TSTP Solution File: NUM844+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 : Mon Jul 18 12:30:53 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 31
% Syntax : Number of formulae : 124 ( 69 unt; 0 def)
% Number of atoms : 204 ( 203 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 162 ( 82 ~; 78 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('holds(266, 415, 3)',conjecture,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ).
fof('holds(266, 415, 2)',axiom,
vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ).
fof('holds(266, 415, 1)',axiom,
vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) ).
fof('holds(266, 415, 0)',axiom,
vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) ).
fof('ass(cond(61, 0), 0)',axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).
fof('ass(cond(52, 0), 0)',axiom,
! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)) ).
fof('ass(cond(33, 0), 0)',axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [Vd42,Vd43] :
( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& vplus(Vd42,v1) = vsucc(Vd42) ) ).
fof(subgoal_0,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(strip,[],['holds(266, 415, 3)']) ).
fof(negate_0_0,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(canonicalize,[],['holds(266, 415, 2)']) ).
fof(normalize_0_2,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],['ass(cond(61, 0), 0)']) ).
fof(normalize_0_3,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],['ass(cond(33, 0), 0)']) ).
fof(normalize_0_5,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( ! [Vd42] : vplus(Vd42,v1) = vsucc(Vd42)
& ! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)) ),
inference(canonicalize,[],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).
fof(normalize_0_7,plain,
! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),
inference(canonicalize,[],['holds(266, 415, 1)']) ).
fof(normalize_0_10,plain,
vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),
inference(canonicalize,[],['holds(266, 415, 0)']) ).
fof(normalize_0_11,plain,
! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
inference(canonicalize,[],['ass(cond(52, 0), 0)']) ).
fof(normalize_0_12,plain,
! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
inference(specialize,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,plain,
vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( vplus(Vd79,Vd78) != vplus(Vd78,Vd79)
| vplus(Vd78,Vd79) = vplus(Vd79,Vd78) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(vplus(Vd79,Vd78))),bind(Y,$fot(vplus(Vd78,Vd79)))]]) ).
cnf(refute_0_7,plain,
vplus(Vd78,Vd79) = vplus(Vd79,Vd78),
inference(resolve,[$cnf( $equal(vplus(Vd79,Vd78),vplus(Vd78,Vd79)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
vplus(vd413,vd411) = vplus(vd411,vd413),
inference(subst,[],[refute_0_7:[bind(Vd78,$fot(vd413)),bind(Vd79,$fot(vd411))]]) ).
cnf(refute_0_9,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vd411)),
introduced(tautology,[refl,[$fot(vplus(vmul(vd411,vd413),vplus(vd413,vd411)))]]) ).
cnf(refute_0_10,plain,
( vplus(vd413,vd411) != vplus(vd411,vd413)
| vplus(vmul(vd411,vd413),vplus(vd413,vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vd411))
| vplus(vmul(vd411,vd413),vplus(vd413,vd411)) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vd411))) ),[1,1],$fot(vplus(vd411,vd413))]]) ).
cnf(refute_0_11,plain,
( vplus(vd413,vd411) != vplus(vd411,vd413)
| vplus(vmul(vd411,vd413),vplus(vd413,vd411)) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vd411))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vd411)) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)),
inference(resolve,[$cnf( $equal(vplus(vd413,vd411),vplus(vd411,vd413)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_14,plain,
vplus(vplus(vmul(vd411,vd413),vd413),vd411) = vplus(vmul(vd411,vd413),vplus(vd413,vd411)),
inference(subst,[],[refute_0_13:[bind(Vd46,$fot(vmul(vd411,vd413))),bind(Vd47,$fot(vd413)),bind(Vd48,$fot(vd411))]]) ).
cnf(refute_0_15,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_5,refute_0_15]) ).
cnf(refute_0_17,plain,
( vplus(vmul(vd411,vd413),vplus(vd413,vd411)) != vplus(vmul(vd411,vd413),vplus(vd411,vd413))
| vplus(vplus(vmul(vd411,vd413),vd413),vd411) != vplus(vmul(vd411,vd413),vplus(vd413,vd411))
| vplus(vplus(vmul(vd411,vd413),vd413),vd411) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vplus(vmul(vd411,vd413),vd413),vd411))),bind(Y,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vd411)))),bind(Z,$fot(vplus(vmul(vd411,vd413),vplus(vd411,vd413))))]]) ).
cnf(refute_0_18,plain,
( vplus(vmul(vd411,vd413),vplus(vd413,vd411)) != vplus(vmul(vd411,vd413),vplus(vd411,vd413))
| vplus(vplus(vmul(vd411,vd413),vd413),vd411) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vd411),vplus(vmul(vd411,vd413),vplus(vd413,vd411))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
vplus(vplus(vmul(vd411,vd413),vd413),vd411) = vplus(vmul(vd411,vd413),vplus(vd411,vd413)),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vd411)),vplus(vmul(vd411,vd413),vplus(vd411,vd413))) )],[refute_0_12,refute_0_18]) ).
cnf(refute_0_20,plain,
vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) = vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),
introduced(tautology,[refl,[$fot(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)))]]) ).
cnf(refute_0_21,plain,
( vplus(vplus(vmul(vd411,vd413),vd413),vd411) != vplus(vmul(vd411,vd413),vplus(vd411,vd413))
| vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) != vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))
| vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) ),
introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))) ),[1,0],$fot(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))]]) ).
cnf(refute_0_22,plain,
( vplus(vplus(vmul(vd411,vd413),vd413),vd411) != vplus(vmul(vd411,vd413),vplus(vd411,vd413))
| vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vd411),vplus(vmul(vd411,vd413),vplus(vd411,vd413))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_25,plain,
vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),
inference(subst,[],[refute_0_24:[bind(Vd42,$fot(vplus(vmul(vd411,vd413),vd413))),bind(Vd43,$fot(vd411))]]) ).
cnf(refute_0_26,plain,
( vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))
| vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) != vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))
| vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)))),bind(Y,$fot(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)))),bind(Z,$fot(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))))]]) ).
cnf(refute_0_27,plain,
( vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)) != vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))
| vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),
inference(resolve,[$cnf( $equal(vsucc(vplus(vplus(vmul(vd411,vd413),vd413),vd411)),vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
( vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
| vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) ),[0],$fot(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))))]]) ).
cnf(refute_0_30,plain,
( vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
vplus(vmul(vsucc(vd411),vd413),vd411) = vplus(vd411,vmul(vsucc(vd411),vd413)),
inference(subst,[],[refute_0_7:[bind(Vd78,$fot(vmul(vsucc(vd411),vd413))),bind(Vd79,$fot(vd411))]]) ).
cnf(refute_0_32,plain,
vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),
introduced(tautology,[refl,[$fot(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)))]]) ).
cnf(refute_0_33,plain,
( vplus(vmul(vsucc(vd411),vd413),vd411) != vplus(vd411,vmul(vsucc(vd411),vd413))
| vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
| vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) ),[1,0],$fot(vplus(vd411,vmul(vsucc(vd411),vd413)))]]) ).
cnf(refute_0_34,plain,
( vplus(vmul(vsucc(vd411),vd413),vd411) != vplus(vd411,vmul(vsucc(vd411),vd413))
| vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vd411),vplus(vd411,vmul(vsucc(vd411),vd413))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),
inference(subst,[],[refute_0_24:[bind(Vd42,$fot(vmul(vsucc(vd411),vd413))),bind(Vd43,$fot(vd411))]]) ).
cnf(refute_0_37,plain,
vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_38,plain,
( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411))
| vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
| vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) ),[0],$fot(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)))]]) ).
cnf(refute_0_39,plain,
( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411))
| vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_1,refute_0_38]) ).
cnf(refute_0_40,plain,
vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411))) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,plain,
( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)))),bind(Y,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))))]]) ).
cnf(refute_0_42,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))
| vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))))),bind(Y,$fot(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)))),bind(Z,$fot(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))))]]) ).
cnf(refute_0_44,plain,
( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) )],[refute_0_36,refute_0_44]) ).
cnf(refute_0_46,plain,
( vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
| vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))))),bind(Y,$fot(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)))),bind(Z,$fot(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))))]]) ).
cnf(refute_0_47,plain,
( vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_35,refute_0_47]) ).
cnf(refute_0_49,plain,
( vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) ),[1],$fot(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))))]]) ).
cnf(refute_0_50,plain,
( vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_30,refute_0_50]) ).
cnf(refute_0_52,plain,
vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd411,vd413),vd413),vsucc(vd411)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_1,refute_0_51]) ).
cnf(refute_0_53,plain,
vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_54,plain,
( vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))
| vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
| vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)))),bind(Y,$fot(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)))),bind(Z,$fot(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))))]]) ).
cnf(refute_0_55,plain,
( vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
| vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vsucc(vplus(vmul(vsucc(vd411),vd413),vd411))) )],[refute_0_36,refute_0_54]) ).
cnf(refute_0_56,plain,
vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vsucc(vd411),vd413),vd411)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_35,refute_0_55]) ).
cnf(refute_0_57,plain,
( vmul(vsucc(vd411),vsucc(vd413)) != vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))
| vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
| vmul(vsucc(vd411),vsucc(vd413)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(vd411),vsucc(vd413)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) ),[0],$fot(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)))]]) ).
cnf(refute_0_58,plain,
( vmul(vsucc(vd411),vsucc(vd413)) != vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))
| vmul(vsucc(vd411),vsucc(vd413)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),vd413),vsucc(vd411)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
vmul(vsucc(vd411),vsucc(vd413)) = vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),
inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(vd413)),vplus(vmul(vsucc(vd411),vd413),vsucc(vd411))) )],[refute_0_53,refute_0_58]) ).
cnf(refute_0_60,plain,
( vmul(vsucc(vd411),vsucc(vd413)) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
| vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(vmul(vsucc(vd411),vsucc(vd413)))),bind(Y,$fot(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))))]]) ).
cnf(refute_0_61,plain,
vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) = vmul(vsucc(vd411),vsucc(vd413)),
inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(vd413)),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))) != vmul(vsucc(vd411),vsucc(vd413))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) ),[1],$fot(vmul(vsucc(vd411),vsucc(vd413)))]]) ).
cnf(refute_0_63,plain,
( vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vd411,vmul(vsucc(vd411),vd413))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)),
inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vsucc(vplus(vd411,vmul(vsucc(vd411),vd413)))) )],[refute_0_52,refute_0_63]) ).
cnf(refute_0_65,plain,
vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) = vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),
inference(subst,[],[refute_0_24:[bind(Vd42,$fot(vmul(vd411,vd413))),bind(Vd43,$fot(vplus(vd411,vd413)))]]) ).
cnf(refute_0_66,plain,
( vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))
| vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
| vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))))),bind(Y,$fot(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))))),bind(Z,$fot(vmul(vsucc(vd411),vsucc(vd413))))]]) ).
cnf(refute_0_67,plain,
( vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
| vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) = vmul(vsucc(vd411),vsucc(vd413)),
inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
vsucc(vplus(vd413,vd411)) = vsucc(vplus(vd413,vd411)),
introduced(tautology,[refl,[$fot(vsucc(vplus(vd413,vd411)))]]) ).
cnf(refute_0_70,plain,
( vplus(vd413,vd411) != vplus(vd411,vd413)
| vsucc(vplus(vd413,vd411)) != vsucc(vplus(vd413,vd411))
| vsucc(vplus(vd413,vd411)) = vsucc(vplus(vd411,vd413)) ),
introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vd413,vd411)),vsucc(vplus(vd413,vd411))) ),[1,0],$fot(vplus(vd411,vd413))]]) ).
cnf(refute_0_71,plain,
( vplus(vd413,vd411) != vplus(vd411,vd413)
| vsucc(vplus(vd413,vd411)) = vsucc(vplus(vd411,vd413)) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vd413,vd411)),vsucc(vplus(vd413,vd411))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
vsucc(vplus(vd413,vd411)) = vsucc(vplus(vd411,vd413)),
inference(resolve,[$cnf( $equal(vplus(vd413,vd411),vplus(vd411,vd413)) )],[refute_0_8,refute_0_71]) ).
cnf(refute_0_73,plain,
vplus(vd413,vsucc(vd411)) = vsucc(vplus(vd413,vd411)),
inference(subst,[],[refute_0_24:[bind(Vd42,$fot(vd413)),bind(Vd43,$fot(vd411))]]) ).
cnf(refute_0_74,plain,
( vplus(vd413,vsucc(vd411)) != vsucc(vplus(vd413,vd411))
| vsucc(vplus(vd413,vd411)) != vsucc(vplus(vd411,vd413))
| vplus(vd413,vsucc(vd411)) = vsucc(vplus(vd411,vd413)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vd413,vsucc(vd411)))),bind(Y,$fot(vsucc(vplus(vd413,vd411)))),bind(Z,$fot(vsucc(vplus(vd411,vd413))))]]) ).
cnf(refute_0_75,plain,
( vsucc(vplus(vd413,vd411)) != vsucc(vplus(vd411,vd413))
| vplus(vd413,vsucc(vd411)) = vsucc(vplus(vd411,vd413)) ),
inference(resolve,[$cnf( $equal(vplus(vd413,vsucc(vd411)),vsucc(vplus(vd413,vd411))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
vplus(vd413,vsucc(vd411)) = vsucc(vplus(vd411,vd413)),
inference(resolve,[$cnf( $equal(vsucc(vplus(vd413,vd411)),vsucc(vplus(vd411,vd413))) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),
introduced(tautology,[refl,[$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))))]]) ).
cnf(refute_0_78,plain,
( vplus(vd413,vsucc(vd411)) != vsucc(vplus(vd411,vd413))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) ),[1,1],$fot(vsucc(vplus(vd411,vd413)))]]) ).
cnf(refute_0_79,plain,
( vplus(vd413,vsucc(vd411)) != vsucc(vplus(vd411,vd413))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),
inference(resolve,[$cnf( $equal(vplus(vd413,vsucc(vd411)),vsucc(vplus(vd411,vd413))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
( vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413)))
| vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vmul(vsucc(vd411),vsucc(vd413)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))))),bind(Y,$fot(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))))),bind(Z,$fot(vmul(vsucc(vd411),vsucc(vd413))))]]) ).
cnf(refute_0_82,plain,
( vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vmul(vsucc(vd411),vsucc(vd413)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vmul(vsucc(vd411),vsucc(vd413)),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_68,refute_0_82]) ).
cnf(refute_0_84,plain,
( vmul(vsucc(vd411),vsucc(vd413)) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) != vmul(vsucc(vd411),vsucc(vd413))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vmul(vsucc(vd411),vsucc(vd413))) ),[1],$fot(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)))]]) ).
cnf(refute_0_85,plain,
( vmul(vsucc(vd411),vsucc(vd413)) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_87,plain,
vplus(vsucc(vd411),vd413) = vsucc(vplus(vd411,vd413)),
inference(subst,[],[refute_0_86:[bind(Vd68,$fot(vd411)),bind(Vd69,$fot(vd413))]]) ).
cnf(refute_0_88,plain,
vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),
introduced(tautology,[refl,[$fot(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)))]]) ).
cnf(refute_0_89,plain,
( vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) != vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))
| vplus(vsucc(vd411),vd413) != vsucc(vplus(vd411,vd413))
| vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) ),[1,1],$fot(vsucc(vplus(vd411,vd413)))]]) ).
cnf(refute_0_90,plain,
( vplus(vsucc(vd411),vd413) != vsucc(vplus(vd411,vd413))
| vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),
inference(resolve,[$cnf( $equal(vplus(vsucc(vd411),vd413),vsucc(vplus(vd411,vd413))) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
( vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) != vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413)))
| vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
| vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vmul(vsucc(vd411),vsucc(vd413)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)))),bind(Y,$fot(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))))),bind(Z,$fot(vmul(vsucc(vd411),vsucc(vd413))))]]) ).
cnf(refute_0_93,plain,
( vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))) != vmul(vsucc(vd411),vsucc(vd413))
| vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vmul(vsucc(vd411),vsucc(vd413)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413)))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) = vmul(vsucc(vd411),vsucc(vd413)),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vsucc(vplus(vd411,vd413))),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_68,refute_0_93]) ).
cnf(refute_0_95,plain,
( vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413))
| vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) != vmul(vsucc(vd411),vsucc(vd413))
| vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(vd411),vsucc(vd413)),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) ),[1],$fot(vmul(vsucc(vd411),vsucc(vd413)))]]) ).
cnf(refute_0_96,plain,
( vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413))
| vmul(vsucc(vd411),vsucc(vd413)) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413))
| vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))) = vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)) ),
inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(vd413)),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) )],[refute_0_96,refute_0_85]) ).
cnf(refute_0_98,plain,
vmul(vsucc(vd411),vsucc(vd413)) != vmul(vsucc(vd411),vsucc(vd413)),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411))),vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413))) )],[refute_0_97,refute_0_0]) ).
cnf(refute_0_99,plain,
vmul(vsucc(vd411),vsucc(vd413)) = vmul(vsucc(vd411),vsucc(vd413)),
introduced(tautology,[refl,[$fot(vmul(vsucc(vd411),vsucc(vd413)))]]) ).
cnf(refute_0_100,plain,
$false,
inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(vd413)),vmul(vsucc(vd411),vsucc(vd413))) )],[refute_0_99,refute_0_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 04:58:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.39
%------------------------------------------------------------------------------