%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM423+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 : n014.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 01:40:29 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 43 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 38 ( 15 ~; 11 |; 10 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa))
& aInteger0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa))
& aInteger0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f26,plain,
aInteger0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f41,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f42,plain,
! [X0] :
( sdtpldt0(X0,smndt0(X0)) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f54,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f55,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f75,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f76,plain,
aInteger0(xq),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f78,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f79,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f89,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(resolution,[status(thm)],[f42,f75]) ).
fof(f91,plain,
! [X0] :
( sdtasdt0(xq,X0) != sz00
| ~ aInteger0(X0) ),
inference(backward_demodulation,[status(thm)],[f89,f79]) ).
fof(f180,plain,
sdtasdt0(xq,sz00) != sz00,
inference(resolution,[status(thm)],[f91,f26]) ).
fof(f293,plain,
sdtasdt0(xq,sz00) = sz00,
inference(resolution,[status(thm)],[f55,f76]) ).
fof(f295,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f293,f180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n014.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 02:28:04 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.49 % Refutation found
% 0.18/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.52 % Elapsed time: 0.058084 seconds
% 0.18/0.52 % CPU time: 0.179960 seconds
% 0.18/0.52 % Total memory used: 41.366 MB
% 0.18/0.52 % Net memory used: 41.251 MB
%------------------------------------------------------------------------------