%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM855+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.23s 0.56s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 38 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 8 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd512)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
vmul(vd512,vd509) = vmul(vd509,vd512),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
vmul(vd509,vd511) = vmul(vd511,vd509),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [Vd337,Vd338,Vd340,Vd341] :
( ( greater(Vd337,Vd338)
& greater(Vd340,Vd341) )
=> greater(vplus(Vd337,Vd340),vplus(Vd338,Vd341)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [Vd328,Vd329,Vd330] :
( greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
=> greater(Vd328,Vd329) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f66,plain,
vmul(vd512,vd509) = vmul(vd509,vd512),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f67,plain,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f68,plain,
vmul(vd509,vd511) = vmul(vd511,vd509),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f69,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f108,plain,
! [Vd337,Vd338,Vd340,Vd341] :
( greater(vplus(Vd337,Vd340),vplus(Vd338,Vd341))
| ~ greater(Vd337,Vd338)
| ~ greater(Vd340,Vd341) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( greater(vplus(X2,X0),vplus(X3,X1))
| ~ greater(X2,X3)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f116,plain,
! [Vd328,Vd329,Vd330] :
( greater(Vd328,Vd329)
| ~ greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330)) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f117,plain,
! [Vd328,Vd329] :
( greater(Vd328,Vd329)
| ! [Vd330] : ~ greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330)) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(vplus(X0,X1),vplus(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f182,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f206,plain,
~ greater(vmul(vd508,vd511),vmul(vd512,vd509)),
inference(backward_demodulation,[status(thm)],[f66,f65]) ).
fof(f207,plain,
greater(vmul(vd508,vd511),vmul(vd511,vd509)),
inference(forward_demodulation,[status(thm)],[f68,f69]) ).
fof(f374,plain,
! [X0] : ~ greater(vplus(vmul(vd508,vd511),X0),vplus(vmul(vd512,vd509),X0)),
inference(resolution,[status(thm)],[f118,f206]) ).
fof(f590,plain,
! [X0] : ~ greater(vplus(vmul(vd508,vd511),X0),vplus(X0,vmul(vd512,vd509))),
inference(paramodulation,[status(thm)],[f182,f374]) ).
fof(f1426,plain,
! [X0] :
( ~ greater(vmul(vd508,vd511),X0)
| ~ greater(X0,vmul(vd512,vd509)) ),
inference(resolution,[status(thm)],[f590,f109]) ).
fof(f1452,plain,
~ greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(resolution,[status(thm)],[f1426,f207]) ).
fof(f1456,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1452,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM855+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 03:11:36 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.23/0.56 % Refutation found
% 0.23/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.59 % Elapsed time: 0.125366 seconds
% 0.23/0.59 % CPU time: 0.669919 seconds
% 0.23/0.59 % Total memory used: 114.752 MB
% 0.23/0.59 % Net memory used: 113.614 MB
%------------------------------------------------------------------------------