TSTP Solution File: SYN074+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN074+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 08:59:19 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 8 unt; 0 def)
% Number of atoms : 156 ( 100 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 183 ( 85 ~; 76 |; 6 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 2 sgn 37 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel51_1,axiom,
? [Z,W] :
! [X,Y] :
( big_f(X,Y)
<=> ( X = Z
& Y = W ) ) ).
fof(pel51,conjecture,
? [Z] :
! [X] :
( ? [W] :
! [Y] :
( big_f(X,Y)
<=> Y = W )
<=> X = Z ) ).
fof(subgoal_0,plain,
? [Z] :
! [X] :
( ? [W] :
! [Y] :
( big_f(X,Y)
<=> Y = W )
<=> X = Z ),
inference(strip,[],[pel51]) ).
fof(negate_0_0,plain,
~ ? [Z] :
! [X] :
( ? [W] :
! [Y] :
( big_f(X,Y)
<=> Y = W )
<=> X = Z ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Z] :
? [X] :
( X != Z
<=> ? [W] :
! [Y] :
( Y != W
<=> ~ big_f(X,Y) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Z] :
? [X] :
( X != Z
<=> ? [W] :
! [Y] :
( Y != W
<=> ~ big_f(X,Y) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Z] :
( skolemFOFtoCNF_X(Z) != Z
<=> ? [W] :
! [Y] :
( Y != W
<=> ~ big_f(skolemFOFtoCNF_X(Z),Y) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [W,Y,Z] :
( ( Y != skolemFOFtoCNF_W_1(Z)
| skolemFOFtoCNF_X(Z) = Z
| big_f(skolemFOFtoCNF_X(Z),Y) )
& ( skolemFOFtoCNF_X(Z) != Z
| skolemFOFtoCNF_Y(W,Z) != W
| ~ big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) )
& ( skolemFOFtoCNF_X(Z) != Z
| skolemFOFtoCNF_Y(W,Z) = W
| big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) )
& ( ~ big_f(skolemFOFtoCNF_X(Z),Y)
| Y = skolemFOFtoCNF_W_1(Z)
| skolemFOFtoCNF_X(Z) = Z ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W,Z] :
( skolemFOFtoCNF_X(Z) != Z
| skolemFOFtoCNF_Y(W,Z) != W
| ~ big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [W,Z] :
! [X,Y] :
( ~ big_f(X,Y)
<=> ( X != Z
| Y != W ) ),
inference(canonicalize,[],[pel51_1]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ big_f(X,Y)
<=> ( X != skolemFOFtoCNF_Z
| Y != skolemFOFtoCNF_W ) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ big_f(X,Y)
<=> ( X != skolemFOFtoCNF_Z
| Y != skolemFOFtoCNF_W ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ( ~ big_f(X,Y)
| X = skolemFOFtoCNF_Z )
& ( ~ big_f(X,Y)
| Y = skolemFOFtoCNF_W )
& ( X != skolemFOFtoCNF_Z
| Y != skolemFOFtoCNF_W
| big_f(X,Y) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ big_f(X,Y)
| Y = skolemFOFtoCNF_W ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [W,Z] :
( skolemFOFtoCNF_X(Z) != Z
| skolemFOFtoCNF_Y(W,Z) = W
| big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_11,plain,
! [Y,Z] :
( Y != skolemFOFtoCNF_W_1(Z)
| skolemFOFtoCNF_X(Z) = Z
| big_f(skolemFOFtoCNF_X(Z),Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ big_f(X,Y)
| X = skolemFOFtoCNF_Z ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( X != skolemFOFtoCNF_Z
| Y != skolemFOFtoCNF_W
| big_f(X,Y) ),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
( skolemFOFtoCNF_X(Z) != Z
| skolemFOFtoCNF_Y(W,Z) != W
| ~ big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_X(Z) != Z
| ~ big_f(Z,skolemFOFtoCNF_Y(W,Z))
| big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) ),
introduced(tautology,[equality,[$cnf( ~ big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) ),[0],$fot(Z)]]) ).
cnf(refute_0_2,plain,
( skolemFOFtoCNF_Y(W,Z) != W
| ~ big_f(Z,W)
| big_f(Z,skolemFOFtoCNF_Y(W,Z)) ),
introduced(tautology,[equality,[$cnf( ~ big_f(Z,skolemFOFtoCNF_Y(W,Z)) ),[1],$fot(W)]]) ).
cnf(refute_0_3,plain,
( skolemFOFtoCNF_X(Z) != Z
| skolemFOFtoCNF_Y(W,Z) != W
| ~ big_f(Z,W)
| big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) ),
inference(resolve,[$cnf( big_f(Z,skolemFOFtoCNF_Y(W,Z)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( skolemFOFtoCNF_X(Z) != Z
| skolemFOFtoCNF_Y(W,Z) != W
| ~ big_f(Z,W) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_X(skolemFOFtoCNF_Z) != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Y(skolemFOFtoCNF_W,skolemFOFtoCNF_Z) != skolemFOFtoCNF_W
| ~ big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_4:[bind(W,$fot(skolemFOFtoCNF_W)),bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_6,plain,
( ~ big_f(X,Y)
| Y = skolemFOFtoCNF_W ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y(X_18,skolemFOFtoCNF_Z))
| skolemFOFtoCNF_Y(X_18,skolemFOFtoCNF_Z) = skolemFOFtoCNF_W ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y(X_18,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_X(Z) != Z
| skolemFOFtoCNF_Y(W,Z) = W
| big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_X(Z) != Z
| ~ big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z))
| big_f(Z,skolemFOFtoCNF_Y(W,Z)) ),
introduced(tautology,[equality,[$cnf( big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) ),[0],$fot(Z)]]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_X(Z) != Z
| skolemFOFtoCNF_Y(W,Z) = W
| big_f(Z,skolemFOFtoCNF_Y(W,Z)) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_Y(W,Z)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_X(skolemFOFtoCNF_Z) != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Y(X_16,skolemFOFtoCNF_Z) = X_16
| big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y(X_16,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_10:[bind(W,$fot(X_16)),bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_12,plain,
( Y != skolemFOFtoCNF_W_1(Z)
| skolemFOFtoCNF_X(Z) = Z
| big_f(skolemFOFtoCNF_X(Z),Y) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
( skolemFOFtoCNF_W_1(Z) != skolemFOFtoCNF_W_1(Z)
| skolemFOFtoCNF_X(Z) = Z
| big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_W_1(Z)) ),
inference(subst,[],[refute_0_12:[bind(Y,$fot(skolemFOFtoCNF_W_1(Z)))]]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_W_1(Z) = skolemFOFtoCNF_W_1(Z),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_W_1(Z))]]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_X(Z) = Z
| big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_W_1(Z)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_1(Z),skolemFOFtoCNF_W_1(Z)) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
( ~ big_f(X,Y)
| X = skolemFOFtoCNF_Z ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_17,plain,
( ~ big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_W_1(Z))
| skolemFOFtoCNF_X(Z) = skolemFOFtoCNF_Z ),
inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_X(Z))),bind(Y,$fot(skolemFOFtoCNF_W_1(Z)))]]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_X(Z) = Z
| skolemFOFtoCNF_X(Z) = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X(Z),skolemFOFtoCNF_W_1(Z)) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
skolemFOFtoCNF_X(skolemFOFtoCNF_Z) = skolemFOFtoCNF_Z,
inference(subst,[],[refute_0_18:[bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_X(skolemFOFtoCNF_Z) != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Z != skolemFOFtoCNF_Z
| skolemFOFtoCNF_X(skolemFOFtoCNF_Z) = skolemFOFtoCNF_Z ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_X(skolemFOFtoCNF_Z),skolemFOFtoCNF_Z) ),[0],$fot(skolemFOFtoCNF_Z)]]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_Z != skolemFOFtoCNF_Z
| skolemFOFtoCNF_X(skolemFOFtoCNF_Z) = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X(skolemFOFtoCNF_Z),skolemFOFtoCNF_Z) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( skolemFOFtoCNF_Z != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Y(X_16,skolemFOFtoCNF_Z) = X_16
| big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y(X_16,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X(skolemFOFtoCNF_Z),skolemFOFtoCNF_Z) )],[refute_0_21,refute_0_11]) ).
cnf(refute_0_23,plain,
skolemFOFtoCNF_Z = skolemFOFtoCNF_Z,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Z)]]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_Y(X_16,skolemFOFtoCNF_Z) = X_16
| big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y(X_16,skolemFOFtoCNF_Z)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_Y(X_18,skolemFOFtoCNF_Z) = X_18
| big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y(X_18,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_24:[bind(X_16,$fot(X_18))]]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_Y(X_18,skolemFOFtoCNF_Z) = X_18
| skolemFOFtoCNF_Y(X_18,skolemFOFtoCNF_Z) = skolemFOFtoCNF_W ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y(X_18,skolemFOFtoCNF_Z)) )],[refute_0_25,refute_0_7]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Y(skolemFOFtoCNF_W,skolemFOFtoCNF_Z) = skolemFOFtoCNF_W,
inference(subst,[],[refute_0_26:[bind(X_18,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_W != skolemFOFtoCNF_W
| skolemFOFtoCNF_Y(skolemFOFtoCNF_W,skolemFOFtoCNF_Z) != skolemFOFtoCNF_W
| skolemFOFtoCNF_Y(skolemFOFtoCNF_W,skolemFOFtoCNF_Z) = skolemFOFtoCNF_W ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y(skolemFOFtoCNF_W,skolemFOFtoCNF_Z),skolemFOFtoCNF_W) ),[0,0],$fot(skolemFOFtoCNF_W)]]) ).
cnf(refute_0_29,plain,
( skolemFOFtoCNF_W != skolemFOFtoCNF_W
| skolemFOFtoCNF_Y(skolemFOFtoCNF_W,skolemFOFtoCNF_Z) = skolemFOFtoCNF_W ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(skolemFOFtoCNF_W,skolemFOFtoCNF_Z),skolemFOFtoCNF_W) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( skolemFOFtoCNF_W != skolemFOFtoCNF_W
| skolemFOFtoCNF_X(skolemFOFtoCNF_Z) != skolemFOFtoCNF_Z
| ~ big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(skolemFOFtoCNF_W,skolemFOFtoCNF_Z),skolemFOFtoCNF_W) )],[refute_0_29,refute_0_5]) ).
cnf(refute_0_31,plain,
skolemFOFtoCNF_W = skolemFOFtoCNF_W,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_W)]]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_X(skolemFOFtoCNF_Z) != skolemFOFtoCNF_Z
| ~ big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W,skolemFOFtoCNF_W) )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_Z != skolemFOFtoCNF_Z
| ~ big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X(skolemFOFtoCNF_Z),skolemFOFtoCNF_Z) )],[refute_0_21,refute_0_32]) ).
cnf(refute_0_34,plain,
~ big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_23,refute_0_33]) ).
cnf(refute_0_35,plain,
( X != skolemFOFtoCNF_Z
| Y != skolemFOFtoCNF_W
| big_f(X,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_36,plain,
( skolemFOFtoCNF_W != skolemFOFtoCNF_W
| skolemFOFtoCNF_Z != skolemFOFtoCNF_Z
| big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_37,plain,
( skolemFOFtoCNF_Z != skolemFOFtoCNF_Z
| big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W,skolemFOFtoCNF_W) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_23,refute_0_37]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W) )],[refute_0_38,refute_0_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN074+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n004.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 : Mon Jul 11 19:13:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------