TSTP Solution File: SWC040+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC040+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 21:26:15 EDT 2022
% Result : Theorem 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 83 ( 32 unt; 0 def)
% Number of atoms : 381 ( 266 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 466 ( 168 ~; 86 |; 182 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 46 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( nil != V
| V != X0
| U != W
| nil = U
| ( nil != W
& nil = X0 )
| ( ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ( app(cons(Y0,nil),Z) != W
| app(Z,cons(Y0,nil)) != X0 ) ) )
& neq(X0,nil) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U
& ~ ( nil != W
& nil = X0 ) )
=> ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ( ssList(Z)
& ~ ( app(cons(Y0,nil),Z) != W ) )
=> app(Z,cons(Y0,nil)) != X0 ) ) ) ) ) ),
inference(strip,[],[co1]) ).
fof(subgoal_1,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U
& ~ ( nil != W
& nil = X0 )
& ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ( app(cons(Y0,nil),Z) != W
| app(Z,cons(Y0,nil)) != X0 ) ) ) )
=> neq(X0,nil) ) ) ) ),
inference(strip,[],[co1]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U
& ~ ( nil != W
& nil = X0 ) )
=> ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ( ssList(Z)
& ~ ( app(cons(Y0,nil),Z) != W ) )
=> app(Z,cons(Y0,nil)) != X0 ) ) ) ) ) ),
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 != X0
| nil = W )
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( app(Z,cons(Y0,nil)) = X0
& app(cons(Y0,nil),Z) = W
& ssList(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 != X0
| nil = W )
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( app(Z,cons(Y0,nil)) = X0
& app(cons(Y0,nil),Z) = W
& ssList(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 != X0
| nil = W )
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( app(Z,cons(Y0,nil)) = X0
& app(cons(Y0,nil),Z) = W
& ssList(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 != X0
| nil = W )
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( app(Z,cons(Y0,nil)) = X0
& app(cons(Y0,nil),Z) = W
& ssList(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 != X0
| nil = W )
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( app(Z,cons(Y0,nil)) = X0
& app(cons(Y0,nil),Z) = W
& ssList(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] :
( ssItem(Y0)
& ? [Z] :
( app(Z,cons(Y0,nil)) = X0
& app(cons(Y0,nil),Z) = skolemFOFtoCNF_W_12
& ssList(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] :
( ssItem(Y0)
& ? [Z] :
( app(Z,cons(Y0,nil)) = X0
& app(cons(Y0,nil),Z) = skolemFOFtoCNF_W_12
& ssList(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_X_9
| nil = skolemFOFtoCNF_W_12 )
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( app(Z,cons(Y0,nil)) = skolemFOFtoCNF_X_9
& app(cons(Y0,nil),Z) = skolemFOFtoCNF_W_12
& ssList(Z) ) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
( nil != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_W_12 ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,plain,
nil = skolemFOFtoCNF_V_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_11,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
nil != skolemFOFtoCNF_U_1,
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( nil != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_W_12 ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
nil = skolemFOFtoCNF_V_12,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( nil != skolemFOFtoCNF_V_12
| skolemFOFtoCNF_V_12 = nil ),
inference(subst,[],[refute_0_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_V_12))]]) ).
cnf(refute_0_7,plain,
skolemFOFtoCNF_V_12 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_12) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_V_12 != nil
| skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) ),[0],$fot(nil)]]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,nil) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
nil = skolemFOFtoCNF_X_9,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( nil != skolemFOFtoCNF_X_9
| skolemFOFtoCNF_X_9 = nil ),
inference(subst,[],[refute_0_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_X_9))]]) ).
cnf(refute_0_12,plain,
skolemFOFtoCNF_X_9 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_9) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( nil != nil
| skolemFOFtoCNF_X_9 != nil
| nil = skolemFOFtoCNF_X_9 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_X_9) ),[1],$fot(nil)]]) ).
cnf(refute_0_14,plain,
( nil != nil
| nil = skolemFOFtoCNF_X_9 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,nil) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( nil != nil
| nil = skolemFOFtoCNF_W_12 ),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_9) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_17,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_18,plain,
skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( nil != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
| nil = skolemFOFtoCNF_U_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_U_1) ),[0],$fot(skolemFOFtoCNF_W_12)]]) ).
cnf(refute_0_20,plain,
( nil != skolemFOFtoCNF_W_12
| nil = skolemFOFtoCNF_U_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( nil != nil
| nil = skolemFOFtoCNF_U_1 ),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_12) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
nil = nil,
introduced(tautology,[refl,[$fot(nil)]]) ).
cnf(refute_0_23,plain,
nil = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(nil,nil) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
nil != skolemFOFtoCNF_U_1,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_1) )],[refute_0_23,refute_0_24]) ).
fof(negate_1_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U
& ~ ( nil != W
& nil = X0 )
& ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ( app(cons(Y0,nil),Z) != W
| app(Z,cons(Y0,nil)) != X0 ) ) ) )
=> neq(X0,nil) ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != U
& ~ neq(X0,nil)
& U = W
& V = X0
& nil = V
& ssList(X0)
& ( nil != X0
| nil = W )
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( app(Z,cons(Y0,nil)) != X0
| app(cons(Y0,nil),Z) != W
| ~ ssList(Z) ) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ssList(skolemFOFtoCNF_U_2)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_2
& ~ neq(X0,nil)
& V = X0
& nil = V
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ( nil != X0
| nil = W )
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( app(Z,cons(Y0,nil)) != X0
| app(cons(Y0,nil),Z) != W
| ~ ssList(Z) ) ) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_2
& ~ neq(X0,nil)
& V = X0
& nil = V
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ( nil != X0
| nil = W )
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( app(Z,cons(Y0,nil)) != X0
| app(cons(Y0,nil),Z) != W
| ~ ssList(Z) ) ) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_2
& ~ neq(X0,nil)
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ( nil != X0
| nil = W )
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( app(Z,cons(Y0,nil)) != X0
| app(cons(Y0,nil),Z) != W
| ~ ssList(Z) ) ) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_2
& ~ neq(X0,nil)
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ( nil != X0
| nil = W )
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( app(Z,cons(Y0,nil)) != X0
| app(cons(Y0,nil),Z) != W
| ~ ssList(Z) ) ) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( nil != skolemFOFtoCNF_U_2
& ~ neq(X0,nil)
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ( nil != X0
| nil = skolemFOFtoCNF_W_13 )
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( app(Z,cons(Y0,nil)) != X0
| app(cons(Y0,nil),Z) != skolemFOFtoCNF_W_13
| ~ ssList(Z) ) ) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X0] :
( nil != skolemFOFtoCNF_U_2
& ~ neq(X0,nil)
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ( nil != X0
| nil = skolemFOFtoCNF_W_13 )
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( app(Z,cons(Y0,nil)) != X0
| app(cons(Y0,nil),Z) != skolemFOFtoCNF_W_13
| ~ ssList(Z) ) ) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( nil != skolemFOFtoCNF_U_2
& ~ neq(skolemFOFtoCNF_X_10,nil)
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10
& ssList(skolemFOFtoCNF_X_10)
& ( nil != skolemFOFtoCNF_X_10
| nil = skolemFOFtoCNF_W_13 )
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( app(Z,cons(Y0,nil)) != skolemFOFtoCNF_X_10
| app(cons(Y0,nil),Z) != skolemFOFtoCNF_W_13
| ~ ssList(Z) ) ) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
( nil != skolemFOFtoCNF_X_10
| nil = skolemFOFtoCNF_W_13 ),
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_V_13,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_11,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_12,plain,
nil != skolemFOFtoCNF_U_2,
inference(conjunct,[],[normalize_1_7]) ).
cnf(refute_1_0,plain,
( nil != skolemFOFtoCNF_X_10
| nil = skolemFOFtoCNF_W_13 ),
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_V_13,
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( $equal(X,X) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
( nil != skolemFOFtoCNF_V_13
| skolemFOFtoCNF_V_13 = nil ),
inference(subst,[],[refute_1_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_V_13))]]) ).
cnf(refute_1_7,plain,
skolemFOFtoCNF_V_13 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_13) )],[refute_1_2,refute_1_6]) ).
cnf(refute_1_8,plain,
( skolemFOFtoCNF_V_13 != nil
| skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| nil = skolemFOFtoCNF_X_10 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) ),[0],$fot(nil)]]) ).
cnf(refute_1_9,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| nil = skolemFOFtoCNF_X_10 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,nil) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
nil = skolemFOFtoCNF_X_10,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) )],[refute_1_1,refute_1_9]) ).
cnf(refute_1_11,plain,
( nil != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 = nil ),
inference(subst,[],[refute_1_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_X_10))]]) ).
cnf(refute_1_12,plain,
skolemFOFtoCNF_X_10 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_10) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
( nil != nil
| skolemFOFtoCNF_X_10 != nil
| nil = skolemFOFtoCNF_X_10 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_X_10) ),[1],$fot(nil)]]) ).
cnf(refute_1_14,plain,
( nil != nil
| nil = skolemFOFtoCNF_X_10 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_10,nil) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
( nil != nil
| nil = skolemFOFtoCNF_W_13 ),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_10) )],[refute_1_14,refute_1_0]) ).
cnf(refute_1_16,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_17,plain,
( skolemFOFtoCNF_U_2 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 = skolemFOFtoCNF_U_2 ),
inference(subst,[],[refute_1_5:[bind(X,$fot(skolemFOFtoCNF_U_2)),bind(Y,$fot(skolemFOFtoCNF_W_13))]]) ).
cnf(refute_1_18,plain,
skolemFOFtoCNF_W_13 = skolemFOFtoCNF_U_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,skolemFOFtoCNF_W_13) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
( nil != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 != skolemFOFtoCNF_U_2
| nil = skolemFOFtoCNF_U_2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_U_2) ),[0],$fot(skolemFOFtoCNF_W_13)]]) ).
cnf(refute_1_20,plain,
( nil != skolemFOFtoCNF_W_13
| nil = skolemFOFtoCNF_U_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_13,skolemFOFtoCNF_U_2) )],[refute_1_18,refute_1_19]) ).
cnf(refute_1_21,plain,
( nil != nil
| nil = skolemFOFtoCNF_U_2 ),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_13) )],[refute_1_15,refute_1_20]) ).
cnf(refute_1_22,plain,
nil = nil,
introduced(tautology,[refl,[$fot(nil)]]) ).
cnf(refute_1_23,plain,
nil = skolemFOFtoCNF_U_2,
inference(resolve,[$cnf( $equal(nil,nil) )],[refute_1_22,refute_1_21]) ).
cnf(refute_1_24,plain,
nil != skolemFOFtoCNF_U_2,
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_25,plain,
$false,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_2) )],[refute_1_23,refute_1_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC040+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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 : Sun Jun 12 02:11:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.49
%------------------------------------------------------------------------------