TSTP Solution File: NUM838+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM838+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 12:30:49 EDT 2022
% Result : Theorem 45.06s 45.28s
% Output : CNFRefutation 45.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 38 unt; 0 def)
% Number of atoms : 111 ( 48 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 84 ( 43 ~; 32 |; 2 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 5 sgn 49 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof('holds(conseq(195), 305, 0)',conjecture,
greater(vplus(vd301,vd303),vplus(vd302,vd303)) ).
fof('holds(antec(195), 304, 0)',axiom,
greater(vd301,vd302) ).
fof('ass(cond(proof(196), 0), 2)',axiom,
! [Vd310,Vd322,Vd323] :
( less(Vd322,Vd323)
=> greater(Vd323,Vd322) ) ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [Vd198,Vd199] :
( less(Vd199,Vd198)
<=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ) ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).
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(subgoal_0,plain,
greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(strip,[],['holds(conseq(195), 305, 0)']) ).
fof(negate_0_0,plain,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Vd322,Vd323] :
( ~ less(Vd322,Vd323)
| greater(Vd323,Vd322) ),
inference(canonicalize,[],['ass(cond(proof(196), 0), 2)']) ).
fof(normalize_0_2,plain,
! [Vd322,Vd323] :
( ~ less(Vd322,Vd323)
| greater(Vd323,Vd322) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Vd198,Vd199] :
( ~ less(Vd199,Vd198)
<=> ! [Vd201] : Vd198 != vplus(Vd199,Vd201) ),
inference(canonicalize,[],['def(cond(conseq(axiom(3)), 12), 1)']) ).
fof(normalize_0_4,plain,
! [Vd198,Vd199] :
( ~ less(Vd199,Vd198)
<=> ! [Vd201] : Vd198 != vplus(Vd199,Vd201) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Vd198,Vd199,Vd201] :
( ( Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ( ~ less(Vd199,Vd198)
| Vd198 = vplus(Vd199,skolemFOFtoCNF_Vd201(Vd198,Vd199)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Vd198,Vd199,Vd201] :
( Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],['ass(cond(33, 0), 0)']) ).
fof(normalize_0_8,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
greater(vd301,vd302),
inference(canonicalize,[],['holds(antec(195), 304, 0)']) ).
fof(normalize_0_10,plain,
! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
<=> ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ),
inference(canonicalize,[],['def(cond(conseq(axiom(3)), 11), 1)']) ).
fof(normalize_0_11,plain,
! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
<=> ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,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_11]) ).
fof(normalize_0_13,plain,
! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,skolemFOFtoCNF_Vd196(Vd193,Vd194)) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],['ass(cond(61, 0), 0)']) ).
fof(normalize_0_15,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ less(Vd322,Vd323)
| greater(Vd323,Vd322) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ less(vplus(X_241,vd302),vplus(X_241,vd301))
| greater(vplus(X_241,vd301),vplus(X_241,vd302)) ),
inference(subst,[],[refute_0_1:[bind(Vd322,$fot(vplus(X_241,vd302))),bind(Vd323,$fot(vplus(X_241,vd301)))]]) ).
cnf(refute_0_3,plain,
( Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( vplus(Vd199,Vd201) != vplus(Vd199,Vd201)
| less(Vd199,vplus(Vd199,Vd201)) ),
inference(subst,[],[refute_0_3:[bind(Vd198,$fot(vplus(Vd199,Vd201)))]]) ).
cnf(refute_0_5,plain,
vplus(Vd199,Vd201) = vplus(Vd199,Vd201),
introduced(tautology,[refl,[$fot(vplus(Vd199,Vd201))]]) ).
cnf(refute_0_6,plain,
less(Vd199,vplus(Vd199,Vd201)),
inference(resolve,[$cnf( $equal(vplus(Vd199,Vd201),vplus(Vd199,Vd201)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
less(vplus(X_91,X_92),vplus(vplus(X_91,X_92),Vd201)),
inference(subst,[],[refute_0_6:[bind(Vd199,$fot(vplus(X_91,X_92)))]]) ).
cnf(refute_0_8,plain,
vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
vplus(vplus(X_91,X_92),Vd201) = vplus(X_91,vplus(X_92,Vd201)),
inference(subst,[],[refute_0_8:[bind(Vd46,$fot(X_91)),bind(Vd47,$fot(X_92)),bind(Vd48,$fot(Vd201))]]) ).
cnf(refute_0_10,plain,
( vplus(vplus(X_91,X_92),Vd201) != vplus(X_91,vplus(X_92,Vd201))
| ~ less(vplus(X_91,X_92),vplus(vplus(X_91,X_92),Vd201))
| less(vplus(X_91,X_92),vplus(X_91,vplus(X_92,Vd201))) ),
introduced(tautology,[equality,[$cnf( less(vplus(X_91,X_92),vplus(vplus(X_91,X_92),Vd201)) ),[1],$fot(vplus(X_91,vplus(X_92,Vd201)))]]) ).
cnf(refute_0_11,plain,
( ~ less(vplus(X_91,X_92),vplus(vplus(X_91,X_92),Vd201))
| less(vplus(X_91,X_92),vplus(X_91,vplus(X_92,Vd201))) ),
inference(resolve,[$cnf( $equal(vplus(vplus(X_91,X_92),Vd201),vplus(X_91,vplus(X_92,Vd201))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
less(vplus(X_91,X_92),vplus(X_91,vplus(X_92,Vd201))),
inference(resolve,[$cnf( less(vplus(X_91,X_92),vplus(vplus(X_91,X_92),Vd201)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
less(vplus(X_91,vd302),vplus(X_91,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)))),
inference(subst,[],[refute_0_12:[bind(Vd201,$fot(skolemFOFtoCNF_Vd196(vd302,vd301))),bind(X_92,$fot(vd302))]]) ).
cnf(refute_0_14,plain,
greater(vd301,vd302),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_15,plain,
( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,skolemFOFtoCNF_Vd196(Vd193,Vd194)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_16,plain,
( ~ greater(vd301,vd302)
| vd301 = vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)) ),
inference(subst,[],[refute_0_15:[bind(Vd193,$fot(vd302)),bind(Vd194,$fot(vd301))]]) ).
cnf(refute_0_17,plain,
vd301 = vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)),
inference(resolve,[$cnf( greater(vd301,vd302) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( vd301 != vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))
| vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)) = vd301 ),
inference(subst,[],[refute_0_20:[bind(X,$fot(vd301)),bind(Y,$fot(vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))))]]) ).
cnf(refute_0_22,plain,
vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)) = vd301,
inference(resolve,[$cnf( $equal(vd301,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)) != vd301
| ~ less(vplus(X_91,vd302),vplus(X_91,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))))
| less(vplus(X_91,vd302),vplus(X_91,vd301)) ),
introduced(tautology,[equality,[$cnf( less(vplus(X_91,vd302),vplus(X_91,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)))) ),[1,1],$fot(vd301)]]) ).
cnf(refute_0_24,plain,
( ~ less(vplus(X_91,vd302),vplus(X_91,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))))
| less(vplus(X_91,vd302),vplus(X_91,vd301)) ),
inference(resolve,[$cnf( $equal(vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)),vd301) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
less(vplus(X_91,vd302),vplus(X_91,vd301)),
inference(resolve,[$cnf( less(vplus(X_91,vd302),vplus(X_91,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)))) )],[refute_0_13,refute_0_24]) ).
cnf(refute_0_26,plain,
less(vplus(X_241,vd302),vplus(X_241,vd301)),
inference(subst,[],[refute_0_25:[bind(X_91,$fot(X_241))]]) ).
cnf(refute_0_27,plain,
greater(vplus(X_241,vd301),vplus(X_241,vd302)),
inference(resolve,[$cnf( less(vplus(X_241,vd302),vplus(X_241,vd301)) )],[refute_0_26,refute_0_2]) ).
cnf(refute_0_28,plain,
greater(vplus(X_265,vd301),vplus(X_265,vd302)),
inference(subst,[],[refute_0_27:[bind(X_241,$fot(X_265))]]) ).
cnf(refute_0_29,plain,
vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_30,plain,
vplus(vd302,X_265) = vplus(X_265,vd302),
inference(subst,[],[refute_0_29:[bind(Vd78,$fot(X_265)),bind(Vd79,$fot(vd302))]]) ).
cnf(refute_0_31,plain,
( vplus(vd302,X_265) != vplus(X_265,vd302)
| vplus(X_265,vd302) = vplus(vd302,X_265) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(vplus(vd302,X_265))),bind(Y,$fot(vplus(X_265,vd302)))]]) ).
cnf(refute_0_32,plain,
vplus(X_265,vd302) = vplus(vd302,X_265),
inference(resolve,[$cnf( $equal(vplus(vd302,X_265),vplus(X_265,vd302)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( vplus(X_265,vd302) != vplus(vd302,X_265)
| ~ greater(vplus(X_265,vd301),vplus(X_265,vd302))
| greater(vplus(X_265,vd301),vplus(vd302,X_265)) ),
introduced(tautology,[equality,[$cnf( greater(vplus(X_265,vd301),vplus(X_265,vd302)) ),[1],$fot(vplus(vd302,X_265))]]) ).
cnf(refute_0_34,plain,
( ~ greater(vplus(X_265,vd301),vplus(X_265,vd302))
| greater(vplus(X_265,vd301),vplus(vd302,X_265)) ),
inference(resolve,[$cnf( $equal(vplus(X_265,vd302),vplus(vd302,X_265)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
greater(vplus(X_265,vd301),vplus(vd302,X_265)),
inference(resolve,[$cnf( greater(vplus(X_265,vd301),vplus(X_265,vd302)) )],[refute_0_28,refute_0_34]) ).
cnf(refute_0_36,plain,
greater(vplus(X_335,vd301),vplus(vd302,X_335)),
inference(subst,[],[refute_0_35:[bind(X_265,$fot(X_335))]]) ).
cnf(refute_0_37,plain,
vplus(vd301,X_335) = vplus(X_335,vd301),
inference(subst,[],[refute_0_29:[bind(Vd78,$fot(X_335)),bind(Vd79,$fot(vd301))]]) ).
cnf(refute_0_38,plain,
( vplus(vd301,X_335) != vplus(X_335,vd301)
| vplus(X_335,vd301) = vplus(vd301,X_335) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(vplus(vd301,X_335))),bind(Y,$fot(vplus(X_335,vd301)))]]) ).
cnf(refute_0_39,plain,
vplus(X_335,vd301) = vplus(vd301,X_335),
inference(resolve,[$cnf( $equal(vplus(vd301,X_335),vplus(X_335,vd301)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( vplus(X_335,vd301) != vplus(vd301,X_335)
| ~ greater(vplus(X_335,vd301),vplus(vd302,X_335))
| greater(vplus(vd301,X_335),vplus(vd302,X_335)) ),
introduced(tautology,[equality,[$cnf( greater(vplus(X_335,vd301),vplus(vd302,X_335)) ),[0],$fot(vplus(vd301,X_335))]]) ).
cnf(refute_0_41,plain,
( ~ greater(vplus(X_335,vd301),vplus(vd302,X_335))
| greater(vplus(vd301,X_335),vplus(vd302,X_335)) ),
inference(resolve,[$cnf( $equal(vplus(X_335,vd301),vplus(vd301,X_335)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
greater(vplus(vd301,X_335),vplus(vd302,X_335)),
inference(resolve,[$cnf( greater(vplus(X_335,vd301),vplus(vd302,X_335)) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(subst,[],[refute_0_42:[bind(X_335,$fot(vd303))]]) ).
cnf(refute_0_44,plain,
$false,
inference(resolve,[$cnf( greater(vplus(vd301,vd303),vplus(vd302,vd303)) )],[refute_0_43,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM838+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % 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 : Wed Jul 6 06:04:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 45.06/45.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.06/45.28
% 45.06/45.28 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 45.06/45.29
%------------------------------------------------------------------------------