TSTP Solution File: GEO498+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO498+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 : Sat Jul 16 05:26:54 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 24 ~; 11 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz7_7,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp ).
fof(aSatz7_8,conjecture,
! [Xa,Xp,Xr,Xq] :
( s(Xa,Xp) != Xr
| s(Xa,Xq) != Xr
| Xp = Xq ) ).
fof(subgoal_0,plain,
! [Xa,Xp,Xr,Xq] :
( ( ~ ( s(Xa,Xp) != Xr )
& ~ ( s(Xa,Xq) != Xr ) )
=> Xp = Xq ),
inference(strip,[],[aSatz7_8]) ).
fof(negate_0_0,plain,
~ ! [Xa,Xp,Xr,Xq] :
( ( ~ ( s(Xa,Xp) != Xr )
& ~ ( s(Xa,Xq) != Xr ) )
=> Xp = Xq ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
inference(canonicalize,[],[aSatz7_7]) ).
fof(normalize_0_1,plain,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [Xa,Xp,Xq,Xr] :
( Xp != Xq
& s(Xa,Xp) = Xr
& s(Xa,Xq) = Xr ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( skolemFOFtoCNF_Xp != skolemFOFtoCNF_Xq
& s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp) = skolemFOFtoCNF_Xr
& s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq) = skolemFOFtoCNF_Xr ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq) = skolemFOFtoCNF_Xr,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp) = skolemFOFtoCNF_Xr,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
skolemFOFtoCNF_Xp != skolemFOFtoCNF_Xq,
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
s(Xa,s(Xa,Xp)) = Xp,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)) = skolemFOFtoCNF_Xq,
inference(subst,[],[refute_0_0:[bind(Xa,$fot(skolemFOFtoCNF_Xa)),bind(Xp,$fot(skolemFOFtoCNF_Xq))]]) ).
cnf(refute_0_2,plain,
s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq) = skolemFOFtoCNF_Xr,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)) != skolemFOFtoCNF_Xq
| s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq) != skolemFOFtoCNF_Xr
| s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xq ),
introduced(tautology,[equality,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),skolemFOFtoCNF_Xq) ),[0,1],$fot(skolemFOFtoCNF_Xr)]]) ).
cnf(refute_0_4,plain,
( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)) != skolemFOFtoCNF_Xq
| s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xq ),
inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),skolemFOFtoCNF_Xr) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xq,
inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),skolemFOFtoCNF_Xq) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) = skolemFOFtoCNF_Xp,
inference(subst,[],[refute_0_0:[bind(Xa,$fot(skolemFOFtoCNF_Xa)),bind(Xp,$fot(skolemFOFtoCNF_Xp))]]) ).
cnf(refute_0_7,plain,
s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp) = skolemFOFtoCNF_Xr,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_8,plain,
( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) != skolemFOFtoCNF_Xp
| s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp) != skolemFOFtoCNF_Xr
| s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xp ),
introduced(tautology,[equality,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)),skolemFOFtoCNF_Xp) ),[0,1],$fot(skolemFOFtoCNF_Xr)]]) ).
cnf(refute_0_9,plain,
( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) != skolemFOFtoCNF_Xp
| s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xp ),
inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp),skolemFOFtoCNF_Xr) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xp,
inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)),skolemFOFtoCNF_Xp) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) != skolemFOFtoCNF_Xp
| s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) != skolemFOFtoCNF_Xq
| skolemFOFtoCNF_Xp = skolemFOFtoCNF_Xq ),
introduced(tautology,[equality,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),skolemFOFtoCNF_Xq) ),[0],$fot(skolemFOFtoCNF_Xp)]]) ).
cnf(refute_0_12,plain,
( s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) != skolemFOFtoCNF_Xq
| skolemFOFtoCNF_Xp = skolemFOFtoCNF_Xq ),
inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),skolemFOFtoCNF_Xp) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_Xp = skolemFOFtoCNF_Xq,
inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),skolemFOFtoCNF_Xq) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_Xp != skolemFOFtoCNF_Xq,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Xp,skolemFOFtoCNF_Xq) )],[refute_0_13,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO498+1 : TPTP v8.1.0. Released v7.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.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 : Sat Jun 18 13:20:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.51
% 0.18/0.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.52
%------------------------------------------------------------------------------