TSTP Solution File: SWC097+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC097+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 21:26:32 EDT 2022
% Result : Theorem 0.21s 0.51s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 73 ( 27 unt; 0 def)
% Number of atoms : 313 ( 147 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 366 ( 126 ~; 71 |; 144 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 43 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( V != X0
| U != W
| ( ( ~ neq(V,nil)
| ? [Y] :
( ssItem(Y)
& app(U,cons(Y,nil)) = V )
| ! [Z] :
( ssItem(Z)
=> app(W,cons(Z,nil)) != X0 ) )
& ( ~ neq(V,nil)
| neq(X0,nil) ) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ~ neq(V,nil)
& ~ ? [Y] :
( ssItem(Y)
& app(U,cons(Y,nil)) = V ) )
=> ! [Z] :
( ssItem(Z)
=> app(W,cons(Z,nil)) != X0 ) ) ) ) ),
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)
| ? [Y] :
( ssItem(Y)
& app(U,cons(Y,nil)) = V )
| ! [Z] :
( ssItem(Z)
=> app(W,cons(Z,nil)) != X0 ) )
& ~ ~ neq(V,nil) )
=> neq(X0,nil) ) ) ) ),
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)
& ~ ? [Y] :
( ssItem(Y)
& app(U,cons(Y,nil)) = V ) )
=> ! [Z] :
( ssItem(Z)
=> app(W,cons(Z,nil)) != X0 ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( U = W
& V = X0
& neq(V,nil)
& ssList(X0)
& ? [Z] :
( app(W,cons(Z,nil)) = X0
& ssItem(Z) )
& ! [Y] :
( app(U,cons(Y,nil)) != V
| ~ ssItem(Y) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ssList(skolemFOFtoCNF_U_1)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( V = X0
& skolemFOFtoCNF_U_1 = W
& neq(V,nil)
& ssList(X0)
& ? [Z] :
( app(W,cons(Z,nil)) = X0
& ssItem(Z) )
& ! [Y] :
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != V
| ~ ssItem(Y) ) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( V = X0
& skolemFOFtoCNF_U_1 = W
& neq(V,nil)
& ssList(X0)
& ? [Z] :
( app(W,cons(Z,nil)) = X0
& ssItem(Z) )
& ! [Y] :
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != V
| ~ ssItem(Y) ) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ssList(skolemFOFtoCNF_V_12)
& ? [W] :
( ssList(W)
& ? [X0] :
( skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(X0)
& ? [Z] :
( app(W,cons(Z,nil)) = X0
& ssItem(Z) )
& ! [Y] :
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != skolemFOFtoCNF_V_12
| ~ ssItem(Y) ) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(X0)
& ? [Z] :
( app(W,cons(Z,nil)) = X0
& ssItem(Z) )
& ! [Y] :
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != skolemFOFtoCNF_V_12
| ~ ssItem(Y) ) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ssList(skolemFOFtoCNF_W_12)
& ? [X0] :
( skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(X0)
& ? [Z] :
( app(skolemFOFtoCNF_W_12,cons(Z,nil)) = X0
& ssItem(Z) )
& ! [Y] :
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != skolemFOFtoCNF_V_12
| ~ ssItem(Y) ) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X0] :
( skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(X0)
& ? [Z] :
( app(skolemFOFtoCNF_W_12,cons(Z,nil)) = X0
& ssItem(Z) )
& ! [Y] :
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != skolemFOFtoCNF_V_12
| ~ ssItem(Y) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
& neq(skolemFOFtoCNF_V_12,nil)
& ssList(skolemFOFtoCNF_X_9)
& ? [Z] :
( app(skolemFOFtoCNF_W_12,cons(Z,nil)) = skolemFOFtoCNF_X_9
& ssItem(Z) )
& ! [Y] :
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != skolemFOFtoCNF_V_12
| ~ ssItem(Y) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Y] :
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != skolemFOFtoCNF_V_12
| ~ ssItem(Y) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Y] :
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != skolemFOFtoCNF_V_12
| ~ ssItem(Y) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [Z] :
( app(skolemFOFtoCNF_W_12,cons(Z,nil)) = skolemFOFtoCNF_X_9
& ssItem(Z) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_11,plain,
( app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_X_9
& ssItem(skolemFOFtoCNF_Z_6) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_X_9,
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_14,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
ssItem(skolemFOFtoCNF_Z_6),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( app(skolemFOFtoCNF_U_1,cons(Y,nil)) != skolemFOFtoCNF_V_12
| ~ ssItem(Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_1,plain,
( app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) != skolemFOFtoCNF_V_12
| ~ ssItem(skolemFOFtoCNF_Z_6) ),
inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_Z_6))]]) ).
cnf(refute_0_2,plain,
app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_X_9,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_3,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y0
| Y0 = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X != Y0
| Y0 = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y0,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_8,plain,
skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) = app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)),
introduced(tautology,[refl,[$fot(app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)))]]) ).
cnf(refute_0_10,plain,
( app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) != app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil))
| skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
| app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) = app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) ),
introduced(tautology,[equality,[$cnf( $equal(app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)),app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil))) ),[1,0],$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
| app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) = app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) ),
inference(resolve,[$cnf( $equal(app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)),app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) = app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) != app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil))
| app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) != skolemFOFtoCNF_X_9
| app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_X_9 ),
introduced(tautology,[equality,[$cnf( $equal(app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)),skolemFOFtoCNF_X_9) ),[0],$fot(app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)))]]) ).
cnf(refute_0_14,plain,
( app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) != skolemFOFtoCNF_X_9
| app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_X_9 ),
inference(resolve,[$cnf( $equal(app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)),app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| skolemFOFtoCNF_X_9 = skolemFOFtoCNF_V_12 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_V_12)),bind(Y0,$fot(skolemFOFtoCNF_X_9))]]) ).
cnf(refute_0_17,plain,
skolemFOFtoCNF_X_9 = skolemFOFtoCNF_V_12,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) != skolemFOFtoCNF_X_9
| skolemFOFtoCNF_X_9 != skolemFOFtoCNF_V_12
| app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_V_12 ),
introduced(tautology,[equality,[$cnf( ~ $equal(app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)),skolemFOFtoCNF_V_12) ),[0],$fot(skolemFOFtoCNF_X_9)]]) ).
cnf(refute_0_19,plain,
( app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) != skolemFOFtoCNF_X_9
| app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_V_12 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,skolemFOFtoCNF_V_12) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)) != skolemFOFtoCNF_X_9
| app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_V_12 ),
inference(resolve,[$cnf( $equal(app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)),skolemFOFtoCNF_X_9) )],[refute_0_14,refute_0_19]) ).
cnf(refute_0_21,plain,
app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_V_12,
inference(resolve,[$cnf( $equal(app(skolemFOFtoCNF_W_12,cons(skolemFOFtoCNF_Z_6,nil)),skolemFOFtoCNF_X_9) )],[refute_0_2,refute_0_20]) ).
cnf(refute_0_22,plain,
( app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) != skolemFOFtoCNF_V_12
| skolemFOFtoCNF_V_12 != skolemFOFtoCNF_V_12
| app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_V_12 ),
introduced(tautology,[equality,[$cnf( ~ $equal(app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)),skolemFOFtoCNF_V_12) ),[0],$fot(skolemFOFtoCNF_V_12)]]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_V_12
| app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)) = skolemFOFtoCNF_V_12 ),
inference(resolve,[$cnf( $equal(app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)),skolemFOFtoCNF_V_12) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_V_12
| ~ ssItem(skolemFOFtoCNF_Z_6) ),
inference(resolve,[$cnf( $equal(app(skolemFOFtoCNF_U_1,cons(skolemFOFtoCNF_Z_6,nil)),skolemFOFtoCNF_V_12) )],[refute_0_23,refute_0_1]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_V_12,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_V_12)]]) ).
cnf(refute_0_26,plain,
~ ssItem(skolemFOFtoCNF_Z_6),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_V_12) )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
ssItem(skolemFOFtoCNF_Z_6),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( ssItem(skolemFOFtoCNF_Z_6) )],[refute_0_27,refute_0_26]) ).
fof(negate_1_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ( ~ neq(V,nil)
| ? [Y] :
( ssItem(Y)
& app(U,cons(Y,nil)) = V )
| ! [Z] :
( ssItem(Z)
=> app(W,cons(Z,nil)) != X0 ) )
& ~ ~ neq(V,nil) )
=> neq(X0,nil) ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& U = W
& V = X0
& neq(V,nil)
& ssList(X0)
& ( ~ neq(V,nil)
| ? [Y] :
( app(U,cons(Y,nil)) = V
& ssItem(Y) )
| ! [Z] :
( app(W,cons(Z,nil)) != X0
| ~ ssItem(Z) ) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ssList(skolemFOFtoCNF_U_2)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& V = X0
& skolemFOFtoCNF_U_2 = W
& neq(V,nil)
& ssList(X0)
& ( ~ neq(V,nil)
| ? [Y] :
( app(skolemFOFtoCNF_U_2,cons(Y,nil)) = V
& ssItem(Y) )
| ! [Z] :
( app(W,cons(Z,nil)) != X0
| ~ ssItem(Z) ) ) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& V = X0
& skolemFOFtoCNF_U_2 = W
& neq(V,nil)
& ssList(X0)
& ( ~ neq(V,nil)
| ? [Y] :
( app(skolemFOFtoCNF_U_2,cons(Y,nil)) = V
& ssItem(Y) )
| ! [Z] :
( app(W,cons(Z,nil)) != X0
| ~ ssItem(Z) ) ) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ? [Y] :
( app(skolemFOFtoCNF_U_2,cons(Y,nil)) = skolemFOFtoCNF_V_13
& ssItem(Y) )
| ! [Z] :
( app(W,cons(Z,nil)) != X0
| ~ ssItem(Z) ) ) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ? [Y] :
( app(skolemFOFtoCNF_U_2,cons(Y,nil)) = skolemFOFtoCNF_V_13
& ssItem(Y) )
| ! [Z] :
( app(W,cons(Z,nil)) != X0
| ~ ssItem(Z) ) ) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( ~ neq(X0,nil)
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ? [Y] :
( app(skolemFOFtoCNF_U_2,cons(Y,nil)) = skolemFOFtoCNF_V_13
& ssItem(Y) )
| ! [Z] :
( app(skolemFOFtoCNF_W_13,cons(Z,nil)) != X0
| ~ ssItem(Z) ) ) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X0] :
( ~ neq(X0,nil)
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ? [Y] :
( app(skolemFOFtoCNF_U_2,cons(Y,nil)) = skolemFOFtoCNF_V_13
& ssItem(Y) )
| ! [Z] :
( app(skolemFOFtoCNF_W_13,cons(Z,nil)) != X0
| ~ ssItem(Z) ) ) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( ~ neq(skolemFOFtoCNF_X_10,nil)
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(skolemFOFtoCNF_X_10)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ? [Y] :
( app(skolemFOFtoCNF_U_2,cons(Y,nil)) = skolemFOFtoCNF_V_13
& ssItem(Y) )
| ! [Z] :
( app(skolemFOFtoCNF_W_13,cons(Z,nil)) != skolemFOFtoCNF_X_10
| ~ ssItem(Z) ) ) ),
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,
~ neq(skolemFOFtoCNF_X_10,nil),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_10,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
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,
~ neq(skolemFOFtoCNF_X_10,nil),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_2,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_4,plain,
( X != X
| X != Y0
| Y0 = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).
cnf(refute_1_5,plain,
( X != Y0
| Y0 = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13 ),
inference(subst,[],[refute_1_5:[bind(X,$fot(skolemFOFtoCNF_V_13)),bind(Y0,$fot(skolemFOFtoCNF_X_10))]]) ).
cnf(refute_1_7,plain,
skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) )],[refute_1_2,refute_1_6]) ).
cnf(refute_1_8,plain,
( skolemFOFtoCNF_X_10 != skolemFOFtoCNF_V_13
| ~ neq(skolemFOFtoCNF_V_13,nil)
| neq(skolemFOFtoCNF_X_10,nil) ),
introduced(tautology,[equality,[$cnf( ~ neq(skolemFOFtoCNF_X_10,nil) ),[0],$fot(skolemFOFtoCNF_V_13)]]) ).
cnf(refute_1_9,plain,
( ~ neq(skolemFOFtoCNF_V_13,nil)
| neq(skolemFOFtoCNF_X_10,nil) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_10,skolemFOFtoCNF_V_13) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
~ neq(skolemFOFtoCNF_V_13,nil),
inference(resolve,[$cnf( neq(skolemFOFtoCNF_X_10,nil) )],[refute_1_9,refute_1_1]) ).
cnf(refute_1_11,plain,
$false,
inference(resolve,[$cnf( neq(skolemFOFtoCNF_V_13,nil) )],[refute_1_0,refute_1_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC097+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 00:09:13 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.51
% 0.21/0.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.36/0.52
%------------------------------------------------------------------------------