%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM476+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 : Fri Sep 25 02:20:08 PM UTC 2026
% Result : Theorem 28.05s 4.54s
% Output : Proof 28.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 18 unt; 0 def)
% Number of atoms : 153 ( 81 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 132 ( 22 ~; 19 |; 85 &)
% ( 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 : 29 ( 0 sgn 8 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f11_nnf,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c15,plain,
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f34,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',m__1324_04) ).
fof(f34_nnf,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& sdtpldt0(xm,xn) = sdtasdt0(xl,sk3)
& aNaturalNumber0(sk3)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sk2)
& aNaturalNumber0(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f34_nnf]) ).
cnf(c60,plain,
aNaturalNumber0(sk2),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p229,plain,
sz00 = sdtasdt0(sz00,sk2),
inference(resolution,[status(thm)],[c15,c60]) ).
fof(f7,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f7_nnf,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f33,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f33_nnf,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c59,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p185,plain,
xn = sdtpldt0(sz00,xn),
inference(resolution,[status(thm)],[c9,c59]) ).
fof(f35,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',m__) ).
fof(f35_neg,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)],[f35]) ).
fof(f35_nnf,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(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
! [W0] :
( ~ doDivides0(xl,xn)
& ( xn != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) )
& ( ( xn = sdtasdt0(xl,sk7)
& sdtpldt0(sdtasdt0(xl,sk4),sdtasdt0(xl,sk7)) = sdtpldt0(sdtasdt0(xl,sk4),xn)
& sk7 = sdtmndt0(sk5,sk4)
& sdtpldt0(sk4,sk7) = sk5
& aNaturalNumber0(sk7)
& sdtlseqdt0(sk4,sk5)
& sdtpldt0(sk4,sk6) = sk5
& aNaturalNumber0(sk6)
& sk5 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,sk5)
& aNaturalNumber0(sk5)
& sk4 = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,sk4)
& aNaturalNumber0(sk4) )
| xl = sz00 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f35_nnf]) ).
cnf(c75,plain,
( aNaturalNumber0(sk7)
| xl = sz00 ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(c61,plain,
xm = sdtasdt0(xl,sk2),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p144,plain,
( xm = sdtasdt0(sz00,sk2)
| aNaturalNumber0(sk7) ),
inference(superposition,[status(thm)],[c75,c61]) ).
cnf(p235,plain,
( xm = sz00
| aNaturalNumber0(sk7) ),
inference(superposition,[status(thm)],[p229,p144]) ).
cnf(c65,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p282,plain,
( doDivides0(xl,sdtpldt0(sz00,xn))
| aNaturalNumber0(sk7) ),
inference(superposition,[status(thm)],[p235,c65]) ).
cnf(p337,plain,
( doDivides0(xl,xn)
| aNaturalNumber0(sk7) ),
inference(superposition,[status(thm)],[p185,p282]) ).
cnf(c81,plain,
~ doDivides0(xl,xn),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p340,plain,
aNaturalNumber0(sk7),
inference(resolution,[status(thm)],[p337,c81]) ).
cnf(c80,plain,
( xn != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p341,plain,
xn != sdtasdt0(xl,sk7),
inference(resolution,[status(thm)],[p340,c80]) ).
cnf(c79,plain,
( xn = sdtasdt0(xl,sk7)
| xl = sz00 ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p349,plain,
xl = sz00,
inference(resolution,[status(thm)],[p341,c79]) ).
cnf(p350,plain,
xm = sdtasdt0(sz00,sk2),
inference(demodulation,[status(thm)],[p349,c61]) ).
cnf(p371,plain,
xm = sz00,
inference(superposition,[status(thm)],[p229,p350]) ).
cnf(c64,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sk3),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(c63,plain,
aNaturalNumber0(sk3),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p132,plain,
xn != sdtasdt0(xl,sk3),
inference(resolution,[status(thm)],[c63,c80]) ).
cnf(p170,plain,
xn != sdtpldt0(xm,xn),
inference(superposition,[status(thm)],[c64,p132]) ).
cnf(p372,plain,
xn != sdtpldt0(sz00,xn),
inference(demodulation,[status(thm)],[p371,p170]) ).
cnf(p376,plain,
$false,
inference(resolution,[status(thm)],[p372,p185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM476+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 04:10:05 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 28.05/4.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.05/4.54 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------