%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM852+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 01:41:50 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 35 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 6 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vd481,vd480),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Vd328,Vd329,Vd330] :
( greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
=> greater(Vd328,Vd329) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Vd295,Vd296] : greater(vplus(Vd295,Vd296),Vd295),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f61,plain,
greater(vd481,vd480),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f71,plain,
! [Vd470,Vd471] :
( Vd470 = vplus(Vd471,vskolem9(Vd470,Vd471))
| ~ greater(Vd470,Vd471) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f72,plain,
! [X0,X1] :
( X0 = vplus(X1,vskolem9(X0,X1))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f74,plain,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f75,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f99,plain,
! [Vd328,Vd329,Vd330] :
( greater(Vd328,Vd329)
| ~ greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330)) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f100,plain,
! [Vd328,Vd329] :
( greater(Vd328,Vd329)
| ! [Vd330] : ~ greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330)) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(vplus(X0,X1),vplus(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f111,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f199,plain,
~ greater(vmul(vd469,vd481),vmul(vd480,vd469)),
inference(paramodulation,[status(thm)],[f75,f60]) ).
fof(f257,plain,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X1,X0),vmul(X0,X2)),
inference(paramodulation,[status(thm)],[f75,f74]) ).
fof(f267,plain,
! [X0,X1,X2,X3] :
( greater(vmul(X0,X1),X3)
| ~ greater(vmul(X0,vplus(X1,X2)),vplus(X3,vmul(X0,X2))) ),
inference(paramodulation,[status(thm)],[f74,f101]) ).
fof(f268,plain,
! [X0,X1,X2] : greater(vmul(X0,vplus(X1,X2)),vmul(X0,X1)),
inference(paramodulation,[status(thm)],[f74,f111]) ).
fof(f457,plain,
vd481 = vplus(vd480,vskolem9(vd481,vd480)),
inference(resolution,[status(thm)],[f72,f61]) ).
fof(f1007,plain,
! [X0] : ~ greater(vmul(vd469,vplus(vd481,X0)),vplus(vmul(vd480,vd469),vmul(vd469,X0))),
inference(resolution,[status(thm)],[f267,f199]) ).
fof(f1031,plain,
! [X0] : ~ greater(vmul(vd469,vplus(vd481,X0)),vmul(vd469,vplus(vd480,X0))),
inference(forward_demodulation,[status(thm)],[f257,f1007]) ).
fof(f1192,plain,
~ greater(vmul(vd469,vplus(vd481,vskolem9(vd481,vd480))),vmul(vd469,vd481)),
inference(paramodulation,[status(thm)],[f457,f1031]) ).
fof(f1199,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1192,f268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM852+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 03:13:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.47 % Elapsed time: 0.089828 seconds
% 0.14/0.47 % CPU time: 0.378906 seconds
% 0.14/0.47 % Total memory used: 108.438 MB
% 0.14/0.47 % Net memory used: 108.181 MB
%------------------------------------------------------------------------------