TSTP Solution File: SWV393+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV393+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 : Wed Jul 20 20:31:28 EDT 2022
% Result : Theorem 0.44s 0.62s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 16 unt; 0 def)
% Number of atoms : 116 ( 45 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 126 ( 48 ~; 34 |; 26 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 4 sgn 67 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax23,axiom,
! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( pair_in_list(U,W,Y)
| ( V = W
& X = Y ) ) ) ).
fof(ax24,axiom,
! [U,V,W] : remove_slb(insert_slb(U,pair(V,W)),V) = U ).
fof(l29_co,conjecture,
! [U] :
( ! [V,W] :
( pair_in_list(U,V,W)
=> ! [X] :
( contains_slb(U,X)
=> ( pair_in_list(remove_slb(U,X),V,W)
| V = X ) ) )
=> ! [Y,Z,X1,X2] :
( pair_in_list(insert_slb(U,pair(X1,X2)),Y,Z)
=> ! [X1] :
( contains_slb(insert_slb(U,pair(X1,X2)),X1)
=> ( pair_in_list(remove_slb(insert_slb(U,pair(X1,X2)),X1),Y,Z)
| Y = X1 ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ! [V,W] :
( pair_in_list(U,V,W)
=> ! [X] :
( contains_slb(U,X)
=> ( pair_in_list(remove_slb(U,X),V,W)
| V = X ) ) )
=> ! [Y,Z,X1,X2] :
( pair_in_list(insert_slb(U,pair(X1,X2)),Y,Z)
=> ! [X1] :
( ( contains_slb(insert_slb(U,pair(X1,X2)),X1)
& ~ pair_in_list(remove_slb(insert_slb(U,pair(X1,X2)),X1),Y,Z) )
=> Y = X1 ) ) ),
inference(strip,[],[l29_co]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ! [V,W] :
( pair_in_list(U,V,W)
=> ! [X] :
( contains_slb(U,X)
=> ( pair_in_list(remove_slb(U,X),V,W)
| V = X ) ) )
=> ! [Y,Z,X1,X2] :
( pair_in_list(insert_slb(U,pair(X1,X2)),Y,Z)
=> ! [X1] :
( ( contains_slb(insert_slb(U,pair(X1,X2)),X1)
& ~ pair_in_list(remove_slb(insert_slb(U,pair(X1,X2)),X1),Y,Z) )
=> Y = X1 ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ? [X1,X2,Y,Z] :
( pair_in_list(insert_slb(U,pair(X1,X2)),Y,Z)
& ? [X1] :
( Y != X1
& ~ pair_in_list(remove_slb(insert_slb(U,pair(X1,X2)),X1),Y,Z)
& contains_slb(insert_slb(U,pair(X1,X2)),X1) ) )
& ! [V,W] :
( ~ pair_in_list(U,V,W)
| ! [X] :
( ~ contains_slb(U,X)
| V = X
| pair_in_list(remove_slb(U,X),V,W) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ? [X1,X2,Y,Z] :
( pair_in_list(insert_slb(skolemFOFtoCNF_U,pair(X1,X2)),Y,Z)
& ? [X1] :
( Y != X1
& ~ pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(X1,X2)),X1),Y,Z)
& contains_slb(insert_slb(skolemFOFtoCNF_U,pair(X1,X2)),X1) ) )
& ! [V,W] :
( ~ pair_in_list(skolemFOFtoCNF_U,V,W)
| ! [X] :
( ~ contains_slb(skolemFOFtoCNF_U,X)
| V = X
| pair_in_list(remove_slb(skolemFOFtoCNF_U,X),V,W) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X1,X2,Y,Z] :
( pair_in_list(insert_slb(skolemFOFtoCNF_U,pair(X1,X2)),Y,Z)
& ? [X1] :
( Y != X1
& ~ pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(X1,X2)),X1),Y,Z)
& contains_slb(insert_slb(skolemFOFtoCNF_U,pair(X1,X2)),X1) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( pair_in_list(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
& ? [X1] :
( skolemFOFtoCNF_Y != skolemFOFtoCNF_X1
& ~ pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
& contains_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
pair_in_list(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [U,V,W,X,Y] :
( ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( ~ pair_in_list(U,W,Y)
& ( V != W
| X != Y ) ) ),
inference(canonicalize,[],[ax23]) ).
fof(normalize_0_6,plain,
! [U,V,W,X,Y] :
( ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( ~ pair_in_list(U,W,Y)
& ( V != W
| X != Y ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [U,V,W,X,Y] :
( ( ~ pair_in_list(U,W,Y)
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ( V != W
| X != Y
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ( ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y)
| V = W
| pair_in_list(U,W,Y) )
& ( ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y)
| X = Y
| pair_in_list(U,W,Y) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [U,V,W,X,Y] :
( ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y)
| V = W
| pair_in_list(U,W,Y) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
? [X1] :
( skolemFOFtoCNF_Y != skolemFOFtoCNF_X1
& ~ pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
& contains_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
( skolemFOFtoCNF_Y != skolemFOFtoCNF_X1
& ~ pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
& contains_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
skolemFOFtoCNF_Y != skolemFOFtoCNF_X1,
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
~ pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_13,plain,
! [U,V,W] : remove_slb(insert_slb(U,pair(V,W)),V) = U,
inference(canonicalize,[],[ax24]) ).
fof(normalize_0_14,plain,
! [U,V,W] : remove_slb(insert_slb(U,pair(V,W)),V) = U,
inference(specialize,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
pair_in_list(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y)
| V = W
| pair_in_list(U,W,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( ~ pair_in_list(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| skolemFOFtoCNF_X1 = skolemFOFtoCNF_Y
| pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_X1)),bind(W,$fot(skolemFOFtoCNF_Y)),bind(X,$fot(skolemFOFtoCNF_X2)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_3,plain,
( skolemFOFtoCNF_X1 = skolemFOFtoCNF_Y
| pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( pair_in_list(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
skolemFOFtoCNF_Y != skolemFOFtoCNF_X1,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_X1 != skolemFOFtoCNF_Y
| skolemFOFtoCNF_Y = skolemFOFtoCNF_X1 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(skolemFOFtoCNF_X1)),bind(Y0,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_9,plain,
skolemFOFtoCNF_X1 != skolemFOFtoCNF_Y,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,skolemFOFtoCNF_X1) )],[refute_0_8,refute_0_4]) ).
cnf(refute_0_10,plain,
pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1,skolemFOFtoCNF_Y) )],[refute_0_3,refute_0_9]) ).
cnf(refute_0_11,plain,
~ pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
remove_slb(insert_slb(U,pair(V,W)),V) = U,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1) = skolemFOFtoCNF_U,
inference(subst,[],[refute_0_12:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_X1)),bind(W,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_14,plain,
( remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1) != skolemFOFtoCNF_U
| ~ pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
introduced(tautology,[equality,[$cnf( ~ pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),[0],$fot(skolemFOFtoCNF_U)]]) ).
cnf(refute_0_15,plain,
( ~ pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( $equal(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_U) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
~ pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( pair_in_list(remove_slb(insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1),skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_15,refute_0_11]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_10,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV393+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 22:23:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.44/0.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.62
% 0.44/0.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.44/0.62
%------------------------------------------------------------------------------