TSTP Solution File: NUM854+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM854+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:31:00 EDT 2022
% Result : Theorem 242.37s 242.59s
% Output : CNFRefutation 242.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 39 unt; 0 def)
% Number of atoms : 114 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 44 ~; 33 |; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 4 sgn 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof('holds(conjunct1(315), 514, 0)',conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd511)) ).
fof('holds(conjunct1(314), 510, 0)',axiom,
greater(vd508,vd509) ).
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(147, 0), 0)',axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ) ).
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(subgoal_0,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(strip,[],['holds(conjunct1(315), 514, 0)']) ).
fof(negate_0_0,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Vd226,Vd227] :
( ~ less(Vd226,Vd227)
| greater(Vd227,Vd226) ),
inference(canonicalize,[],['ass(cond(147, 0), 0)']) ).
fof(normalize_0_2,plain,
! [Vd226,Vd227] :
( ~ less(Vd226,Vd227)
| greater(Vd227,Vd226) ),
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,
! [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(vd508,vd509),
inference(canonicalize,[],['holds(conjunct1(314), 510, 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,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(canonicalize,[],['ass(cond(270, 0), 0)']) ).
fof(normalize_0_15,plain,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ less(Vd226,Vd227)
| greater(Vd227,Vd226) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ less(vmul(X_733,vd509),vmul(X_733,vd508))
| greater(vmul(X_733,vd508),vmul(X_733,vd509)) ),
inference(subst,[],[refute_0_1:[bind(Vd226,$fot(vmul(X_733,vd509))),bind(Vd227,$fot(vmul(X_733,vd508)))]]) ).
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( $equal(vplus(Vd199,Vd201),vplus(Vd199,Vd201)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
less(vmul(X_163,X_164),vplus(vmul(X_163,X_164),vmul(X_163,X_165))),
inference(subst,[],[refute_0_6:[bind(Vd199,$fot(vmul(X_163,X_164))),bind(Vd201,$fot(vmul(X_163,X_165)))]]) ).
cnf(refute_0_8,plain,
vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
vmul(X_163,vplus(X_164,X_165)) = vplus(vmul(X_163,X_164),vmul(X_163,X_165)),
inference(subst,[],[refute_0_8:[bind(Vd432,$fot(X_163)),bind(Vd433,$fot(X_164)),bind(Vd434,$fot(X_165))]]) ).
cnf(refute_0_10,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( vmul(X_163,vplus(X_164,X_165)) != vplus(vmul(X_163,X_164),vmul(X_163,X_165))
| vplus(vmul(X_163,X_164),vmul(X_163,X_165)) = vmul(X_163,vplus(X_164,X_165)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(vmul(X_163,vplus(X_164,X_165)))),bind(Y,$fot(vplus(vmul(X_163,X_164),vmul(X_163,X_165))))]]) ).
cnf(refute_0_14,plain,
vplus(vmul(X_163,X_164),vmul(X_163,X_165)) = vmul(X_163,vplus(X_164,X_165)),
inference(resolve,[$cnf( $equal(vmul(X_163,vplus(X_164,X_165)),vplus(vmul(X_163,X_164),vmul(X_163,X_165))) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( vplus(vmul(X_163,X_164),vmul(X_163,X_165)) != vmul(X_163,vplus(X_164,X_165))
| ~ less(vmul(X_163,X_164),vplus(vmul(X_163,X_164),vmul(X_163,X_165)))
| less(vmul(X_163,X_164),vmul(X_163,vplus(X_164,X_165))) ),
introduced(tautology,[equality,[$cnf( less(vmul(X_163,X_164),vplus(vmul(X_163,X_164),vmul(X_163,X_165))) ),[1],$fot(vmul(X_163,vplus(X_164,X_165)))]]) ).
cnf(refute_0_16,plain,
( ~ less(vmul(X_163,X_164),vplus(vmul(X_163,X_164),vmul(X_163,X_165)))
| less(vmul(X_163,X_164),vmul(X_163,vplus(X_164,X_165))) ),
inference(resolve,[$cnf( $equal(vplus(vmul(X_163,X_164),vmul(X_163,X_165)),vmul(X_163,vplus(X_164,X_165))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
less(vmul(X_163,X_164),vmul(X_163,vplus(X_164,X_165))),
inference(resolve,[$cnf( less(vmul(X_163,X_164),vplus(vmul(X_163,X_164),vmul(X_163,X_165))) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
less(vmul(X_729,vd509),vmul(X_729,vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508)))),
inference(subst,[],[refute_0_17:[bind(X_163,$fot(X_729)),bind(X_164,$fot(vd509)),bind(X_165,$fot(skolemFOFtoCNF_Vd196(vd509,vd508)))]]) ).
cnf(refute_0_19,plain,
greater(vd508,vd509),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_20,plain,
( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,skolemFOFtoCNF_Vd196(Vd193,Vd194)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_21,plain,
( ~ greater(vd508,vd509)
| vd508 = vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508)) ),
inference(subst,[],[refute_0_20:[bind(Vd193,$fot(vd509)),bind(Vd194,$fot(vd508))]]) ).
cnf(refute_0_22,plain,
vd508 = vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508)),
inference(resolve,[$cnf( greater(vd508,vd509) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( vd508 != vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508))
| vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508)) = vd508 ),
inference(subst,[],[refute_0_12:[bind(X,$fot(vd508)),bind(Y,$fot(vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508))))]]) ).
cnf(refute_0_24,plain,
vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508)) = vd508,
inference(resolve,[$cnf( $equal(vd508,vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508)) != vd508
| ~ less(vmul(X_729,vd509),vmul(X_729,vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508))))
| less(vmul(X_729,vd509),vmul(X_729,vd508)) ),
introduced(tautology,[equality,[$cnf( less(vmul(X_729,vd509),vmul(X_729,vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508)))) ),[1,1],$fot(vd508)]]) ).
cnf(refute_0_26,plain,
( ~ less(vmul(X_729,vd509),vmul(X_729,vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508))))
| less(vmul(X_729,vd509),vmul(X_729,vd508)) ),
inference(resolve,[$cnf( $equal(vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508)),vd508) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
less(vmul(X_729,vd509),vmul(X_729,vd508)),
inference(resolve,[$cnf( less(vmul(X_729,vd509),vmul(X_729,vplus(vd509,skolemFOFtoCNF_Vd196(vd509,vd508)))) )],[refute_0_18,refute_0_26]) ).
cnf(refute_0_28,plain,
less(vmul(X_733,vd509),vmul(X_733,vd508)),
inference(subst,[],[refute_0_27:[bind(X_729,$fot(X_733))]]) ).
cnf(refute_0_29,plain,
greater(vmul(X_733,vd508),vmul(X_733,vd509)),
inference(resolve,[$cnf( less(vmul(X_733,vd509),vmul(X_733,vd508)) )],[refute_0_28,refute_0_2]) ).
cnf(refute_0_30,plain,
greater(vmul(X_734,vd508),vmul(X_734,vd509)),
inference(subst,[],[refute_0_29:[bind(X_733,$fot(X_734))]]) ).
cnf(refute_0_31,plain,
vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_32,plain,
vmul(vd509,X_734) = vmul(X_734,vd509),
inference(subst,[],[refute_0_31:[bind(Vd418,$fot(vd509)),bind(Vd419,$fot(X_734))]]) ).
cnf(refute_0_33,plain,
( vmul(vd509,X_734) != vmul(X_734,vd509)
| vmul(X_734,vd509) = vmul(vd509,X_734) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(vmul(vd509,X_734))),bind(Y,$fot(vmul(X_734,vd509)))]]) ).
cnf(refute_0_34,plain,
vmul(X_734,vd509) = vmul(vd509,X_734),
inference(resolve,[$cnf( $equal(vmul(vd509,X_734),vmul(X_734,vd509)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( vmul(X_734,vd509) != vmul(vd509,X_734)
| ~ greater(vmul(X_734,vd508),vmul(X_734,vd509))
| greater(vmul(X_734,vd508),vmul(vd509,X_734)) ),
introduced(tautology,[equality,[$cnf( greater(vmul(X_734,vd508),vmul(X_734,vd509)) ),[1],$fot(vmul(vd509,X_734))]]) ).
cnf(refute_0_36,plain,
( ~ greater(vmul(X_734,vd508),vmul(X_734,vd509))
| greater(vmul(X_734,vd508),vmul(vd509,X_734)) ),
inference(resolve,[$cnf( $equal(vmul(X_734,vd509),vmul(vd509,X_734)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
greater(vmul(X_734,vd508),vmul(vd509,X_734)),
inference(resolve,[$cnf( greater(vmul(X_734,vd508),vmul(X_734,vd509)) )],[refute_0_30,refute_0_36]) ).
cnf(refute_0_38,plain,
greater(vmul(X_741,vd508),vmul(vd509,X_741)),
inference(subst,[],[refute_0_37:[bind(X_734,$fot(X_741))]]) ).
cnf(refute_0_39,plain,
vmul(vd508,X_741) = vmul(X_741,vd508),
inference(subst,[],[refute_0_31:[bind(Vd418,$fot(vd508)),bind(Vd419,$fot(X_741))]]) ).
cnf(refute_0_40,plain,
( vmul(vd508,X_741) != vmul(X_741,vd508)
| vmul(X_741,vd508) = vmul(vd508,X_741) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(vmul(vd508,X_741))),bind(Y,$fot(vmul(X_741,vd508)))]]) ).
cnf(refute_0_41,plain,
vmul(X_741,vd508) = vmul(vd508,X_741),
inference(resolve,[$cnf( $equal(vmul(vd508,X_741),vmul(X_741,vd508)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( vmul(X_741,vd508) != vmul(vd508,X_741)
| ~ greater(vmul(X_741,vd508),vmul(vd509,X_741))
| greater(vmul(vd508,X_741),vmul(vd509,X_741)) ),
introduced(tautology,[equality,[$cnf( greater(vmul(X_741,vd508),vmul(vd509,X_741)) ),[0],$fot(vmul(vd508,X_741))]]) ).
cnf(refute_0_43,plain,
( ~ greater(vmul(X_741,vd508),vmul(vd509,X_741))
| greater(vmul(vd508,X_741),vmul(vd509,X_741)) ),
inference(resolve,[$cnf( $equal(vmul(X_741,vd508),vmul(vd508,X_741)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
greater(vmul(vd508,X_741),vmul(vd509,X_741)),
inference(resolve,[$cnf( greater(vmul(X_741,vd508),vmul(vd509,X_741)) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(subst,[],[refute_0_44:[bind(X_741,$fot(vd511))]]) ).
cnf(refute_0_46,plain,
$false,
inference(resolve,[$cnf( greater(vmul(vd508,vd511),vmul(vd509,vd511)) )],[refute_0_45,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM854+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 : n026.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 : Wed Jul 6 23:53:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 242.37/242.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 242.37/242.59
% 242.37/242.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 242.37/242.60
%------------------------------------------------------------------------------