TSTP Solution File: NUM846+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM846+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 12:30:54 EDT 2022
% Result : Theorem 54.51s 54.76s
% Output : CNFRefutation 54.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 34
% Syntax : Number of formulae : 167 ( 90 unt; 0 def)
% Number of atoms : 272 ( 271 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 211 ( 106 ~; 100 |; 4 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 291 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('holds(286, 441, 2)',conjecture,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ).
fof('holds(285, 440, 0)',axiom,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)) ).
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(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('ass(cond(6, 0), 0)',axiom,
! [Vd7,Vd8] :
( Vd7 != Vd8
=> vsucc(Vd7) != vsucc(Vd8) ) ).
fof(subgoal_0,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(strip,[],['holds(286, 441, 2)']) ).
fof(negate_0_0,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Vd7,Vd8] :
( vsucc(Vd7) != vsucc(Vd8)
| Vd7 = Vd8 ),
inference(canonicalize,[],['ass(cond(6, 0), 0)']) ).
fof(normalize_0_1,plain,
! [Vd7,Vd8] :
( vsucc(Vd7) != vsucc(Vd8)
| Vd7 = Vd8 ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
inference(canonicalize,[],['ass(cond(52, 0), 0)']) ).
fof(normalize_0_3,plain,
! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],['ass(cond(61, 0), 0)']) ).
fof(normalize_0_5,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
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,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],['ass(cond(33, 0), 0)']) ).
fof(normalize_0_10,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
inference(canonicalize,[],['holds(285, 440, 0)']) ).
fof(normalize_0_12,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_13,plain,
! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( vsucc(Vd7) != vsucc(Vd8)
| Vd7 = Vd8 ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( vsucc(vplus(X_25,vplus(X_24,Vd69))) != vsucc(X_78)
| vplus(X_25,vplus(X_24,Vd69)) = X_78 ),
inference(subst,[],[refute_0_0:[bind(Vd7,$fot(vplus(X_25,vplus(X_24,Vd69)))),bind(Vd8,$fot(X_78))]]) ).
cnf(refute_0_2,plain,
vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
vplus(vsucc(vplus(X_25,X_24)),Vd69) = vsucc(vplus(vplus(X_25,X_24),Vd69)),
inference(subst,[],[refute_0_2:[bind(Vd68,$fot(vplus(X_25,X_24)))]]) ).
cnf(refute_0_4,plain,
vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
vplus(vsucc(Vd68),Vd69) = vplus(Vd69,vsucc(Vd68)),
inference(subst,[],[refute_0_4:[bind(Vd78,$fot(Vd69)),bind(Vd79,$fot(vsucc(Vd68)))]]) ).
cnf(refute_0_6,plain,
( vplus(vsucc(Vd68),Vd69) != vplus(Vd69,vsucc(Vd68))
| vplus(vsucc(Vd68),Vd69) != vsucc(vplus(Vd68,Vd69))
| vplus(Vd69,vsucc(Vd68)) = vsucc(vplus(Vd68,Vd69)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vsucc(Vd68),Vd69),vsucc(vplus(Vd68,Vd69))) ),[0],$fot(vplus(Vd69,vsucc(Vd68)))]]) ).
cnf(refute_0_7,plain,
( vplus(vsucc(Vd68),Vd69) != vsucc(vplus(Vd68,Vd69))
| vplus(Vd69,vsucc(Vd68)) = vsucc(vplus(Vd68,Vd69)) ),
inference(resolve,[$cnf( $equal(vplus(vsucc(Vd68),Vd69),vplus(Vd69,vsucc(Vd68))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
vplus(Vd69,vsucc(Vd68)) = vsucc(vplus(Vd68,Vd69)),
inference(resolve,[$cnf( $equal(vplus(vsucc(Vd68),Vd69),vsucc(vplus(Vd68,Vd69))) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
vplus(Vd69,vsucc(Vd68)) = vsucc(vplus(Vd69,Vd68)),
inference(subst,[],[refute_0_9:[bind(Vd42,$fot(Vd69)),bind(Vd43,$fot(Vd68))]]) ).
cnf(refute_0_11,plain,
( vplus(Vd69,vsucc(Vd68)) != vsucc(vplus(Vd68,Vd69))
| vplus(Vd69,vsucc(Vd68)) != vsucc(vplus(Vd69,Vd68))
| vsucc(vplus(Vd69,Vd68)) = vsucc(vplus(Vd68,Vd69)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(Vd69,vsucc(Vd68)),vsucc(vplus(Vd68,Vd69))) ),[0],$fot(vsucc(vplus(Vd69,Vd68)))]]) ).
cnf(refute_0_12,plain,
( vplus(Vd69,vsucc(Vd68)) != vsucc(vplus(Vd68,Vd69))
| vsucc(vplus(Vd69,Vd68)) = vsucc(vplus(Vd68,Vd69)) ),
inference(resolve,[$cnf( $equal(vplus(Vd69,vsucc(Vd68)),vsucc(vplus(Vd69,Vd68))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
vsucc(vplus(Vd69,Vd68)) = vsucc(vplus(Vd68,Vd69)),
inference(resolve,[$cnf( $equal(vplus(Vd69,vsucc(Vd68)),vsucc(vplus(Vd68,Vd69))) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
vsucc(vplus(X_25,X_24)) = vsucc(vplus(X_24,X_25)),
inference(subst,[],[refute_0_13:[bind(Vd68,$fot(X_24)),bind(Vd69,$fot(X_25))]]) ).
cnf(refute_0_15,plain,
( vplus(vsucc(vplus(X_25,X_24)),Vd69) != vsucc(vplus(vplus(X_25,X_24),Vd69))
| vsucc(vplus(X_25,X_24)) != vsucc(vplus(X_24,X_25))
| vplus(vsucc(vplus(X_24,X_25)),Vd69) = vsucc(vplus(vplus(X_25,X_24),Vd69)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vsucc(vplus(X_25,X_24)),Vd69),vsucc(vplus(vplus(X_25,X_24),Vd69))) ),[0,0],$fot(vsucc(vplus(X_24,X_25)))]]) ).
cnf(refute_0_16,plain,
( vplus(vsucc(vplus(X_25,X_24)),Vd69) != vsucc(vplus(vplus(X_25,X_24),Vd69))
| vplus(vsucc(vplus(X_24,X_25)),Vd69) = vsucc(vplus(vplus(X_25,X_24),Vd69)) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(X_25,X_24)),vsucc(vplus(X_24,X_25))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
vplus(vsucc(vplus(X_24,X_25)),Vd69) = vsucc(vplus(vplus(X_25,X_24),Vd69)),
inference(resolve,[$cnf( $equal(vplus(vsucc(vplus(X_25,X_24)),Vd69),vsucc(vplus(vplus(X_25,X_24),Vd69))) )],[refute_0_3,refute_0_16]) ).
cnf(refute_0_18,plain,
vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_19,plain,
vplus(vplus(X_24,X_25),Vd69) = vplus(X_24,vplus(X_25,Vd69)),
inference(subst,[],[refute_0_18:[bind(Vd46,$fot(X_24)),bind(Vd47,$fot(X_25)),bind(Vd48,$fot(Vd69))]]) ).
cnf(refute_0_20,plain,
vsucc(vplus(vplus(X_24,X_25),Vd69)) = vsucc(vplus(vplus(X_24,X_25),Vd69)),
introduced(tautology,[refl,[$fot(vsucc(vplus(vplus(X_24,X_25),Vd69)))]]) ).
cnf(refute_0_21,plain,
( vplus(vplus(X_24,X_25),Vd69) != vplus(X_24,vplus(X_25,Vd69))
| vsucc(vplus(vplus(X_24,X_25),Vd69)) != vsucc(vplus(vplus(X_24,X_25),Vd69))
| vsucc(vplus(vplus(X_24,X_25),Vd69)) = vsucc(vplus(X_24,vplus(X_25,Vd69))) ),
introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vplus(X_24,X_25),Vd69)),vsucc(vplus(vplus(X_24,X_25),Vd69))) ),[1,0],$fot(vplus(X_24,vplus(X_25,Vd69)))]]) ).
cnf(refute_0_22,plain,
( vplus(vplus(X_24,X_25),Vd69) != vplus(X_24,vplus(X_25,Vd69))
| vsucc(vplus(vplus(X_24,X_25),Vd69)) = vsucc(vplus(X_24,vplus(X_25,Vd69))) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vplus(X_24,X_25),Vd69)),vsucc(vplus(vplus(X_24,X_25),Vd69))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
vsucc(vplus(vplus(X_24,X_25),Vd69)) = vsucc(vplus(X_24,vplus(X_25,Vd69))),
inference(resolve,[$cnf( $equal(vplus(vplus(X_24,X_25),Vd69),vplus(X_24,vplus(X_25,Vd69))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
vplus(vsucc(vplus(X_24,X_25)),Vd69) = vsucc(vplus(vplus(X_24,X_25),Vd69)),
inference(subst,[],[refute_0_2:[bind(Vd68,$fot(vplus(X_24,X_25)))]]) ).
cnf(refute_0_25,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_26,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_27,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_29,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( vplus(vsucc(vplus(X_24,X_25)),Vd69) != vsucc(vplus(vplus(X_24,X_25),Vd69))
| vsucc(vplus(vplus(X_24,X_25),Vd69)) != vsucc(vplus(X_24,vplus(X_25,Vd69)))
| vplus(vsucc(vplus(X_24,X_25)),Vd69) = vsucc(vplus(X_24,vplus(X_25,Vd69))) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(vplus(vsucc(vplus(X_24,X_25)),Vd69))),bind(Y,$fot(vsucc(vplus(vplus(X_24,X_25),Vd69)))),bind(Z,$fot(vsucc(vplus(X_24,vplus(X_25,Vd69)))))]]) ).
cnf(refute_0_31,plain,
( vsucc(vplus(vplus(X_24,X_25),Vd69)) != vsucc(vplus(X_24,vplus(X_25,Vd69)))
| vplus(vsucc(vplus(X_24,X_25)),Vd69) = vsucc(vplus(X_24,vplus(X_25,Vd69))) ),
inference(resolve,[$cnf( $equal(vplus(vsucc(vplus(X_24,X_25)),Vd69),vsucc(vplus(vplus(X_24,X_25),Vd69))) )],[refute_0_24,refute_0_30]) ).
cnf(refute_0_32,plain,
vplus(vsucc(vplus(X_24,X_25)),Vd69) = vsucc(vplus(X_24,vplus(X_25,Vd69))),
inference(resolve,[$cnf( $equal(vsucc(vplus(vplus(X_24,X_25),Vd69)),vsucc(vplus(X_24,vplus(X_25,Vd69)))) )],[refute_0_23,refute_0_31]) ).
cnf(refute_0_33,plain,
( vplus(vsucc(vplus(X_24,X_25)),Vd69) != vsucc(vplus(X_24,vplus(X_25,Vd69)))
| vplus(vsucc(vplus(X_24,X_25)),Vd69) != vsucc(vplus(vplus(X_25,X_24),Vd69))
| vsucc(vplus(X_24,vplus(X_25,Vd69))) = vsucc(vplus(vplus(X_25,X_24),Vd69)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vsucc(vplus(X_24,X_25)),Vd69),vsucc(vplus(vplus(X_25,X_24),Vd69))) ),[0],$fot(vsucc(vplus(X_24,vplus(X_25,Vd69))))]]) ).
cnf(refute_0_34,plain,
( vplus(vsucc(vplus(X_24,X_25)),Vd69) != vsucc(vplus(vplus(X_25,X_24),Vd69))
| vsucc(vplus(X_24,vplus(X_25,Vd69))) = vsucc(vplus(vplus(X_25,X_24),Vd69)) ),
inference(resolve,[$cnf( $equal(vplus(vsucc(vplus(X_24,X_25)),Vd69),vsucc(vplus(X_24,vplus(X_25,Vd69)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
vplus(vplus(X_25,X_24),Vd69) = vplus(X_25,vplus(X_24,Vd69)),
inference(subst,[],[refute_0_18:[bind(Vd46,$fot(X_25)),bind(Vd47,$fot(X_24)),bind(Vd48,$fot(Vd69))]]) ).
cnf(refute_0_36,plain,
vsucc(vplus(vplus(X_25,X_24),Vd69)) = vsucc(vplus(vplus(X_25,X_24),Vd69)),
introduced(tautology,[refl,[$fot(vsucc(vplus(vplus(X_25,X_24),Vd69)))]]) ).
cnf(refute_0_37,plain,
( vplus(vplus(X_25,X_24),Vd69) != vplus(X_25,vplus(X_24,Vd69))
| vsucc(vplus(vplus(X_25,X_24),Vd69)) != vsucc(vplus(vplus(X_25,X_24),Vd69))
| vsucc(vplus(vplus(X_25,X_24),Vd69)) = vsucc(vplus(X_25,vplus(X_24,Vd69))) ),
introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vplus(X_25,X_24),Vd69)),vsucc(vplus(vplus(X_25,X_24),Vd69))) ),[1,0],$fot(vplus(X_25,vplus(X_24,Vd69)))]]) ).
cnf(refute_0_38,plain,
( vplus(vplus(X_25,X_24),Vd69) != vplus(X_25,vplus(X_24,Vd69))
| vsucc(vplus(vplus(X_25,X_24),Vd69)) = vsucc(vplus(X_25,vplus(X_24,Vd69))) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vplus(X_25,X_24),Vd69)),vsucc(vplus(vplus(X_25,X_24),Vd69))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
vsucc(vplus(vplus(X_25,X_24),Vd69)) = vsucc(vplus(X_25,vplus(X_24,Vd69))),
inference(resolve,[$cnf( $equal(vplus(vplus(X_25,X_24),Vd69),vplus(X_25,vplus(X_24,Vd69))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
( vsucc(vplus(X_24,vplus(X_25,Vd69))) != vsucc(vplus(vplus(X_25,X_24),Vd69))
| vsucc(vplus(vplus(X_25,X_24),Vd69)) != vsucc(vplus(X_25,vplus(X_24,Vd69)))
| vsucc(vplus(X_24,vplus(X_25,Vd69))) = vsucc(vplus(X_25,vplus(X_24,Vd69))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vsucc(vplus(X_24,vplus(X_25,Vd69))),vsucc(vplus(X_25,vplus(X_24,Vd69)))) ),[0],$fot(vsucc(vplus(vplus(X_25,X_24),Vd69)))]]) ).
cnf(refute_0_41,plain,
( vsucc(vplus(X_24,vplus(X_25,Vd69))) != vsucc(vplus(vplus(X_25,X_24),Vd69))
| vsucc(vplus(X_24,vplus(X_25,Vd69))) = vsucc(vplus(X_25,vplus(X_24,Vd69))) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vplus(X_25,X_24),Vd69)),vsucc(vplus(X_25,vplus(X_24,Vd69)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( vplus(vsucc(vplus(X_24,X_25)),Vd69) != vsucc(vplus(vplus(X_25,X_24),Vd69))
| vsucc(vplus(X_24,vplus(X_25,Vd69))) = vsucc(vplus(X_25,vplus(X_24,Vd69))) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(X_24,vplus(X_25,Vd69))),vsucc(vplus(vplus(X_25,X_24),Vd69))) )],[refute_0_34,refute_0_41]) ).
cnf(refute_0_43,plain,
vsucc(vplus(X_24,vplus(X_25,Vd69))) = vsucc(vplus(X_25,vplus(X_24,Vd69))),
inference(resolve,[$cnf( $equal(vplus(vsucc(vplus(X_24,X_25)),Vd69),vsucc(vplus(vplus(X_25,X_24),Vd69))) )],[refute_0_17,refute_0_42]) ).
cnf(refute_0_44,plain,
( vsucc(vplus(X_24,vplus(X_25,Vd69))) != vsucc(vplus(X_25,vplus(X_24,Vd69)))
| vsucc(vplus(X_25,vplus(X_24,Vd69))) = vsucc(vplus(X_24,vplus(X_25,Vd69))) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vsucc(vplus(X_24,vplus(X_25,Vd69))))),bind(Y,$fot(vsucc(vplus(X_25,vplus(X_24,Vd69)))))]]) ).
cnf(refute_0_45,plain,
vsucc(vplus(X_25,vplus(X_24,Vd69))) = vsucc(vplus(X_24,vplus(X_25,Vd69))),
inference(resolve,[$cnf( $equal(vsucc(vplus(X_24,vplus(X_25,Vd69))),vsucc(vplus(X_25,vplus(X_24,Vd69)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( vsucc(vplus(X_24,vplus(X_25,Vd69))) != vsucc(X_78)
| vsucc(vplus(X_25,vplus(X_24,Vd69))) != vsucc(vplus(X_24,vplus(X_25,Vd69)))
| vsucc(vplus(X_25,vplus(X_24,Vd69))) = vsucc(X_78) ),
introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(X_25,vplus(X_24,Vd69))),vsucc(vplus(X_24,vplus(X_25,Vd69)))) ),[1],$fot(vsucc(X_78))]]) ).
cnf(refute_0_47,plain,
( vsucc(vplus(X_24,vplus(X_25,Vd69))) != vsucc(X_78)
| vsucc(vplus(X_25,vplus(X_24,Vd69))) = vsucc(X_78) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(X_25,vplus(X_24,Vd69))),vsucc(vplus(X_24,vplus(X_25,Vd69)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( vsucc(vplus(X_24,vplus(X_25,Vd69))) != vsucc(X_78)
| vplus(X_25,vplus(X_24,Vd69)) = X_78 ),
inference(resolve,[$cnf( $equal(vsucc(vplus(X_25,vplus(X_24,Vd69))),vsucc(X_78)) )],[refute_0_47,refute_0_1]) ).
cnf(refute_0_49,plain,
( vsucc(vplus(X_24,vplus(X_25,Vd69))) != vsucc(vplus(X_24,vplus(X_25,Vd69)))
| vplus(X_25,vplus(X_24,Vd69)) = vplus(X_24,vplus(X_25,Vd69)) ),
inference(subst,[],[refute_0_48:[bind(X_78,$fot(vplus(X_24,vplus(X_25,Vd69))))]]) ).
cnf(refute_0_50,plain,
vsucc(vplus(X_24,vplus(X_25,Vd69))) = vsucc(vplus(X_24,vplus(X_25,Vd69))),
introduced(tautology,[refl,[$fot(vsucc(vplus(X_24,vplus(X_25,Vd69))))]]) ).
cnf(refute_0_51,plain,
vplus(X_25,vplus(X_24,Vd69)) = vplus(X_24,vplus(X_25,Vd69)),
inference(resolve,[$cnf( $equal(vsucc(vplus(X_24,vplus(X_25,Vd69))),vsucc(vplus(X_24,vplus(X_25,Vd69)))) )],[refute_0_50,refute_0_49]) ).
cnf(refute_0_52,plain,
vplus(X_81,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vplus(X_81,vmul(vd436,vd439))),
inference(subst,[],[refute_0_51:[bind(Vd69,$fot(vmul(vd436,vd439))),bind(X_24,$fot(vmul(vd436,vd437))),bind(X_25,$fot(X_81))]]) ).
cnf(refute_0_53,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_54,plain,
( vmul(vd436,vplus(vd437,vd439)) != vplus(vmul(vd436,vd437),vmul(vd436,vd439))
| vplus(vmul(vd436,vd437),vmul(vd436,vd439)) = vmul(vd436,vplus(vd437,vd439)) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vmul(vd436,vplus(vd437,vd439)))),bind(Y,$fot(vplus(vmul(vd436,vd437),vmul(vd436,vd439))))]]) ).
cnf(refute_0_55,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vd439)) = vmul(vd436,vplus(vd437,vd439)),
inference(resolve,[$cnf( $equal(vmul(vd436,vplus(vd437,vd439)),vplus(vmul(vd436,vd437),vmul(vd436,vd439))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( vplus(X_81,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vplus(X_81,vmul(vd436,vd439)))
| vplus(vmul(vd436,vd437),vmul(vd436,vd439)) != vmul(vd436,vplus(vd437,vd439))
| vplus(X_81,vmul(vd436,vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(X_81,vmul(vd436,vd439))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(X_81,vplus(vmul(vd436,vd437),vmul(vd436,vd439))),vplus(vmul(vd436,vd437),vplus(X_81,vmul(vd436,vd439)))) ),[0,1],$fot(vmul(vd436,vplus(vd437,vd439)))]]) ).
cnf(refute_0_57,plain,
( vplus(X_81,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vplus(X_81,vmul(vd436,vd439)))
| vplus(X_81,vmul(vd436,vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(X_81,vmul(vd436,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vmul(vd436,vplus(vd437,vd439))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
vplus(X_81,vmul(vd436,vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(X_81,vmul(vd436,vd439))),
inference(resolve,[$cnf( $equal(vplus(X_81,vplus(vmul(vd436,vd437),vmul(vd436,vd439))),vplus(vmul(vd436,vd437),vplus(X_81,vmul(vd436,vd439)))) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(subst,[],[refute_0_58:[bind(X_81,$fot(vd436))]]) ).
cnf(refute_0_60,plain,
vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_61,plain,
( vplus(Vd79,Vd78) != vplus(Vd78,Vd79)
| vplus(Vd78,Vd79) = vplus(Vd79,Vd78) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vplus(Vd79,Vd78))),bind(Y,$fot(vplus(Vd78,Vd79)))]]) ).
cnf(refute_0_62,plain,
vplus(Vd78,Vd79) = vplus(Vd79,Vd78),
inference(resolve,[$cnf( $equal(vplus(Vd79,Vd78),vplus(Vd78,Vd79)) )],[refute_0_4,refute_0_61]) ).
cnf(refute_0_63,plain,
vplus(vmul(Vd396,Vd397),Vd396) = vplus(Vd396,vmul(Vd396,Vd397)),
inference(subst,[],[refute_0_62:[bind(Vd78,$fot(vmul(Vd396,Vd397))),bind(Vd79,$fot(Vd396))]]) ).
cnf(refute_0_64,plain,
( vmul(Vd396,vsucc(Vd397)) != vplus(vmul(Vd396,Vd397),Vd396)
| vplus(vmul(Vd396,Vd397),Vd396) != vplus(Vd396,vmul(Vd396,Vd397))
| vmul(Vd396,vsucc(Vd397)) = vplus(Vd396,vmul(Vd396,Vd397)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(Vd396,vsucc(Vd397)),vplus(Vd396,vmul(Vd396,Vd397))) ),[0],$fot(vplus(vmul(Vd396,Vd397),Vd396))]]) ).
cnf(refute_0_65,plain,
( vmul(Vd396,vsucc(Vd397)) != vplus(vmul(Vd396,Vd397),Vd396)
| vmul(Vd396,vsucc(Vd397)) = vplus(Vd396,vmul(Vd396,Vd397)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(Vd396,Vd397),Vd396),vplus(Vd396,vmul(Vd396,Vd397))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
vmul(Vd396,vsucc(Vd397)) = vplus(Vd396,vmul(Vd396,Vd397)),
inference(resolve,[$cnf( $equal(vmul(Vd396,vsucc(Vd397)),vplus(vmul(Vd396,Vd397),Vd396)) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(subst,[],[refute_0_66:[bind(Vd396,$fot(vd436)),bind(Vd397,$fot(vplus(vd437,vd439)))]]) ).
cnf(refute_0_68,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vd436,vmul(vd436,vplus(vd437,vd439)))
| vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vmul(vd436,vsucc(vplus(vd437,vd439))))),bind(Y,$fot(vplus(vd436,vmul(vd436,vplus(vd437,vd439)))))]]) ).
cnf(refute_0_69,plain,
vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vmul(vd436,vsucc(vplus(vd437,vd439))),
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vd436,vmul(vd436,vplus(vd437,vd439)))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) ),
introduced(tautology,[equality,[$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_71,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( $equal(vplus(vd436,vmul(vd436,vplus(vd437,vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(resolve,[$cnf( $equal(vplus(vd436,vmul(vd436,vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) )],[refute_0_59,refute_0_71]) ).
cnf(refute_0_73,plain,
vplus(X_81,vplus(X_80,vmul(X_80,Vd397))) = vplus(X_80,vplus(X_81,vmul(X_80,Vd397))),
inference(subst,[],[refute_0_51:[bind(Vd69,$fot(vmul(X_80,Vd397))),bind(X_24,$fot(X_80)),bind(X_25,$fot(X_81))]]) ).
cnf(refute_0_74,plain,
vmul(X_80,vsucc(Vd397)) = vplus(X_80,vmul(X_80,Vd397)),
inference(subst,[],[refute_0_66:[bind(Vd396,$fot(X_80))]]) ).
cnf(refute_0_75,plain,
( vmul(X_80,vsucc(Vd397)) != vplus(X_80,vmul(X_80,Vd397))
| vplus(X_80,vmul(X_80,Vd397)) = vmul(X_80,vsucc(Vd397)) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vmul(X_80,vsucc(Vd397)))),bind(Y,$fot(vplus(X_80,vmul(X_80,Vd397))))]]) ).
cnf(refute_0_76,plain,
vplus(X_80,vmul(X_80,Vd397)) = vmul(X_80,vsucc(Vd397)),
inference(resolve,[$cnf( $equal(vmul(X_80,vsucc(Vd397)),vplus(X_80,vmul(X_80,Vd397))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( vplus(X_80,vmul(X_80,Vd397)) != vmul(X_80,vsucc(Vd397))
| vplus(X_81,vplus(X_80,vmul(X_80,Vd397))) != vplus(X_80,vplus(X_81,vmul(X_80,Vd397)))
| vplus(X_81,vmul(X_80,vsucc(Vd397))) = vplus(X_80,vplus(X_81,vmul(X_80,Vd397))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(X_81,vplus(X_80,vmul(X_80,Vd397))),vplus(X_80,vplus(X_81,vmul(X_80,Vd397)))) ),[0,1],$fot(vmul(X_80,vsucc(Vd397)))]]) ).
cnf(refute_0_78,plain,
( vplus(X_81,vplus(X_80,vmul(X_80,Vd397))) != vplus(X_80,vplus(X_81,vmul(X_80,Vd397)))
| vplus(X_81,vmul(X_80,vsucc(Vd397))) = vplus(X_80,vplus(X_81,vmul(X_80,Vd397))) ),
inference(resolve,[$cnf( $equal(vplus(X_80,vmul(X_80,Vd397)),vmul(X_80,vsucc(Vd397))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
vplus(X_81,vmul(X_80,vsucc(Vd397))) = vplus(X_80,vplus(X_81,vmul(X_80,Vd397))),
inference(resolve,[$cnf( $equal(vplus(X_81,vplus(X_80,vmul(X_80,Vd397))),vplus(X_80,vplus(X_81,vmul(X_80,Vd397)))) )],[refute_0_73,refute_0_78]) ).
cnf(refute_0_80,plain,
( vplus(X_81,vmul(X_80,vsucc(Vd397))) != vplus(X_80,vplus(X_81,vmul(X_80,Vd397)))
| vplus(X_80,vplus(X_81,vmul(X_80,Vd397))) = vplus(X_81,vmul(X_80,vsucc(Vd397))) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vplus(X_81,vmul(X_80,vsucc(Vd397))))),bind(Y,$fot(vplus(X_80,vplus(X_81,vmul(X_80,Vd397)))))]]) ).
cnf(refute_0_81,plain,
vplus(X_80,vplus(X_81,vmul(X_80,Vd397))) = vplus(X_81,vmul(X_80,vsucc(Vd397))),
inference(resolve,[$cnf( $equal(vplus(X_81,vmul(X_80,vsucc(Vd397))),vplus(X_80,vplus(X_81,vmul(X_80,Vd397)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(subst,[],[refute_0_81:[bind(Vd397,$fot(vd439)),bind(X_80,$fot(vd436)),bind(X_81,$fot(vmul(vd436,vd437)))]]) ).
cnf(refute_0_83,plain,
vplus(Vd79,vplus(X_26,X_27)) = vplus(vplus(X_26,X_27),Vd79),
inference(subst,[],[refute_0_4:[bind(Vd78,$fot(vplus(X_26,X_27)))]]) ).
cnf(refute_0_84,plain,
vplus(vplus(X_26,X_27),Vd79) = vplus(X_26,vplus(X_27,Vd79)),
inference(subst,[],[refute_0_18:[bind(Vd46,$fot(X_26)),bind(Vd47,$fot(X_27)),bind(Vd48,$fot(Vd79))]]) ).
cnf(refute_0_85,plain,
( vplus(Vd79,vplus(X_26,X_27)) != vplus(vplus(X_26,X_27),Vd79)
| vplus(vplus(X_26,X_27),Vd79) != vplus(X_26,vplus(X_27,Vd79))
| vplus(Vd79,vplus(X_26,X_27)) = vplus(X_26,vplus(X_27,Vd79)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vplus(Vd79,vplus(X_26,X_27)),vplus(X_26,vplus(X_27,Vd79))) ),[0],$fot(vplus(vplus(X_26,X_27),Vd79))]]) ).
cnf(refute_0_86,plain,
( vplus(Vd79,vplus(X_26,X_27)) != vplus(vplus(X_26,X_27),Vd79)
| vplus(Vd79,vplus(X_26,X_27)) = vplus(X_26,vplus(X_27,Vd79)) ),
inference(resolve,[$cnf( $equal(vplus(vplus(X_26,X_27),Vd79),vplus(X_26,vplus(X_27,Vd79))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
vplus(Vd79,vplus(X_26,X_27)) = vplus(X_26,vplus(X_27,Vd79)),
inference(resolve,[$cnf( $equal(vplus(Vd79,vplus(X_26,X_27)),vplus(vplus(X_26,X_27),Vd79)) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
vplus(X_24,vplus(X_25,Vd69)) = vplus(X_25,vplus(Vd69,X_24)),
inference(subst,[],[refute_0_87:[bind(Vd79,$fot(X_24)),bind(X_26,$fot(X_25)),bind(X_27,$fot(Vd69))]]) ).
cnf(refute_0_89,plain,
( vplus(X_24,vplus(X_25,Vd69)) != vplus(X_25,vplus(Vd69,X_24))
| vplus(X_25,vplus(X_24,Vd69)) != vplus(X_24,vplus(X_25,Vd69))
| vplus(X_25,vplus(X_24,Vd69)) = vplus(X_25,vplus(Vd69,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(X_25,vplus(X_24,Vd69)),vplus(X_24,vplus(X_25,Vd69))) ),[1],$fot(vplus(X_25,vplus(Vd69,X_24)))]]) ).
cnf(refute_0_90,plain,
( vplus(X_25,vplus(X_24,Vd69)) != vplus(X_24,vplus(X_25,Vd69))
| vplus(X_25,vplus(X_24,Vd69)) = vplus(X_25,vplus(Vd69,X_24)) ),
inference(resolve,[$cnf( $equal(vplus(X_24,vplus(X_25,Vd69)),vplus(X_25,vplus(Vd69,X_24))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
vplus(X_25,vplus(X_24,Vd69)) = vplus(X_25,vplus(Vd69,X_24)),
inference(resolve,[$cnf( $equal(vplus(X_25,vplus(X_24,Vd69)),vplus(X_24,vplus(X_25,Vd69))) )],[refute_0_51,refute_0_90]) ).
cnf(refute_0_92,plain,
( vplus(X_25,vplus(X_24,Vd69)) != vplus(X_25,vplus(Vd69,X_24))
| vplus(X_25,vplus(Vd69,X_24)) = vplus(X_25,vplus(X_24,Vd69)) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vplus(X_25,vplus(X_24,Vd69)))),bind(Y,$fot(vplus(X_25,vplus(Vd69,X_24))))]]) ).
cnf(refute_0_93,plain,
vplus(X_25,vplus(Vd69,X_24)) = vplus(X_25,vplus(X_24,Vd69)),
inference(resolve,[$cnf( $equal(vplus(X_25,vplus(X_24,Vd69)),vplus(X_25,vplus(Vd69,X_24))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))) = vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))),
inference(subst,[],[refute_0_93:[bind(Vd69,$fot(vmul(vd436,vd439))),bind(X_24,$fot(vmul(vd436,vd437))),bind(X_25,$fot(vd436))]]) ).
cnf(refute_0_95,plain,
( vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))) != vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439)))
| vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))))),bind(Y,$fot(vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))))),bind(Z,$fot(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))))]]) ).
cnf(refute_0_96,plain,
( vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))),vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(resolve,[$cnf( $equal(vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd436,vd439))),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) )],[refute_0_82,refute_0_96]) ).
cnf(refute_0_98,plain,
vplus(X_81,vplus(X_80,X_79)) = vplus(X_80,vplus(X_81,X_79)),
inference(subst,[],[refute_0_51:[bind(Vd69,$fot(X_79)),bind(X_24,$fot(X_80)),bind(X_25,$fot(X_81))]]) ).
cnf(refute_0_99,plain,
vplus(X_79,X_80) = vplus(X_80,X_79),
inference(subst,[],[refute_0_4:[bind(Vd78,$fot(X_80)),bind(Vd79,$fot(X_79))]]) ).
cnf(refute_0_100,plain,
( vplus(X_79,X_80) != vplus(X_80,X_79)
| vplus(X_80,X_79) = vplus(X_79,X_80) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vplus(X_79,X_80))),bind(Y,$fot(vplus(X_80,X_79)))]]) ).
cnf(refute_0_101,plain,
vplus(X_80,X_79) = vplus(X_79,X_80),
inference(resolve,[$cnf( $equal(vplus(X_79,X_80),vplus(X_80,X_79)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( vplus(X_80,X_79) != vplus(X_79,X_80)
| vplus(X_81,vplus(X_80,X_79)) != vplus(X_80,vplus(X_81,X_79))
| vplus(X_81,vplus(X_79,X_80)) = vplus(X_80,vplus(X_81,X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(X_81,vplus(X_80,X_79)),vplus(X_80,vplus(X_81,X_79))) ),[0,1],$fot(vplus(X_79,X_80))]]) ).
cnf(refute_0_103,plain,
( vplus(X_81,vplus(X_80,X_79)) != vplus(X_80,vplus(X_81,X_79))
| vplus(X_81,vplus(X_79,X_80)) = vplus(X_80,vplus(X_81,X_79)) ),
inference(resolve,[$cnf( $equal(vplus(X_80,X_79),vplus(X_79,X_80)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
vplus(X_81,vplus(X_79,X_80)) = vplus(X_80,vplus(X_81,X_79)),
inference(resolve,[$cnf( $equal(vplus(X_81,vplus(X_80,X_79)),vplus(X_80,vplus(X_81,X_79))) )],[refute_0_98,refute_0_103]) ).
cnf(refute_0_105,plain,
( vplus(X_81,vplus(X_79,X_80)) != vplus(X_80,vplus(X_81,X_79))
| vplus(X_80,vplus(X_81,X_79)) = vplus(X_81,vplus(X_79,X_80)) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vplus(X_81,vplus(X_79,X_80)))),bind(Y,$fot(vplus(X_80,vplus(X_81,X_79))))]]) ).
cnf(refute_0_106,plain,
vplus(X_80,vplus(X_81,X_79)) = vplus(X_81,vplus(X_79,X_80)),
inference(resolve,[$cnf( $equal(vplus(X_81,vplus(X_79,X_80)),vplus(X_80,vplus(X_81,X_79))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))),
inference(subst,[],[refute_0_106:[bind(X_79,$fot(vmul(vd436,vd439))),bind(X_80,$fot(vmul(vd436,vd437))),bind(X_81,$fot(vd436))]]) ).
cnf(refute_0_108,plain,
( vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437)))
| vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))))),bind(Y,$fot(vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))))),bind(Z,$fot(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))))]]) ).
cnf(refute_0_109,plain,
( vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437)))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(resolve,[$cnf( $equal(vplus(vd436,vplus(vmul(vd436,vd439),vmul(vd436,vd437))),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) )],[refute_0_97,refute_0_109]) ).
cnf(refute_0_111,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))
| vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
introduced(tautology,[equality,[$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_112,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( $equal(vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439)))) )],[refute_0_72,refute_0_112]) ).
cnf(refute_0_114,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_115,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(subst,[],[refute_0_62:[bind(Vd78,$fot(vmul(vd436,vplus(vd437,vd439)))),bind(Vd79,$fot(vd436))]]) ).
cnf(refute_0_116,plain,
( vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vd436,vmul(vd436,vplus(vd437,vd439)))
| vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vmul(vd436,vsucc(vplus(vd437,vd439))) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(vplus(vmul(vd436,vplus(vd437,vd439)),vd436))),bind(Y,$fot(vplus(vd436,vmul(vd436,vplus(vd437,vd439))))),bind(Z,$fot(vmul(vd436,vsucc(vplus(vd437,vd439)))))]]) ).
cnf(refute_0_117,plain,
( vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vmul(vd436,vsucc(vplus(vd437,vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vplus(vd437,vd439)),vd436),vplus(vd436,vmul(vd436,vplus(vd437,vd439)))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vmul(vd436,vsucc(vplus(vd437,vd439))),
inference(resolve,[$cnf( $equal(vplus(vd436,vmul(vd436,vplus(vd437,vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))) )],[refute_0_69,refute_0_117]) ).
cnf(refute_0_119,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)
| vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vmul(vd436,vsucc(vplus(vd437,vd439)))
| vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd436,vplus(vd437,vd439)),vd436),vmul(vd436,vsucc(vplus(vd437,vd439)))) ),[1],$fot(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436))]]) ).
cnf(refute_0_120,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)
| vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vplus(vd437,vd439)),vd436),vmul(vd436,vsucc(vplus(vd437,vd439)))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( vmul(Vd396,vsucc(Vd397)) != vplus(Vd396,vmul(Vd396,Vd397))
| vplus(Vd396,vmul(Vd396,Vd397)) = vmul(Vd396,vsucc(Vd397)) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(vmul(Vd396,vsucc(Vd397)))),bind(Y,$fot(vplus(Vd396,vmul(Vd396,Vd397))))]]) ).
cnf(refute_0_122,plain,
vplus(Vd396,vmul(Vd396,Vd397)) = vmul(Vd396,vsucc(Vd397)),
inference(resolve,[$cnf( $equal(vmul(Vd396,vsucc(Vd397)),vplus(Vd396,vmul(Vd396,Vd397))) )],[refute_0_66,refute_0_121]) ).
cnf(refute_0_123,plain,
vplus(vd436,vmul(vd436,vd439)) = vmul(vd436,vsucc(vd439)),
inference(subst,[],[refute_0_122:[bind(Vd396,$fot(vd436)),bind(Vd397,$fot(vd439))]]) ).
cnf(refute_0_124,plain,
vplus(vmul(vd436,vd439),vd436) = vplus(vd436,vmul(vd436,vd439)),
inference(subst,[],[refute_0_62:[bind(Vd78,$fot(vmul(vd436,vd439))),bind(Vd79,$fot(vd436))]]) ).
cnf(refute_0_125,plain,
( vplus(vd436,vmul(vd436,vd439)) != vmul(vd436,vsucc(vd439))
| vplus(vmul(vd436,vd439),vd436) != vplus(vd436,vmul(vd436,vd439))
| vplus(vmul(vd436,vd439),vd436) = vmul(vd436,vsucc(vd439)) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(vplus(vmul(vd436,vd439),vd436))),bind(Y,$fot(vplus(vd436,vmul(vd436,vd439)))),bind(Z,$fot(vmul(vd436,vsucc(vd439))))]]) ).
cnf(refute_0_126,plain,
( vplus(vd436,vmul(vd436,vd439)) != vmul(vd436,vsucc(vd439))
| vplus(vmul(vd436,vd439),vd436) = vmul(vd436,vsucc(vd439)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd439),vd436),vplus(vd436,vmul(vd436,vd439))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
vplus(vmul(vd436,vd439),vd436) = vmul(vd436,vsucc(vd439)),
inference(resolve,[$cnf( $equal(vplus(vd436,vmul(vd436,vd439)),vmul(vd436,vsucc(vd439))) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
introduced(tautology,[refl,[$fot(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)))]]) ).
cnf(refute_0_129,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_130,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( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd439),vd436),vmul(vd436,vsucc(vd439))) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(subst,[],[refute_0_18:[bind(Vd46,$fot(vmul(vd436,vd437))),bind(Vd47,$fot(vmul(vd436,vd439))),bind(Vd48,$fot(vd436))]]) ).
cnf(refute_0_133,plain,
( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(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),vmul(vd436,vsucc(vd439))) ),
inference(subst,[],[refute_0_29:[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,$fot(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))))]]) ).
cnf(refute_0_134,plain,
( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)) ),[1],$fot(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))))]]) ).
cnf(refute_0_137,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ),
inference(resolve,[$cnf( $equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))
| vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) ),
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)) )],[refute_0_137,refute_0_120]) ).
cnf(refute_0_139,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd436,vplus(vd437,vd439)),vd436),vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)) )],[refute_0_138,refute_0_114]) ).
cnf(refute_0_140,plain,
$false,
inference(resolve,[$cnf( $equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))) )],[refute_0_113,refute_0_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM846+2 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 14:34:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 54.51/54.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.51/54.76
% 54.51/54.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 54.59/54.77
%------------------------------------------------------------------------------