TSTP Solution File: NUM852+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM852+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:30:59 EDT 2022
% Result : Theorem 0.39s 0.61s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 33 unt; 0 def)
% Number of atoms : 88 ( 43 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 35 ~; 27 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 4 sgn 31 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)',conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)) ).
fof('holds(conseq_conjunct1(conseq(304)), 483, 0)',axiom,
greater(vd481,vd480) ).
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('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).
fof(subgoal_0,plain,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(strip,[],['holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)']) ).
fof(negate_0_0,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(canonicalize,[],['ass(cond(270, 0), 0)']) ).
fof(normalize_0_2,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
<=> ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ),
inference(canonicalize,[],['def(cond(conseq(axiom(3)), 11), 1)']) ).
fof(normalize_0_4,plain,
! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
<=> ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Vd193,Vd194,Vd196] :
( ( Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,skolemFOFtoCNF_Vd196(Vd193,Vd194)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Vd193,Vd194,Vd196] :
( Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,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_8,plain,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
greater(vd481,vd480),
inference(canonicalize,[],['holds(conseq_conjunct1(conseq(304)), 483, 0)']) ).
fof(normalize_0_10,plain,
! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,skolemFOFtoCNF_Vd196(Vd193,Vd194)) ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(canonicalize,[],[normalize_0_2]) ).
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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( vmul(Vd418,Vd419) != vmul(Vd419,Vd418)
| vmul(Vd419,Vd418) = vmul(Vd418,Vd419) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vmul(Vd418,Vd419))),bind(Y,$fot(vmul(Vd419,Vd418)))]]) ).
cnf(refute_0_6,plain,
vmul(Vd419,Vd418) = vmul(Vd418,Vd419),
inference(resolve,[$cnf( $equal(vmul(Vd418,Vd419),vmul(Vd419,Vd418)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
vmul(vd481,vd469) = vmul(vd469,vd481),
inference(subst,[],[refute_0_6:[bind(Vd418,$fot(vd469)),bind(Vd419,$fot(vd481))]]) ).
cnf(refute_0_8,plain,
( vmul(vd481,vd469) != vmul(vd469,vd481)
| ~ greater(vmul(vd469,vd481),vmul(vd480,vd469))
| greater(vmul(vd481,vd469),vmul(vd480,vd469)) ),
introduced(tautology,[equality,[$cnf( ~ greater(vmul(vd481,vd469),vmul(vd480,vd469)) ),[0],$fot(vmul(vd469,vd481))]]) ).
cnf(refute_0_9,plain,
( ~ greater(vmul(vd469,vd481),vmul(vd480,vd469))
| greater(vmul(vd481,vd469),vmul(vd480,vd469)) ),
inference(resolve,[$cnf( $equal(vmul(vd481,vd469),vmul(vd469,vd481)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
vmul(vd480,vd469) = vmul(vd469,vd480),
inference(subst,[],[refute_0_6:[bind(Vd418,$fot(vd469)),bind(Vd419,$fot(vd480))]]) ).
cnf(refute_0_11,plain,
( vmul(vd480,vd469) != vmul(vd469,vd480)
| ~ greater(vmul(vd469,vd481),vmul(vd469,vd480))
| greater(vmul(vd469,vd481),vmul(vd480,vd469)) ),
introduced(tautology,[equality,[$cnf( ~ greater(vmul(vd469,vd481),vmul(vd480,vd469)) ),[1],$fot(vmul(vd469,vd480))]]) ).
cnf(refute_0_12,plain,
( ~ greater(vmul(vd469,vd481),vmul(vd469,vd480))
| greater(vmul(vd469,vd481),vmul(vd480,vd469)) ),
inference(resolve,[$cnf( $equal(vmul(vd480,vd469),vmul(vd469,vd480)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ greater(vmul(vd469,vd481),vmul(vd469,vd480))
| greater(vmul(vd481,vd469),vmul(vd480,vd469)) ),
inference(resolve,[$cnf( greater(vmul(vd469,vd481),vmul(vd480,vd469)) )],[refute_0_12,refute_0_9]) ).
cnf(refute_0_14,plain,
~ greater(vmul(vd469,vd481),vmul(vd469,vd480)),
inference(resolve,[$cnf( greater(vmul(vd481,vd469),vmul(vd480,vd469)) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
( Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_16,plain,
( vplus(Vd193,Vd196) != vplus(Vd193,Vd196)
| greater(vplus(Vd193,Vd196),Vd193) ),
inference(subst,[],[refute_0_15:[bind(Vd194,$fot(vplus(Vd193,Vd196)))]]) ).
cnf(refute_0_17,plain,
vplus(Vd193,Vd196) = vplus(Vd193,Vd196),
introduced(tautology,[refl,[$fot(vplus(Vd193,Vd196))]]) ).
cnf(refute_0_18,plain,
greater(vplus(Vd193,Vd196),Vd193),
inference(resolve,[$cnf( $equal(vplus(Vd193,Vd196),vplus(Vd193,Vd196)) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
greater(vplus(vmul(X_74,X_75),vmul(X_74,X_76)),vmul(X_74,X_75)),
inference(subst,[],[refute_0_18:[bind(Vd193,$fot(vmul(X_74,X_75))),bind(Vd196,$fot(vmul(X_74,X_76)))]]) ).
cnf(refute_0_20,plain,
vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_21,plain,
vmul(X_74,vplus(X_75,X_76)) = vplus(vmul(X_74,X_75),vmul(X_74,X_76)),
inference(subst,[],[refute_0_20:[bind(Vd432,$fot(X_74)),bind(Vd433,$fot(X_75)),bind(Vd434,$fot(X_76))]]) ).
cnf(refute_0_22,plain,
( vmul(X_74,vplus(X_75,X_76)) != vplus(vmul(X_74,X_75),vmul(X_74,X_76))
| vplus(vmul(X_74,X_75),vmul(X_74,X_76)) = vmul(X_74,vplus(X_75,X_76)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vmul(X_74,vplus(X_75,X_76)))),bind(Y,$fot(vplus(vmul(X_74,X_75),vmul(X_74,X_76))))]]) ).
cnf(refute_0_23,plain,
vplus(vmul(X_74,X_75),vmul(X_74,X_76)) = vmul(X_74,vplus(X_75,X_76)),
inference(resolve,[$cnf( $equal(vmul(X_74,vplus(X_75,X_76)),vplus(vmul(X_74,X_75),vmul(X_74,X_76))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( vplus(vmul(X_74,X_75),vmul(X_74,X_76)) != vmul(X_74,vplus(X_75,X_76))
| ~ greater(vplus(vmul(X_74,X_75),vmul(X_74,X_76)),vmul(X_74,X_75))
| greater(vmul(X_74,vplus(X_75,X_76)),vmul(X_74,X_75)) ),
introduced(tautology,[equality,[$cnf( greater(vplus(vmul(X_74,X_75),vmul(X_74,X_76)),vmul(X_74,X_75)) ),[0],$fot(vmul(X_74,vplus(X_75,X_76)))]]) ).
cnf(refute_0_25,plain,
( ~ greater(vplus(vmul(X_74,X_75),vmul(X_74,X_76)),vmul(X_74,X_75))
| greater(vmul(X_74,vplus(X_75,X_76)),vmul(X_74,X_75)) ),
inference(resolve,[$cnf( $equal(vplus(vmul(X_74,X_75),vmul(X_74,X_76)),vmul(X_74,vplus(X_75,X_76))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
greater(vmul(X_74,vplus(X_75,X_76)),vmul(X_74,X_75)),
inference(resolve,[$cnf( greater(vplus(vmul(X_74,X_75),vmul(X_74,X_76)),vmul(X_74,X_75)) )],[refute_0_19,refute_0_25]) ).
cnf(refute_0_27,plain,
greater(vmul(X_77,vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481))),vmul(X_77,vd480)),
inference(subst,[],[refute_0_26:[bind(X_74,$fot(X_77)),bind(X_75,$fot(vd480)),bind(X_76,$fot(skolemFOFtoCNF_Vd196(vd480,vd481)))]]) ).
cnf(refute_0_28,plain,
greater(vd481,vd480),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_29,plain,
( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,skolemFOFtoCNF_Vd196(Vd193,Vd194)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_30,plain,
( ~ greater(vd481,vd480)
| vd481 = vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481)) ),
inference(subst,[],[refute_0_29:[bind(Vd193,$fot(vd480)),bind(Vd194,$fot(vd481))]]) ).
cnf(refute_0_31,plain,
vd481 = vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481)),
inference(resolve,[$cnf( greater(vd481,vd480) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( vd481 != vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481))
| vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481)) = vd481 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(vd481)),bind(Y,$fot(vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481))))]]) ).
cnf(refute_0_33,plain,
vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481)) = vd481,
inference(resolve,[$cnf( $equal(vd481,vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481)) != vd481
| ~ greater(vmul(X_77,vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481))),vmul(X_77,vd480))
| greater(vmul(X_77,vd481),vmul(X_77,vd480)) ),
introduced(tautology,[equality,[$cnf( greater(vmul(X_77,vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481))),vmul(X_77,vd480)) ),[0,1],$fot(vd481)]]) ).
cnf(refute_0_35,plain,
( ~ greater(vmul(X_77,vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481))),vmul(X_77,vd480))
| greater(vmul(X_77,vd481),vmul(X_77,vd480)) ),
inference(resolve,[$cnf( $equal(vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481)),vd481) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
greater(vmul(X_77,vd481),vmul(X_77,vd480)),
inference(resolve,[$cnf( greater(vmul(X_77,vplus(vd480,skolemFOFtoCNF_Vd196(vd480,vd481))),vmul(X_77,vd480)) )],[refute_0_27,refute_0_35]) ).
cnf(refute_0_37,plain,
greater(vmul(vd469,vd481),vmul(vd469,vd480)),
inference(subst,[],[refute_0_36:[bind(X_77,$fot(vd469))]]) ).
cnf(refute_0_38,plain,
$false,
inference(resolve,[$cnf( greater(vmul(vd469,vd481),vmul(vd469,vd480)) )],[refute_0_37,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM852+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 21:30:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.61
% 0.39/0.61 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.39/0.62
%------------------------------------------------------------------------------