%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM128+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 : Fri Sep 25 01:03:39 PM UTC 2026
% Result : Theorem 27.49s 9.13s
% Output : Proof 27.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 84 ( 41 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 99 ( 43 ~; 35 |; 12 &)
% ( 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 : 72 ( 5 sgn 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,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/sandbox2/benchmark/theBenchmark.p',isFreeVar2) ).
fof(f11_nnf,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(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [VVar0,Vv,VExp0,Ve1,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(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c21,plain,
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X4)
| X1 != vapp(X2,X4)
| X0 != X3 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p556,plain,
( visFreeVar(X3,X0)
| ~ visFreeVar(X3,X2)
| X0 != vapp(X1,X2) ),
inference(equality_resolution,[status(thm)],[c21]) ).
cnf(p855,plain,
( visFreeVar(X0,vapp(X2,X1))
| ~ visFreeVar(X0,X1) ),
inference(equality_resolution,[status(thm)],[p556]) ).
fof(f9,axiom,
! [VVar0,VExp0,Vx,Vv] :
( ( VExp0 = vvar(Vx)
& VVar0 = Vv )
=> ( ( visFreeVar(VVar0,VExp0)
=> Vx = Vv )
& ( Vx = Vv
=> visFreeVar(VVar0,VExp0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar0) ).
fof(f9_nnf,plain,
! [VVar0,VExp0,Vx,Vv] :
( ( ( Vx = Vv
| ~ visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
| Vx != Vv ) )
| VExp0 != vvar(Vx)
| VVar0 != Vv ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [VVar0,Vv,VExp0,Vx] :
( ( ( Vx = Vv
| ~ visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
| Vx != Vv ) )
| VExp0 != vvar(Vx)
| VVar0 != Vv ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c15,plain,
( visFreeVar(X0,X1)
| X2 != X3
| X1 != vvar(X2)
| X0 != X3 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p362,plain,
( visFreeVar(X0,X2)
| X2 != vvar(X0)
| X0 != X1 ),
inference(factoring,[status(thm)],[c15]) ).
cnf(p743,plain,
( visFreeVar(X1,X0)
| X0 != vvar(X1) ),
inference(equality_resolution,[status(thm)],[p362]) ).
cnf(p745,plain,
visFreeVar(X0,vvar(X0)),
inference(equality_resolution,[status(thm)],[p743]) ).
cnf(p856,plain,
visFreeVar(X0,vapp(X1,vvar(X0))),
inference(resolution,[status(thm)],[p855,p745]) ).
fof(f64,conjecture,
! [Ve,Ve1,Vx,Vfresh] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> Vx != Vfresh ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd36) ).
fof(f64_neg,negated_conjecture,
~ ! [Ve,Ve1,Vx,Vfresh] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> Vx != Vfresh ),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f64_nnf,plain,
? [Ve,Ve1,Vx,Vfresh] :
( Vx = Vfresh
& Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx))) ),
inference(nnf_transformation,[status(thm)],[f64_neg]) ).
fof(f64_sk,plain,
( sk76 = sk77
& sk77 = vgensym(vapp(vapp(sk74,sk75),vvar(sk76))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk74,sk75,sk76,sk77])],[f64_nnf]) ).
cnf(c330,plain,
sk76 = sk77,
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(c329,plain,
sk77 = vgensym(vapp(vapp(sk74,sk75),vvar(sk76))),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
fof(f27,axiom,
! [Vv,Ve] :
( vgensym(Ve) = Vv
=> ~ visFreeVar(Vv,Ve) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qtd15) ).
fof(f27_nnf,plain,
! [Vv,Ve] :
( ~ visFreeVar(Vv,Ve)
| vgensym(Ve) != Vv ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [Ve,Vv] :
( ~ visFreeVar(Vv,Ve)
| vgensym(Ve) != Vv ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c91,plain,
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p370,plain,
~ visFreeVar(vgensym(X0),X0),
inference(equality_resolution,[status(thm)],[c91]) ).
cnf(p546,plain,
~ visFreeVar(sk77,vapp(vapp(sk74,sk75),vvar(sk76))),
inference(superposition,[status(thm)],[c329,p370]) ).
cnf(p554,plain,
~ visFreeVar(sk76,vapp(vapp(sk74,sk75),vvar(sk76))),
inference(superposition,[status(thm)],[c330,p546]) ).
cnf(p861,plain,
$false,
inference(resolution,[status(thm)],[p856,p554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM128+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.58 % Computer : n002.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Fri Sep 25 07:56:58 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.49/9.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.49/9.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------