%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM466+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 01:40:37 PM UTC 2026
% Result : Theorem 0.15s 5.55s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 9 unt; 1 def)
% Number of atoms : 136 ( 27 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 161 ( 61 ~; 55 |; 38 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 35 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
( ( doDivides0(xm,xn)
& ? [W0] :
( xn = sdtasdt0(xm,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) )
=> ( doDivides0(xl,xn)
| ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ( ( doDivides0(xm,xn)
& ? [W0] :
( xn = sdtasdt0(xm,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) )
=> ( doDivides0(xl,xn)
| ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f43,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f44,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f54,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f55,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f116,plain,
! [W0,W1] :
( ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f117,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( W1 = sdtasdt0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f117]) ).
fof(f121,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f128,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f130,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f131,plain,
( ~ doDivides0(xl,xn)
& ! [W0] :
( xn != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) )
& doDivides0(xm,xn)
& ? [W0] :
( xn = sdtasdt0(xm,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f132,plain,
( ~ doDivides0(xl,xn)
& ! [W0] :
( xn != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) )
& doDivides0(xm,xn)
& xn = sdtasdt0(xm,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)],[f131]) ).
fof(f133,plain,
aNaturalNumber0(sK2_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
xm = sdtasdt0(xl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f136,plain,
aNaturalNumber0(sK3_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f137,plain,
xn = sdtasdt0(xm,sK3_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f140,plain,
~ doDivides0(xl,xn),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f186,plain,
! [X0] :
( sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK2_skl,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2_skl)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f134,f55]) ).
fof(f198,plain,
! [X0] :
( sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK2_skl,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f128]) ).
fof(f517,plain,
! [X0] :
( sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK2_skl,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f133]) ).
fof(f518,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(sK2_skl,X0))
| doDivides0(xl,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f517,f121]) ).
fof(f522,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(sK2_skl,X0))
| doDivides0(xl,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f128]) ).
fof(f528,plain,
( ~ aNaturalNumber0(sdtasdt0(sK2_skl,sK3_skl))
| doDivides0(xl,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,sK3_skl))
| ~ aNaturalNumber0(sK3_skl) ),
inference(paramodulation,[status(thm)],[f137,f522]) ).
fof(f531,plain,
( ~ aNaturalNumber0(sdtasdt0(sK2_skl,sK3_skl))
| doDivides0(xl,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f137,f528]) ).
fof(f532,plain,
( ~ aNaturalNumber0(sdtasdt0(sK2_skl,sK3_skl))
| doDivides0(xl,xn)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f136]) ).
fof(f533,plain,
( ~ aNaturalNumber0(sdtasdt0(sK2_skl,sK3_skl))
| doDivides0(xl,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f130]) ).
fof(f534,plain,
( ~ aNaturalNumber0(sK3_skl)
| ~ aNaturalNumber0(sK2_skl)
| doDivides0(xl,xn) ),
inference(resolution,[status(thm)],[f533,f44]) ).
fof(f535,plain,
( ~ aNaturalNumber0(sK3_skl)
| ~ aNaturalNumber0(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f140]) ).
fof(f537,plain,
~ aNaturalNumber0(sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f535,f133]) ).
fof(f538,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f136,f537]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM466+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.37 % Computer : n008.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Mon Sep 21 02:33:02 UTC 2026
% 0.12/5.37 % CPUTime :
% 0.12/5.39 % Drodi V4.1.1
% 0.15/5.55 % Refutation found
% 0.15/5.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.57 % Elapsed time: 0.187948 seconds
% 0.15/5.57 % CPU time: 1.218500 seconds
% 0.15/5.57 % Total memory used: 120.882 MB
% 0.15/5.57 % Net memory used: 119.312 MB
%------------------------------------------------------------------------------