TSTP Solution File: NUM845+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM845+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 24
% Syntax : Number of formulae : 118 ( 64 unt; 0 def)
% Number of atoms : 192 ( 191 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 145 ( 71 ~; 65 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 136 ( 0 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('qu(ind(267), imp(267))',conjecture,
! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ) ).
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('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [Vd42,Vd43] :
( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& vplus(Vd42,v1) = vsucc(Vd42) ) ).
fof(subgoal_0,plain,
! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
inference(strip,[],['qu(ind(267), imp(267))']) ).
fof(negate_0_0,plain,
~ ! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],['ass(cond(61, 0), 0)']) ).
fof(normalize_0_1,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_3,plain,
! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],['ass(cond(33, 0), 0)']) ).
fof(normalize_0_6,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [Vd416] :
( vmul(vsucc(vd411),vsucc(Vd416)) != vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416))
& vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
( vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) != vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416))
& vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) = vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) = vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,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_11,plain,
! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) != vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
vplus(vsucc(X_11),Vd78) = vplus(Vd78,vsucc(X_11)),
inference(subst,[],[refute_0_0:[bind(Vd79,$fot(vsucc(X_11)))]]) ).
cnf(refute_0_2,plain,
vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
vplus(Vd78,vsucc(X_11)) = vsucc(vplus(Vd78,X_11)),
inference(subst,[],[refute_0_2:[bind(Vd42,$fot(Vd78)),bind(Vd43,$fot(X_11))]]) ).
cnf(refute_0_4,plain,
( vplus(Vd78,vsucc(X_11)) != vsucc(vplus(Vd78,X_11))
| vplus(vsucc(X_11),Vd78) != vplus(Vd78,vsucc(X_11))
| vplus(vsucc(X_11),Vd78) = vsucc(vplus(Vd78,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vsucc(X_11),Vd78),vplus(Vd78,vsucc(X_11))) ),[1],$fot(vsucc(vplus(Vd78,X_11)))]]) ).
cnf(refute_0_5,plain,
( vplus(vsucc(X_11),Vd78) != vplus(Vd78,vsucc(X_11))
| vplus(vsucc(X_11),Vd78) = vsucc(vplus(Vd78,X_11)) ),
inference(resolve,[$cnf( $equal(vplus(Vd78,vsucc(X_11)),vsucc(vplus(Vd78,X_11))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
vplus(vsucc(X_11),Vd78) = vsucc(vplus(Vd78,X_11)),
inference(resolve,[$cnf( $equal(vplus(vsucc(X_11),Vd78),vplus(Vd78,vsucc(X_11))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) = vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))),
inference(subst,[],[refute_0_6:[bind(Vd78,$fot(vd411)),bind(X_11,$fot(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)))]]) ).
cnf(refute_0_8,plain,
vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_9,plain,
vplus(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)),X_21) = vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_21)),
inference(subst,[],[refute_0_8:[bind(Vd46,$fot(skolemFOFtoCNF_Vd416)),bind(Vd47,$fot(vmul(vd411,skolemFOFtoCNF_Vd416))),bind(Vd48,$fot(X_21))]]) ).
cnf(refute_0_10,plain,
vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) = vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( vplus(Vd79,Vd78) != vplus(Vd78,Vd79)
| vplus(Vd78,Vd79) = vplus(Vd79,Vd78) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(vplus(Vd79,Vd78))),bind(Y,$fot(vplus(Vd78,Vd79)))]]) ).
cnf(refute_0_15,plain,
vplus(Vd78,Vd79) = vplus(Vd79,Vd78),
inference(resolve,[$cnf( $equal(vplus(Vd79,Vd78),vplus(Vd78,Vd79)) )],[refute_0_0,refute_0_14]) ).
cnf(refute_0_16,plain,
vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)),
inference(subst,[],[refute_0_15:[bind(Vd78,$fot(vmul(vd411,skolemFOFtoCNF_Vd416))),bind(Vd79,$fot(skolemFOFtoCNF_Vd416))]]) ).
cnf(refute_0_17,plain,
( vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) != vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416)
| vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416) != vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416))
| vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416))) ),[0],$fot(vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416))]]) ).
cnf(refute_0_18,plain,
( vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) != vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416)
| vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416),vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)),
inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vplus(vmul(vd411,skolemFOFtoCNF_Vd416),skolemFOFtoCNF_Vd416)) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
( vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) != vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416))
| vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)) = vmul(vsucc(vd411),skolemFOFtoCNF_Vd416) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))),bind(Y,$fot(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416))))]]) ).
cnf(refute_0_21,plain,
vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)) = vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),
inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)) != vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)
| vplus(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)),X_21) != vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_21))
| vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_21) = vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)),X_21),vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_21))) ),[0,0],$fot(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))]]) ).
cnf(refute_0_23,plain,
( vplus(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)),X_21) != vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_21))
| vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_21) = vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_21)) ),
inference(resolve,[$cnf( $equal(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)),vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_21) = vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_21)),
inference(resolve,[$cnf( $equal(vplus(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,skolemFOFtoCNF_Vd416)),X_21),vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_21))) )],[refute_0_9,refute_0_23]) ).
cnf(refute_0_25,plain,
vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_22) = vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22)),
inference(subst,[],[refute_0_24:[bind(X_21,$fot(X_22))]]) ).
cnf(refute_0_26,plain,
vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416)) = vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22),
inference(subst,[],[refute_0_0:[bind(Vd78,$fot(vmul(vd411,skolemFOFtoCNF_Vd416))),bind(Vd79,$fot(X_22))]]) ).
cnf(refute_0_27,plain,
( vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416)) != vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22)
| vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22) = vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416)))),bind(Y,$fot(vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22)))]]) ).
cnf(refute_0_28,plain,
vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22) = vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416)),
inference(resolve,[$cnf( $equal(vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416)),vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22) != vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416))
| vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_22) != vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22))
| vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_22) = vplus(skolemFOFtoCNF_Vd416,vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_22),vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22))) ),[1,1],$fot(vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416)))]]) ).
cnf(refute_0_30,plain,
( vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_22) != vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22))
| vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_22) = vplus(skolemFOFtoCNF_Vd416,vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22),vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_22) = vplus(skolemFOFtoCNF_Vd416,vplus(X_22,vmul(vd411,skolemFOFtoCNF_Vd416))),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),X_22),vplus(skolemFOFtoCNF_Vd416,vplus(vmul(vd411,skolemFOFtoCNF_Vd416),X_22))) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) = vplus(skolemFOFtoCNF_Vd416,vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416))),
inference(subst,[],[refute_0_31:[bind(X_22,$fot(vd411))]]) ).
cnf(refute_0_33,plain,
vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_34,plain,
vplus(vmul(Vd396,Vd397),Vd396) = vplus(Vd396,vmul(Vd396,Vd397)),
inference(subst,[],[refute_0_15:[bind(Vd78,$fot(vmul(Vd396,Vd397))),bind(Vd79,$fot(Vd396))]]) ).
cnf(refute_0_35,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_36,plain,
( vmul(Vd396,vsucc(Vd397)) != vplus(vmul(Vd396,Vd397),Vd396)
| vmul(Vd396,vsucc(Vd397)) = vplus(Vd396,vmul(Vd396,Vd397)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(Vd396,Vd397),Vd396),vplus(Vd396,vmul(Vd396,Vd397))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
vmul(Vd396,vsucc(Vd397)) = vplus(Vd396,vmul(Vd396,Vd397)),
inference(resolve,[$cnf( $equal(vmul(Vd396,vsucc(Vd397)),vplus(vmul(Vd396,Vd397),Vd396)) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)) = vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416)),
inference(subst,[],[refute_0_37:[bind(Vd396,$fot(vd411)),bind(Vd397,$fot(skolemFOFtoCNF_Vd416))]]) ).
cnf(refute_0_39,plain,
( vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)) != vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416))
| vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416)) = vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))),bind(Y,$fot(vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416))))]]) ).
cnf(refute_0_40,plain,
vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416)) = vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),
inference(resolve,[$cnf( $equal(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416)) != vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))
| vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) != vplus(skolemFOFtoCNF_Vd416,vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416)))
| vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411),vplus(skolemFOFtoCNF_Vd416,vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416)))) ),[1,1],$fot(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))]]) ).
cnf(refute_0_42,plain,
( vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) != vplus(skolemFOFtoCNF_Vd416,vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416)))
| vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))) ),
inference(resolve,[$cnf( $equal(vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416)),vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411),vplus(skolemFOFtoCNF_Vd416,vplus(vd411,vmul(vd411,skolemFOFtoCNF_Vd416)))) )],[refute_0_32,refute_0_42]) ).
cnf(refute_0_44,plain,
vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) = vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),
inference(subst,[],[refute_0_15:[bind(Vd78,$fot(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))),bind(Vd79,$fot(vd411))]]) ).
cnf(refute_0_45,plain,
( vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) != vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))
| vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) != vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))
| vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411),vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) ),[0],$fot(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)))]]) ).
cnf(refute_0_46,plain,
( vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411) != vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))
| vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411),vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))),
inference(resolve,[$cnf( $equal(vplus(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416),vd411),vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)) != vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))
| vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) != vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)))
| vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411),vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)))) ),[1,0],$fot(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))]]) ).
cnf(refute_0_49,plain,
( vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) != vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)))
| vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) ),
inference(resolve,[$cnf( $equal(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))),
inference(resolve,[$cnf( $equal(vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411),vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)))) )],[refute_0_7,refute_0_49]) ).
cnf(refute_0_51,plain,
vmul(vsucc(X_15),vsucc(Vd397)) = vplus(vsucc(X_15),vmul(vsucc(X_15),Vd397)),
inference(subst,[],[refute_0_37:[bind(Vd396,$fot(vsucc(X_15)))]]) ).
cnf(refute_0_52,plain,
vplus(vsucc(X_15),vmul(vsucc(X_15),Vd397)) = vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15)),
inference(subst,[],[refute_0_6:[bind(Vd78,$fot(vmul(vsucc(X_15),Vd397))),bind(X_11,$fot(X_15))]]) ).
cnf(refute_0_53,plain,
( vmul(vsucc(X_15),vsucc(Vd397)) != vplus(vsucc(X_15),vmul(vsucc(X_15),Vd397))
| vplus(vsucc(X_15),vmul(vsucc(X_15),Vd397)) != vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15))
| vmul(vsucc(X_15),vsucc(Vd397)) = vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(X_15),vsucc(Vd397)),vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15))) ),[0],$fot(vplus(vsucc(X_15),vmul(vsucc(X_15),Vd397)))]]) ).
cnf(refute_0_54,plain,
( vmul(vsucc(X_15),vsucc(Vd397)) != vplus(vsucc(X_15),vmul(vsucc(X_15),Vd397))
| vmul(vsucc(X_15),vsucc(Vd397)) = vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15)) ),
inference(resolve,[$cnf( $equal(vplus(vsucc(X_15),vmul(vsucc(X_15),Vd397)),vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
vmul(vsucc(X_15),vsucc(Vd397)) = vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15)),
inference(resolve,[$cnf( $equal(vmul(vsucc(X_15),vsucc(Vd397)),vplus(vsucc(X_15),vmul(vsucc(X_15),Vd397))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
vplus(X_10,vsucc(X_11)) = vsucc(vplus(X_10,X_11)),
inference(subst,[],[refute_0_2:[bind(Vd42,$fot(X_10)),bind(Vd43,$fot(X_11))]]) ).
cnf(refute_0_57,plain,
vplus(X_11,X_10) = vplus(X_10,X_11),
inference(subst,[],[refute_0_0:[bind(Vd78,$fot(X_10)),bind(Vd79,$fot(X_11))]]) ).
cnf(refute_0_58,plain,
( vplus(X_11,X_10) != vplus(X_10,X_11)
| vplus(X_10,X_11) = vplus(X_11,X_10) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(vplus(X_11,X_10))),bind(Y,$fot(vplus(X_10,X_11)))]]) ).
cnf(refute_0_59,plain,
vplus(X_10,X_11) = vplus(X_11,X_10),
inference(resolve,[$cnf( $equal(vplus(X_11,X_10),vplus(X_10,X_11)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( vplus(X_10,X_11) != vplus(X_11,X_10)
| vplus(X_10,vsucc(X_11)) != vsucc(vplus(X_10,X_11))
| vplus(X_10,vsucc(X_11)) = vsucc(vplus(X_11,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(X_10,vsucc(X_11)),vsucc(vplus(X_10,X_11))) ),[1,0],$fot(vplus(X_11,X_10))]]) ).
cnf(refute_0_61,plain,
( vplus(X_10,vsucc(X_11)) != vsucc(vplus(X_10,X_11))
| vplus(X_10,vsucc(X_11)) = vsucc(vplus(X_11,X_10)) ),
inference(resolve,[$cnf( $equal(vplus(X_10,X_11),vplus(X_11,X_10)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
vplus(X_10,vsucc(X_11)) = vsucc(vplus(X_11,X_10)),
inference(resolve,[$cnf( $equal(vplus(X_10,vsucc(X_11)),vsucc(vplus(X_10,X_11))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
( vplus(X_10,vsucc(X_11)) != vsucc(vplus(X_10,X_11))
| vplus(X_10,vsucc(X_11)) != vsucc(vplus(X_11,X_10))
| vsucc(vplus(X_10,X_11)) = vsucc(vplus(X_11,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(X_10,vsucc(X_11)),vsucc(vplus(X_11,X_10))) ),[0],$fot(vsucc(vplus(X_10,X_11)))]]) ).
cnf(refute_0_64,plain,
( vplus(X_10,vsucc(X_11)) != vsucc(vplus(X_11,X_10))
| vsucc(vplus(X_10,X_11)) = vsucc(vplus(X_11,X_10)) ),
inference(resolve,[$cnf( $equal(vplus(X_10,vsucc(X_11)),vsucc(vplus(X_10,X_11))) )],[refute_0_56,refute_0_63]) ).
cnf(refute_0_65,plain,
vsucc(vplus(X_10,X_11)) = vsucc(vplus(X_11,X_10)),
inference(resolve,[$cnf( $equal(vplus(X_10,vsucc(X_11)),vsucc(vplus(X_11,X_10))) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
( vsucc(vplus(X_10,X_11)) != vsucc(vplus(X_11,X_10))
| vsucc(vplus(X_11,X_10)) = vsucc(vplus(X_10,X_11)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(vsucc(vplus(X_10,X_11)))),bind(Y,$fot(vsucc(vplus(X_11,X_10))))]]) ).
cnf(refute_0_67,plain,
vsucc(vplus(X_11,X_10)) = vsucc(vplus(X_10,X_11)),
inference(resolve,[$cnf( $equal(vsucc(vplus(X_10,X_11)),vsucc(vplus(X_11,X_10))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15)) = vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397))),
inference(subst,[],[refute_0_67:[bind(X_10,$fot(X_15)),bind(X_11,$fot(vmul(vsucc(X_15),Vd397)))]]) ).
cnf(refute_0_69,plain,
( vmul(vsucc(X_15),vsucc(Vd397)) != vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15))
| vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15)) != vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397)))
| vmul(vsucc(X_15),vsucc(Vd397)) = vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(X_15),vsucc(Vd397)),vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397)))) ),[0],$fot(vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15)))]]) ).
cnf(refute_0_70,plain,
( vmul(vsucc(X_15),vsucc(Vd397)) != vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15))
| vmul(vsucc(X_15),vsucc(Vd397)) = vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397))) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15)),vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397)))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
vmul(vsucc(X_15),vsucc(Vd397)) = vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397))),
inference(resolve,[$cnf( $equal(vmul(vsucc(X_15),vsucc(Vd397)),vsucc(vplus(vmul(vsucc(X_15),Vd397),X_15))) )],[refute_0_55,refute_0_70]) ).
cnf(refute_0_72,plain,
( vmul(vsucc(X_15),vsucc(Vd397)) != vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397)))
| vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397))) = vmul(vsucc(X_15),vsucc(Vd397)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(vmul(vsucc(X_15),vsucc(Vd397)))),bind(Y,$fot(vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397)))))]]) ).
cnf(refute_0_73,plain,
vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397))) = vmul(vsucc(X_15),vsucc(Vd397)),
inference(resolve,[$cnf( $equal(vmul(vsucc(X_15),vsucc(Vd397)),vsucc(vplus(X_15,vmul(vsucc(X_15),Vd397)))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))) = vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)),
inference(subst,[],[refute_0_73:[bind(Vd397,$fot(skolemFOFtoCNF_Vd416)),bind(X_15,$fot(vd411))]]) ).
cnf(refute_0_75,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_76,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_13,refute_0_75]) ).
cnf(refute_0_77,plain,
( vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) != vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)))
| vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))) != vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416))
| vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) = vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) ),
inference(subst,[],[refute_0_76:[bind(X,$fot(vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411))),bind(Y,$fot(vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))))),bind(Z,$fot(vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416))))]]) ).
cnf(refute_0_78,plain,
( vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))) != vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416))
| vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) = vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) ),
inference(resolve,[$cnf( $equal(vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411),vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)))) )],[refute_0_7,refute_0_77]) ).
cnf(refute_0_79,plain,
vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) = vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)),
inference(resolve,[$cnf( $equal(vsucc(vplus(vd411,vmul(vsucc(vd411),skolemFOFtoCNF_Vd416))),vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416))) )],[refute_0_74,refute_0_78]) ).
cnf(refute_0_80,plain,
( vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) != vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416))
| vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) != vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))
| vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411),vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))) ),[0],$fot(vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)))]]) ).
cnf(refute_0_81,plain,
( vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411) != vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))
| vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) ),
inference(resolve,[$cnf( $equal(vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411),vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))),
inference(resolve,[$cnf( $equal(vplus(vsucc(vmul(vsucc(vd411),skolemFOFtoCNF_Vd416)),vd411),vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))) )],[refute_0_50,refute_0_81]) ).
cnf(refute_0_83,plain,
vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) != vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_84,plain,
vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416) = vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))),
inference(subst,[],[refute_0_15:[bind(Vd78,$fot(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))),bind(Vd79,$fot(skolemFOFtoCNF_Vd416))]]) ).
cnf(refute_0_85,plain,
vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)) = vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)),
introduced(tautology,[refl,[$fot(vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)))]]) ).
cnf(refute_0_86,plain,
( vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416) != vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))
| vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)) != vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416))
| vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) ),
introduced(tautology,[equality,[$cnf( $equal(vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)),vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416))) ),[1,0],$fot(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))]]) ).
cnf(refute_0_87,plain,
( vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416) != vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))
| vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) ),
inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)),vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416),vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)) = vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)),
inference(subst,[],[refute_0_2:[bind(Vd42,$fot(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))),bind(Vd43,$fot(skolemFOFtoCNF_Vd416))]]) ).
cnf(refute_0_90,plain,
( vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)) != vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416))
| vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)) != vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))
| vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) ),
inference(subst,[],[refute_0_76:[bind(X,$fot(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)))),bind(Y,$fot(vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)))),bind(Z,$fot(vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))))]]) ).
cnf(refute_0_91,plain,
( vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)) != vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))
| vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)),vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)) = vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))),
inference(resolve,[$cnf( $equal(vsucc(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),skolemFOFtoCNF_Vd416)),vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
( vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) != vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))
| vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)) != vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))
| vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) = vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)),vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416))) ),[1],$fot(vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))))]]) ).
cnf(refute_0_94,plain,
( vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) != vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))
| vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) = vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416)),vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)) != vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)))),
inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)),vplus(vmul(vd411,vsucc(skolemFOFtoCNF_Vd416)),vsucc(skolemFOFtoCNF_Vd416))) )],[refute_0_94,refute_0_83]) ).
cnf(refute_0_96,plain,
$false,
inference(resolve,[$cnf( $equal(vmul(vsucc(vd411),vsucc(skolemFOFtoCNF_Vd416)),vsucc(vplus(skolemFOFtoCNF_Vd416,vmul(vd411,vsucc(skolemFOFtoCNF_Vd416))))) )],[refute_0_82,refute_0_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM845+2 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n004.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 : Thu Jul 7 03:22:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.50
% 0.20/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.51
%------------------------------------------------------------------------------