TSTP Solution File: SWC256+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC256+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 21:27:22 EDT 2022
% Result : Theorem 9.55s 9.75s
% Output : CNFRefutation 9.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 103 ( 38 unt; 0 def)
% Number of atoms : 407 ( 160 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 491 ( 187 ~; 103 |; 167 &)
% ( 6 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn 52 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( V != X0
| U != W
| ~ neq(V,nil)
| singletonP(U)
| ( ! [Y0] :
( ssItem(Y0)
=> ( cons(Y0,nil) != W
| ~ memberP(X0,Y0) ) )
& ( nil != X0
| nil != W ) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ~ neq(V,nil)
& ~ singletonP(U) )
=> ! [Y0] :
( ( ssItem(Y0)
& ~ ( cons(Y0,nil) != W ) )
=> ~ memberP(X0,Y0) ) ) ) ) ),
inference(strip,[],[co1]) ).
fof(subgoal_1,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ~ neq(V,nil)
& ~ singletonP(U)
& ! [Y0] :
( ssItem(Y0)
=> ( cons(Y0,nil) != W
| ~ memberP(X0,Y0) ) )
& ~ ( nil != X0 ) )
=> nil != W ) ) ) ),
inference(strip,[],[co1]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ~ neq(V,nil)
& ~ singletonP(U) )
=> ! [Y0] :
( ( ssItem(Y0)
& ~ ( cons(Y0,nil) != W ) )
=> ~ memberP(X0,Y0) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [U] :
( ~ ssList(U)
| ( ~ singletonP(U)
<=> ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) ) ) ),
inference(canonicalize,[],[ax4]) ).
fof(normalize_0_1,plain,
! [U] :
( ~ ssList(U)
| ( ~ singletonP(U)
<=> ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_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_0_1]) ).
fof(normalize_0_3,plain,
! [U,V] :
( cons(V,nil) != U
| ~ ssItem(V)
| ~ ssList(U)
| singletonP(U) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(U)
& U = W
& V = X0
& neq(V,nil)
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ssList(skolemFOFtoCNF_U_1)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& V = X0
& skolemFOFtoCNF_U_1 = W
& neq(V,nil)
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0) ) ) ) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& V = X0
& skolemFOFtoCNF_U_1 = W
& neq(V,nil)
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0) ) ) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ssList(skolemFOFtoCNF_V_12)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0) ) ) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0) ) ) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( ssList(skolemFOFtoCNF_W_12)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(X0,Y0)
& ssItem(Y0) ) ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(X0,Y0)
& ssItem(Y0) ) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(skolemFOFtoCNF_X_9)
& ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(skolemFOFtoCNF_X_9,Y0)
& ssItem(Y0) ) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(skolemFOFtoCNF_X_9,Y0)
& ssItem(Y0) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7)
& ssItem(skolemFOFtoCNF_Y_7) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_16,plain,
ssItem(skolemFOFtoCNF_Y_7),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_17,plain,
ssList(skolemFOFtoCNF_U_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_18,plain,
~ singletonP(skolemFOFtoCNF_U_1),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( cons(V,nil) != U
| ~ ssItem(V)
| ~ ssList(U)
| singletonP(U) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( cons(V,nil) != cons(V,nil)
| ~ ssItem(V)
| ~ ssList(cons(V,nil))
| singletonP(cons(V,nil)) ),
inference(subst,[],[refute_0_0:[bind(U,$fot(cons(V,nil)))]]) ).
cnf(refute_0_2,plain,
cons(V,nil) = cons(V,nil),
introduced(tautology,[refl,[$fot(cons(V,nil))]]) ).
cnf(refute_0_3,plain,
( ~ ssItem(V)
| ~ ssList(cons(V,nil))
| singletonP(cons(V,nil)) ),
inference(resolve,[$cnf( $equal(cons(V,nil),cons(V,nil)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ ssItem(skolemFOFtoCNF_Y_7)
| ~ ssList(cons(skolemFOFtoCNF_Y_7,nil))
| singletonP(cons(skolemFOFtoCNF_Y_7,nil)) ),
inference(subst,[],[refute_0_3:[bind(V,$fot(skolemFOFtoCNF_Y_7))]]) ).
cnf(refute_0_5,plain,
cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_7,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_8,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_9,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_11,plain,
skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( cons(skolemFOFtoCNF_Y_7,nil) != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
| cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_U_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(cons(skolemFOFtoCNF_Y_7,nil),skolemFOFtoCNF_U_1) ),[0],$fot(skolemFOFtoCNF_W_12)]]) ).
cnf(refute_0_13,plain,
( cons(skolemFOFtoCNF_Y_7,nil) != skolemFOFtoCNF_W_12
| cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_U_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(cons(skolemFOFtoCNF_Y_7,nil),skolemFOFtoCNF_W_12) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
( cons(skolemFOFtoCNF_Y_7,nil) != skolemFOFtoCNF_U_1
| ~ ssList(skolemFOFtoCNF_U_1)
| ssList(cons(skolemFOFtoCNF_Y_7,nil)) ),
introduced(tautology,[equality,[$cnf( ~ ssList(cons(skolemFOFtoCNF_Y_7,nil)) ),[0],$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_0_16,plain,
( ~ ssList(skolemFOFtoCNF_U_1)
| ssList(cons(skolemFOFtoCNF_Y_7,nil)) ),
inference(resolve,[$cnf( $equal(cons(skolemFOFtoCNF_Y_7,nil),skolemFOFtoCNF_U_1) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ ssItem(skolemFOFtoCNF_Y_7)
| ~ ssList(skolemFOFtoCNF_U_1)
| singletonP(cons(skolemFOFtoCNF_Y_7,nil)) ),
inference(resolve,[$cnf( ssList(cons(skolemFOFtoCNF_Y_7,nil)) )],[refute_0_16,refute_0_4]) ).
cnf(refute_0_18,plain,
( cons(skolemFOFtoCNF_Y_7,nil) != skolemFOFtoCNF_U_1
| ~ singletonP(cons(skolemFOFtoCNF_Y_7,nil))
| singletonP(skolemFOFtoCNF_U_1) ),
introduced(tautology,[equality,[$cnf( singletonP(cons(skolemFOFtoCNF_Y_7,nil)) ),[0],$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_0_19,plain,
( ~ singletonP(cons(skolemFOFtoCNF_Y_7,nil))
| singletonP(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( $equal(cons(skolemFOFtoCNF_Y_7,nil),skolemFOFtoCNF_U_1) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ ssItem(skolemFOFtoCNF_Y_7)
| ~ ssList(skolemFOFtoCNF_U_1)
| singletonP(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( singletonP(cons(skolemFOFtoCNF_Y_7,nil)) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
ssItem(skolemFOFtoCNF_Y_7),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_22,plain,
( ~ ssList(skolemFOFtoCNF_U_1)
| singletonP(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( ssItem(skolemFOFtoCNF_Y_7) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
ssList(skolemFOFtoCNF_U_1),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_24,plain,
singletonP(skolemFOFtoCNF_U_1),
inference(resolve,[$cnf( ssList(skolemFOFtoCNF_U_1) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
~ singletonP(skolemFOFtoCNF_U_1),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( singletonP(skolemFOFtoCNF_U_1) )],[refute_0_24,refute_0_25]) ).
fof(negate_1_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ~ neq(V,nil)
& ~ singletonP(U)
& ! [Y0] :
( ssItem(Y0)
=> ( cons(Y0,nil) != W
| ~ memberP(X0,Y0) ) )
& ~ ( nil != X0 ) )
=> nil != W ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(U)
& U = W
& V = X0
& nil = W
& nil = X0
& neq(V,nil)
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ssList(skolemFOFtoCNF_U_2)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_2)
& V = X0
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& neq(V,nil)
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0) ) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_2)
& V = X0
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& neq(V,nil)
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0) ) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_2)
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0) ) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_2)
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0) ) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_2)
& nil = X0
& nil = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| ~ memberP(X0,Y0)
| ~ ssItem(Y0) ) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_2)
& nil = X0
& nil = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| ~ memberP(X0,Y0)
| ~ ssItem(Y0) ) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( ~ singletonP(skolemFOFtoCNF_U_2)
& nil = skolemFOFtoCNF_W_13
& nil = skolemFOFtoCNF_X_10
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(skolemFOFtoCNF_X_10)
& ! [Y0] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| ~ memberP(skolemFOFtoCNF_X_10,Y0)
| ~ ssItem(Y0) ) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
neq(skolemFOFtoCNF_V_13,nil),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_10,plain,
nil = skolemFOFtoCNF_X_10,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_11,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( U != V
<=> neq(U,V) ) ) ),
inference(canonicalize,[],[ax15]) ).
fof(normalize_1_12,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( U != V
<=> neq(U,V) ) ) ),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [U,V] :
( ( U != V
| ~ neq(U,V)
| ~ ssList(U)
| ~ ssList(V) )
& ( ~ ssList(U)
| ~ ssList(V)
| U = V
| neq(U,V) ) ),
inference(clausify,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [U,V] :
( U != V
| ~ neq(U,V)
| ~ ssList(U)
| ~ ssList(V) ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
ssList(skolemFOFtoCNF_U_2),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_16,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_17,plain,
nil = skolemFOFtoCNF_W_13,
inference(conjunct,[],[normalize_1_7]) ).
cnf(refute_1_0,plain,
neq(skolemFOFtoCNF_V_13,nil),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_1,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_2,plain,
nil = skolemFOFtoCNF_X_10,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
( nil != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 = nil ),
inference(subst,[],[refute_1_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_X_10))]]) ).
cnf(refute_1_7,plain,
skolemFOFtoCNF_X_10 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_10) )],[refute_1_2,refute_1_6]) ).
cnf(refute_1_8,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 != nil
| skolemFOFtoCNF_V_13 = nil ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_V_13,nil) ),[0],$fot(skolemFOFtoCNF_X_10)]]) ).
cnf(refute_1_9,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_V_13 = nil ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_10,nil) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
skolemFOFtoCNF_V_13 = nil,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) )],[refute_1_1,refute_1_9]) ).
cnf(refute_1_11,plain,
( skolemFOFtoCNF_V_13 != nil
| ~ neq(skolemFOFtoCNF_V_13,nil)
| neq(nil,nil) ),
introduced(tautology,[equality,[$cnf( neq(skolemFOFtoCNF_V_13,nil) ),[0],$fot(nil)]]) ).
cnf(refute_1_12,plain,
( ~ neq(skolemFOFtoCNF_V_13,nil)
| neq(nil,nil) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,nil) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
neq(nil,nil),
inference(resolve,[$cnf( neq(skolemFOFtoCNF_V_13,nil) )],[refute_1_0,refute_1_12]) ).
cnf(refute_1_14,plain,
( U != V
| ~ neq(U,V)
| ~ ssList(U)
| ~ ssList(V) ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_15,plain,
( V != V
| ~ neq(V,V)
| ~ ssList(V) ),
inference(subst,[],[refute_1_14:[bind(U,$fot(V))]]) ).
cnf(refute_1_16,plain,
V = V,
introduced(tautology,[refl,[$fot(V)]]) ).
cnf(refute_1_17,plain,
( ~ neq(V,V)
| ~ ssList(V) ),
inference(resolve,[$cnf( $equal(V,V) )],[refute_1_16,refute_1_15]) ).
cnf(refute_1_18,plain,
( ~ neq(nil,nil)
| ~ ssList(nil) ),
inference(subst,[],[refute_1_17:[bind(V,$fot(nil))]]) ).
cnf(refute_1_19,plain,
~ ssList(nil),
inference(resolve,[$cnf( neq(nil,nil) )],[refute_1_13,refute_1_18]) ).
cnf(refute_1_20,plain,
ssList(skolemFOFtoCNF_U_2),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_21,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_22,plain,
nil = skolemFOFtoCNF_W_13,
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_23,plain,
( nil != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 = nil ),
inference(subst,[],[refute_1_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_W_13))]]) ).
cnf(refute_1_24,plain,
skolemFOFtoCNF_W_13 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_13) )],[refute_1_22,refute_1_23]) ).
cnf(refute_1_25,plain,
( skolemFOFtoCNF_U_2 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 != nil
| skolemFOFtoCNF_U_2 = nil ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_U_2,nil) ),[0],$fot(skolemFOFtoCNF_W_13)]]) ).
cnf(refute_1_26,plain,
( skolemFOFtoCNF_U_2 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_U_2 = nil ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_13,nil) )],[refute_1_24,refute_1_25]) ).
cnf(refute_1_27,plain,
skolemFOFtoCNF_U_2 = nil,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,skolemFOFtoCNF_W_13) )],[refute_1_21,refute_1_26]) ).
cnf(refute_1_28,plain,
( skolemFOFtoCNF_U_2 != nil
| ~ ssList(skolemFOFtoCNF_U_2)
| ssList(nil) ),
introduced(tautology,[equality,[$cnf( ssList(skolemFOFtoCNF_U_2) ),[0],$fot(nil)]]) ).
cnf(refute_1_29,plain,
( ~ ssList(skolemFOFtoCNF_U_2)
| ssList(nil) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,nil) )],[refute_1_27,refute_1_28]) ).
cnf(refute_1_30,plain,
ssList(nil),
inference(resolve,[$cnf( ssList(skolemFOFtoCNF_U_2) )],[refute_1_20,refute_1_29]) ).
cnf(refute_1_31,plain,
$false,
inference(resolve,[$cnf( ssList(nil) )],[refute_1_30,refute_1_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC256+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 12 16:07:33 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.55/9.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.55/9.75
% 9.55/9.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.55/9.76
%------------------------------------------------------------------------------