TSTP Solution File: SWC254+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC254+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 21:27:21 EDT 2022
% Result : Theorem 9.32s 9.51s
% Output : CNFRefutation 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 77 ( 26 unt; 0 def)
% Number of atoms : 372 ( 134 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 453 ( 158 ~; 103 |; 158 &)
% ( 3 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn 55 !; 53 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( V != X0
| U != W
| ( ( ~ neq(V,nil)
| ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0 ) ) )
| singletonP(U) )
& ( ~ 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)
& ~ ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0 ) ) ) )
=> singletonP(U) ) ) ) ),
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)
| ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0 ) ) )
| singletonP(U) )
& ~ ~ 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)
& ~ ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0 ) ) ) )
=> singletonP(U) ) ) ) ),
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] :
( ssItem(Y0)
& ? [Z] :
( cons(Y0,nil) = W
& app(Z,cons(Y0,nil)) = X0
& ssList(Z) ) ) ) ) ) ),
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] :
( ssItem(Y0)
& ? [Z] :
( cons(Y0,nil) = W
& app(Z,cons(Y0,nil)) = X0
& ssList(Z) ) ) ) ) ) ),
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] :
( ssItem(Y0)
& ? [Z] :
( cons(Y0,nil) = W
& app(Z,cons(Y0,nil)) = X0
& ssList(Z) ) ) ) ) ),
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] :
( ssItem(Y0)
& ? [Z] :
( cons(Y0,nil) = W
& app(Z,cons(Y0,nil)) = X0
& ssList(Z) ) ) ) ) ),
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] :
( ssItem(Y0)
& ? [Z] :
( cons(Y0,nil) = W
& app(Z,cons(Y0,nil)) = X0
& ssList(Z) ) ) ) ),
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] :
( ssItem(Y0)
& ? [Z] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& app(Z,cons(Y0,nil)) = X0
& ssList(Z) ) ) ) ),
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] :
( ssItem(Y0)
& ? [Z] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& app(Z,cons(Y0,nil)) = X0
& ssList(Z) ) ) ),
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] :
( ssItem(Y0)
& ? [Z] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& app(Z,cons(Y0,nil)) = skolemFOFtoCNF_X_9
& ssList(Z) ) ) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
? [Y0] :
( ssItem(Y0)
& ? [Z] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& app(Z,cons(Y0,nil)) = skolemFOFtoCNF_X_9
& ssList(Z) ) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
( ssItem(skolemFOFtoCNF_Y_7)
& ? [Z] :
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& app(Z,cons(skolemFOFtoCNF_Y_7,nil)) = skolemFOFtoCNF_X_9
& ssList(Z) ) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
? [Z] :
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& app(Z,cons(skolemFOFtoCNF_Y_7,nil)) = skolemFOFtoCNF_X_9
& ssList(Z) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& app(skolemFOFtoCNF_Z_6,cons(skolemFOFtoCNF_Y_7,nil)) = skolemFOFtoCNF_X_9
& ssList(skolemFOFtoCNF_Z_6) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_18,plain,
ssItem(skolemFOFtoCNF_Y_7),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_19,plain,
ssList(skolemFOFtoCNF_U_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_20,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_16]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_17]) ).
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_18]) ).
cnf(refute_0_22,plain,
( ~ ssList(skolemFOFtoCNF_U_1)
| singletonP(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( ssItem(skolemFOFtoCNF_Y_7) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
ssList(skolemFOFtoCNF_U_1),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_24,plain,
singletonP(skolemFOFtoCNF_U_1),
inference(resolve,[$cnf( ssList(skolemFOFtoCNF_U_1) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
~ singletonP(skolemFOFtoCNF_U_1),
inference(canonicalize,[],[normalize_0_20]) ).
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)
| ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0 ) ) )
| singletonP(U) )
& ~ ~ 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)
| singletonP(U)
| ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0
| ~ ssList(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)
| singletonP(skolemFOFtoCNF_U_2)
| ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0
| ~ ssList(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)
| singletonP(skolemFOFtoCNF_U_2)
| ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0
| ~ ssList(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)
| singletonP(skolemFOFtoCNF_U_2)
| ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0
| ~ ssList(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)
| singletonP(skolemFOFtoCNF_U_2)
| ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( cons(Y0,nil) != W
| app(Z,cons(Y0,nil)) != X0
| ~ ssList(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)
| singletonP(skolemFOFtoCNF_U_2)
| ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| app(Z,cons(Y0,nil)) != X0
| ~ ssList(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)
| singletonP(skolemFOFtoCNF_U_2)
| ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| app(Z,cons(Y0,nil)) != X0
| ~ ssList(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)
| singletonP(skolemFOFtoCNF_U_2)
| ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| app(Z,cons(Y0,nil)) != skolemFOFtoCNF_X_10
| ~ ssList(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,[$fot(X)]]) ).
cnf(refute_1_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13 ),
inference(subst,[],[refute_1_5:[bind(X,$fot(skolemFOFtoCNF_V_13)),bind(Y,$fot(skolemFOFtoCNF_X_10))]]) ).
cnf(refute_1_7,plain,
skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13,
inference(resolve,[$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
% 0.03/0.12 % Problem : SWC254+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n007.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 06:03:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.32/9.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.32/9.51
% 9.32/9.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.36/9.52
%------------------------------------------------------------------------------