TSTP Solution File: SYN415+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 : Thu Jul 21 09:02:14 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 82 ( 31 unt; 0 def)
% Number of atoms : 193 ( 87 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 188 ( 77 ~; 54 |; 38 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 86 ( 1 sgn 40 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kalish317,conjecture,
( ( ? [X] : f(X)
& ! [Y,Z] :
( ( f(Y)
& f(Z) )
=> Y = Z ) )
<=> ? [U] :
( f(U)
& ! [V] :
( f(V)
=> U = V ) ) ) ).
fof(subgoal_0,plain,
( ( ? [X] : f(X)
& ! [Y,Z] :
( ( f(Y)
& f(Z) )
=> Y = Z ) )
=> ? [U] :
( f(U)
& ! [V] :
( f(V)
=> U = V ) ) ),
inference(strip,[],[kalish317]) ).
fof(subgoal_1,plain,
( ? [U] :
( f(U)
& ! [V] :
( f(V)
=> U = V ) )
=> ? [X] : f(X) ),
inference(strip,[],[kalish317]) ).
fof(subgoal_2,plain,
( ( ? [U] :
( f(U)
& ! [V] :
( f(V)
=> U = V ) )
& ? [X] : f(X) )
=> ! [Y,Z] :
( ( f(Y)
& f(Z) )
=> Y = Z ) ),
inference(strip,[],[kalish317]) ).
fof(negate_0_0,plain,
~ ( ( ? [X] : f(X)
& ! [Y,Z] :
( ( f(Y)
& f(Z) )
=> Y = Z ) )
=> ? [U] :
( f(U)
& ! [V] :
( f(V)
=> U = V ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X] : f(X)
& ! [U] :
( ~ f(U)
| ? [V] :
( U != V
& f(V) ) )
& ! [Y,Z] :
( ~ f(Y)
| ~ f(Z)
| Y = Z ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [U] :
( ~ f(U)
| ? [V] :
( U != V
& f(V) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [U] :
( ~ f(U)
| ? [V] :
( U != V
& f(V) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [U] :
( ( U != skolemFOFtoCNF_V(U)
| ~ f(U) )
& ( ~ f(U)
| f(skolemFOFtoCNF_V(U)) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [U] :
( U != skolemFOFtoCNF_V(U)
| ~ f(U) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [X] : f(X),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
f(skolemFOFtoCNF_X),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [U] :
( ~ f(U)
| f(skolemFOFtoCNF_V(U)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_8,plain,
! [Y,Z] :
( ~ f(Y)
| ~ f(Z)
| Y = Z ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_9,plain,
! [Y,Z] :
( ~ f(Y)
| ~ f(Z)
| Y = Z ),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
( U != skolemFOFtoCNF_V(U)
| ~ f(U) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_X != skolemFOFtoCNF_V(skolemFOFtoCNF_X)
| ~ f(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_0:[bind(U,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
f(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ f(U)
| f(skolemFOFtoCNF_V(U)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ f(skolemFOFtoCNF_X)
| f(skolemFOFtoCNF_V(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_3:[bind(U,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_5,plain,
f(skolemFOFtoCNF_V(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( f(skolemFOFtoCNF_X) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ f(Y)
| ~ f(Z)
| Y = Z ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ f(X_3)
| ~ f(skolemFOFtoCNF_X)
| skolemFOFtoCNF_X = X_3 ),
inference(subst,[],[refute_0_6:[bind(Y,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(X_3))]]) ).
cnf(refute_0_8,plain,
( ~ f(X_3)
| skolemFOFtoCNF_X = X_3 ),
inference(resolve,[$cnf( f(skolemFOFtoCNF_X) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ f(skolemFOFtoCNF_V(skolemFOFtoCNF_X))
| skolemFOFtoCNF_X = skolemFOFtoCNF_V(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_8:[bind(X_3,$fot(skolemFOFtoCNF_V(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_10,plain,
skolemFOFtoCNF_X = skolemFOFtoCNF_V(skolemFOFtoCNF_X),
inference(resolve,[$cnf( f(skolemFOFtoCNF_V(skolemFOFtoCNF_X)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_X != skolemFOFtoCNF_V(skolemFOFtoCNF_X)
| skolemFOFtoCNF_V(skolemFOFtoCNF_X) = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(skolemFOFtoCNF_X)),bind(Y0,$fot(skolemFOFtoCNF_V(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_15,plain,
skolemFOFtoCNF_V(skolemFOFtoCNF_X) = skolemFOFtoCNF_X,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,skolemFOFtoCNF_V(skolemFOFtoCNF_X)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_V(skolemFOFtoCNF_X) != skolemFOFtoCNF_X
| skolemFOFtoCNF_X != skolemFOFtoCNF_X
| skolemFOFtoCNF_X = skolemFOFtoCNF_V(skolemFOFtoCNF_X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_X,skolemFOFtoCNF_V(skolemFOFtoCNF_X)) ),[1],$fot(skolemFOFtoCNF_X)]]) ).
cnf(refute_0_17,plain,
( skolemFOFtoCNF_X != skolemFOFtoCNF_X
| skolemFOFtoCNF_X = skolemFOFtoCNF_V(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V(skolemFOFtoCNF_X),skolemFOFtoCNF_X) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_X != skolemFOFtoCNF_X
| ~ f(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,skolemFOFtoCNF_V(skolemFOFtoCNF_X)) )],[refute_0_17,refute_0_1]) ).
cnf(refute_0_19,plain,
skolemFOFtoCNF_X = skolemFOFtoCNF_X,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X)]]) ).
cnf(refute_0_20,plain,
~ f(skolemFOFtoCNF_X),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( f(skolemFOFtoCNF_X) )],[refute_0_2,refute_0_20]) ).
fof(negate_1_0,plain,
~ ( ? [U] :
( f(U)
& ! [V] :
( f(V)
=> U = V ) )
=> ? [X] : f(X) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [U] :
( f(U)
& ! [V] :
( ~ f(V)
| U = V ) )
& ! [X] : ~ f(X) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [U] :
( f(U)
& ! [V] :
( ~ f(V)
| U = V ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( f(skolemFOFtoCNF_U)
& ! [V] :
( ~ f(V)
| skolemFOFtoCNF_U = V ) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
f(skolemFOFtoCNF_U),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X] : ~ f(X),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_5,plain,
! [X] : ~ f(X),
inference(specialize,[],[normalize_1_4]) ).
cnf(refute_1_0,plain,
f(skolemFOFtoCNF_U),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
~ f(X),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_2,plain,
~ f(skolemFOFtoCNF_U),
inference(subst,[],[refute_1_1:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_1_3,plain,
$false,
inference(resolve,[$cnf( f(skolemFOFtoCNF_U) )],[refute_1_0,refute_1_2]) ).
fof(negate_2_0,plain,
~ ( ( ? [U] :
( f(U)
& ! [V] :
( f(V)
=> U = V ) )
& ? [X] : f(X) )
=> ! [Y,Z] :
( ( f(Y)
& f(Z) )
=> Y = Z ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ? [U] :
( f(U)
& ! [V] :
( ~ f(V)
| U = V ) )
& ? [X] : f(X)
& ? [Y,Z] :
( Y != Z
& f(Y)
& f(Z) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
? [Y,Z] :
( Y != Z
& f(Y)
& f(Z) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
( skolemFOFtoCNF_Y != skolemFOFtoCNF_Z
& f(skolemFOFtoCNF_Y)
& f(skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
skolemFOFtoCNF_Y != skolemFOFtoCNF_Z,
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
f(skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_5,plain,
? [U] :
( f(U)
& ! [V] :
( ~ f(V)
| U = V ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_6,plain,
( f(skolemFOFtoCNF_U_1)
& ! [V] :
( ~ f(V)
| skolemFOFtoCNF_U_1 = V ) ),
inference(skolemize,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [V] :
( ~ f(V)
| skolemFOFtoCNF_U_1 = V ),
inference(conjunct,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
! [V] :
( ~ f(V)
| skolemFOFtoCNF_U_1 = V ),
inference(specialize,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
f(skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_2_2]) ).
cnf(refute_2_0,plain,
skolemFOFtoCNF_Y != skolemFOFtoCNF_Z,
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
f(skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_2,plain,
( ~ f(V)
| skolemFOFtoCNF_U_1 = V ),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_3,plain,
( ~ f(skolemFOFtoCNF_Y)
| skolemFOFtoCNF_U_1 = skolemFOFtoCNF_Y ),
inference(subst,[],[refute_2_2:[bind(V,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_2_4,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_Y,
inference(resolve,[$cnf( f(skolemFOFtoCNF_Y) )],[refute_2_1,refute_2_3]) ).
cnf(refute_2_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_2_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_2_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_2_5,refute_2_6]) ).
cnf(refute_2_8,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_Y
| skolemFOFtoCNF_Y = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_2_7:[bind(X0,$fot(skolemFOFtoCNF_U_1)),bind(Y0,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_2_9,plain,
skolemFOFtoCNF_Y = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Y) )],[refute_2_4,refute_2_8]) ).
cnf(refute_2_10,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Y != skolemFOFtoCNF_U_1
| skolemFOFtoCNF_Y = skolemFOFtoCNF_Z ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y,skolemFOFtoCNF_U_1) ),[1],$fot(skolemFOFtoCNF_Z)]]) ).
cnf(refute_2_11,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Y = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,skolemFOFtoCNF_U_1) )],[refute_2_9,refute_2_10]) ).
cnf(refute_2_12,plain,
f(skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_13,plain,
( ~ f(skolemFOFtoCNF_Z)
| skolemFOFtoCNF_U_1 = skolemFOFtoCNF_Z ),
inference(subst,[],[refute_2_2:[bind(V,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_2_14,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_Z,
inference(resolve,[$cnf( f(skolemFOFtoCNF_Z) )],[refute_2_12,refute_2_13]) ).
cnf(refute_2_15,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Z = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_2_7:[bind(X0,$fot(skolemFOFtoCNF_U_1)),bind(Y0,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_2_16,plain,
skolemFOFtoCNF_Z = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z) )],[refute_2_14,refute_2_15]) ).
cnf(refute_2_17,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_U_1
| skolemFOFtoCNF_Z != skolemFOFtoCNF_U_1
| skolemFOFtoCNF_U_1 = skolemFOFtoCNF_Z ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z) ),[1],$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_2_18,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_U_1
| skolemFOFtoCNF_U_1 = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,skolemFOFtoCNF_U_1) )],[refute_2_16,refute_2_17]) ).
cnf(refute_2_19,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_U_1
| skolemFOFtoCNF_Y = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z) )],[refute_2_18,refute_2_11]) ).
cnf(refute_2_20,plain,
skolemFOFtoCNF_U_1 != skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_2_19,refute_2_0]) ).
cnf(refute_2_21,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_U_1,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_2_22,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_U_1) )],[refute_2_21,refute_2_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.12/0.35 % Computer : n003.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 600
% 0.12/0.35 % DateTime : Tue Jul 12 04:19:45 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.50
%------------------------------------------------------------------------------