TSTP Solution File: GEO499+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO499+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 5.88s 6.04s
% Output : CNFRefutation 5.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 19 unt; 0 def)
% Number of atoms : 70 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 32 ~; 23 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 43 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz3_2,axiom,
! [Xa,Xb,Xc] :
( ~ s_t(Xa,Xb,Xc)
| s_t(Xc,Xb,Xa) ) ).
fof(aSatz7_7,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp ).
fof(aSatz7_15a,axiom,
! [Xp,Xq,Xr,Xa] :
( ~ s_t(Xp,Xq,Xr)
| s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ) ).
fof(aSatz7_15b,conjecture,
! [Xp,Xq,Xr,Xa] :
( s_t(Xp,Xq,Xr)
| ~ s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ) ).
fof(subgoal_0,plain,
! [Xp,Xq,Xr,Xa] :
( ~ s_t(Xp,Xq,Xr)
=> ~ s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
inference(strip,[],[aSatz7_15b]) ).
fof(negate_0_0,plain,
~ ! [Xp,Xq,Xr,Xa] :
( ~ s_t(Xp,Xq,Xr)
=> ~ s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Xa,Xb,Xc] :
( ~ s_t(Xa,Xb,Xc)
| s_t(Xc,Xb,Xa) ),
inference(canonicalize,[],[aSatz3_2]) ).
fof(normalize_0_1,plain,
! [Xa,Xb,Xc] :
( ~ s_t(Xa,Xb,Xc)
| s_t(Xc,Xb,Xa) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [Xp,Xq,Xr] :
( ~ s_t(Xp,Xq,Xr)
& ? [Xa] : s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( ~ s_t(skolemFOFtoCNF_Xp,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xr)
& ? [Xa] : s_t(s(Xa,skolemFOFtoCNF_Xp),s(Xa,skolemFOFtoCNF_Xq),s(Xa,skolemFOFtoCNF_Xr)) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [Xa] : s_t(s(Xa,skolemFOFtoCNF_Xp),s(Xa,skolemFOFtoCNF_Xq),s(Xa,skolemFOFtoCNF_Xr)),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
s_t(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Xp,Xq,Xr] :
( ~ s_t(Xp,Xq,Xr)
| ! [Xa] : s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
inference(canonicalize,[],[aSatz7_15a]) ).
fof(normalize_0_7,plain,
! [Xp,Xq,Xr] :
( ~ s_t(Xp,Xq,Xr)
| ! [Xa] : s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Xa,Xp,Xq,Xr] :
( ~ s_t(Xp,Xq,Xr)
| s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
inference(canonicalize,[],[aSatz7_7]) ).
fof(normalize_0_10,plain,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
~ s_t(skolemFOFtoCNF_Xp,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xr),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( ~ s_t(Xa,Xb,Xc)
| s_t(Xc,Xb,Xa) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xp)
| s_t(skolemFOFtoCNF_Xp,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xr) ),
inference(subst,[],[refute_0_0:[bind(Xa,$fot(skolemFOFtoCNF_Xr)),bind(Xb,$fot(skolemFOFtoCNF_Xq)),bind(Xc,$fot(skolemFOFtoCNF_Xp))]]) ).
cnf(refute_0_2,plain,
s_t(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ s_t(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr))
| s_t(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) ),
inference(subst,[],[refute_0_0:[bind(Xa,$fot(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))),bind(Xb,$fot(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq))),bind(Xc,$fot(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)))]]) ).
cnf(refute_0_4,plain,
s_t(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)),
inference(resolve,[$cnf( s_t(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ s_t(Xp,Xq,Xr)
| s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
( ~ s_t(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))
| s_t(s(X_2417,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),s(X_2417,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(X_2417,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) ),
inference(subst,[],[refute_0_5:[bind(Xa,$fot(X_2417)),bind(Xp,$fot(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr))),bind(Xq,$fot(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq))),bind(Xr,$fot(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)))]]) ).
cnf(refute_0_7,plain,
s_t(s(X_2417,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),s(X_2417,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(X_2417,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))),
inference(resolve,[$cnf( s_t(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
s_t(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))),
inference(subst,[],[refute_0_7:[bind(X_2417,$fot(skolemFOFtoCNF_Xa))]]) ).
cnf(refute_0_9,plain,
s(Xa,s(Xa,Xp)) = Xp,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)) = skolemFOFtoCNF_Xr,
inference(subst,[],[refute_0_9:[bind(Xa,$fot(skolemFOFtoCNF_Xa)),bind(Xp,$fot(skolemFOFtoCNF_Xr))]]) ).
cnf(refute_0_11,plain,
( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)) != skolemFOFtoCNF_Xr
| ~ s_t(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)))
| s_t(skolemFOFtoCNF_Xr,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) ),
introduced(tautology,[equality,[$cnf( s_t(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) ),[0],$fot(skolemFOFtoCNF_Xr)]]) ).
cnf(refute_0_12,plain,
( ~ s_t(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)))
| s_t(skolemFOFtoCNF_Xr,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) ),
inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),skolemFOFtoCNF_Xr) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
s_t(skolemFOFtoCNF_Xr,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))),
inference(resolve,[$cnf( s_t(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)) = skolemFOFtoCNF_Xq,
inference(subst,[],[refute_0_9:[bind(Xa,$fot(skolemFOFtoCNF_Xa)),bind(Xp,$fot(skolemFOFtoCNF_Xq))]]) ).
cnf(refute_0_15,plain,
( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)) != skolemFOFtoCNF_Xq
| ~ s_t(skolemFOFtoCNF_Xr,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)))
| s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) ),
introduced(tautology,[equality,[$cnf( s_t(skolemFOFtoCNF_Xr,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) ),[1],$fot(skolemFOFtoCNF_Xq)]]) ).
cnf(refute_0_16,plain,
( ~ s_t(skolemFOFtoCNF_Xr,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)))
| s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) ),
inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),skolemFOFtoCNF_Xq) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) = skolemFOFtoCNF_Xp,
inference(subst,[],[refute_0_9:[bind(Xa,$fot(skolemFOFtoCNF_Xa)),bind(Xp,$fot(skolemFOFtoCNF_Xp))]]) ).
cnf(refute_0_18,plain,
( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) != skolemFOFtoCNF_Xp
| ~ s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)))
| s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xp) ),
introduced(tautology,[equality,[$cnf( s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) ),[2],$fot(skolemFOFtoCNF_Xp)]]) ).
cnf(refute_0_19,plain,
( ~ s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)))
| s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xp) ),
inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)),skolemFOFtoCNF_Xp) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ s_t(skolemFOFtoCNF_Xr,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)))
| s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xp) ),
inference(resolve,[$cnf( s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xp),
inference(resolve,[$cnf( s_t(skolemFOFtoCNF_Xr,s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp))) )],[refute_0_13,refute_0_20]) ).
cnf(refute_0_22,plain,
s_t(skolemFOFtoCNF_Xp,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xr),
inference(resolve,[$cnf( s_t(skolemFOFtoCNF_Xr,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xp) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
~ s_t(skolemFOFtoCNF_Xp,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xr),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( s_t(skolemFOFtoCNF_Xp,skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xr) )],[refute_0_22,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO499+1 : TPTP v8.1.0. Released v7.0.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 10:22:43 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.88/6.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.88/6.04
% 5.88/6.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.88/6.05
%------------------------------------------------------------------------------