TSTP Solution File: COM128+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM128+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 01:32:54 EDT 2022
% Result : Theorem 0.52s 0.68s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 66 ( 25 unt; 0 def)
% Number of atoms : 172 ( 106 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 196 ( 90 ~; 81 |; 15 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 4 sgn 63 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(isFreeVar0,axiom,
! [VVar0,VExp0,Vx,Vv] :
( ( VVar0 = Vv
& VExp0 = vvar(Vx) )
=> ( ( Vx = Vv
=> visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
=> Vx = Vv ) ) ) ).
fof(isFreeVar2,axiom,
! [VVar0,VExp0,Ve1,Vv,Ve2] :
( ( VVar0 = Vv
& VExp0 = vapp(Ve1,Ve2) )
=> ( ( ( visFreeVar(Vv,Ve1)
| visFreeVar(Vv,Ve2) )
=> visFreeVar(VVar0,VExp0) )
& ( visFreeVar(VVar0,VExp0)
=> ( visFreeVar(Vv,Ve1)
| visFreeVar(Vv,Ve2) ) ) ) ) ).
fof('gensym-is-fresh',axiom,
! [Vv,Ve] :
( vgensym(Ve) = Vv
=> ~ visFreeVar(Vv,Ve) ) ).
fof('fresh-unequal-var-3',conjecture,
! [Ve,Ve1,Vx,Vfresh] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> Vx != Vfresh ) ).
fof(subgoal_0,plain,
! [Ve,Ve1,Vx,Vfresh] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> Vx != Vfresh ),
inference(strip,[],['fresh-unequal-var-3']) ).
fof(negate_0_0,plain,
~ ! [Ve,Ve1,Vx,Vfresh] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> Vx != Vfresh ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Ve,Vv] :
( vgensym(Ve) != Vv
| ~ visFreeVar(Vv,Ve) ),
inference(canonicalize,[],['gensym-is-fresh']) ).
fof(normalize_0_1,plain,
! [Ve,Vv] :
( vgensym(Ve) != Vv
| ~ visFreeVar(Vv,Ve) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [Ve,Ve1,Vfresh,Vx] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
& Vx = Vfresh ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( skolemFOFtoCNF_Vfresh_1 = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))
& skolemFOFtoCNF_Vx_16 = skolemFOFtoCNF_Vfresh_1 ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
skolemFOFtoCNF_Vfresh_1 = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
skolemFOFtoCNF_Vx_16 = skolemFOFtoCNF_Vfresh_1,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [VExp0,VVar0,Vv,Vx] :
( VExp0 != vvar(Vx)
| VVar0 != Vv
| ( ( Vx != Vv
| visFreeVar(VVar0,VExp0) )
& ( ~ visFreeVar(VVar0,VExp0)
| Vx = Vv ) ) ),
inference(canonicalize,[],[isFreeVar0]) ).
fof(normalize_0_7,plain,
! [VExp0,VVar0,Vv,Vx] :
( VExp0 != vvar(Vx)
| VVar0 != Vv
| ( ( Vx != Vv
| visFreeVar(VVar0,VExp0) )
& ( ~ visFreeVar(VVar0,VExp0)
| Vx = Vv ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [VExp0,VVar0,Vv,Vx] :
( ( VExp0 != vvar(Vx)
| VVar0 != Vv
| Vx != Vv
| visFreeVar(VVar0,VExp0) )
& ( VExp0 != vvar(Vx)
| VVar0 != Vv
| ~ visFreeVar(VVar0,VExp0)
| Vx = Vv ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [VExp0,VVar0,Vv,Vx] :
( VExp0 != vvar(Vx)
| VVar0 != Vv
| Vx != Vv
| visFreeVar(VVar0,VExp0) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [VExp0,VVar0,Ve1,Ve2,Vv] :
( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ( ( visFreeVar(VVar0,VExp0)
| ( ~ visFreeVar(Vv,Ve1)
& ~ visFreeVar(Vv,Ve2) ) )
& ( ~ visFreeVar(VVar0,VExp0)
| visFreeVar(Vv,Ve1)
| visFreeVar(Vv,Ve2) ) ) ),
inference(canonicalize,[],[isFreeVar2]) ).
fof(normalize_0_11,plain,
! [VExp0,VVar0,Ve1,Ve2,Vv] :
( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ( ( visFreeVar(VVar0,VExp0)
| ( ~ visFreeVar(Vv,Ve1)
& ~ visFreeVar(Vv,Ve2) ) )
& ( ~ visFreeVar(VVar0,VExp0)
| visFreeVar(Vv,Ve1)
| visFreeVar(Vv,Ve2) ) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [VExp0,VVar0,Ve1,Ve2,Vv] :
( ( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ~ visFreeVar(Vv,Ve1)
| visFreeVar(VVar0,VExp0) )
& ( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ~ visFreeVar(Vv,Ve2)
| visFreeVar(VVar0,VExp0) )
& ( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ~ visFreeVar(VVar0,VExp0)
| visFreeVar(Vv,Ve1)
| visFreeVar(Vv,Ve2) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [VExp0,VVar0,Ve1,Ve2,Vv] :
( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ~ visFreeVar(Vv,Ve2)
| visFreeVar(VVar0,VExp0) ),
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
( vgensym(Ve) != Vv
| ~ visFreeVar(Vv,Ve) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( vgensym(Ve) != vgensym(Ve)
| ~ visFreeVar(vgensym(Ve),Ve) ),
inference(subst,[],[refute_0_0:[bind(Vv,$fot(vgensym(Ve)))]]) ).
cnf(refute_0_2,plain,
vgensym(Ve) = vgensym(Ve),
introduced(tautology,[refl,[$fot(vgensym(Ve))]]) ).
cnf(refute_0_3,plain,
~ visFreeVar(vgensym(Ve),Ve),
inference(resolve,[$cnf( $equal(vgensym(Ve),vgensym(Ve)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
~ visFreeVar(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),
inference(subst,[],[refute_0_3:[bind(Ve,$fot(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))))]]) ).
cnf(refute_0_5,plain,
skolemFOFtoCNF_Vfresh_1 = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_Vx_16 = skolemFOFtoCNF_Vfresh_1,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_7,plain,
vvar(skolemFOFtoCNF_Vx_16) = vvar(skolemFOFtoCNF_Vx_16),
introduced(tautology,[refl,[$fot(vvar(skolemFOFtoCNF_Vx_16))]]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_Vx_16 != skolemFOFtoCNF_Vfresh_1
| vvar(skolemFOFtoCNF_Vx_16) != vvar(skolemFOFtoCNF_Vx_16)
| vvar(skolemFOFtoCNF_Vx_16) = vvar(skolemFOFtoCNF_Vfresh_1) ),
introduced(tautology,[equality,[$cnf( $equal(vvar(skolemFOFtoCNF_Vx_16),vvar(skolemFOFtoCNF_Vx_16)) ),[1,0],$fot(skolemFOFtoCNF_Vfresh_1)]]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_Vx_16 != skolemFOFtoCNF_Vfresh_1
| vvar(skolemFOFtoCNF_Vx_16) = vvar(skolemFOFtoCNF_Vfresh_1) ),
inference(resolve,[$cnf( $equal(vvar(skolemFOFtoCNF_Vx_16),vvar(skolemFOFtoCNF_Vx_16)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
vvar(skolemFOFtoCNF_Vx_16) = vvar(skolemFOFtoCNF_Vfresh_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Vx_16,skolemFOFtoCNF_Vfresh_1) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)) = vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)),
introduced(tautology,[refl,[$fot(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))]]) ).
cnf(refute_0_12,plain,
( vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)) != vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))
| vvar(skolemFOFtoCNF_Vx_16) != vvar(skolemFOFtoCNF_Vfresh_1)
| vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)) = vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)) ),
introduced(tautology,[equality,[$cnf( $equal(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) ),[1,1],$fot(vvar(skolemFOFtoCNF_Vfresh_1))]]) ).
cnf(refute_0_13,plain,
( vvar(skolemFOFtoCNF_Vx_16) != vvar(skolemFOFtoCNF_Vfresh_1)
| vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)) = vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)) ),
inference(resolve,[$cnf( $equal(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)) = vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)),
inference(resolve,[$cnf( $equal(vvar(skolemFOFtoCNF_Vx_16),vvar(skolemFOFtoCNF_Vfresh_1)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),
introduced(tautology,[refl,[$fot(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))))]]) ).
cnf(refute_0_16,plain,
( vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)) != vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))
| vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) != vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))
| vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) ),
introduced(tautology,[equality,[$cnf( $equal(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))) ),[1,0],$fot(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)))]]) ).
cnf(refute_0_17,plain,
( vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)) != vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))
| vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) ),
inference(resolve,[$cnf( $equal(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),
inference(resolve,[$cnf( $equal(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_Vfresh_1 != vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))
| vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) != vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)))
| skolemFOFtoCNF_Vfresh_1 = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_Vfresh_1,vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)))) ),[0],$fot(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))))]]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_Vfresh_1 != vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))
| skolemFOFtoCNF_Vfresh_1 = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) ),
inference(resolve,[$cnf( $equal(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
skolemFOFtoCNF_Vfresh_1 = vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Vfresh_1,vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))) )],[refute_0_5,refute_0_20]) ).
cnf(refute_0_22,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_23,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_24,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_Vfresh_1 != vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)))
| vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) = skolemFOFtoCNF_Vfresh_1 ),
inference(subst,[],[refute_0_24:[bind(X,$fot(skolemFOFtoCNF_Vfresh_1)),bind(Y,$fot(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)))))]]) ).
cnf(refute_0_26,plain,
vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) = skolemFOFtoCNF_Vfresh_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Vfresh_1,vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)))) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) != skolemFOFtoCNF_Vfresh_1
| ~ visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)))
| visFreeVar(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) ),
introduced(tautology,[equality,[$cnf( ~ visFreeVar(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) ),[0],$fot(skolemFOFtoCNF_Vfresh_1)]]) ).
cnf(refute_0_28,plain,
( ~ visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1)))
| visFreeVar(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) ),
inference(resolve,[$cnf( $equal(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),skolemFOFtoCNF_Vfresh_1) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
~ visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),
inference(resolve,[$cnf( visFreeVar(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) )],[refute_0_28,refute_0_4]) ).
cnf(refute_0_30,plain,
( VExp0 != vvar(Vx)
| VVar0 != Vv
| Vx != Vv
| visFreeVar(VVar0,VExp0) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_31,plain,
( Vv != Vv
| vvar(Vv) != vvar(Vv)
| visFreeVar(Vv,vvar(Vv)) ),
inference(subst,[],[refute_0_30:[bind(VExp0,$fot(vvar(Vv))),bind(VVar0,$fot(Vv)),bind(Vx,$fot(Vv))]]) ).
cnf(refute_0_32,plain,
Vv = Vv,
introduced(tautology,[refl,[$fot(Vv)]]) ).
cnf(refute_0_33,plain,
( vvar(Vv) != vvar(Vv)
| visFreeVar(Vv,vvar(Vv)) ),
inference(resolve,[$cnf( $equal(Vv,Vv) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
vvar(Vv) = vvar(Vv),
introduced(tautology,[refl,[$fot(vvar(Vv))]]) ).
cnf(refute_0_35,plain,
visFreeVar(Vv,vvar(Vv)),
inference(resolve,[$cnf( $equal(vvar(Vv),vvar(Vv)) )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
visFreeVar(X_167,vvar(X_167)),
inference(subst,[],[refute_0_35:[bind(Vv,$fot(X_167))]]) ).
cnf(refute_0_37,plain,
( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ~ visFreeVar(Vv,Ve2)
| visFreeVar(VVar0,VExp0) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_38,plain,
( Vv != Vv
| vapp(Ve1,Ve2) != vapp(Ve1,Ve2)
| ~ visFreeVar(Vv,Ve2)
| visFreeVar(Vv,vapp(Ve1,Ve2)) ),
inference(subst,[],[refute_0_37:[bind(VExp0,$fot(vapp(Ve1,Ve2))),bind(VVar0,$fot(Vv))]]) ).
cnf(refute_0_39,plain,
( vapp(Ve1,Ve2) != vapp(Ve1,Ve2)
| ~ visFreeVar(Vv,Ve2)
| visFreeVar(Vv,vapp(Ve1,Ve2)) ),
inference(resolve,[$cnf( $equal(Vv,Vv) )],[refute_0_32,refute_0_38]) ).
cnf(refute_0_40,plain,
vapp(Ve1,Ve2) = vapp(Ve1,Ve2),
introduced(tautology,[refl,[$fot(vapp(Ve1,Ve2))]]) ).
cnf(refute_0_41,plain,
( ~ visFreeVar(Vv,Ve2)
| visFreeVar(Vv,vapp(Ve1,Ve2)) ),
inference(resolve,[$cnf( $equal(vapp(Ve1,Ve2),vapp(Ve1,Ve2)) )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
( ~ visFreeVar(X_167,vvar(X_167))
| visFreeVar(X_167,vapp(X_165,vvar(X_167))) ),
inference(subst,[],[refute_0_41:[bind(Ve1,$fot(X_165)),bind(Ve2,$fot(vvar(X_167))),bind(Vv,$fot(X_167))]]) ).
cnf(refute_0_43,plain,
visFreeVar(X_167,vapp(X_165,vvar(X_167))),
inference(resolve,[$cnf( visFreeVar(X_167,vvar(X_167)) )],[refute_0_36,refute_0_42]) ).
cnf(refute_0_44,plain,
visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))),
inference(subst,[],[refute_0_43:[bind(X_165,$fot(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10))),bind(X_167,$fot(skolemFOFtoCNF_Vfresh_1))]]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vfresh_1))) )],[refute_0_44,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM128+1 : TPTP v8.1.0. Released v6.4.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 16 17:37:33 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.52/0.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.68
% 0.52/0.68 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.52/0.68
%------------------------------------------------------------------------------