TSTP Solution File: NUM851+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM851+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 12:30:58 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 63 ( 37 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 42 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('holds(conseq_conjunct2(conseq(302)), 475, 1)',conjecture,
vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)) ).
fof('holds(conseq_conjunct1(conseq(302)), 474, 0)',axiom,
vd470 = vplus(vd471,vd473) ).
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(subgoal_0,plain,
vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(strip,[],['holds(conseq_conjunct2(conseq(302)), 475, 1)']) ).
fof(negate_0_0,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
vd470 = vplus(vd471,vd473),
inference(canonicalize,[],['holds(conseq_conjunct1(conseq(302)), 474, 0)']) ).
fof(normalize_0_2,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(canonicalize,[],['ass(cond(270, 0), 0)']) ).
fof(normalize_0_3,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
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]) ).
cnf(refute_0_0,plain,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
vd470 = vplus(vd471,vd473),
inference(canonicalize,[],[normalize_0_1]) ).
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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( vd470 != vplus(vd471,vd473)
| vplus(vd471,vd473) = vd470 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vd470)),bind(Y,$fot(vplus(vd471,vd473)))]]) ).
cnf(refute_0_6,plain,
vplus(vd471,vd473) = vd470,
inference(resolve,[$cnf( $equal(vd470,vplus(vd471,vd473)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
vmul(vd469,vplus(vd471,vd473)) = vmul(vd469,vplus(vd471,vd473)),
introduced(tautology,[refl,[$fot(vmul(vd469,vplus(vd471,vd473)))]]) ).
cnf(refute_0_8,plain,
( vmul(vd469,vplus(vd471,vd473)) != vmul(vd469,vplus(vd471,vd473))
| vplus(vd471,vd473) != vd470
| vmul(vd469,vplus(vd471,vd473)) = vmul(vd469,vd470) ),
introduced(tautology,[equality,[$cnf( $equal(vmul(vd469,vplus(vd471,vd473)),vmul(vd469,vplus(vd471,vd473))) ),[1,1],$fot(vd470)]]) ).
cnf(refute_0_9,plain,
( vplus(vd471,vd473) != vd470
| vmul(vd469,vplus(vd471,vd473)) = vmul(vd469,vd470) ),
inference(resolve,[$cnf( $equal(vmul(vd469,vplus(vd471,vd473)),vmul(vd469,vplus(vd471,vd473))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
vmul(vd469,vplus(vd471,vd473)) = vmul(vd469,vd470),
inference(resolve,[$cnf( $equal(vplus(vd471,vd473),vd470) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_12,plain,
( vmul(Vd418,Vd419) != vmul(Vd419,Vd418)
| vmul(Vd419,Vd418) = vmul(Vd418,Vd419) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vmul(Vd418,Vd419))),bind(Y,$fot(vmul(Vd419,Vd418)))]]) ).
cnf(refute_0_13,plain,
vmul(Vd419,Vd418) = vmul(Vd418,Vd419),
inference(resolve,[$cnf( $equal(vmul(Vd418,Vd419),vmul(Vd419,Vd418)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
vmul(vplus(vd471,vd473),vd469) = vmul(vd469,vplus(vd471,vd473)),
inference(subst,[],[refute_0_13:[bind(Vd418,$fot(vd469)),bind(Vd419,$fot(vplus(vd471,vd473)))]]) ).
cnf(refute_0_15,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_15]) ).
cnf(refute_0_17,plain,
( vmul(vd469,vplus(vd471,vd473)) != vmul(vd469,vd470)
| vmul(vplus(vd471,vd473),vd469) != vmul(vd469,vplus(vd471,vd473))
| vmul(vplus(vd471,vd473),vd469) = vmul(vd469,vd470) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vmul(vplus(vd471,vd473),vd469))),bind(Y,$fot(vmul(vd469,vplus(vd471,vd473)))),bind(Z,$fot(vmul(vd469,vd470)))]]) ).
cnf(refute_0_18,plain,
( vmul(vd469,vplus(vd471,vd473)) != vmul(vd469,vd470)
| vmul(vplus(vd471,vd473),vd469) = vmul(vd469,vd470) ),
inference(resolve,[$cnf( $equal(vmul(vplus(vd471,vd473),vd469),vmul(vd469,vplus(vd471,vd473))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
vmul(vplus(vd471,vd473),vd469) = vmul(vd469,vd470),
inference(resolve,[$cnf( $equal(vmul(vd469,vplus(vd471,vd473)),vmul(vd469,vd470)) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
( vmul(vd469,vd470) != vplus(vmul(vd471,vd469),vmul(vd473,vd469))
| vmul(vplus(vd471,vd473),vd469) != vmul(vd469,vd470)
| vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)) ),
introduced(tautology,[equality,[$cnf( $equal(vmul(vplus(vd471,vd473),vd469),vmul(vd469,vd470)) ),[1],$fot(vplus(vmul(vd471,vd469),vmul(vd473,vd469)))]]) ).
cnf(refute_0_21,plain,
( vmul(vd469,vd470) != vplus(vmul(vd471,vd469),vmul(vd473,vd469))
| vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)) ),
inference(resolve,[$cnf( $equal(vmul(vplus(vd471,vd473),vd469),vmul(vd469,vd470)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_23,plain,
( vmul(Vd432,vplus(Vd433,Vd434)) != vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434))
| vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) = vmul(Vd432,vplus(Vd433,Vd434)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vmul(Vd432,vplus(Vd433,Vd434)))),bind(Y,$fot(vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434))))]]) ).
cnf(refute_0_24,plain,
vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) = vmul(Vd432,vplus(Vd433,Vd434)),
inference(resolve,[$cnf( $equal(vmul(Vd432,vplus(Vd433,Vd434)),vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
vplus(vmul(vd469,vd471),vmul(vd469,vd473)) = vmul(vd469,vplus(vd471,vd473)),
inference(subst,[],[refute_0_24:[bind(Vd432,$fot(vd469)),bind(Vd433,$fot(vd471)),bind(Vd434,$fot(vd473))]]) ).
cnf(refute_0_26,plain,
( vmul(vd469,vplus(vd471,vd473)) != vmul(vd469,vd470)
| vplus(vmul(vd469,vd471),vmul(vd469,vd473)) != vmul(vd469,vplus(vd471,vd473))
| vplus(vmul(vd469,vd471),vmul(vd469,vd473)) = vmul(vd469,vd470) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd469,vd471),vmul(vd469,vd473)))),bind(Y,$fot(vmul(vd469,vplus(vd471,vd473)))),bind(Z,$fot(vmul(vd469,vd470)))]]) ).
cnf(refute_0_27,plain,
( vmul(vd469,vplus(vd471,vd473)) != vmul(vd469,vd470)
| vplus(vmul(vd469,vd471),vmul(vd469,vd473)) = vmul(vd469,vd470) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd469,vd471),vmul(vd469,vd473)),vmul(vd469,vplus(vd471,vd473))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
vplus(vmul(vd469,vd471),vmul(vd469,vd473)) = vmul(vd469,vd470),
inference(resolve,[$cnf( $equal(vmul(vd469,vplus(vd471,vd473)),vmul(vd469,vd470)) )],[refute_0_10,refute_0_27]) ).
cnf(refute_0_29,plain,
vmul(vd473,vd469) = vmul(vd469,vd473),
inference(subst,[],[refute_0_13:[bind(Vd418,$fot(vd469)),bind(Vd419,$fot(vd473))]]) ).
cnf(refute_0_30,plain,
vplus(vmul(vd469,vd471),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd473,vd469)),
introduced(tautology,[refl,[$fot(vplus(vmul(vd469,vd471),vmul(vd473,vd469)))]]) ).
cnf(refute_0_31,plain,
( vmul(vd473,vd469) != vmul(vd469,vd473)
| vplus(vmul(vd469,vd471),vmul(vd473,vd469)) != vplus(vmul(vd469,vd471),vmul(vd473,vd469))
| vplus(vmul(vd469,vd471),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd469,vd473)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd469,vd471),vmul(vd473,vd469)),vplus(vmul(vd469,vd471),vmul(vd473,vd469))) ),[1,1],$fot(vmul(vd469,vd473))]]) ).
cnf(refute_0_32,plain,
( vmul(vd473,vd469) != vmul(vd469,vd473)
| vplus(vmul(vd469,vd471),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd469,vd473)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd469,vd471),vmul(vd473,vd469)),vplus(vmul(vd469,vd471),vmul(vd473,vd469))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
vplus(vmul(vd469,vd471),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd469,vd473)),
inference(resolve,[$cnf( $equal(vmul(vd473,vd469),vmul(vd469,vd473)) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
vmul(vd471,vd469) = vmul(vd469,vd471),
inference(subst,[],[refute_0_13:[bind(Vd418,$fot(vd469)),bind(Vd419,$fot(vd471))]]) ).
cnf(refute_0_35,plain,
vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
introduced(tautology,[refl,[$fot(vplus(vmul(vd471,vd469),vmul(vd473,vd469)))]]) ).
cnf(refute_0_36,plain,
( vmul(vd471,vd469) != vmul(vd469,vd471)
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) != vplus(vmul(vd471,vd469),vmul(vd473,vd469))
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd473,vd469)) ),
introduced(tautology,[equality,[$cnf( $equal(vplus(vmul(vd471,vd469),vmul(vd473,vd469)),vplus(vmul(vd471,vd469),vmul(vd473,vd469))) ),[1,0],$fot(vmul(vd469,vd471))]]) ).
cnf(refute_0_37,plain,
( vmul(vd471,vd469) != vmul(vd469,vd471)
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd473,vd469)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd471,vd469),vmul(vd473,vd469)),vplus(vmul(vd471,vd469),vmul(vd473,vd469))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd473,vd469)),
inference(resolve,[$cnf( $equal(vmul(vd471,vd469),vmul(vd469,vd471)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( vplus(vmul(vd469,vd471),vmul(vd473,vd469)) != vplus(vmul(vd469,vd471),vmul(vd469,vd473))
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) != vplus(vmul(vd469,vd471),vmul(vd473,vd469))
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd469,vd473)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd471,vd469),vmul(vd473,vd469)))),bind(Y,$fot(vplus(vmul(vd469,vd471),vmul(vd473,vd469)))),bind(Z,$fot(vplus(vmul(vd469,vd471),vmul(vd469,vd473))))]]) ).
cnf(refute_0_40,plain,
( vplus(vmul(vd469,vd471),vmul(vd473,vd469)) != vplus(vmul(vd469,vd471),vmul(vd469,vd473))
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd469,vd473)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd471,vd469),vmul(vd473,vd469)),vplus(vmul(vd469,vd471),vmul(vd473,vd469))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vplus(vmul(vd469,vd471),vmul(vd469,vd473)),
inference(resolve,[$cnf( $equal(vplus(vmul(vd469,vd471),vmul(vd473,vd469)),vplus(vmul(vd469,vd471),vmul(vd469,vd473))) )],[refute_0_33,refute_0_40]) ).
cnf(refute_0_42,plain,
( vplus(vmul(vd469,vd471),vmul(vd469,vd473)) != vmul(vd469,vd470)
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) != vplus(vmul(vd469,vd471),vmul(vd469,vd473))
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vmul(vd469,vd470) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(vplus(vmul(vd471,vd469),vmul(vd473,vd469)))),bind(Y,$fot(vplus(vmul(vd469,vd471),vmul(vd469,vd473)))),bind(Z,$fot(vmul(vd469,vd470)))]]) ).
cnf(refute_0_43,plain,
( vplus(vmul(vd469,vd471),vmul(vd469,vd473)) != vmul(vd469,vd470)
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vmul(vd469,vd470) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd471,vd469),vmul(vd473,vd469)),vplus(vmul(vd469,vd471),vmul(vd469,vd473))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
vplus(vmul(vd471,vd469),vmul(vd473,vd469)) = vmul(vd469,vd470),
inference(resolve,[$cnf( $equal(vplus(vmul(vd469,vd471),vmul(vd469,vd473)),vmul(vd469,vd470)) )],[refute_0_28,refute_0_43]) ).
cnf(refute_0_45,plain,
( vmul(vd469,vd470) != vmul(vd469,vd470)
| vplus(vmul(vd471,vd469),vmul(vd473,vd469)) != vmul(vd469,vd470)
| vmul(vd469,vd470) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(vmul(vd469,vd470),vplus(vmul(vd471,vd469),vmul(vd473,vd469))) ),[1],$fot(vmul(vd469,vd470))]]) ).
cnf(refute_0_46,plain,
( vmul(vd469,vd470) != vmul(vd469,vd470)
| vmul(vd469,vd470) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(vd471,vd469),vmul(vd473,vd469)),vmul(vd469,vd470)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( vmul(vd469,vd470) != vmul(vd469,vd470)
| vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)) ),
inference(resolve,[$cnf( $equal(vmul(vd469,vd470),vplus(vmul(vd471,vd469),vmul(vd473,vd469))) )],[refute_0_46,refute_0_21]) ).
cnf(refute_0_48,plain,
vmul(vd469,vd470) != vmul(vd469,vd470),
inference(resolve,[$cnf( $equal(vmul(vplus(vd471,vd473),vd469),vplus(vmul(vd471,vd469),vmul(vd473,vd469))) )],[refute_0_47,refute_0_0]) ).
cnf(refute_0_49,plain,
vmul(vd469,vd470) = vmul(vd469,vd470),
introduced(tautology,[refl,[$fot(vmul(vd469,vd470))]]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( $equal(vmul(vd469,vd470),vmul(vd469,vd470)) )],[refute_0_49,refute_0_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM851+1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 20:35:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.40
%------------------------------------------------------------------------------