%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM476+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 : 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 01:40:40 PM UTC 2026
% Result : Theorem 0.14s 5.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 133 ( 73 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 116 ( 20 ~; 16 |; 74 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 25 ( 9 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
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,conjecture,
( ( xl != sz00
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( xn = sdtasdt0(xl,W2)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& W2 = sdtmndt0(W1,W0)
& sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& sdtlseqdt0(W0,W1)
& ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& aNaturalNumber0(W1) )
& W0 = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) )
=> ( doDivides0(xl,xn)
| ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ( ( xl != sz00
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( xn = sdtasdt0(xl,W2)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& W2 = sdtmndt0(W1,W0)
& sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& sdtlseqdt0(W0,W1)
& ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& aNaturalNumber0(W1) )
& W0 = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) )
=> ( doDivides0(xl,xn)
| ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f52,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f54,plain,
! [X0] :
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f62,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f64,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f137,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f138,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(f139,plain,
aNaturalNumber0(sK2_skl),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
xm = sdtasdt0(xl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f143,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f144,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f145,plain,
( ~ doDivides0(xl,xn)
& ! [W0] :
( xn != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) )
& ( ? [W0] :
( ? [W1] :
( ? [W2] :
( xn = sdtasdt0(xl,W2)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& W2 = sdtmndt0(W1,W0)
& sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& sdtlseqdt0(W0,W1)
& ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& aNaturalNumber0(W1) )
& W0 = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
| xl = sz00 ) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f146,plain,
( ~ doDivides0(xl,xn)
& ! [W0] :
( xn != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) )
& ( ( xn = sdtasdt0(xl,sK7_skl)
& sdtpldt0(sdtasdt0(xl,sK4_skl),sdtasdt0(xl,sK7_skl)) = sdtpldt0(sdtasdt0(xl,sK4_skl),xn)
& sK7_skl = sdtmndt0(sK5_skl,sK4_skl)
& sdtpldt0(sK4_skl,sK7_skl) = sK5_skl
& aNaturalNumber0(sK7_skl)
& sdtlseqdt0(sK4_skl,sK5_skl)
& sdtpldt0(sK4_skl,sK6_skl) = sK5_skl
& aNaturalNumber0(sK6_skl)
& sK5_skl = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,sK5_skl)
& aNaturalNumber0(sK5_skl)
& sK4_skl = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,sK4_skl)
& aNaturalNumber0(sK4_skl) )
| xl = sz00 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(W0,sK4_skl),skolemize(W1,sK5_skl),skolemize(W2,sK6_skl),skolemize(W2,sK7_skl)],[f145]) ).
fof(f156,plain,
( aNaturalNumber0(sK7_skl)
| xl = sz00 ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f160,plain,
( xn = sdtasdt0(xl,sK7_skl)
| xl = sz00 ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f161,plain,
! [X0] :
( xn != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f162,plain,
~ doDivides0(xl,xn),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f189,plain,
doDivides0(xl,sdtasdt0(xl,sK3_skl)),
inference(backward_demodulation,[status(thm)],[f143,f144]) ).
fof(f194,plain,
( ~ aNaturalNumber0(sK7_skl)
| xl = sz00 ),
inference(resolution,[status(thm)],[f160,f161]) ).
fof(f198,plain,
xl = sz00,
inference(forward_subsumption_resolution,[status(thm)],[f194,f156]) ).
fof(f204,plain,
doDivides0(xl,sdtasdt0(sz00,sK3_skl)),
inference(backward_demodulation,[status(thm)],[f198,f189]) ).
fof(f205,plain,
sdtpldt0(xm,xn) = sdtasdt0(sz00,sK3_skl),
inference(backward_demodulation,[status(thm)],[f198,f143]) ).
fof(f213,plain,
xm = sdtasdt0(sz00,sK2_skl),
inference(backward_demodulation,[status(thm)],[f198,f140]) ).
fof(f219,plain,
~ doDivides0(sz00,xn),
inference(backward_demodulation,[status(thm)],[f198,f162]) ).
fof(f220,plain,
doDivides0(sz00,sdtasdt0(sz00,sK3_skl)),
inference(forward_demodulation,[status(thm)],[f198,f204]) ).
fof(f228,plain,
( sz00 = xm
| ~ aNaturalNumber0(sK2_skl) ),
inference(paramodulation,[status(thm)],[f213,f64]) ).
fof(f235,plain,
sz00 = xm,
inference(forward_subsumption_resolution,[status(thm)],[f228,f139]) ).
fof(f276,plain,
sdtpldt0(sz00,xn) = sdtasdt0(sz00,sK3_skl),
inference(forward_demodulation,[status(thm)],[f235,f205]) ).
fof(f277,plain,
( xn = sdtasdt0(sz00,sK3_skl)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f276,f54]) ).
fof(f284,plain,
xn = sdtasdt0(sz00,sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f277,f137]) ).
fof(f292,plain,
doDivides0(sz00,xn),
inference(backward_demodulation,[status(thm)],[f284,f220]) ).
fof(f304,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f292,f219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM476+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n008.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 02:34:15 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.42 % Refutation found
% 0.14/5.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.45 % Elapsed time: 0.065579 seconds
% 0.14/5.45 % CPU time: 0.202173 seconds
% 0.14/5.45 % Total memory used: 105.132 MB
% 0.14/5.45 % Net memory used: 104.972 MB
%------------------------------------------------------------------------------