%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM128+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:10:27 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 62 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 27 ~; 20 |; 10 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 46 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [VVar0,VExp0,Vx,Vv] :
( ( VExp0 = vvar(Vx)
& VVar0 = Vv )
=> ( ( visFreeVar(VVar0,VExp0)
=> Vx = Vv )
& ( Vx = Vv
=> visFreeVar(VVar0,VExp0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [VVar0,VExp0,Ve1,Vv,Ve2] :
( ( VExp0 = vapp(Ve1,Ve2)
& VVar0 = Vv )
=> ( ( visFreeVar(VVar0,VExp0)
=> ( visFreeVar(Vv,Ve2)
| visFreeVar(Vv,Ve1) ) )
& ( ( visFreeVar(Vv,Ve2)
| visFreeVar(Vv,Ve1) )
=> visFreeVar(VVar0,VExp0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Vv,Ve] :
( vgensym(Ve) = Vv
=> ~ visFreeVar(Vv,Ve) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,conjecture,
! [Ve,Ve1,Vx,Vfresh] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> Vx != Vfresh ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
~ ! [Ve,Ve1,Vx,Vfresh] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> Vx != Vfresh ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f94,plain,
! [VVar0,VExp0,Vx,Vv] :
( ( ( Vx = Vv
| ~ visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
| Vx != Vv ) )
| VExp0 != vvar(Vx)
| VVar0 != Vv ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( visFreeVar(X0,X2)
| X3 != X1
| X2 != vvar(X3)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f102,plain,
! [VVar0,VExp0,Ve1,Vv,Ve2] :
( ( ( visFreeVar(Vv,Ve2)
| visFreeVar(Vv,Ve1)
| ~ visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
| ( ~ visFreeVar(Vv,Ve2)
& ~ visFreeVar(Vv,Ve1) ) ) )
| VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4] :
( visFreeVar(X0,X2)
| ~ visFreeVar(X1,X4)
| X2 != vapp(X3,X4)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f155,plain,
! [Vv,Ve] :
( ~ visFreeVar(Vv,Ve)
| vgensym(Ve) != Vv ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f156,plain,
! [X0,X1] :
( ~ visFreeVar(X1,X0)
| vgensym(X0) != X1 ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f281,plain,
? [Ve,Ve1,Vx,Vfresh] :
( Vx = Vfresh
& Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx))) ),
inference(pre_NNF_transformation,[status(thm)],[f66]) ).
fof(f282,plain,
? [Vx,Vfresh] :
( Vx = Vfresh
& ? [Ve,Ve1] : Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx))) ),
inference(miniscoping,[status(thm)],[f281]) ).
fof(f283,plain,
( sK21_skl = sK22_skl
& sK22_skl = vgensym(vapp(vapp(sK23_skl,sK24_skl),vvar(sK21_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl,sK23_skl,sK24_skl]),skolemize(Vx,sK21_skl),skolemize(Vfresh,sK22_skl),skolemize(Ve,sK23_skl),skolemize(Ve1,sK24_skl)],[f282]) ).
fof(f284,plain,
sK22_skl = vgensym(vapp(vapp(sK23_skl,sK24_skl),vvar(sK21_skl))),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f285,plain,
sK21_skl = sK22_skl,
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f434,plain,
! [X0] : visFreeVar(X0,vvar(X0)),
inference(destructive_equality_resolution,[status(thm)],[f95]) ).
fof(f440,plain,
! [X0,X1,X2] :
( visFreeVar(X0,vapp(X2,X1))
| ~ visFreeVar(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f104]) ).
fof(f453,plain,
! [X0] : ~ visFreeVar(vgensym(X0),X0),
inference(destructive_equality_resolution,[status(thm)],[f156]) ).
fof(f497,plain,
sK21_skl = vgensym(vapp(vapp(sK23_skl,sK24_skl),vvar(sK21_skl))),
inference(forward_demodulation,[status(thm)],[f285,f284]) ).
fof(f499,plain,
~ visFreeVar(sK21_skl,vapp(vapp(sK23_skl,sK24_skl),vvar(sK21_skl))),
inference(paramodulation,[status(thm)],[f497,f453]) ).
fof(f541,plain,
~ visFreeVar(sK21_skl,vvar(sK21_skl)),
inference(resolution,[status(thm)],[f440,f499]) ).
fof(f550,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f541,f434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM128+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 14:17:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.063361 seconds
% 0.12/0.44 % CPU time: 0.184230 seconds
% 0.12/0.44 % Total memory used: 111.821 MB
% 0.12/0.44 % Net memory used: 111.549 MB
%------------------------------------------------------------------------------