TSTP Solution File: SWC288+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC288+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 21:27:33 EDT 2022
% Result : Theorem 0.21s 0.51s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 74 ( 28 unt; 0 def)
% Number of atoms : 508 ( 158 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 667 ( 233 ~; 145 |; 257 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 192 ( 0 sgn 90 !; 91 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ) ).
fof(ax69,axiom,
strictorderedP(nil) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ~ ssList(X0)
| V != X0
| U != W
| strictorderedP(U)
| ( ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ~ ssList(X1)
| cons(Y0,nil) != W
| app(app(Z,W),X1) != X0
| ? [X2] :
( ssItem(X2)
& memberP(Z,X2)
& lt(Y0,X2) )
| ? [X3] :
( ssItem(X3)
& memberP(X1,X3)
& lt(X3,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 )
& ~ strictorderedP(U) )
=> ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ( ~ ~ ssList(X1)
& ~ ( cons(Y0,nil) != W )
& ~ ( app(app(Z,W),X1) != X0 )
& ~ ? [X2] :
( ssItem(X2)
& memberP(Z,X2)
& lt(Y0,X2) ) )
=> ? [X3] :
( ssItem(X3)
& memberP(X1,X3)
& lt(X3,Y0) ) ) ) ) ) ) ) ),
inference(strip,[],[co1]) ).
fof(subgoal_1,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ~ ~ ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ strictorderedP(U)
& ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ~ ssList(X1)
| cons(Y0,nil) != W
| app(app(Z,W),X1) != X0
| ? [X2] :
( ssItem(X2)
& memberP(Z,X2)
& lt(Y0,X2) )
| ? [X3] :
( ssItem(X3)
& memberP(X1,X3)
& lt(X3,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 )
& ~ strictorderedP(U) )
=> ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ( ~ ~ ssList(X1)
& ~ ( cons(Y0,nil) != W )
& ~ ( app(app(Z,W),X1) != X0 )
& ~ ? [X2] :
( ssItem(X2)
& memberP(Z,X2)
& lt(Y0,X2) ) )
=> ? [X3] :
( ssItem(X3)
& memberP(X1,X3)
& lt(X3,Y0) ) ) ) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(U)
& U = W
& V = X0
& ssList(X0)
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(Y0,nil) = W
& app(app(Z,W),X1) = X0
& ssList(X1)
& ! [X2] :
( ~ lt(Y0,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,Y0)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ssList(skolemFOFtoCNF_U_1)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_1)
& V = X0
& skolemFOFtoCNF_U_1 = W
& ssList(X0)
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(Y0,nil) = W
& app(app(Z,W),X1) = X0
& ssList(X1)
& ! [X2] :
( ~ lt(Y0,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,Y0)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_1)
& V = X0
& skolemFOFtoCNF_U_1 = W
& ssList(X0)
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(Y0,nil) = W
& app(app(Z,W),X1) = X0
& ssList(X1)
& ! [X2] :
( ~ lt(Y0,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,Y0)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ssList(skolemFOFtoCNF_V_12)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(Y0,nil) = W
& app(app(Z,W),X1) = X0
& ssList(X1)
& ! [X2] :
( ~ lt(Y0,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,Y0)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(Y0,nil) = W
& app(app(Z,W),X1) = X0
& ssList(X1)
& ! [X2] :
( ~ lt(Y0,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,Y0)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ssList(skolemFOFtoCNF_W_12)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& app(app(Z,skolemFOFtoCNF_W_12),X1) = X0
& ssList(X1)
& ! [X2] :
( ~ lt(Y0,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,Y0)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& app(app(Z,skolemFOFtoCNF_W_12),X1) = X0
& ssList(X1)
& ! [X2] :
( ~ lt(Y0,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,Y0)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ~ strictorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
& ssList(skolemFOFtoCNF_X_9)
& ? [Y0] :
( ssItem(Y0)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& app(app(Z,skolemFOFtoCNF_W_12),X1) = skolemFOFtoCNF_X_9
& ssList(X1)
& ! [X2] :
( ~ lt(Y0,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,Y0)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [Y0] :
( ssItem(Y0)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& app(app(Z,skolemFOFtoCNF_W_12),X1) = skolemFOFtoCNF_X_9
& ssList(X1)
& ! [X2] :
( ~ lt(Y0,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,Y0)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( ssItem(skolemFOFtoCNF_Y_7)
& ? [Z] :
( ssList(Z)
& ? [X1] :
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& app(app(Z,skolemFOFtoCNF_W_12),X1) = skolemFOFtoCNF_X_9
& ssList(X1)
& ! [X2] :
( ~ lt(skolemFOFtoCNF_Y_7,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,skolemFOFtoCNF_Y_7)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
ssItem(skolemFOFtoCNF_Y_7),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [U] :
( ~ ssItem(U)
| strictorderedP(cons(U,nil)) ),
inference(canonicalize,[],[ax68]) ).
fof(normalize_0_12,plain,
! [U] :
( ~ ssItem(U)
| strictorderedP(cons(U,nil)) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
? [Z] :
( ssList(Z)
& ? [X1] :
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& app(app(Z,skolemFOFtoCNF_W_12),X1) = skolemFOFtoCNF_X_9
& ssList(X1)
& ! [X2] :
( ~ lt(skolemFOFtoCNF_Y_7,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,skolemFOFtoCNF_Y_7)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_14,plain,
( ssList(skolemFOFtoCNF_Z_6)
& ? [X1] :
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& app(app(skolemFOFtoCNF_Z_6,skolemFOFtoCNF_W_12),X1) = skolemFOFtoCNF_X_9
& ssList(X1)
& ! [X2] :
( ~ lt(skolemFOFtoCNF_Y_7,X2)
| ~ memberP(skolemFOFtoCNF_Z_6,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,skolemFOFtoCNF_Y_7)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ) ),
inference(skolemize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
? [X1] :
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& app(app(skolemFOFtoCNF_Z_6,skolemFOFtoCNF_W_12),X1) = skolemFOFtoCNF_X_9
& ssList(X1)
& ! [X2] :
( ~ lt(skolemFOFtoCNF_Y_7,X2)
| ~ memberP(skolemFOFtoCNF_Z_6,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,skolemFOFtoCNF_Y_7)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& app(app(skolemFOFtoCNF_Z_6,skolemFOFtoCNF_W_12),skolemFOFtoCNF_X1) = skolemFOFtoCNF_X_9
& ssList(skolemFOFtoCNF_X1)
& ! [X2] :
( ~ lt(skolemFOFtoCNF_Y_7,X2)
| ~ memberP(skolemFOFtoCNF_Z_6,X2)
| ~ ssItem(X2) )
& ! [X3] :
( ~ lt(X3,skolemFOFtoCNF_Y_7)
| ~ memberP(skolemFOFtoCNF_X1,X3)
| ~ ssItem(X3) ) ),
inference(skolemize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_19,plain,
~ strictorderedP(skolemFOFtoCNF_U_1),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
ssItem(skolemFOFtoCNF_Y_7),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_1,plain,
( ~ ssItem(U)
| strictorderedP(cons(U,nil)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_2,plain,
( ~ ssItem(skolemFOFtoCNF_Y_7)
| strictorderedP(cons(skolemFOFtoCNF_Y_7,nil)) ),
inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_Y_7))]]) ).
cnf(refute_0_3,plain,
strictorderedP(cons(skolemFOFtoCNF_Y_7,nil)),
inference(resolve,[$cnf( ssItem(skolemFOFtoCNF_Y_7) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_5,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_10,plain,
skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( cons(skolemFOFtoCNF_Y_7,nil) != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
| cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_U_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(cons(skolemFOFtoCNF_Y_7,nil),skolemFOFtoCNF_U_1) ),[0],$fot(skolemFOFtoCNF_W_12)]]) ).
cnf(refute_0_12,plain,
( cons(skolemFOFtoCNF_Y_7,nil) != skolemFOFtoCNF_W_12
| cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_U_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(cons(skolemFOFtoCNF_Y_7,nil),skolemFOFtoCNF_W_12) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( cons(skolemFOFtoCNF_Y_7,nil) != skolemFOFtoCNF_U_1
| ~ strictorderedP(cons(skolemFOFtoCNF_Y_7,nil))
| strictorderedP(skolemFOFtoCNF_U_1) ),
introduced(tautology,[equality,[$cnf( strictorderedP(cons(skolemFOFtoCNF_Y_7,nil)) ),[0],$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_0_15,plain,
( ~ strictorderedP(cons(skolemFOFtoCNF_Y_7,nil))
| strictorderedP(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( $equal(cons(skolemFOFtoCNF_Y_7,nil),skolemFOFtoCNF_U_1) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
strictorderedP(skolemFOFtoCNF_U_1),
inference(resolve,[$cnf( strictorderedP(cons(skolemFOFtoCNF_Y_7,nil)) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
~ strictorderedP(skolemFOFtoCNF_U_1),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( strictorderedP(skolemFOFtoCNF_U_1) )],[refute_0_16,refute_0_17]) ).
fof(negate_1_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ~ ~ ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ strictorderedP(U)
& ! [Y0] :
( ssItem(Y0)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ~ ssList(X1)
| cons(Y0,nil) != W
| app(app(Z,W),X1) != X0
| ? [X2] :
( ssItem(X2)
& memberP(Z,X2)
& lt(Y0,X2) )
| ? [X3] :
( ssItem(X3)
& memberP(X1,X3)
& lt(X3,Y0) ) ) ) )
& ~ ( nil != X0 ) )
=> nil != W ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(U)
& U = W
& V = X0
& nil = W
& nil = X0
& ssList(X0)
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( cons(Y0,nil) != W
| app(app(Z,W),X1) != X0
| ~ ssList(X1)
| ? [X2] :
( lt(Y0,X2)
& memberP(Z,X2)
& ssItem(X2) )
| ? [X3] :
( lt(X3,Y0)
& memberP(X1,X3)
& ssItem(X3) ) ) ) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ssList(skolemFOFtoCNF_U_2)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_2)
& V = X0
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( cons(Y0,nil) != W
| app(app(Z,W),X1) != X0
| ~ ssList(X1)
| ? [X2] :
( lt(Y0,X2)
& memberP(Z,X2)
& ssItem(X2) )
| ? [X3] :
( lt(X3,Y0)
& memberP(X1,X3)
& ssItem(X3) ) ) ) ) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_2)
& V = X0
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( cons(Y0,nil) != W
| app(app(Z,W),X1) != X0
| ~ ssList(X1)
| ? [X2] :
( lt(Y0,X2)
& memberP(Z,X2)
& ssItem(X2) )
| ? [X3] :
( lt(X3,Y0)
& memberP(X1,X3)
& ssItem(X3) ) ) ) ) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_2)
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( cons(Y0,nil) != W
| app(app(Z,W),X1) != X0
| ~ ssList(X1)
| ? [X2] :
( lt(Y0,X2)
& memberP(Z,X2)
& ssItem(X2) )
| ? [X3] :
( lt(X3,Y0)
& memberP(X1,X3)
& ssItem(X3) ) ) ) ) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_2)
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( cons(Y0,nil) != W
| app(app(Z,W),X1) != X0
| ~ ssList(X1)
| ? [X2] :
( lt(Y0,X2)
& memberP(Z,X2)
& ssItem(X2) )
| ? [X3] :
( lt(X3,Y0)
& memberP(X1,X3)
& ssItem(X3) ) ) ) ) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_2)
& nil = X0
& nil = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| app(app(Z,skolemFOFtoCNF_W_13),X1) != X0
| ~ ssList(X1)
| ? [X2] :
( lt(Y0,X2)
& memberP(Z,X2)
& ssItem(X2) )
| ? [X3] :
( lt(X3,Y0)
& memberP(X1,X3)
& ssItem(X3) ) ) ) ) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X0] :
( ~ strictorderedP(skolemFOFtoCNF_U_2)
& nil = X0
& nil = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| app(app(Z,skolemFOFtoCNF_W_13),X1) != X0
| ~ ssList(X1)
| ? [X2] :
( lt(Y0,X2)
& memberP(Z,X2)
& ssItem(X2) )
| ? [X3] :
( lt(X3,Y0)
& memberP(X1,X3)
& ssItem(X3) ) ) ) ) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( ~ strictorderedP(skolemFOFtoCNF_U_2)
& nil = skolemFOFtoCNF_W_13
& nil = skolemFOFtoCNF_X_10
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10
& ssList(skolemFOFtoCNF_X_10)
& ! [Y0] :
( ~ ssItem(Y0)
| ! [Z] :
( ~ ssList(Z)
| ! [X1] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| app(app(Z,skolemFOFtoCNF_W_13),X1) != skolemFOFtoCNF_X_10
| ~ ssList(X1)
| ? [X2] :
( lt(Y0,X2)
& memberP(Z,X2)
& ssItem(X2) )
| ? [X3] :
( lt(X3,Y0)
& memberP(X1,X3)
& ssItem(X3) ) ) ) ) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
~ strictorderedP(skolemFOFtoCNF_U_2),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_10,plain,
nil = skolemFOFtoCNF_W_13,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_11,plain,
strictorderedP(nil),
inference(canonicalize,[],[ax69]) ).
cnf(refute_1_0,plain,
~ strictorderedP(skolemFOFtoCNF_U_2),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_1,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_2,plain,
nil = skolemFOFtoCNF_W_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( $equal(X,X) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
( nil != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 = nil ),
inference(subst,[],[refute_1_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_W_13))]]) ).
cnf(refute_1_7,plain,
skolemFOFtoCNF_W_13 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_13) )],[refute_1_2,refute_1_6]) ).
cnf(refute_1_8,plain,
( skolemFOFtoCNF_U_2 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 != nil
| skolemFOFtoCNF_U_2 = nil ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_U_2,nil) ),[0],$fot(skolemFOFtoCNF_W_13)]]) ).
cnf(refute_1_9,plain,
( skolemFOFtoCNF_U_2 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_U_2 = nil ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_13,nil) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
skolemFOFtoCNF_U_2 = nil,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,skolemFOFtoCNF_W_13) )],[refute_1_1,refute_1_9]) ).
cnf(refute_1_11,plain,
( skolemFOFtoCNF_U_2 != nil
| ~ strictorderedP(nil)
| strictorderedP(skolemFOFtoCNF_U_2) ),
introduced(tautology,[equality,[$cnf( ~ strictorderedP(skolemFOFtoCNF_U_2) ),[0],$fot(nil)]]) ).
cnf(refute_1_12,plain,
( ~ strictorderedP(nil)
| strictorderedP(skolemFOFtoCNF_U_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,nil) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
~ strictorderedP(nil),
inference(resolve,[$cnf( strictorderedP(skolemFOFtoCNF_U_2) )],[refute_1_12,refute_1_0]) ).
cnf(refute_1_14,plain,
strictorderedP(nil),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_15,plain,
$false,
inference(resolve,[$cnf( strictorderedP(nil) )],[refute_1_14,refute_1_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC288+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jun 12 03:06:34 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
% 0.21/0.53
%------------------------------------------------------------------------------