%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM857+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 01:41:51 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 16 unt; 0 def)
% Number of atoms : 62 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 28 ~; 23 |; 7 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
geq(vmul(vd526,vd529),vmul(vd527,vd530)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
geq(vd529,vd530),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
geq(vd526,vd527),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Vd517,Vd518,Vd519,Vd520] :
( ( ( greater(Vd517,Vd518)
& geq(Vd519,Vd520) )
| ( geq(Vd517,Vd518)
& greater(Vd519,Vd520) ) )
=> greater(vmul(Vd517,Vd519),vmul(Vd518,Vd520)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [Vd244,Vd245] :
( geq(Vd245,Vd244)
<=> ( Vd245 = Vd244
| greater(Vd245,Vd244) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,plain,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f64,plain,
geq(vd529,vd530),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f65,plain,
geq(vd526,vd527),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f66,plain,
! [Vd517,Vd518,Vd519,Vd520] :
( greater(vmul(Vd517,Vd519),vmul(Vd518,Vd520))
| ( ( ~ greater(Vd517,Vd518)
| ~ geq(Vd519,Vd520) )
& ( ~ geq(Vd517,Vd518)
| ~ greater(Vd519,Vd520) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( greater(vmul(X2,X0),vmul(X3,X1))
| ~ geq(X2,X3)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( greater(vmul(X2,X0),vmul(X3,X1))
| ~ greater(X2,X3)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f147,plain,
! [Vd244,Vd245] :
( ( ( Vd245 != Vd244
& ~ greater(Vd245,Vd244) )
| geq(Vd245,Vd244) )
& ( Vd245 = Vd244
| greater(Vd245,Vd244)
| ~ geq(Vd245,Vd244) ) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f148,plain,
( ! [Vd244,Vd245] :
( ( Vd245 != Vd244
& ~ greater(Vd245,Vd244) )
| geq(Vd245,Vd244) )
& ! [Vd244,Vd245] :
( Vd245 = Vd244
| greater(Vd245,Vd244)
| ~ geq(Vd245,Vd244) ) ),
inference(miniscoping,[status(thm)],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f151,plain,
! [X0,X1] :
( X0 != X1
| geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f197,plain,
! [X0] : geq(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f151]) ).
fof(f209,plain,
~ greater(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(resolution,[status(thm)],[f150,f63]) ).
fof(f217,plain,
( vd526 = vd527
| greater(vd526,vd527) ),
inference(resolution,[status(thm)],[f149,f65]) ).
fof(f218,plain,
( vd529 = vd530
| greater(vd529,vd530) ),
inference(resolution,[status(thm)],[f149,f64]) ).
fof(f256,plain,
( ~ greater(vd526,vd527)
| ~ geq(vd529,vd530) ),
inference(resolution,[status(thm)],[f209,f68]) ).
fof(f257,plain,
( ~ geq(vd526,vd527)
| ~ greater(vd529,vd530) ),
inference(resolution,[status(thm)],[f209,f67]) ).
fof(f258,plain,
~ greater(vd526,vd527),
inference(forward_subsumption_resolution,[status(thm)],[f256,f64]) ).
fof(f259,plain,
~ greater(vd529,vd530),
inference(forward_subsumption_resolution,[status(thm)],[f257,f65]) ).
fof(f264,plain,
~ geq(vmul(vd526,vd529),vmul(vd526,vd530)),
inference(backward_demodulation,[status(thm)],[f265,f63]) ).
fof(f265,plain,
vd526 = vd527,
inference(forward_subsumption_resolution,[status(thm)],[f217,f258]) ).
fof(f268,plain,
vd529 = vd530,
inference(forward_subsumption_resolution,[status(thm)],[f218,f259]) ).
fof(f419,plain,
~ geq(vmul(vd526,vd529),vmul(vd526,vd529)),
inference(forward_demodulation,[status(thm)],[f268,f264]) ).
fof(f420,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f419,f197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM857+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 03:13:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.059159 seconds
% 0.13/0.42 % CPU time: 0.182273 seconds
% 0.13/0.42 % Total memory used: 104.242 MB
% 0.13/0.42 % Net memory used: 104.132 MB
%------------------------------------------------------------------------------