%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC027+1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Tue Jul 19 21:26:09 EDT 2022
% Result : Theorem 5.30s 5.47s
% Output : CNFRefutation 5.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of formulae : 125 ( 41 unt; 0 def)
% Number of atoms : 611 ( 327 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 726 ( 240 ~; 216 |; 240 &)
% ( 3 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 57 !; 56 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ) ).
fof(ax38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ) ).
fof(ax39,axiom,
~ singletonP(nil) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( V != X0
| U != W
| ( ! [Y0] :
( ssItem(Y0)
=> ( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) ) )
& ( nil != X0
| nil != W ) )
| ( ( nil != V
| nil = U )
& ( nil != U
| nil = V ) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ( ! [Y0] :
( ssItem(Y0)
=> ( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) ) )
& ( nil != X0
| nil != W ) )
& ~ ( nil != V ) )
=> nil = U ) ) ) ),
inference(strip,[],[co1]) ).
fof(subgoal_1,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ( ! [Y0] :
( ssItem(Y0)
=> ( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) ) )
& ( nil != X0
| nil != W ) )
& ( nil != V
| nil = U )
& ~ ( nil != U ) )
=> nil = V ) ) ) ),
inference(strip,[],[co1]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ( ! [Y0] :
( ssItem(Y0)
=> ( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) ) )
& ( nil != X0
| nil != W ) )
& ~ ( nil != V ) )
=> nil = U ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != U
& U = W
& V = X0
& nil = V
& ssList(X0)
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ssList(skolemFOFtoCNF_U_1)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& V = X0
& nil = V
& skolemFOFtoCNF_U_1 = W
& ssList(X0)
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& V = X0
& nil = V
& skolemFOFtoCNF_U_1 = W
& ssList(X0)
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ssList(skolemFOFtoCNF_V_12)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ssList(skolemFOFtoCNF_W_12)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ( ( nil = X0
& nil = skolemFOFtoCNF_W_12 )
| ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ( ( nil = X0
& nil = skolemFOFtoCNF_W_12 )
| ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
& ssList(skolemFOFtoCNF_X_9)
& ( ( nil = skolemFOFtoCNF_W_12
& nil = skolemFOFtoCNF_X_9 )
| ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(skolemFOFtoCNF_X_9,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(skolemFOFtoCNF_X_9,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
( ( nil = skolemFOFtoCNF_W_12
& nil = skolemFOFtoCNF_X_9 )
| ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(skolemFOFtoCNF_X_9,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(skolemFOFtoCNF_X_9,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Z] :
( ( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
| nil = skolemFOFtoCNF_W_12 )
& ( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
| nil = skolemFOFtoCNF_X_9 )
& ( nil = skolemFOFtoCNF_W_12
| memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7) )
& ( nil = skolemFOFtoCNF_W_12
| ssItem(skolemFOFtoCNF_Y_7) )
& ( nil = skolemFOFtoCNF_X_9
| memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7) )
& ( nil = skolemFOFtoCNF_X_9
| ssItem(skolemFOFtoCNF_Y_7) )
& ( ~ leq(skolemFOFtoCNF_Y_7,Z)
| ~ memberP(skolemFOFtoCNF_X_9,Z)
| ~ ssItem(Z)
| nil = skolemFOFtoCNF_W_12
| skolemFOFtoCNF_Y_7 = Z )
& ( ~ leq(skolemFOFtoCNF_Y_7,Z)
| ~ memberP(skolemFOFtoCNF_X_9,Z)
| ~ ssItem(Z)
| nil = skolemFOFtoCNF_X_9
| skolemFOFtoCNF_Y_7 = Z ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( nil = skolemFOFtoCNF_W_12
| memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_13,plain,
nil = skolemFOFtoCNF_V_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_14,plain,
nil != skolemFOFtoCNF_U_1,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(canonicalize,[],[ax38]) ).
fof(normalize_0_16,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
( nil = skolemFOFtoCNF_W_12
| ssItem(skolemFOFtoCNF_Y_7) ),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( nil = skolemFOFtoCNF_W_12
| memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( nil != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
| nil = skolemFOFtoCNF_U_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_U_1) ),[0],$fot(skolemFOFtoCNF_W_12)]]) ).
cnf(refute_0_8,plain,
( nil != skolemFOFtoCNF_W_12
| nil = skolemFOFtoCNF_U_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( nil = skolemFOFtoCNF_U_1
| memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7) ),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_12) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
nil = skolemFOFtoCNF_V_12,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
( nil != skolemFOFtoCNF_V_12
| skolemFOFtoCNF_V_12 = nil ),
inference(subst,[],[refute_0_4:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_V_12))]]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_V_12 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_12) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_V_12 != nil
| skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) ),[0],$fot(nil)]]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,nil) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
nil = skolemFOFtoCNF_X_9,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
( nil != skolemFOFtoCNF_X_9
| skolemFOFtoCNF_X_9 = nil ),
inference(subst,[],[refute_0_4:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_X_9))]]) ).
cnf(refute_0_18,plain,
skolemFOFtoCNF_X_9 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_9) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_X_9 != nil
| ~ memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7)
| memberP(nil,skolemFOFtoCNF_Y_7) ),
introduced(tautology,[equality,[$cnf( memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7) ),[0],$fot(nil)]]) ).
cnf(refute_0_20,plain,
( ~ memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7)
| memberP(nil,skolemFOFtoCNF_Y_7) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,nil) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( nil = skolemFOFtoCNF_U_1
| memberP(nil,skolemFOFtoCNF_Y_7) ),
inference(resolve,[$cnf( memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
nil != skolemFOFtoCNF_U_1,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_23,plain,
memberP(nil,skolemFOFtoCNF_Y_7),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_1) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_25,plain,
( ~ memberP(nil,skolemFOFtoCNF_Y_7)
| ~ ssItem(skolemFOFtoCNF_Y_7) ),
inference(subst,[],[refute_0_24:[bind(U,$fot(skolemFOFtoCNF_Y_7))]]) ).
cnf(refute_0_26,plain,
~ ssItem(skolemFOFtoCNF_Y_7),
inference(resolve,[$cnf( memberP(nil,skolemFOFtoCNF_Y_7) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
( nil = skolemFOFtoCNF_W_12
| ssItem(skolemFOFtoCNF_Y_7) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_28,plain,
( nil = skolemFOFtoCNF_U_1
| ssItem(skolemFOFtoCNF_Y_7) ),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_12) )],[refute_0_27,refute_0_8]) ).
cnf(refute_0_29,plain,
ssItem(skolemFOFtoCNF_Y_7),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_1) )],[refute_0_28,refute_0_22]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( ssItem(skolemFOFtoCNF_Y_7) )],[refute_0_29,refute_0_26]) ).
fof(negate_1_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ( ! [Y0] :
( ssItem(Y0)
=> ( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) ) )
& ( nil != X0
| nil != W ) )
& ( nil != V
| nil = U )
& ~ ( nil != U ) )
=> nil = V ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [U] :
( ~ ssList(U)
| ( ~ singletonP(U)
<=> ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) ) ) ),
inference(canonicalize,[],[ax4]) ).
fof(normalize_1_1,plain,
! [U] :
( ~ ssList(U)
| ( ~ singletonP(U)
<=> ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) ) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [U,V] :
( ( ~ singletonP(U)
| ~ ssList(U)
| cons(skolemFOFtoCNF_V_1(U),nil) = U )
& ( ~ singletonP(U)
| ~ ssList(U)
| ssItem(skolemFOFtoCNF_V_1(U)) )
& ( cons(V,nil) != U
| ~ ssItem(V)
| ~ ssList(U)
| singletonP(U) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [U,V] :
( cons(V,nil) != U
| ~ ssItem(V)
| ~ ssList(U)
| singletonP(U) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != V
& U = W
& V = X0
& nil = U
& ssList(X0)
& ( nil != V
| nil = U )
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ssList(skolemFOFtoCNF_U_2)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != V
& V = X0
& nil = skolemFOFtoCNF_U_2
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ( nil != V
| nil = skolemFOFtoCNF_U_2 )
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != V
& V = X0
& nil = skolemFOFtoCNF_U_2
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ( nil != V
| nil = skolemFOFtoCNF_U_2 )
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_V_13
& nil = skolemFOFtoCNF_U_2
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_V_13
& nil = skolemFOFtoCNF_U_2
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ( ( nil = W
& nil = X0 )
| ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( nil != skolemFOFtoCNF_V_13
& nil = skolemFOFtoCNF_U_2
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ( ( nil = X0
& nil = skolemFOFtoCNF_W_13 )
| ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_13
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ),
inference(skolemize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
? [X0] :
( nil != skolemFOFtoCNF_V_13
& nil = skolemFOFtoCNF_U_2
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ( ( nil = X0
& nil = skolemFOFtoCNF_W_13 )
| ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_13
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
( nil != skolemFOFtoCNF_V_13
& nil = skolemFOFtoCNF_U_2
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10
& ssList(skolemFOFtoCNF_X_10)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ( ( nil = skolemFOFtoCNF_W_13
& nil = skolemFOFtoCNF_X_10 )
| ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_13
& memberP(skolemFOFtoCNF_X_10,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(skolemFOFtoCNF_X_10,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ),
inference(skolemize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
( ( nil = skolemFOFtoCNF_W_13
& nil = skolemFOFtoCNF_X_10 )
| ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_13
& memberP(skolemFOFtoCNF_X_10,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(skolemFOFtoCNF_X_10,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [Z] :
( ( cons(skolemFOFtoCNF_Y_8,nil) = skolemFOFtoCNF_W_13
| nil = skolemFOFtoCNF_W_13 )
& ( cons(skolemFOFtoCNF_Y_8,nil) = skolemFOFtoCNF_W_13
| nil = skolemFOFtoCNF_X_10 )
& ( nil = skolemFOFtoCNF_W_13
| memberP(skolemFOFtoCNF_X_10,skolemFOFtoCNF_Y_8) )
& ( nil = skolemFOFtoCNF_W_13
| ssItem(skolemFOFtoCNF_Y_8) )
& ( nil = skolemFOFtoCNF_X_10
| memberP(skolemFOFtoCNF_X_10,skolemFOFtoCNF_Y_8) )
& ( nil = skolemFOFtoCNF_X_10
| ssItem(skolemFOFtoCNF_Y_8) )
& ( ~ leq(skolemFOFtoCNF_Y_8,Z)
| ~ memberP(skolemFOFtoCNF_X_10,Z)
| ~ ssItem(Z)
| nil = skolemFOFtoCNF_W_13
| skolemFOFtoCNF_Y_8 = Z )
& ( ~ leq(skolemFOFtoCNF_Y_8,Z)
| ~ memberP(skolemFOFtoCNF_X_10,Z)
| ~ ssItem(Z)
| nil = skolemFOFtoCNF_X_10
| skolemFOFtoCNF_Y_8 = Z ) ),
inference(clausify,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
( cons(skolemFOFtoCNF_Y_8,nil) = skolemFOFtoCNF_W_13
| nil = skolemFOFtoCNF_X_10 ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_16,plain,
nil = skolemFOFtoCNF_U_2,
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_17,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_18,plain,
nil != skolemFOFtoCNF_V_13,
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_19,plain,
( nil = skolemFOFtoCNF_X_10
| ssItem(skolemFOFtoCNF_Y_8) ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_20,plain,
ssList(skolemFOFtoCNF_U_2),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_21,plain,
~ singletonP(nil),
inference(canonicalize,[],[ax39]) ).
cnf(refute_1_0,plain,
( cons(V,nil) != U
| ~ ssItem(V)
| ~ ssList(U)
| singletonP(U) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( cons(V,nil) != cons(V,nil)
| ~ ssItem(V)
| ~ ssList(cons(V,nil))
| singletonP(cons(V,nil)) ),
inference(subst,[],[refute_1_0:[bind(U,$fot(cons(V,nil)))]]) ).
cnf(refute_1_2,plain,
cons(V,nil) = cons(V,nil),
introduced(tautology,[refl,[$fot(cons(V,nil))]]) ).
cnf(refute_1_3,plain,
( ~ ssItem(V)
| ~ ssList(cons(V,nil))
| singletonP(cons(V,nil)) ),
inference(resolve,[$cnf( $equal(cons(V,nil),cons(V,nil)) )],[refute_1_2,refute_1_1]) ).
cnf(refute_1_4,plain,
( ~ ssItem(skolemFOFtoCNF_Y_8)
| ~ ssList(cons(skolemFOFtoCNF_Y_8,nil))
| singletonP(cons(skolemFOFtoCNF_Y_8,nil)) ),
inference(subst,[],[refute_1_3:[bind(V,$fot(skolemFOFtoCNF_Y_8))]]) ).
cnf(refute_1_5,plain,
( cons(skolemFOFtoCNF_Y_8,nil) = skolemFOFtoCNF_W_13
| nil = skolemFOFtoCNF_X_10 ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_6,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_7,plain,
nil = skolemFOFtoCNF_U_2,
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_8,refute_1_9]) ).
cnf(refute_1_11,plain,
( nil != skolemFOFtoCNF_U_2
| skolemFOFtoCNF_U_2 = nil ),
inference(subst,[],[refute_1_10:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_U_2))]]) ).
cnf(refute_1_12,plain,
skolemFOFtoCNF_U_2 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_2) )],[refute_1_7,refute_1_11]) ).
cnf(refute_1_13,plain,
( skolemFOFtoCNF_U_2 != nil
| skolemFOFtoCNF_U_2 != skolemFOFtoCNF_W_13
| nil = skolemFOFtoCNF_W_13 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_U_2,skolemFOFtoCNF_W_13) ),[0],$fot(nil)]]) ).
cnf(refute_1_14,plain,
( skolemFOFtoCNF_U_2 != skolemFOFtoCNF_W_13
| nil = skolemFOFtoCNF_W_13 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,nil) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
nil = skolemFOFtoCNF_W_13,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,skolemFOFtoCNF_W_13) )],[refute_1_6,refute_1_14]) ).
cnf(refute_1_16,plain,
( nil != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 = nil ),
inference(subst,[],[refute_1_10:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_W_13))]]) ).
cnf(refute_1_17,plain,
skolemFOFtoCNF_W_13 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_13) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
( cons(skolemFOFtoCNF_Y_8,nil) != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 != nil
| cons(skolemFOFtoCNF_Y_8,nil) = nil ),
introduced(tautology,[equality,[$cnf( ~ $equal(cons(skolemFOFtoCNF_Y_8,nil),nil) ),[0],$fot(skolemFOFtoCNF_W_13)]]) ).
cnf(refute_1_19,plain,
( cons(skolemFOFtoCNF_Y_8,nil) != skolemFOFtoCNF_W_13
| cons(skolemFOFtoCNF_Y_8,nil) = nil ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_13,nil) )],[refute_1_17,refute_1_18]) ).
cnf(refute_1_20,plain,
( cons(skolemFOFtoCNF_Y_8,nil) = nil
| nil = skolemFOFtoCNF_X_10 ),
inference(resolve,[$cnf( $equal(cons(skolemFOFtoCNF_Y_8,nil),skolemFOFtoCNF_W_13) )],[refute_1_5,refute_1_19]) ).
cnf(refute_1_21,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_22,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13 ),
inference(subst,[],[refute_1_10:[bind(X,$fot(skolemFOFtoCNF_V_13)),bind(Y,$fot(skolemFOFtoCNF_X_10))]]) ).
cnf(refute_1_23,plain,
skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) )],[refute_1_21,refute_1_22]) ).
cnf(refute_1_24,plain,
( nil != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_V_13 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_V_13) ),[0],$fot(skolemFOFtoCNF_X_10)]]) ).
cnf(refute_1_25,plain,
( nil != skolemFOFtoCNF_X_10
| nil = skolemFOFtoCNF_V_13 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_10,skolemFOFtoCNF_V_13) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
( cons(skolemFOFtoCNF_Y_8,nil) = nil
| nil = skolemFOFtoCNF_V_13 ),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_10) )],[refute_1_20,refute_1_25]) ).
cnf(refute_1_27,plain,
nil != skolemFOFtoCNF_V_13,
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_28,plain,
cons(skolemFOFtoCNF_Y_8,nil) = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_13) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
( cons(skolemFOFtoCNF_Y_8,nil) != nil
| ~ ssList(nil)
| ssList(cons(skolemFOFtoCNF_Y_8,nil)) ),
introduced(tautology,[equality,[$cnf( ~ ssList(cons(skolemFOFtoCNF_Y_8,nil)) ),[0],$fot(nil)]]) ).
cnf(refute_1_30,plain,
( ~ ssList(nil)
| ssList(cons(skolemFOFtoCNF_Y_8,nil)) ),
inference(resolve,[$cnf( $equal(cons(skolemFOFtoCNF_Y_8,nil),nil) )],[refute_1_28,refute_1_29]) ).
cnf(refute_1_31,plain,
( ~ ssItem(skolemFOFtoCNF_Y_8)
| ~ ssList(nil)
| singletonP(cons(skolemFOFtoCNF_Y_8,nil)) ),
inference(resolve,[$cnf( ssList(cons(skolemFOFtoCNF_Y_8,nil)) )],[refute_1_30,refute_1_4]) ).
cnf(refute_1_32,plain,
( cons(skolemFOFtoCNF_Y_8,nil) != nil
| ~ singletonP(cons(skolemFOFtoCNF_Y_8,nil))
| singletonP(nil) ),
introduced(tautology,[equality,[$cnf( singletonP(cons(skolemFOFtoCNF_Y_8,nil)) ),[0],$fot(nil)]]) ).
cnf(refute_1_33,plain,
( ~ singletonP(cons(skolemFOFtoCNF_Y_8,nil))
| singletonP(nil) ),
inference(resolve,[$cnf( $equal(cons(skolemFOFtoCNF_Y_8,nil),nil) )],[refute_1_28,refute_1_32]) ).
cnf(refute_1_34,plain,
( ~ ssItem(skolemFOFtoCNF_Y_8)
| ~ ssList(nil)
| singletonP(nil) ),
inference(resolve,[$cnf( singletonP(cons(skolemFOFtoCNF_Y_8,nil)) )],[refute_1_31,refute_1_33]) ).
cnf(refute_1_35,plain,
( nil = skolemFOFtoCNF_X_10
| ssItem(skolemFOFtoCNF_Y_8) ),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_36,plain,
( nil = skolemFOFtoCNF_V_13
| ssItem(skolemFOFtoCNF_Y_8) ),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_10) )],[refute_1_35,refute_1_25]) ).
cnf(refute_1_37,plain,
ssItem(skolemFOFtoCNF_Y_8),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_13) )],[refute_1_36,refute_1_27]) ).
cnf(refute_1_38,plain,
( ~ ssList(nil)
| singletonP(nil) ),
inference(resolve,[$cnf( ssItem(skolemFOFtoCNF_Y_8) )],[refute_1_37,refute_1_34]) ).
cnf(refute_1_39,plain,
ssList(skolemFOFtoCNF_U_2),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_40,plain,
( skolemFOFtoCNF_U_2 != nil
| ~ ssList(skolemFOFtoCNF_U_2)
| ssList(nil) ),
introduced(tautology,[equality,[$cnf( ssList(skolemFOFtoCNF_U_2) ),[0],$fot(nil)]]) ).
cnf(refute_1_41,plain,
( ~ ssList(skolemFOFtoCNF_U_2)
| ssList(nil) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,nil) )],[refute_1_12,refute_1_40]) ).
cnf(refute_1_42,plain,
ssList(nil),
inference(resolve,[$cnf( ssList(skolemFOFtoCNF_U_2) )],[refute_1_39,refute_1_41]) ).
cnf(refute_1_43,plain,
singletonP(nil),
inference(resolve,[$cnf( ssList(nil) )],[refute_1_42,refute_1_38]) ).
cnf(refute_1_44,plain,
~ singletonP(nil),
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_45,plain,
$false,
inference(resolve,[$cnf( singletonP(nil) )],[refute_1_43,refute_1_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC027+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % 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 : Sun Jun 12 16:05:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.30/5.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.30/5.47
% 5.30/5.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.30/5.47
%------------------------------------------------------------------------------