%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM129+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 37.26s 5.11s
% Output : Proof 37.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 65 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 75 ( 34 ~; 27 |; 8 &)
% ( 0 <=>; 6 =>; 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 : 63 ( 9 sgn 29 !; 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/sandbox/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(p388,plain,
( visFreeVar(X3,X0)
| ~ visFreeVar(X3,X2)
| X0 != vapp(X1,X2) ),
inference(equality_resolution,[status(thm)],[c21]) ).
cnf(p661,plain,
( visFreeVar(X0,vapp(X2,X1))
| ~ visFreeVar(X0,X1) ),
inference(equality_resolution,[status(thm)],[p388]) ).
fof(f65,conjecture,
! [Ve,Vx,Vfresh,Ve1] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> ~ visFreeVar(Vfresh,Ve1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qtd37) ).
fof(f65_neg,negated_conjecture,
~ ! [Ve,Vx,Vfresh,Ve1] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> ~ visFreeVar(Vfresh,Ve1) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f65_nnf,plain,
? [Ve,Vx,Vfresh,Ve1] :
( visFreeVar(Vfresh,Ve1)
& Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx))) ),
inference(nnf_transformation,[status(thm)],[f65_neg]) ).
fof(f65_sk,plain,
( visFreeVar(sk76,sk77)
& sk76 = vgensym(vapp(vapp(sk74,sk77),vvar(sk75))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk74,sk75,sk76,sk77])],[f65_nnf]) ).
cnf(c331,plain,
visFreeVar(sk76,sk77),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(p662,plain,
visFreeVar(sk76,vapp(X0,sk77)),
inference(resolution,[status(thm)],[p661,c331]) ).
cnf(c20,plain,
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| X1 != vapp(X2,X4)
| X0 != X3 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p384,plain,
( visFreeVar(X3,X0)
| ~ visFreeVar(X3,X1)
| X0 != vapp(X1,X2) ),
inference(equality_resolution,[status(thm)],[c20]) ).
cnf(p634,plain,
( visFreeVar(X0,vapp(X1,X2))
| ~ visFreeVar(X0,X1) ),
inference(equality_resolution,[status(thm)],[p384]) ).
cnf(p672,plain,
visFreeVar(sk76,vapp(vapp(X0,sk77),X1)),
inference(resolution,[status(thm)],[p662,p634]) ).
cnf(c330,plain,
sk76 = vgensym(vapp(vapp(sk74,sk77),vvar(sk75))),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
fof(f27,axiom,
! [Vv,Ve] :
( vgensym(Ve) = Vv
=> ~ visFreeVar(Vv,Ve) ),
file('/export/starexec/sandbox/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(p349,plain,
~ visFreeVar(vgensym(X0),X0),
inference(equality_resolution,[status(thm)],[c91]) ).
cnf(p367,plain,
~ visFreeVar(sk76,vapp(vapp(sk74,sk77),vvar(sk75))),
inference(superposition,[status(thm)],[c330,p349]) ).
cnf(p683,plain,
$false,
inference(resolution,[status(thm)],[p672,p367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM129+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n004.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 : Fri Sep 25 07:54:07 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 37.26/5.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.26/5.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------