
~ sQ70_spl,
inference(contradiction_clause,[status(thm)],[f779]) ).
fof(f781,plain,
$false,
inference(sat_refutation,[status(thm)],[f362,f417,f431,f448,f502,f506,f705,f707,f709,f778,f780]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM504+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:37:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.14/0.54 % Refutation found
% 0.14/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.01/0.56 % Elapsed time: 0.190747 seconds
% 1.01/0.56 % CPU time: 1.184843 seconds
% 1.01/0.56 % Total memory used: 119.775 MB
% 1.01/0.56 % Net memory used: 118.062 MB
%------------------------------------------------------------------------------