%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO085+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 05:24:10 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 10 unt; 0 def)
% Number of atoms : 130 ( 37 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 137 ( 64 ~; 48 |; 14 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 36 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(closed_defn,axiom,
! [C] :
( closed(C)
<=> ~ ? [P] : end_point(P,C) ) ).
fof(open_defn,axiom,
! [C] :
( open(C)
<=> ? [P] : end_point(P,C) ) ).
fof(c6,axiom,
! [C,P] :
( end_point(P,C)
=> ? [Q] :
( end_point(Q,C)
& P != Q ) ) ).
fof(theorem_2_7_1,conjecture,
! [C] :
( open(C)
=> ? [P,Q] :
( P != Q
& end_point(P,C)
& end_point(Q,C) ) ) ).
fof(subgoal_0,plain,
! [C] :
( open(C)
=> ? [P,Q] :
( P != Q
& end_point(P,C)
& end_point(Q,C) ) ),
inference(strip,[],[theorem_2_7_1]) ).
fof(negate_0_0,plain,
~ ! [C] :
( open(C)
=> ? [P,Q] :
( P != Q
& end_point(P,C)
& end_point(Q,C) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [C] :
( ~ closed(C)
<=> ? [P] : end_point(P,C) ),
inference(canonicalize,[],[closed_defn]) ).
fof(normalize_0_1,plain,
! [C] :
( ~ closed(C)
<=> ? [P] : end_point(P,C) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [C,P] :
( ( ~ closed(C)
| ~ end_point(P,C) )
& ( closed(C)
| end_point(skolemFOFtoCNF_P_1(C),C) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [C] :
( closed(C)
| end_point(skolemFOFtoCNF_P_1(C),C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [C] :
( open(C)
& ! [P,Q] :
( ~ end_point(P,C)
| ~ end_point(Q,C)
| P = Q ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( open(skolemFOFtoCNF_C_1)
& ! [P,Q] :
( ~ end_point(P,skolemFOFtoCNF_C_1)
| ~ end_point(Q,skolemFOFtoCNF_C_1)
| P = Q ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
open(skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [C] :
( ~ open(C)
<=> ! [P] : ~ end_point(P,C) ),
inference(canonicalize,[],[open_defn]) ).
fof(normalize_0_8,plain,
! [C] :
( ~ closed(C)
<=> open(C) ),
inference(simplify,[],[normalize_0_7,normalize_0_1]) ).
fof(normalize_0_9,plain,
! [C] :
( ~ closed(C)
<=> open(C) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [C] :
( ( ~ closed(C)
| ~ open(C) )
& ( closed(C)
| open(C) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [C] :
( ~ closed(C)
| ~ open(C) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [C,P] :
( ~ end_point(P,C)
| ? [Q] :
( P != Q
& end_point(Q,C) ) ),
inference(canonicalize,[],[c6]) ).
fof(normalize_0_13,plain,
! [C,P] :
( ~ end_point(P,C)
| ? [Q] :
( P != Q
& end_point(Q,C) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [C,P] :
( ( P != skolemFOFtoCNF_Q_2(C,P)
| ~ end_point(P,C) )
& ( ~ end_point(P,C)
| end_point(skolemFOFtoCNF_Q_2(C,P),C) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [C,P] :
( P != skolemFOFtoCNF_Q_2(C,P)
| ~ end_point(P,C) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [C,P] :
( ~ end_point(P,C)
| end_point(skolemFOFtoCNF_Q_2(C,P),C) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_17,plain,
! [P,Q] :
( ~ end_point(P,skolemFOFtoCNF_C_1)
| ~ end_point(Q,skolemFOFtoCNF_C_1)
| P = Q ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_18,plain,
! [P,Q] :
( ~ end_point(P,skolemFOFtoCNF_C_1)
| ~ end_point(Q,skolemFOFtoCNF_C_1)
| P = Q ),
inference(specialize,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
( closed(C)
| end_point(skolemFOFtoCNF_P_1(C),C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( closed(skolemFOFtoCNF_C_1)
| end_point(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_2,plain,
open(skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ closed(C)
| ~ open(C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_4,plain,
( ~ closed(skolemFOFtoCNF_C_1)
| ~ open(skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_3:[bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_5,plain,
~ closed(skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( open(skolemFOFtoCNF_C_1) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
end_point(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( closed(skolemFOFtoCNF_C_1) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( P != skolemFOFtoCNF_Q_2(C,P)
| ~ end_point(P,C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) != skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))
| ~ end_point(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(skolemFOFtoCNF_C_1)),bind(P,$fot(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_0_9,plain,
( closed(X_23)
| end_point(skolemFOFtoCNF_P_1(X_23),X_23) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(X_23))]]) ).
cnf(refute_0_10,plain,
( ~ end_point(P,C)
| end_point(skolemFOFtoCNF_Q_2(C,P),C) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_11,plain,
( ~ end_point(skolemFOFtoCNF_P_1(X_23),X_23)
| end_point(skolemFOFtoCNF_Q_2(X_23,skolemFOFtoCNF_P_1(X_23)),X_23) ),
inference(subst,[],[refute_0_10:[bind(C,$fot(X_23)),bind(P,$fot(skolemFOFtoCNF_P_1(X_23)))]]) ).
cnf(refute_0_12,plain,
( closed(X_23)
| end_point(skolemFOFtoCNF_Q_2(X_23,skolemFOFtoCNF_P_1(X_23)),X_23) ),
inference(resolve,[$cnf( end_point(skolemFOFtoCNF_P_1(X_23),X_23) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( closed(skolemFOFtoCNF_C_1)
| end_point(skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_12:[bind(X_23,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_14,plain,
( ~ end_point(P,skolemFOFtoCNF_C_1)
| ~ end_point(Q,skolemFOFtoCNF_C_1)
| P = Q ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_15,plain,
( ~ end_point(X_194,skolemFOFtoCNF_C_1)
| ~ end_point(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) = X_194 ),
inference(subst,[],[refute_0_14:[bind(P,$fot(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))),bind(Q,$fot(X_194))]]) ).
cnf(refute_0_16,plain,
( ~ end_point(X_194,skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) = X_194
| closed(skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( end_point(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) )],[refute_0_1,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ end_point(X_194,skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) = X_194 ),
inference(resolve,[$cnf( closed(skolemFOFtoCNF_C_1) )],[refute_0_16,refute_0_5]) ).
cnf(refute_0_18,plain,
( ~ end_point(skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)),skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) = skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_0_17:[bind(X_194,$fot(skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))))]]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) = skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))
| closed(skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( end_point(skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)),skolemFOFtoCNF_C_1) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) = skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)),
inference(resolve,[$cnf( closed(skolemFOFtoCNF_C_1) )],[refute_0_19,refute_0_5]) ).
cnf(refute_0_21,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_22,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_23,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) != skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))
| skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)) = skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))),bind(Y,$fot(skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))))]]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)) = skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) != skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)) != skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) = skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))) ),[1],$fot(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) != skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) = skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)),skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) != skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)
| ~ end_point(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_Q_2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))) )],[refute_0_27,refute_0_8]) ).
cnf(refute_0_29,plain,
skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1) = skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_30,plain,
~ end_point(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1)) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( end_point(skolemFOFtoCNF_P_1(skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) )],[refute_0_6,refute_0_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO085+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 10:02:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43
% 0.20/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.44
%------------------------------------------------------------------------------