%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM849+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 : n013.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 01:41:49 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 4 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Vd396,Vd397] :
( vmul(Vd396,v1) = Vd396
& vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,plain,
? [Vd454] :
( vmul(vmul(vd448,vd449),vsucc(Vd454)) != vmul(vd448,vmul(vd449,vsucc(Vd454)))
& vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454)) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f59,plain,
( vmul(vmul(vd448,vd449),vsucc(sK0_skl)) != vmul(vd448,vmul(vd449,vsucc(sK0_skl)))
& vmul(vmul(vd448,vd449),sK0_skl) = vmul(vd448,vmul(vd449,sK0_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd454,sK0_skl)],[f58]) ).
fof(f60,plain,
vmul(vmul(vd448,vd449),sK0_skl) = vmul(vd448,vmul(vd449,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
vmul(vmul(vd448,vd449),vsucc(sK0_skl)) != vmul(vd448,vmul(vd449,vsucc(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f72,plain,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f76,plain,
( ! [Vd396] : vmul(Vd396,v1) = Vd396
& ! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f77,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f221,plain,
vmul(vmul(vd448,vd449),vsucc(sK0_skl)) = vplus(vmul(vd448,vmul(vd449,sK0_skl)),vmul(vd448,vd449)),
inference(paramodulation,[status(thm)],[f60,f77]) ).
fof(f225,plain,
vmul(vmul(vd448,vd449),vsucc(sK0_skl)) = vmul(vd448,vplus(vmul(vd449,sK0_skl),vd449)),
inference(forward_demodulation,[status(thm)],[f72,f221]) ).
fof(f226,plain,
vmul(vmul(vd448,vd449),vsucc(sK0_skl)) = vmul(vd448,vmul(vd449,vsucc(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f77,f225]) ).
fof(f227,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f226,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 03:12:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.054124 seconds
% 0.10/0.43 % CPU time: 0.157067 seconds
% 0.10/0.43 % Total memory used: 103.993 MB
% 0.10/0.43 % Net memory used: 103.920 MB
%------------------------------------------------------------------------------