TSTP Solution File: NUM838+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM838+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 8.18s 8.37s
% Output : CNFRefutation 8.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 38 unt; 0 def)
% Number of atoms : 85 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 30 ~; 23 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 3 sgn 34 !; 1 ?)
% 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(189, 0), 0)',axiom,
! [Vd295,Vd296] : greater(vplus(Vd295,Vd296),Vd295) ).
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,
! [Vd295,Vd296] : greater(vplus(Vd295,Vd296),Vd295),
inference(canonicalize,[],['ass(cond(189, 0), 0)']) ).
fof(normalize_0_2,plain,
! [Vd295,Vd296] : greater(vplus(Vd295,Vd296),Vd295),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],['ass(cond(33, 0), 0)']) ).
fof(normalize_0_4,plain,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
greater(vd301,vd302),
inference(canonicalize,[],['holds(antec(195), 304, 0)']) ).
fof(normalize_0_6,plain,
! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
<=> ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ),
inference(canonicalize,[],['def(cond(conseq(axiom(3)), 11), 1)']) ).
fof(normalize_0_7,plain,
! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
<=> ! [Vd196] : Vd194 != vplus(Vd193,Vd196) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,plain,
! [Vd193,Vd194] :
( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,skolemFOFtoCNF_Vd196(Vd193,Vd194)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],['ass(cond(61, 0), 0)']) ).
fof(normalize_0_11,plain,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(specialize,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
greater(vplus(Vd295,Vd296),Vd295),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
greater(vplus(vplus(X_134,X_135),Vd296),vplus(X_134,X_135)),
inference(subst,[],[refute_0_1:[bind(Vd295,$fot(vplus(X_134,X_135)))]]) ).
cnf(refute_0_3,plain,
vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_4,plain,
vplus(vplus(X_134,X_135),Vd296) = vplus(X_134,vplus(X_135,Vd296)),
inference(subst,[],[refute_0_3:[bind(Vd46,$fot(X_134)),bind(Vd47,$fot(X_135)),bind(Vd48,$fot(Vd296))]]) ).
cnf(refute_0_5,plain,
( vplus(vplus(X_134,X_135),Vd296) != vplus(X_134,vplus(X_135,Vd296))
| ~ greater(vplus(vplus(X_134,X_135),Vd296),vplus(X_134,X_135))
| greater(vplus(X_134,vplus(X_135,Vd296)),vplus(X_134,X_135)) ),
introduced(tautology,[equality,[$cnf( greater(vplus(vplus(X_134,X_135),Vd296),vplus(X_134,X_135)) ),[0],$fot(vplus(X_134,vplus(X_135,Vd296)))]]) ).
cnf(refute_0_6,plain,
( ~ greater(vplus(vplus(X_134,X_135),Vd296),vplus(X_134,X_135))
| greater(vplus(X_134,vplus(X_135,Vd296)),vplus(X_134,X_135)) ),
inference(resolve,[$cnf( $equal(vplus(vplus(X_134,X_135),Vd296),vplus(X_134,vplus(X_135,Vd296))) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
greater(vplus(X_134,vplus(X_135,Vd296)),vplus(X_134,X_135)),
inference(resolve,[$cnf( greater(vplus(vplus(X_134,X_135),Vd296),vplus(X_134,X_135)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
greater(vplus(X_134,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))),vplus(X_134,vd302)),
inference(subst,[],[refute_0_7:[bind(Vd296,$fot(skolemFOFtoCNF_Vd196(vd302,vd301))),bind(X_135,$fot(vd302))]]) ).
cnf(refute_0_9,plain,
greater(vd301,vd302),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_10,plain,
( ~ greater(Vd194,Vd193)
| Vd194 = vplus(Vd193,skolemFOFtoCNF_Vd196(Vd193,Vd194)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_11,plain,
( ~ greater(vd301,vd302)
| vd301 = vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)) ),
inference(subst,[],[refute_0_10:[bind(Vd193,$fot(vd302)),bind(Vd194,$fot(vd301))]]) ).
cnf(refute_0_12,plain,
vd301 = vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)),
inference(resolve,[$cnf( greater(vd301,vd302) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_14,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_15,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( vd301 != vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))
| vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)) = vd301 ),
inference(subst,[],[refute_0_15:[bind(X,$fot(vd301)),bind(Y,$fot(vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))))]]) ).
cnf(refute_0_17,plain,
vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)) = vd301,
inference(resolve,[$cnf( $equal(vd301,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
( vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)) != vd301
| ~ greater(vplus(X_134,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))),vplus(X_134,vd302))
| greater(vplus(X_134,vd301),vplus(X_134,vd302)) ),
introduced(tautology,[equality,[$cnf( greater(vplus(X_134,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))),vplus(X_134,vd302)) ),[0,1],$fot(vd301)]]) ).
cnf(refute_0_19,plain,
( ~ greater(vplus(X_134,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))),vplus(X_134,vd302))
| greater(vplus(X_134,vd301),vplus(X_134,vd302)) ),
inference(resolve,[$cnf( $equal(vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301)),vd301) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
greater(vplus(X_134,vd301),vplus(X_134,vd302)),
inference(resolve,[$cnf( greater(vplus(X_134,vplus(vd302,skolemFOFtoCNF_Vd196(vd302,vd301))),vplus(X_134,vd302)) )],[refute_0_8,refute_0_19]) ).
cnf(refute_0_21,plain,
greater(vplus(X_810,vd301),vplus(X_810,vd302)),
inference(subst,[],[refute_0_20:[bind(X_134,$fot(X_810))]]) ).
cnf(refute_0_22,plain,
vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_23,plain,
vplus(vd301,X_810) = vplus(X_810,vd301),
inference(subst,[],[refute_0_22:[bind(Vd78,$fot(X_810)),bind(Vd79,$fot(vd301))]]) ).
cnf(refute_0_24,plain,
( vplus(vd301,X_810) != vplus(X_810,vd301)
| vplus(X_810,vd301) = vplus(vd301,X_810) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(vplus(vd301,X_810))),bind(Y,$fot(vplus(X_810,vd301)))]]) ).
cnf(refute_0_25,plain,
vplus(X_810,vd301) = vplus(vd301,X_810),
inference(resolve,[$cnf( $equal(vplus(vd301,X_810),vplus(X_810,vd301)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( vplus(X_810,vd301) != vplus(vd301,X_810)
| ~ greater(vplus(X_810,vd301),vplus(X_810,vd302))
| greater(vplus(vd301,X_810),vplus(X_810,vd302)) ),
introduced(tautology,[equality,[$cnf( greater(vplus(X_810,vd301),vplus(X_810,vd302)) ),[0],$fot(vplus(vd301,X_810))]]) ).
cnf(refute_0_27,plain,
( ~ greater(vplus(X_810,vd301),vplus(X_810,vd302))
| greater(vplus(vd301,X_810),vplus(X_810,vd302)) ),
inference(resolve,[$cnf( $equal(vplus(X_810,vd301),vplus(vd301,X_810)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
greater(vplus(vd301,X_810),vplus(X_810,vd302)),
inference(resolve,[$cnf( greater(vplus(X_810,vd301),vplus(X_810,vd302)) )],[refute_0_21,refute_0_27]) ).
cnf(refute_0_29,plain,
greater(vplus(vd301,X_822),vplus(X_822,vd302)),
inference(subst,[],[refute_0_28:[bind(X_810,$fot(X_822))]]) ).
cnf(refute_0_30,plain,
vplus(vd302,X_822) = vplus(X_822,vd302),
inference(subst,[],[refute_0_22:[bind(Vd78,$fot(X_822)),bind(Vd79,$fot(vd302))]]) ).
cnf(refute_0_31,plain,
( vplus(vd302,X_822) != vplus(X_822,vd302)
| vplus(X_822,vd302) = vplus(vd302,X_822) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(vplus(vd302,X_822))),bind(Y,$fot(vplus(X_822,vd302)))]]) ).
cnf(refute_0_32,plain,
vplus(X_822,vd302) = vplus(vd302,X_822),
inference(resolve,[$cnf( $equal(vplus(vd302,X_822),vplus(X_822,vd302)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( vplus(X_822,vd302) != vplus(vd302,X_822)
| ~ greater(vplus(vd301,X_822),vplus(X_822,vd302))
| greater(vplus(vd301,X_822),vplus(vd302,X_822)) ),
introduced(tautology,[equality,[$cnf( greater(vplus(vd301,X_822),vplus(X_822,vd302)) ),[1],$fot(vplus(vd302,X_822))]]) ).
cnf(refute_0_34,plain,
( ~ greater(vplus(vd301,X_822),vplus(X_822,vd302))
| greater(vplus(vd301,X_822),vplus(vd302,X_822)) ),
inference(resolve,[$cnf( $equal(vplus(X_822,vd302),vplus(vd302,X_822)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
greater(vplus(vd301,X_822),vplus(vd302,X_822)),
inference(resolve,[$cnf( greater(vplus(vd301,X_822),vplus(X_822,vd302)) )],[refute_0_29,refute_0_34]) ).
cnf(refute_0_36,plain,
greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(subst,[],[refute_0_35:[bind(X_822,$fot(vd303))]]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( greater(vplus(vd301,vd303),vplus(vd302,vd303)) )],[refute_0_36,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM838+1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jul 7 08:34:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.18/8.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.18/8.37
% 8.18/8.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.18/8.37
%------------------------------------------------------------------------------