TSTP Solution File: COM129+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM129+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 0.40s 0.56s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 17 unt; 0 def)
% Number of atoms : 124 ( 51 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 144 ( 68 ~; 59 |; 10 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 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 : 100 ( 10 sgn 48 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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-free-2',conjecture,
! [Ve,Vx,Vfresh,Ve1] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> ~ visFreeVar(Vfresh,Ve1) ) ).
fof(subgoal_0,plain,
! [Ve,Vx,Vfresh,Ve1] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> ~ visFreeVar(Vfresh,Ve1) ),
inference(strip,[],['fresh-free-2']) ).
fof(negate_0_0,plain,
~ ! [Ve,Vx,Vfresh,Ve1] :
( Vfresh = vgensym(vapp(vapp(Ve,Ve1),vvar(Vx)))
=> ~ visFreeVar(Vfresh,Ve1) ),
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)))
& visFreeVar(Vfresh,Ve1) ),
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)))
& visFreeVar(skolemFOFtoCNF_Vfresh_1,skolemFOFtoCNF_Ve1_10) ),
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,
! [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_6,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_5]) ).
fof(normalize_0_7,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_6]) ).
fof(normalize_0_8,plain,
! [VExp0,VVar0,Ve1,Ve2,Vv] :
( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ~ visFreeVar(Vv,Ve1)
| visFreeVar(VVar0,VExp0) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
visFreeVar(skolemFOFtoCNF_Vfresh_1,skolemFOFtoCNF_Ve1_10),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
! [VExp0,VVar0,Ve1,Ve2,Vv] :
( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ~ visFreeVar(Vv,Ve2)
| visFreeVar(VVar0,VExp0) ),
inference(conjunct,[],[normalize_0_7]) ).
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( $equal(vgensym(Ve),vgensym(Ve)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
~ visFreeVar(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),
inference(subst,[],[refute_0_3:[bind(Ve,$fot(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))))]]) ).
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,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_Vfresh_1 != vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))
| vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) = skolemFOFtoCNF_Vfresh_1 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Vfresh_1)),bind(Y,$fot(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))))]]) ).
cnf(refute_0_10,plain,
vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) = skolemFOFtoCNF_Vfresh_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Vfresh_1,vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) != skolemFOFtoCNF_Vfresh_1
| ~ visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))
| visFreeVar(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) ),
introduced(tautology,[equality,[$cnf( ~ visFreeVar(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) ),[0],$fot(skolemFOFtoCNF_Vfresh_1)]]) ).
cnf(refute_0_12,plain,
( ~ visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16)))
| visFreeVar(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) ),
inference(resolve,[$cnf( $equal(vgensym(vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),skolemFOFtoCNF_Vfresh_1) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
~ visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),
inference(resolve,[$cnf( visFreeVar(vgensym(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_12,refute_0_4]) ).
cnf(refute_0_14,plain,
( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ~ visFreeVar(Vv,Ve1)
| visFreeVar(VVar0,VExp0) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_15,plain,
( Vv != Vv
| vapp(Ve1,Ve2) != vapp(Ve1,Ve2)
| ~ visFreeVar(Vv,Ve1)
| visFreeVar(Vv,vapp(Ve1,Ve2)) ),
inference(subst,[],[refute_0_14:[bind(VExp0,$fot(vapp(Ve1,Ve2))),bind(VVar0,$fot(Vv))]]) ).
cnf(refute_0_16,plain,
Vv = Vv,
introduced(tautology,[refl,[$fot(Vv)]]) ).
cnf(refute_0_17,plain,
( vapp(Ve1,Ve2) != vapp(Ve1,Ve2)
| ~ visFreeVar(Vv,Ve1)
| visFreeVar(Vv,vapp(Ve1,Ve2)) ),
inference(resolve,[$cnf( $equal(Vv,Vv) )],[refute_0_16,refute_0_15]) ).
cnf(refute_0_18,plain,
vapp(Ve1,Ve2) = vapp(Ve1,Ve2),
introduced(tautology,[refl,[$fot(vapp(Ve1,Ve2))]]) ).
cnf(refute_0_19,plain,
( ~ visFreeVar(Vv,Ve1)
| visFreeVar(Vv,vapp(Ve1,Ve2)) ),
inference(resolve,[$cnf( $equal(vapp(Ve1,Ve2),vapp(Ve1,Ve2)) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
( ~ visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(X_138,skolemFOFtoCNF_Ve1_10))
| visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(X_138,skolemFOFtoCNF_Ve1_10),Ve2)) ),
inference(subst,[],[refute_0_19:[bind(Ve1,$fot(vapp(X_138,skolemFOFtoCNF_Ve1_10))),bind(Vv,$fot(skolemFOFtoCNF_Vfresh_1))]]) ).
cnf(refute_0_21,plain,
visFreeVar(skolemFOFtoCNF_Vfresh_1,skolemFOFtoCNF_Ve1_10),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_22,plain,
( VExp0 != vapp(Ve1,Ve2)
| VVar0 != Vv
| ~ visFreeVar(Vv,Ve2)
| visFreeVar(VVar0,VExp0) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_23,plain,
( Vv != Vv
| vapp(Ve1,Ve2) != vapp(Ve1,Ve2)
| ~ visFreeVar(Vv,Ve2)
| visFreeVar(Vv,vapp(Ve1,Ve2)) ),
inference(subst,[],[refute_0_22:[bind(VExp0,$fot(vapp(Ve1,Ve2))),bind(VVar0,$fot(Vv))]]) ).
cnf(refute_0_24,plain,
( vapp(Ve1,Ve2) != vapp(Ve1,Ve2)
| ~ visFreeVar(Vv,Ve2)
| visFreeVar(Vv,vapp(Ve1,Ve2)) ),
inference(resolve,[$cnf( $equal(Vv,Vv) )],[refute_0_16,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ visFreeVar(Vv,Ve2)
| visFreeVar(Vv,vapp(Ve1,Ve2)) ),
inference(resolve,[$cnf( $equal(vapp(Ve1,Ve2),vapp(Ve1,Ve2)) )],[refute_0_18,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ visFreeVar(skolemFOFtoCNF_Vfresh_1,skolemFOFtoCNF_Ve1_10)
| visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(X_135,skolemFOFtoCNF_Ve1_10)) ),
inference(subst,[],[refute_0_25:[bind(Ve1,$fot(X_135)),bind(Ve2,$fot(skolemFOFtoCNF_Ve1_10)),bind(Vv,$fot(skolemFOFtoCNF_Vfresh_1))]]) ).
cnf(refute_0_27,plain,
visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(X_135,skolemFOFtoCNF_Ve1_10)),
inference(resolve,[$cnf( visFreeVar(skolemFOFtoCNF_Vfresh_1,skolemFOFtoCNF_Ve1_10) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(X_138,skolemFOFtoCNF_Ve1_10)),
inference(subst,[],[refute_0_27:[bind(X_135,$fot(X_138))]]) ).
cnf(refute_0_29,plain,
visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(X_138,skolemFOFtoCNF_Ve1_10),Ve2)),
inference(resolve,[$cnf( visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(X_138,skolemFOFtoCNF_Ve1_10)) )],[refute_0_28,refute_0_20]) ).
cnf(refute_0_30,plain,
visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))),
inference(subst,[],[refute_0_29:[bind(Ve2,$fot(vvar(skolemFOFtoCNF_Vx_16))),bind(X_138,$fot(skolemFOFtoCNF_Ve_7))]]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( visFreeVar(skolemFOFtoCNF_Vfresh_1,vapp(vapp(skolemFOFtoCNF_Ve_7,skolemFOFtoCNF_Ve1_10),vvar(skolemFOFtoCNF_Vx_16))) )],[refute_0_30,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COM129+1 : TPTP v8.1.0. Released v6.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n026.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jun 16 18:04:08 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.56
% 0.40/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.40/0.56
%------------------------------------------------------------------------------