TSTP Solution File: NUM847+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 12:30:55 EDT 2022
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 91 ( 49 unt; 0 def)
% Number of atoms : 151 ( 150 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 122 ( 62 ~; 58 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('holds(286, 441, 3)',conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) ).
fof('holds(286, 441, 2)',axiom,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ).
fof('holds(286, 441, 1)',axiom,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436) ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [Vd396,Vd397] :
( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
& vmul(Vd396,v1) = Vd396 ) ).
fof('ass(cond(61, 0), 0)',axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).
fof('ass(cond(33, 0), 0)',axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) ).
fof(subgoal_0,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(strip,[],['holds(286, 441, 3)']) ).
fof(negate_0_0,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(canonicalize,[],['holds(286, 441, 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,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
inference(canonicalize,[],['holds(286, 441, 1)']) ).
fof(normalize_0_7,plain,
( ! [Vd396] : vmul(Vd396,v1) = Vd396
& ! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396) ),
inference(canonicalize,[],['qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))']) ).
fof(normalize_0_8,plain,
! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
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( $equal(vplus(Vd79,Vd78),vplus(Vd78,Vd79)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(subst,[],[refute_0_7:[bind(Vd78,$fot(vmul(vd436,vplus(vd437,vd439)))),bind(Vd79,$fot(vd436))]]) ).
cnf(refute_0_9,plain,
( vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vd436,vmul(vd436,vplus(vd437,vd439)))
| vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)
| vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd436,vplus(vd437,vd439)),vd436),vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)) ),[0],$fot(vplus(vd436,vmul(vd436,vplus(vd437,vd439))))]]) ).
cnf(refute_0_10,plain,
( vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)
| vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vplus(vd437,vd439)),vd436),vplus(vd436,vmul(vd436,vplus(vd437,vd439)))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
vplus(vmul(vd436,vd439),vd436) = vplus(vd436,vmul(vd436,vd439)),
inference(subst,[],[refute_0_7:[bind(Vd78,$fot(vmul(vd436,vd439))),bind(Vd79,$fot(vd436))]]) ).
cnf(refute_0_12,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
introduced(tautology,[refl,[$fot(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)))]]) ).
cnf(refute_0_13,plain,
( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))
| vplus(vmul(vd436,vd439),vd436) != vplus(vd436,vmul(vd436,vd439))
| vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) ),[1,1],$fot(vplus(vd436,vmul(vd436,vd439)))]]) ).
cnf(refute_0_14,plain,
( vplus(vmul(vd436,vd439),vd436) != vplus(vd436,vmul(vd436,vd439))
| vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd439),vd436),vplus(vd436,vmul(vd436,vd439))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_17,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(subst,[],[refute_0_16:[bind(Vd46,$fot(vmul(vd436,vd437))),bind(Vd47,$fot(vmul(vd436,vd439))),bind(Vd48,$fot(vd436))]]) ).
cnf(refute_0_18,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_5,refute_0_18]) ).
cnf(refute_0_20,plain,
( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436))),bind(Y,$fot(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)))),bind(Z,$fot(vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))))]]) ).
cnf(refute_0_21,plain,
( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) )],[refute_0_15,refute_0_21]) ).
cnf(refute_0_23,plain,
( vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vplus(vd436,vmul(vd436,vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) ),[0],$fot(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436))]]) ).
cnf(refute_0_24,plain,
( vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)
| vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)
| vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vd436,vmul(vd436,vplus(vd437,vd439))),vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)) )],[refute_0_10,refute_0_24]) ).
cnf(refute_0_26,plain,
vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vplus(vd437,vd439)),vd436),vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)) )],[refute_0_1,refute_0_25]) ).
cnf(refute_0_27,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_28,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vplus(vd437,vd439)),vd436)
| vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vd436,vmul(vd436,vplus(vd437,vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vd436,vmul(vd436,vplus(vd437,vd439)))) ),[0],$fot(vplus(vmul(vd436,vplus(vd437,vd439)),vd436))]]) ).
cnf(refute_0_29,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vplus(vd437,vd439)),vd436)
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vplus(vd437,vd439)),vd436),vplus(vd436,vmul(vd436,vplus(vd437,vd439)))) )],[refute_0_8,refute_0_28]) ).
cnf(refute_0_30,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vmul(vd436,vplus(vd437,vd439)),vd436)) )],[refute_0_27,refute_0_29]) ).
cnf(refute_0_31,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vd436,vmul(vd436,vplus(vd437,vd439)))
| vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(vmul(vd436,vsucc(vplus(vd437,vd439))))),bind(Y,$fot(vplus(vd436,vmul(vd436,vplus(vd437,vd439)))))]]) ).
cnf(refute_0_32,plain,
vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))),
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vd436,vmul(vd436,vplus(vd437,vd439)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vd436,vmul(vd436,vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) ),[0],$fot(vmul(vd436,vsucc(vplus(vd437,vd439))))]]) ).
cnf(refute_0_34,plain,
( vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vd436,vmul(vd436,vplus(vd437,vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(resolve,[$cnf( $equal(vplus(vd436,vmul(vd436,vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) )],[refute_0_26,refute_0_34]) ).
cnf(refute_0_36,plain,
vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_37,plain,
vplus(vmul(Vd396,Vd397),Vd396) = vplus(Vd396,vmul(Vd396,Vd397)),
inference(subst,[],[refute_0_7:[bind(Vd78,$fot(vmul(Vd396,Vd397))),bind(Vd79,$fot(Vd396))]]) ).
cnf(refute_0_38,plain,
( vmul(Vd396,vsucc(Vd397)) != vplus(vmul(Vd396,Vd397),Vd396)
| vplus(vmul(Vd396,Vd397),Vd396) != vplus(Vd396,vmul(Vd396,Vd397))
| vmul(Vd396,vsucc(Vd397)) = vplus(Vd396,vmul(Vd396,Vd397)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(Vd396,vsucc(Vd397)),vplus(Vd396,vmul(Vd396,Vd397))) ),[0],$fot(vplus(vmul(Vd396,Vd397),Vd396))]]) ).
cnf(refute_0_39,plain,
( vmul(Vd396,vsucc(Vd397)) != vplus(vmul(Vd396,Vd397),Vd396)
| vmul(Vd396,vsucc(Vd397)) = vplus(Vd396,vmul(Vd396,Vd397)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(Vd396,Vd397),Vd396),vplus(Vd396,vmul(Vd396,Vd397))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
vmul(Vd396,vsucc(Vd397)) = vplus(Vd396,vmul(Vd396,Vd397)),
inference(resolve,[$cnf( $equal(vmul(Vd396,vsucc(Vd397)),vplus(vmul(Vd396,Vd397),Vd396)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( vmul(Vd396,vsucc(Vd397)) != vplus(Vd396,vmul(Vd396,Vd397))
| vplus(Vd396,vmul(Vd396,Vd397)) = vmul(Vd396,vsucc(Vd397)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(vmul(Vd396,vsucc(Vd397)))),bind(Y,$fot(vplus(Vd396,vmul(Vd396,Vd397))))]]) ).
cnf(refute_0_42,plain,
vplus(Vd396,vmul(Vd396,Vd397)) = vmul(Vd396,vsucc(Vd397)),
inference(resolve,[$cnf( $equal(vmul(Vd396,vsucc(Vd397)),vplus(Vd396,vmul(Vd396,Vd397))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
vplus(vd436,vmul(vd436,vd439)) = vmul(vd436,vsucc(vd439)),
inference(subst,[],[refute_0_42:[bind(Vd396,$fot(vd436)),bind(Vd397,$fot(vd439))]]) ).
cnf(refute_0_44,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
introduced(tautology,[refl,[$fot(vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))))]]) ).
cnf(refute_0_45,plain,
( vplus(vd436,vmul(vd436,vd439)) != vmul(vd436,vsucc(vd439))
| vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) ),[1,1],$fot(vmul(vd436,vsucc(vd439)))]]) ).
cnf(refute_0_46,plain,
( vplus(vd436,vmul(vd436,vd439)) != vmul(vd436,vsucc(vd439))
| vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(resolve,[$cnf( $equal(vplus(vd436,vmul(vd436,vd439)),vmul(vd436,vsucc(vd439))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) ),[0],$fot(vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))))]]) ).
cnf(refute_0_49,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) )],[refute_0_35,refute_0_49]) ).
cnf(refute_0_51,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(vmul(vd436,vsucc(vplus(vd437,vd439))))),bind(Y,$fot(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))))]]) ).
cnf(refute_0_52,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))),
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( vplus(vd436,vmul(vd436,vd439)) != vmul(vd436,vsucc(vd439))
| vplus(vmul(vd436,vd439),vd436) != vplus(vd436,vmul(vd436,vd439))
| vplus(vmul(vd436,vd439),vd436) = vmul(vd436,vsucc(vd439)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(vplus(vmul(vd436,vd439),vd436))),bind(Y,$fot(vplus(vd436,vmul(vd436,vd439)))),bind(Z,$fot(vmul(vd436,vsucc(vd439))))]]) ).
cnf(refute_0_54,plain,
( vplus(vd436,vmul(vd436,vd439)) != vmul(vd436,vsucc(vd439))
| vplus(vmul(vd436,vd439),vd436) = vmul(vd436,vsucc(vd439)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd439),vd436),vplus(vd436,vmul(vd436,vd439))) )],[refute_0_11,refute_0_53]) ).
cnf(refute_0_55,plain,
vplus(vmul(vd436,vd439),vd436) = vmul(vd436,vsucc(vd439)),
inference(resolve,[$cnf( $equal(vplus(vd436,vmul(vd436,vd439)),vmul(vd436,vsucc(vd439))) )],[refute_0_43,refute_0_54]) ).
cnf(refute_0_56,plain,
( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))
| vplus(vmul(vd436,vd439),vd436) != vmul(vd436,vsucc(vd439))
| vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) ),[1,1],$fot(vmul(vd436,vsucc(vd439)))]]) ).
cnf(refute_0_57,plain,
( vplus(vmul(vd436,vd439),vd436) != vmul(vd436,vsucc(vd439))
| vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) )],[refute_0_12,refute_0_56]) ).
cnf(refute_0_58,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd439),vd436),vmul(vd436,vsucc(vd439))) )],[refute_0_55,refute_0_57]) ).
cnf(refute_0_59,plain,
( vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vmul(vd436,vsucc(vplus(vd437,vd439))) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)))),bind(Y,$fot(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))))),bind(Z,$fot(vmul(vd436,vsucc(vplus(vd437,vd439)))))]]) ).
cnf(refute_0_60,plain,
( vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vmul(vd436,vsucc(vplus(vd437,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vmul(vd436,vsucc(vplus(vd437,vd439))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))) )],[refute_0_52,refute_0_60]) ).
cnf(refute_0_62,plain,
( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vmul(vd436,vsucc(vplus(vd437,vd439))) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436))),bind(Y,$fot(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)))),bind(Z,$fot(vmul(vd436,vsucc(vplus(vd437,vd439)))))]]) ).
cnf(refute_0_63,plain,
( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vmul(vd436,vsucc(vplus(vd437,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) )],[refute_0_17,refute_0_62]) ).
cnf(refute_0_64,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vmul(vd436,vsucc(vplus(vd437,vd439))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vmul(vd436,vsucc(vplus(vd437,vd439)))) )],[refute_0_61,refute_0_63]) ).
cnf(refute_0_65,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vmul(vd436,vsucc(vplus(vd437,vd439)))) ),[1],$fot(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)))]]) ).
cnf(refute_0_66,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vmul(vd436,vsucc(vplus(vd437,vd439)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) ),[1],$fot(vmul(vd436,vsucc(vplus(vd437,vd439))))]]) ).
cnf(refute_0_68,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vmul(vd436,vsucc(vplus(vd437,vd439)))) )],[refute_0_61,refute_0_67]) ).
cnf(refute_0_69,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) ),
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) )],[refute_0_68,refute_0_66]) ).
cnf(refute_0_70,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439))),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) )],[refute_0_69,refute_0_0]) ).
cnf(refute_0_71,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))),
introduced(tautology,[refl,[$fot(vmul(vd436,vsucc(vplus(vd437,vd439))))]]) ).
cnf(refute_0_72,plain,
$false,
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))) )],[refute_0_71,refute_0_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Fri Jul 8 01:45:26 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.38
%------------------------------------------------------------------------------