%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM487+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 01:40:42 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 83 ( 14 unt; 12 def)
% Number of atoms : 264 ( 86 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 311 ( 130 ~; 123 |; 41 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 43 ( 37 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
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(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( ( ( doDivides0(W0,xp)
| ? [W1] :
( xp = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xp
| W0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( sdtlseqdt0(xp,xn)
& ? [W0] :
( sdtpldt0(xp,W0) = xn
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
( ( sdtlseqdt0(xr,xn)
| ? [W0] :
( sdtpldt0(xr,W0) = xn
& aNaturalNumber0(W0) ) )
& xr != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ( ( sdtlseqdt0(xr,xn)
| ? [W0] :
( sdtpldt0(xr,W0) = xn
& aNaturalNumber0(W0) ) )
& xr != xn ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f56,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f57,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f62,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f76,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f78,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f166,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f178,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ! [W1] :
( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f179,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK5_skl)
& aNaturalNumber0(sK5_skl)
& isPrime0(xp)
& ! [W0] :
( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ! [W1] :
( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W0,sK5_skl)],[f178]) ).
fof(f180,plain,
xp != sz00,
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f188,plain,
( sdtlseqdt0(xp,xn)
& sdtpldt0(xp,sK6_skl) = xn
& aNaturalNumber0(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W0,sK6_skl)],[f42]) ).
fof(f189,plain,
aNaturalNumber0(sK6_skl),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f190,plain,
sdtpldt0(xp,sK6_skl) = xn,
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f192,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f193,plain,
sdtpldt0(xp,xr) = xn,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f195,plain,
( ( ~ sdtlseqdt0(xr,xn)
& ! [W0] :
( sdtpldt0(xr,W0) != xn
| ~ aNaturalNumber0(W0) ) )
| xr = xn ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f196,plain,
! [X0] :
( sdtpldt0(xr,X0) != xn
| ~ aNaturalNumber0(X0)
| xr = xn ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f218,definition,
( sQ0_spl
<=> xr = xn ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( ~ sQ0_spl
| xr = xn ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,definition,
! [X0] :
( sQ1_spl
<=> ( sdtpldt0(xr,X0) != xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f222,plain,
! [X0] :
( ~ sQ1_spl
| sdtpldt0(xr,X0) != xn
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f196,f218,f221]) ).
fof(f249,definition,
( sQ3_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( sQ3_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,definition,
( sQ4_spl
<=> aNaturalNumber0(xr) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ4_spl
| ~ aNaturalNumber0(xr) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f283,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f192]) ).
fof(f284,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f298,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f251,f166]) ).
fof(f299,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f298]) ).
fof(f306,definition,
( sQ12_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ12_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f326,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f49]) ).
fof(f327,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f341,definition,
( sQ17_spl
<=> aNaturalNumber0(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ17_spl
| ~ aNaturalNumber0(sK6_skl) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f350,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f189]) ).
fof(f351,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f359,plain,
! [X0] :
( X0 = xp
| sdtpldt0(X0,xr) != xn
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(paramodulation,[status(thm)],[f193,f78]) ).
fof(f365,definition,
! [X0] :
( sQ20_spl
<=> ( X0 = xp
| sdtpldt0(X0,xr) != xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f366,plain,
! [X0] :
( ~ sQ20_spl
| X0 = xp
| sdtpldt0(X0,xr) != xn
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( ~ sQ3_spl
| sQ20_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f359,f252,f365,f249]) ).
fof(f486,plain,
( xn = sdtpldt0(xr,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f193,f57]) ).
fof(f487,plain,
( xn = sdtpldt0(sK6_skl,xp)
| ~ aNaturalNumber0(sK6_skl)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f190,f57]) ).
fof(f490,definition,
( sQ34_spl
<=> xn = sdtpldt0(xr,xp) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( ~ sQ34_spl
| xn = sdtpldt0(xr,xp) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( sQ34_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f486,f249,f252,f490]) ).
fof(f494,definition,
( sQ35_spl
<=> xn = sdtpldt0(sK6_skl,xp) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( ~ sQ35_spl
| xn = sdtpldt0(sK6_skl,xp) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,plain,
( sQ35_spl
| ~ sQ17_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f487,f249,f341,f494]) ).
fof(f500,plain,
( ~ sQ1_spl
| ~ sQ34_spl
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f491,f222]) ).
fof(f504,plain,
! [X0] :
( ~ sQ34_spl
| X0 = xr
| sdtpldt0(X0,xp) != xn
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f491,f78]) ).
fof(f506,plain,
( ~ sQ1_spl
| ~ sQ34_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f500,f249,f490,f221]) ).
fof(f510,definition,
! [X0] :
( sQ36_spl
<=> ( X0 = xr
| sdtpldt0(X0,xp) != xn
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f511,plain,
! [X0] :
( ~ sQ36_spl
| X0 = xr
| sdtpldt0(X0,xp) != xn
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,plain,
( ~ sQ34_spl
| ~ sQ4_spl
| sQ36_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f504,f249,f510,f252,f490]) ).
fof(f603,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ0_spl
| X0 = xp
| sdtpldt0(X0,xr) != xr
| ~ aNaturalNumber0(X0) ),
inference(backward_demodulation,[status(thm)],[f219,f366]) ).
fof(f629,plain,
( ~ sQ35_spl
| ~ sQ0_spl
| xr = sdtpldt0(sK6_skl,xp) ),
inference(forward_demodulation,[status(thm)],[f219,f495]) ).
fof(f851,plain,
! [X0] :
( ~ sQ36_spl
| ~ sQ0_spl
| X0 = xr
| sdtpldt0(X0,xp) != xr
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f219,f511]) ).
fof(f852,plain,
( ~ sQ35_spl
| ~ sQ0_spl
| ~ sQ36_spl
| sK6_skl = xr
| ~ aNaturalNumber0(sK6_skl) ),
inference(resolution,[status(thm)],[f851,f629]) ).
fof(f856,definition,
( sQ87_spl
<=> sK6_skl = xr ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f857,plain,
( ~ sQ87_spl
| sK6_skl = xr ),
inference(component_clause,[status(thm)],[f856]) ).
fof(f859,plain,
( ~ sQ35_spl
| ~ sQ0_spl
| ~ sQ36_spl
| sQ87_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f852,f341,f856,f510,f218,f494]) ).
fof(f1004,definition,
( sQ109_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
( ~ sQ109_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f1004]) ).
fof(f1048,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ0_spl
| ~ sQ87_spl
| X0 = xp
| sdtpldt0(X0,sK6_skl) != xr
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f857,f603]) ).
fof(f1049,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ0_spl
| ~ sQ87_spl
| X0 = xp
| sdtpldt0(X0,sK6_skl) != sK6_skl
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f857,f1048]) ).
fof(f1051,plain,
( ~ sQ20_spl
| ~ sQ0_spl
| ~ sQ87_spl
| ~ aNaturalNumber0(sK6_skl)
| sz00 = xp
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[f1049,f62]) ).
fof(f1054,plain,
( ~ sQ20_spl
| ~ sQ0_spl
| ~ sQ87_spl
| ~ sQ17_spl
| sQ109_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1051,f306,f1004,f341,f856,f218,f365]) ).
fof(f1059,plain,
( ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1005,f180]) ).
fof(f1060,plain,
~ sQ109_spl,
inference(contradiction_clause,[status(thm)],[f1059]) ).
fof(f1061,plain,
$false,
inference(sat_refutation,[status(thm)],[f224,f284,f299,f327,f351,f368,f493,f497,f506,f513,f859,f1054,f1060]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM487+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:34:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.47 % Elapsed time: 0.094080 seconds
% 0.13/0.47 % CPU time: 0.236870 seconds
% 0.13/0.47 % Total memory used: 60.521 MB
% 0.13/0.47 % Net memory used: 60.354 MB
%------------------------------------------------------------------------------