%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO524+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 05:27:00 EDT 2022
% Result : Theorem 0.92s 1.15s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 22 |; 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; 0-3 aty)
% Number of variables : 36 ( 0 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz10_5,axiom,
! [Xa,Xb,Xp] :
( Xa = Xb
| reflect(Xa,Xb,reflect(Xa,Xb,Xp)) = Xp ) ).
fof(aSatz10_7,conjecture,
! [Xa,Xb,Xp,Xq] :
( Xa = Xb
| reflect(Xa,Xb,Xp) != reflect(Xa,Xb,Xq)
| Xp = Xq ) ).
fof(subgoal_0,plain,
! [Xa,Xb,Xp,Xq] :
( ( Xa != Xb
& ~ ( reflect(Xa,Xb,Xp) != reflect(Xa,Xb,Xq) ) )
=> Xp = Xq ),
inference(strip,[],[aSatz10_7]) ).
fof(negate_0_0,plain,
~ ! [Xa,Xb,Xp,Xq] :
( ( Xa != Xb
& ~ ( reflect(Xa,Xb,Xp) != reflect(Xa,Xb,Xq) ) )
=> Xp = Xq ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Xa,Xb] :
( Xa = Xb
| ! [Xp] : reflect(Xa,Xb,reflect(Xa,Xb,Xp)) = Xp ),
inference(canonicalize,[],[aSatz10_5]) ).
fof(normalize_0_1,plain,
! [Xa,Xb] :
( Xa = Xb
| ! [Xp] : reflect(Xa,Xb,reflect(Xa,Xb,Xp)) = Xp ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Xa,Xb,Xp] :
( Xa = Xb
| reflect(Xa,Xb,reflect(Xa,Xb,Xp)) = Xp ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [Xa,Xb,Xp,Xq] :
( Xa != Xb
& Xp != Xq
& reflect(Xa,Xb,Xp) = reflect(Xa,Xb,Xq) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( skolemFOFtoCNF_Xa != skolemFOFtoCNF_Xb
& skolemFOFtoCNF_Xp != skolemFOFtoCNF_Xq
& reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp) = reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp) = reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
skolemFOFtoCNF_Xa != skolemFOFtoCNF_Xb,
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_7,plain,
skolemFOFtoCNF_Xp != skolemFOFtoCNF_Xq,
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
( Xa = Xb
| reflect(Xa,Xb,reflect(Xa,Xb,Xp)) = Xp ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)) = skolemFOFtoCNF_Xp
| skolemFOFtoCNF_Xa = skolemFOFtoCNF_Xb ),
inference(subst,[],[refute_0_0:[bind(Xa,$fot(skolemFOFtoCNF_Xa)),bind(Xb,$fot(skolemFOFtoCNF_Xb)),bind(Xp,$fot(skolemFOFtoCNF_Xp))]]) ).
cnf(refute_0_2,plain,
( reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq)) = skolemFOFtoCNF_Xq
| skolemFOFtoCNF_Xa = skolemFOFtoCNF_Xb ),
inference(subst,[],[refute_0_0:[bind(Xa,$fot(skolemFOFtoCNF_Xa)),bind(Xb,$fot(skolemFOFtoCNF_Xb)),bind(Xp,$fot(skolemFOFtoCNF_Xq))]]) ).
cnf(refute_0_3,plain,
reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp) = reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp) != reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq)
| reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq) = reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp))),bind(Y,$fot(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq)))]]) ).
cnf(refute_0_8,plain,
reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq) = reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp),
inference(resolve,[$cnf( $equal(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp),reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq)) != skolemFOFtoCNF_Xq
| reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq) != reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)
| reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)) = skolemFOFtoCNF_Xq ),
introduced(tautology,[equality,[$cnf( $equal(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq)),skolemFOFtoCNF_Xq) ),[0,2],$fot(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp))]]) ).
cnf(refute_0_10,plain,
( reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq)) != skolemFOFtoCNF_Xq
| reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)) = skolemFOFtoCNF_Xq ),
inference(resolve,[$cnf( $equal(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq),reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)) = skolemFOFtoCNF_Xq
| skolemFOFtoCNF_Xa = skolemFOFtoCNF_Xb ),
inference(resolve,[$cnf( $equal(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xq)),skolemFOFtoCNF_Xq) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
skolemFOFtoCNF_Xa != skolemFOFtoCNF_Xb,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_13,plain,
reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)) = skolemFOFtoCNF_Xq,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)) != skolemFOFtoCNF_Xp
| reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)) != skolemFOFtoCNF_Xq
| skolemFOFtoCNF_Xq = skolemFOFtoCNF_Xp ),
introduced(tautology,[equality,[$cnf( $equal(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)),skolemFOFtoCNF_Xp) ),[0],$fot(skolemFOFtoCNF_Xq)]]) ).
cnf(refute_0_15,plain,
( reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)) != skolemFOFtoCNF_Xp
| skolemFOFtoCNF_Xq = skolemFOFtoCNF_Xp ),
inference(resolve,[$cnf( $equal(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)),skolemFOFtoCNF_Xq) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_Xa = skolemFOFtoCNF_Xb
| skolemFOFtoCNF_Xq = skolemFOFtoCNF_Xp ),
inference(resolve,[$cnf( $equal(reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,reflect(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb,skolemFOFtoCNF_Xp)),skolemFOFtoCNF_Xp) )],[refute_0_1,refute_0_15]) ).
cnf(refute_0_17,plain,
skolemFOFtoCNF_Xq = skolemFOFtoCNF_Xp,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xb) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
skolemFOFtoCNF_Xp != skolemFOFtoCNF_Xq,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_Xq != skolemFOFtoCNF_Xp
| skolemFOFtoCNF_Xp = skolemFOFtoCNF_Xq ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_Xq)),bind(Y,$fot(skolemFOFtoCNF_Xp))]]) ).
cnf(refute_0_20,plain,
skolemFOFtoCNF_Xq != skolemFOFtoCNF_Xp,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Xp,skolemFOFtoCNF_Xq) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Xq,skolemFOFtoCNF_Xp) )],[refute_0_17,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO524+1 : TPTP v8.1.0. Released v7.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 08:03:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.92/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.15
% 0.92/1.15 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.92/1.15
%------------------------------------------------------------------------------