TSTP Solution File: SWC257+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC257+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 21:27:23 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 28 unt; 0 def)
% Number of atoms : 378 ( 150 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 482 ( 174 ~; 92 |; 194 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 46 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ) ).
fof(ax66,axiom,
totalorderedP(nil) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ~ ssList(X0)
| V != X0
| U != W
| totalorderedP(U)
| ( ! [Y0] :
( ~ ssItem(Y0)
| cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) )
& ( nil != X0
| nil != W ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ~ ~ ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ totalorderedP(U) )
=> ! [Y0] :
( ( ~ ~ ssItem(Y0)
& ~ ( cons(Y0,nil) != W )
& ~ ~ memberP(X0,Y0) )
=> ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) ) ) ) ) ),
inference(strip,[],[co1]) ).
fof(subgoal_1,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ~ ~ ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ totalorderedP(U)
& ! [Y0] :
( ~ ssItem(Y0)
| cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) )
& ~ ( 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 )
& ~ totalorderedP(U) )
=> ! [Y0] :
( ( ~ ~ ssItem(Y0)
& ~ ( cons(Y0,nil) != W )
& ~ ~ memberP(X0,Y0) )
=> ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(U)
& U = W
& V = X0
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ssList(skolemFOFtoCNF_U_1)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_1)
& V = X0
& skolemFOFtoCNF_U_1 = W
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_1)
& V = X0
& skolemFOFtoCNF_U_1 = W
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ssList(skolemFOFtoCNF_V_12)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = W
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ssList(skolemFOFtoCNF_W_12)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(X0,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(X0,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ~ totalorderedP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
& ssList(skolemFOFtoCNF_X_9)
& ? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(skolemFOFtoCNF_X_9,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(skolemFOFtoCNF_X_9,Z)
| ~ ssItem(Z)
| Y0 = Z ) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [Y0] :
( cons(Y0,nil) = skolemFOFtoCNF_W_12
& memberP(skolemFOFtoCNF_X_9,Y0)
& ssItem(Y0)
& ! [Z] :
( ~ leq(Y0,Z)
| ~ memberP(skolemFOFtoCNF_X_9,Z)
| ~ ssItem(Z)
| Y0 = Z ) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12
& memberP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7)
& ssItem(skolemFOFtoCNF_Y_7)
& ! [Z] :
( ~ leq(skolemFOFtoCNF_Y_7,Z)
| ~ memberP(skolemFOFtoCNF_X_9,Z)
| ~ ssItem(Z)
| skolemFOFtoCNF_Y_7 = Z ) ),
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)
| totalorderedP(cons(U,nil)) ),
inference(canonicalize,[],[ax65]) ).
fof(normalize_0_12,plain,
! [U] :
( ~ ssItem(U)
| totalorderedP(cons(U,nil)) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
cons(skolemFOFtoCNF_Y_7,nil) = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_14,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
~ totalorderedP(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)
| totalorderedP(cons(U,nil)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_2,plain,
( ~ ssItem(skolemFOFtoCNF_Y_7)
| totalorderedP(cons(skolemFOFtoCNF_Y_7,nil)) ),
inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_Y_7))]]) ).
cnf(refute_0_3,plain,
totalorderedP(cons(skolemFOFtoCNF_Y_7,nil)),
inference(resolve,[$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_13]) ).
cnf(refute_0_5,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_14]) ).
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( $equal(cons(skolemFOFtoCNF_Y_7,nil),skolemFOFtoCNF_W_12) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( cons(skolemFOFtoCNF_Y_7,nil) != skolemFOFtoCNF_U_1
| ~ totalorderedP(cons(skolemFOFtoCNF_Y_7,nil))
| totalorderedP(skolemFOFtoCNF_U_1) ),
introduced(tautology,[equality,[$cnf( totalorderedP(cons(skolemFOFtoCNF_Y_7,nil)) ),[0],$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_0_15,plain,
( ~ totalorderedP(cons(skolemFOFtoCNF_Y_7,nil))
| totalorderedP(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( $equal(cons(skolemFOFtoCNF_Y_7,nil),skolemFOFtoCNF_U_1) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
totalorderedP(skolemFOFtoCNF_U_1),
inference(resolve,[$cnf( totalorderedP(cons(skolemFOFtoCNF_Y_7,nil)) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
~ totalorderedP(skolemFOFtoCNF_U_1),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( totalorderedP(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 )
& ~ totalorderedP(U)
& ! [Y0] :
( ~ ssItem(Y0)
| cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ? [Z] :
( ssItem(Z)
& Y0 != Z
& memberP(X0,Z)
& leq(Y0,Z) ) )
& ~ ( nil != X0 ) )
=> nil != W ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(U)
& U = W
& V = X0
& nil = W
& nil = X0
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0)
| ? [Z] :
( Y0 != Z
& leq(Y0,Z)
& memberP(X0,Z)
& ssItem(Z) ) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ssList(skolemFOFtoCNF_U_2)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_2)
& V = X0
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0)
| ? [Z] :
( Y0 != Z
& leq(Y0,Z)
& memberP(X0,Z)
& ssItem(Z) ) ) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_2)
& V = X0
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0)
| ? [Z] :
( Y0 != Z
& leq(Y0,Z)
& memberP(X0,Z)
& ssItem(Z) ) ) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_2)
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0)
| ? [Z] :
( Y0 != Z
& leq(Y0,Z)
& memberP(X0,Z)
& ssItem(Z) ) ) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_2)
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != W
| ~ memberP(X0,Y0)
| ~ ssItem(Y0)
| ? [Z] :
( Y0 != Z
& leq(Y0,Z)
& memberP(X0,Z)
& ssItem(Z) ) ) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_2)
& nil = X0
& nil = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| ~ memberP(X0,Y0)
| ~ ssItem(Y0)
| ? [Z] :
( Y0 != Z
& leq(Y0,Z)
& memberP(X0,Z)
& ssItem(Z) ) ) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X0] :
( ~ totalorderedP(skolemFOFtoCNF_U_2)
& nil = X0
& nil = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| ~ memberP(X0,Y0)
| ~ ssItem(Y0)
| ? [Z] :
( Y0 != Z
& leq(Y0,Z)
& memberP(X0,Z)
& ssItem(Z) ) ) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( ~ totalorderedP(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] :
( cons(Y0,nil) != skolemFOFtoCNF_W_13
| ~ memberP(skolemFOFtoCNF_X_10,Y0)
| ~ ssItem(Y0)
| ? [Z] :
( Y0 != Z
& leq(Y0,Z)
& memberP(skolemFOFtoCNF_X_10,Z)
& ssItem(Z) ) ) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
~ totalorderedP(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,
totalorderedP(nil),
inference(canonicalize,[],[ax66]) ).
cnf(refute_1_0,plain,
~ totalorderedP(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( $equal(skolemFOFtoCNF_U_2,skolemFOFtoCNF_W_13) )],[refute_1_1,refute_1_9]) ).
cnf(refute_1_11,plain,
( skolemFOFtoCNF_U_2 != nil
| ~ totalorderedP(nil)
| totalorderedP(skolemFOFtoCNF_U_2) ),
introduced(tautology,[equality,[$cnf( ~ totalorderedP(skolemFOFtoCNF_U_2) ),[0],$fot(nil)]]) ).
cnf(refute_1_12,plain,
( ~ totalorderedP(nil)
| totalorderedP(skolemFOFtoCNF_U_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,nil) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
~ totalorderedP(nil),
inference(resolve,[$cnf( totalorderedP(skolemFOFtoCNF_U_2) )],[refute_1_12,refute_1_0]) ).
cnf(refute_1_14,plain,
totalorderedP(nil),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_15,plain,
$false,
inference(resolve,[$cnf( totalorderedP(nil) )],[refute_1_14,refute_1_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC257+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 12 09:06:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.49
%------------------------------------------------------------------------------