TSTP Solution File: NUM849+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM849+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:30:57 EDT 2022
% Result : Theorem 0.48s 0.63s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 82 ( 47 unt; 0 def)
% Number of atoms : 130 ( 129 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 97 ( 49 ~; 43 |; 2 &)
% ( 0 <=>; 3 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 30 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('qu(ind(296), imp(296))',conjecture,
! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ) ).
fof('ass(cond(281, 0), 0)',axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) ).
fof('ass(cond(270, 0), 0)',axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418) ).
fof('ass(cond(261, 0), 0)',axiom,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409) ).
fof('ass(cond(61, 0), 0)',axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).
fof(subgoal_0,plain,
! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
inference(strip,[],['qu(ind(296), imp(296))']) ).
fof(negate_0_0,plain,
~ ! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409),
inference(canonicalize,[],['ass(cond(261, 0), 0)']) ).
fof(normalize_0_1,plain,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409),
inference(specialize,[],[normalize_0_0]) ).
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,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(canonicalize,[],['ass(cond(281, 0), 0)']) ).
fof(normalize_0_5,plain,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [Vd454] :
( vmul(vmul(vd448,vd449),vsucc(Vd454)) != vmul(vd448,vmul(vd449,vsucc(Vd454)))
& vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
( vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)) != vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)))
& vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454) = vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454) = vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(canonicalize,[],['ass(cond(270, 0), 0)']) ).
fof(normalize_0_10,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)) != vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( vplus(Vd79,Vd78) != vplus(Vd78,Vd79)
| vplus(Vd78,Vd79) = vplus(Vd79,Vd78) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vplus(Vd79,Vd78))),bind(Y,$fot(vplus(Vd78,Vd79)))]]) ).
cnf(refute_0_6,plain,
vplus(Vd78,Vd79) = vplus(Vd79,Vd78),
inference(resolve,[$cnf( $equal(vplus(Vd79,Vd78),vplus(Vd78,Vd79)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
vplus(vmul(Vd408,Vd409),Vd409) = vplus(Vd409,vmul(Vd408,Vd409)),
inference(subst,[],[refute_0_6:[bind(Vd78,$fot(vmul(Vd408,Vd409))),bind(Vd79,$fot(Vd409))]]) ).
cnf(refute_0_8,plain,
( vmul(vsucc(Vd408),Vd409) != vplus(vmul(Vd408,Vd409),Vd409)
| vplus(vmul(Vd408,Vd409),Vd409) != vplus(Vd409,vmul(Vd408,Vd409))
| vmul(vsucc(Vd408),Vd409) = vplus(Vd409,vmul(Vd408,Vd409)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(Vd408),Vd409),vplus(Vd409,vmul(Vd408,Vd409))) ),[0],$fot(vplus(vmul(Vd408,Vd409),Vd409))]]) ).
cnf(refute_0_9,plain,
( vmul(vsucc(Vd408),Vd409) != vplus(vmul(Vd408,Vd409),Vd409)
| vmul(vsucc(Vd408),Vd409) = vplus(Vd409,vmul(Vd408,Vd409)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(Vd408,Vd409),Vd409),vplus(Vd409,vmul(Vd408,Vd409))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
vmul(vsucc(Vd408),Vd409) = vplus(Vd409,vmul(Vd408,Vd409)),
inference(resolve,[$cnf( $equal(vmul(vsucc(Vd408),Vd409),vplus(vmul(Vd408,Vd409),Vd409)) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) = vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))),
inference(subst,[],[refute_0_10:[bind(Vd408,$fot(skolemFOFtoCNF_Vd454)),bind(Vd409,$fot(vmul(vd448,vd449)))]]) ).
cnf(refute_0_12,plain,
vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_13,plain,
vmul(vd448,vplus(X_29,vmul(skolemFOFtoCNF_Vd454,vd449))) = vplus(vmul(vd448,X_29),vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449))),
inference(subst,[],[refute_0_12:[bind(Vd432,$fot(vd448)),bind(Vd433,$fot(X_29)),bind(Vd434,$fot(vmul(skolemFOFtoCNF_Vd454,vd449)))]]) ).
cnf(refute_0_14,plain,
vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454) = vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_15,plain,
vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_16,plain,
( vmul(Vd418,Vd419) != vmul(Vd419,Vd418)
| vmul(Vd419,Vd418) = vmul(Vd418,Vd419) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vmul(Vd418,Vd419))),bind(Y,$fot(vmul(Vd419,Vd418)))]]) ).
cnf(refute_0_17,plain,
vmul(Vd419,Vd418) = vmul(Vd418,Vd419),
inference(resolve,[$cnf( $equal(vmul(Vd418,Vd419),vmul(Vd419,Vd418)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454) = vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)),
inference(subst,[],[refute_0_17:[bind(Vd418,$fot(skolemFOFtoCNF_Vd454)),bind(Vd419,$fot(vmul(vd448,vd449)))]]) ).
cnf(refute_0_19,plain,
( vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454) != vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))
| vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454) != vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))
| vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)) ),
introduced(tautology,[equality,[$cnf( $equal(vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454),vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))) ),[0],$fot(vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)))]]) ).
cnf(refute_0_20,plain,
( vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454) != vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))
| vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)) ),
inference(resolve,[$cnf( $equal(vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
vmul(vd449,skolemFOFtoCNF_Vd454) = vmul(skolemFOFtoCNF_Vd454,vd449),
inference(subst,[],[refute_0_17:[bind(Vd418,$fot(skolemFOFtoCNF_Vd454)),bind(Vd419,$fot(vd449))]]) ).
cnf(refute_0_22,plain,
vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)) = vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)),
introduced(tautology,[refl,[$fot(vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)))]]) ).
cnf(refute_0_23,plain,
( vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)) != vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))
| vmul(vd449,skolemFOFtoCNF_Vd454) != vmul(skolemFOFtoCNF_Vd454,vd449)
| vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)) = vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)) ),
introduced(tautology,[equality,[$cnf( $equal(vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)),vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))) ),[1,1],$fot(vmul(skolemFOFtoCNF_Vd454,vd449))]]) ).
cnf(refute_0_24,plain,
( vmul(vd449,skolemFOFtoCNF_Vd454) != vmul(skolemFOFtoCNF_Vd454,vd449)
| vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)) = vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)) ),
inference(resolve,[$cnf( $equal(vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)),vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)) = vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)),
inference(resolve,[$cnf( $equal(vmul(vd449,skolemFOFtoCNF_Vd454),vmul(skolemFOFtoCNF_Vd454,vd449)) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) != vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))
| vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)) != vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449))
| vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) = vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)),vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449))) ),[0],$fot(vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)))]]) ).
cnf(refute_0_27,plain,
( vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) != vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))
| vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) = vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)) ),
inference(resolve,[$cnf( $equal(vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454)),vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454) != vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))
| vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) = vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)) ),
inference(resolve,[$cnf( $equal(vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)),vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))) )],[refute_0_20,refute_0_27]) ).
cnf(refute_0_29,plain,
vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) = vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)),
inference(resolve,[$cnf( $equal(vmul(vmul(vd448,vd449),skolemFOFtoCNF_Vd454),vmul(vd448,vmul(vd449,skolemFOFtoCNF_Vd454))) )],[refute_0_14,refute_0_28]) ).
cnf(refute_0_30,plain,
( vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) != vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449))
| vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)) = vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)))),bind(Y,$fot(vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449))))]]) ).
cnf(refute_0_31,plain,
vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)) = vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)),
inference(resolve,[$cnf( $equal(vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)),vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)) != vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))
| vmul(vd448,vplus(X_29,vmul(skolemFOFtoCNF_Vd454,vd449))) != vplus(vmul(vd448,X_29),vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)))
| vmul(vd448,vplus(X_29,vmul(skolemFOFtoCNF_Vd454,vd449))) = vplus(vmul(vd448,X_29),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))) ),
introduced(tautology,[equality,[$cnf( $equal(vmul(vd448,vplus(X_29,vmul(skolemFOFtoCNF_Vd454,vd449))),vplus(vmul(vd448,X_29),vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)))) ),[1,1],$fot(vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)))]]) ).
cnf(refute_0_33,plain,
( vmul(vd448,vplus(X_29,vmul(skolemFOFtoCNF_Vd454,vd449))) != vplus(vmul(vd448,X_29),vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)))
| vmul(vd448,vplus(X_29,vmul(skolemFOFtoCNF_Vd454,vd449))) = vplus(vmul(vd448,X_29),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))) ),
inference(resolve,[$cnf( $equal(vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
vmul(vd448,vplus(X_29,vmul(skolemFOFtoCNF_Vd454,vd449))) = vplus(vmul(vd448,X_29),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))),
inference(resolve,[$cnf( $equal(vmul(vd448,vplus(X_29,vmul(skolemFOFtoCNF_Vd454,vd449))),vplus(vmul(vd448,X_29),vmul(vd448,vmul(skolemFOFtoCNF_Vd454,vd449)))) )],[refute_0_13,refute_0_33]) ).
cnf(refute_0_35,plain,
vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) = vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))),
inference(subst,[],[refute_0_34:[bind(X_29,$fot(vd449))]]) ).
cnf(refute_0_36,plain,
( vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) != vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)))
| vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))) = vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))))),bind(Y,$fot(vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)))))]]) ).
cnf(refute_0_37,plain,
vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))) = vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))),
inference(resolve,[$cnf( $equal(vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))),vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) != vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)))
| vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))) != vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))
| vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) = vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)),vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))) ),[0],$fot(vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))))]]) ).
cnf(refute_0_39,plain,
( vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) != vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)))
| vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) = vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449))),vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) = vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))),
inference(resolve,[$cnf( $equal(vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)),vplus(vmul(vd448,vd449),vmul(skolemFOFtoCNF_Vd454,vmul(vd448,vd449)))) )],[refute_0_11,refute_0_39]) ).
cnf(refute_0_41,plain,
vmul(vsucc(skolemFOFtoCNF_Vd454),vd449) = vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)),
inference(subst,[],[refute_0_17:[bind(Vd418,$fot(vd449)),bind(Vd419,$fot(vsucc(skolemFOFtoCNF_Vd454)))]]) ).
cnf(refute_0_42,plain,
( vmul(vsucc(Vd408),Vd409) != vplus(Vd409,vmul(Vd408,Vd409))
| vplus(Vd409,vmul(Vd408,Vd409)) = vmul(vsucc(Vd408),Vd409) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vmul(vsucc(Vd408),Vd409))),bind(Y,$fot(vplus(Vd409,vmul(Vd408,Vd409))))]]) ).
cnf(refute_0_43,plain,
vplus(Vd409,vmul(Vd408,Vd409)) = vmul(vsucc(Vd408),Vd409),
inference(resolve,[$cnf( $equal(vmul(vsucc(Vd408),Vd409),vplus(Vd409,vmul(Vd408,Vd409))) )],[refute_0_10,refute_0_42]) ).
cnf(refute_0_44,plain,
vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)) = vmul(vsucc(skolemFOFtoCNF_Vd454),vd449),
inference(subst,[],[refute_0_43:[bind(Vd408,$fot(skolemFOFtoCNF_Vd454)),bind(Vd409,$fot(vd449))]]) ).
cnf(refute_0_45,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_46,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_45]) ).
cnf(refute_0_47,plain,
( vmul(vsucc(skolemFOFtoCNF_Vd454),vd449) != vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))
| vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)) != vmul(vsucc(skolemFOFtoCNF_Vd454),vd449)
| vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)) = vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)) ),
inference(subst,[],[refute_0_46:[bind(X,$fot(vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))),bind(Y,$fot(vmul(vsucc(skolemFOFtoCNF_Vd454),vd449))),bind(Z,$fot(vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))))]]) ).
cnf(refute_0_48,plain,
( vmul(vsucc(skolemFOFtoCNF_Vd454),vd449) != vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))
| vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)) = vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)) ),
inference(resolve,[$cnf( $equal(vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)),vmul(vsucc(skolemFOFtoCNF_Vd454),vd449)) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)) = vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)),
inference(resolve,[$cnf( $equal(vmul(vsucc(skolemFOFtoCNF_Vd454),vd449),vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))) )],[refute_0_41,refute_0_48]) ).
cnf(refute_0_50,plain,
vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) = vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))),
introduced(tautology,[refl,[$fot(vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))))]]) ).
cnf(refute_0_51,plain,
( vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) != vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))
| vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)) != vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))
| vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) = vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))) ),
introduced(tautology,[equality,[$cnf( $equal(vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))),vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))) ),[1,1],$fot(vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)))]]) ).
cnf(refute_0_52,plain,
( vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)) != vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))
| vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) = vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))) ),
inference(resolve,[$cnf( $equal(vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))),vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) = vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))),
inference(resolve,[$cnf( $equal(vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)),vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
( vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))) != vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)))
| vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) != vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))
| vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))) ),
introduced(tautology,[equality,[$cnf( $equal(vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)),vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))) ),[1],$fot(vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))))]]) ).
cnf(refute_0_55,plain,
( vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) != vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))
| vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))) ),
inference(resolve,[$cnf( $equal(vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449))),vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))),
inference(resolve,[$cnf( $equal(vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)),vmul(vd448,vplus(vd449,vmul(skolemFOFtoCNF_Vd454,vd449)))) )],[refute_0_40,refute_0_55]) ).
cnf(refute_0_57,plain,
vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)) != vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_58,plain,
vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)) = vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)),
inference(subst,[],[refute_0_17:[bind(Vd418,$fot(vsucc(skolemFOFtoCNF_Vd454))),bind(Vd419,$fot(vmul(vd448,vd449)))]]) ).
cnf(refute_0_59,plain,
( vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)) != vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449))
| vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) != vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)))
| vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)) = vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)),vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)))) ),[0],$fot(vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)))]]) ).
cnf(refute_0_60,plain,
( vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) != vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)))
| vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)) = vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))) ),
inference(resolve,[$cnf( $equal(vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)),vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)) != vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454))),
inference(resolve,[$cnf( $equal(vmul(vmul(vd448,vd449),vsucc(skolemFOFtoCNF_Vd454)),vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)))) )],[refute_0_60,refute_0_57]) ).
cnf(refute_0_62,plain,
$false,
inference(resolve,[$cnf( $equal(vmul(vsucc(skolemFOFtoCNF_Vd454),vmul(vd448,vd449)),vmul(vd448,vmul(vd449,vsucc(skolemFOFtoCNF_Vd454)))) )],[refute_0_56,refute_0_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM849+2 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jul 7 22:20:57 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.63
% 0.48/0.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.48/0.64
%------------------------------------------------------------------------------