%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC037+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 21:26:13 EDT 2022
% Result : Theorem 3.43s 3.66s
% Output : CNFRefutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 96 ( 36 unt; 0 def)
% Number of atoms : 403 ( 181 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 492 ( 185 ~; 96 |; 177 &)
% ( 6 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 105 ( 0 sgn 48 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ) ).
fof(ax58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( nil != V
| V != X0
| U != W
| nil = U
| ( ! [Y0] :
( ssList(Y0)
=> ( ~ neq(Y0,nil)
| ~ segmentP(X0,Y0)
| ~ segmentP(W,Y0) ) )
& ( nil != X0
| nil != W ) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U )
=> ! [Y0] :
( ( ssList(Y0)
& ~ ~ neq(Y0,nil)
& ~ ~ segmentP(X0,Y0) )
=> ~ segmentP(W,Y0) ) ) ) ) ),
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
& ! [Y0] :
( ssList(Y0)
=> ( ~ neq(Y0,nil)
| ~ segmentP(X0,Y0)
| ~ segmentP(W,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)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U )
=> ! [Y0] :
( ( ssList(Y0)
& ~ ~ neq(Y0,nil)
& ~ ~ segmentP(X0,Y0) )
=> ~ segmentP(W,Y0) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( U != V
<=> neq(U,V) ) ) ),
inference(canonicalize,[],[ax15]) ).
fof(normalize_0_1,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( U != V
<=> neq(U,V) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [U,V] :
( ( U != V
| ~ neq(U,V)
| ~ ssList(U)
| ~ ssList(V) )
& ( ~ ssList(U)
| ~ ssList(V)
| U = V
| neq(U,V) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [U,V] :
( U != V
| ~ neq(U,V)
| ~ ssList(U)
| ~ ssList(V) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != U
& U = W
& V = X0
& nil = V
& ssList(X0)
& ? [Y0] :
( neq(Y0,nil)
& segmentP(W,Y0)
& segmentP(X0,Y0)
& ssList(Y0) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,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)
& ? [Y0] :
( neq(Y0,nil)
& segmentP(W,Y0)
& segmentP(X0,Y0)
& ssList(Y0) ) ) ) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& V = X0
& nil = V
& skolemFOFtoCNF_U_1 = W
& ssList(X0)
& ? [Y0] :
( neq(Y0,nil)
& segmentP(W,Y0)
& segmentP(X0,Y0)
& ssList(Y0) ) ) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,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)
& ? [Y0] :
( neq(Y0,nil)
& segmentP(W,Y0)
& segmentP(X0,Y0)
& ssList(Y0) ) ) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( neq(Y0,nil)
& segmentP(W,Y0)
& segmentP(X0,Y0)
& ssList(Y0) ) ) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,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)
& ? [Y0] :
( neq(Y0,nil)
& segmentP(X0,Y0)
& segmentP(skolemFOFtoCNF_W_12,Y0)
& ssList(Y0) ) ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Y0] :
( neq(Y0,nil)
& segmentP(X0,Y0)
& segmentP(skolemFOFtoCNF_W_12,Y0)
& ssList(Y0) ) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,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)
& ? [Y0] :
( neq(Y0,nil)
& segmentP(skolemFOFtoCNF_W_12,Y0)
& segmentP(skolemFOFtoCNF_X_9,Y0)
& ssList(Y0) ) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
? [Y0] :
( neq(Y0,nil)
& segmentP(skolemFOFtoCNF_W_12,Y0)
& segmentP(skolemFOFtoCNF_X_9,Y0)
& ssList(Y0) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
( neq(skolemFOFtoCNF_Y_7,nil)
& segmentP(skolemFOFtoCNF_W_12,skolemFOFtoCNF_Y_7)
& segmentP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7)
& ssList(skolemFOFtoCNF_Y_7) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
neq(skolemFOFtoCNF_Y_7,nil),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
segmentP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_16,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_17,plain,
nil = skolemFOFtoCNF_V_12,
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_18,plain,
! [U] :
( ~ ssList(U)
| ( nil != U
<=> ~ segmentP(nil,U) ) ),
inference(canonicalize,[],[ax58]) ).
fof(normalize_0_19,plain,
! [U] :
( ~ ssList(U)
| ( nil != U
<=> ~ segmentP(nil,U) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [U] :
( ( nil != U
| ~ ssList(U)
| segmentP(nil,U) )
& ( ~ segmentP(nil,U)
| ~ ssList(U)
| nil = U ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [U] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| nil = U ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
ssList(skolemFOFtoCNF_Y_7),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_23,plain,
ssList(skolemFOFtoCNF_V_12),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( U != V
| ~ neq(U,V)
| ~ ssList(U)
| ~ ssList(V) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( V != V
| ~ neq(V,V)
| ~ ssList(V) ),
inference(subst,[],[refute_0_0:[bind(U,$fot(V))]]) ).
cnf(refute_0_2,plain,
V = V,
introduced(tautology,[refl,[$fot(V)]]) ).
cnf(refute_0_3,plain,
( ~ neq(V,V)
| ~ ssList(V) ),
inference(resolve,[$cnf( $equal(V,V) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ neq(nil,nil)
| ~ ssList(nil) ),
inference(subst,[],[refute_0_3:[bind(V,$fot(nil))]]) ).
cnf(refute_0_5,plain,
neq(skolemFOFtoCNF_Y_7,nil),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_6,plain,
segmentP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_7,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_8,plain,
nil = skolemFOFtoCNF_V_12,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_9,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_10,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_11,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( nil != skolemFOFtoCNF_V_12
| skolemFOFtoCNF_V_12 = nil ),
inference(subst,[],[refute_0_11:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_V_12))]]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_V_12 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_12) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_V_12 != nil
| skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) ),[0],$fot(nil)]]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,nil) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
nil = skolemFOFtoCNF_X_9,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
( nil != skolemFOFtoCNF_X_9
| skolemFOFtoCNF_X_9 = nil ),
inference(subst,[],[refute_0_11:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_X_9))]]) ).
cnf(refute_0_18,plain,
skolemFOFtoCNF_X_9 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_9) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_X_9 != nil
| ~ segmentP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7)
| segmentP(nil,skolemFOFtoCNF_Y_7) ),
introduced(tautology,[equality,[$cnf( segmentP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7) ),[0],$fot(nil)]]) ).
cnf(refute_0_20,plain,
( ~ segmentP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7)
| segmentP(nil,skolemFOFtoCNF_Y_7) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,nil) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
segmentP(nil,skolemFOFtoCNF_Y_7),
inference(resolve,[$cnf( segmentP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_7) )],[refute_0_6,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ segmentP(nil,U)
| ~ ssList(U)
| nil = U ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_23,plain,
( ~ segmentP(nil,skolemFOFtoCNF_Y_7)
| ~ ssList(skolemFOFtoCNF_Y_7)
| nil = skolemFOFtoCNF_Y_7 ),
inference(subst,[],[refute_0_22:[bind(U,$fot(skolemFOFtoCNF_Y_7))]]) ).
cnf(refute_0_24,plain,
( ~ ssList(skolemFOFtoCNF_Y_7)
| nil = skolemFOFtoCNF_Y_7 ),
inference(resolve,[$cnf( segmentP(nil,skolemFOFtoCNF_Y_7) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
ssList(skolemFOFtoCNF_Y_7),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_26,plain,
nil = skolemFOFtoCNF_Y_7,
inference(resolve,[$cnf( ssList(skolemFOFtoCNF_Y_7) )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
( nil != skolemFOFtoCNF_Y_7
| skolemFOFtoCNF_Y_7 = nil ),
inference(subst,[],[refute_0_11:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_Y_7))]]) ).
cnf(refute_0_28,plain,
skolemFOFtoCNF_Y_7 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_Y_7) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( skolemFOFtoCNF_Y_7 != nil
| ~ neq(skolemFOFtoCNF_Y_7,nil)
| neq(nil,nil) ),
introduced(tautology,[equality,[$cnf( neq(skolemFOFtoCNF_Y_7,nil) ),[0],$fot(nil)]]) ).
cnf(refute_0_30,plain,
( ~ neq(skolemFOFtoCNF_Y_7,nil)
| neq(nil,nil) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_7,nil) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
neq(nil,nil),
inference(resolve,[$cnf( neq(skolemFOFtoCNF_Y_7,nil) )],[refute_0_5,refute_0_30]) ).
cnf(refute_0_32,plain,
~ ssList(nil),
inference(resolve,[$cnf( neq(nil,nil) )],[refute_0_31,refute_0_4]) ).
cnf(refute_0_33,plain,
ssList(skolemFOFtoCNF_V_12),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_V_12 != nil
| ~ ssList(skolemFOFtoCNF_V_12)
| ssList(nil) ),
introduced(tautology,[equality,[$cnf( ssList(skolemFOFtoCNF_V_12) ),[0],$fot(nil)]]) ).
cnf(refute_0_35,plain,
( ~ ssList(skolemFOFtoCNF_V_12)
| ssList(nil) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,nil) )],[refute_0_13,refute_0_34]) ).
cnf(refute_0_36,plain,
ssList(nil),
inference(resolve,[$cnf( ssList(skolemFOFtoCNF_V_12) )],[refute_0_33,refute_0_35]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( ssList(nil) )],[refute_0_36,refute_0_32]) ).
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
& ! [Y0] :
( ssList(Y0)
=> ( ~ neq(Y0,nil)
| ~ segmentP(X0,Y0)
| ~ segmentP(W,Y0) ) )
& ~ ( nil != X0 ) )
=> nil != W ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != U
& U = W
& V = X0
& nil = V
& nil = W
& nil = X0
& ssList(X0)
& ! [Y0] :
( ~ neq(Y0,nil)
| ~ segmentP(W,Y0)
| ~ segmentP(X0,Y0)
| ~ ssList(Y0) ) ) ) ) ),
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
& V = X0
& nil = V
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ! [Y0] :
( ~ neq(Y0,nil)
| ~ segmentP(W,Y0)
| ~ segmentP(X0,Y0)
| ~ ssList(Y0) ) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_2
& V = X0
& nil = V
& nil = W
& nil = X0
& skolemFOFtoCNF_U_2 = W
& ssList(X0)
& ! [Y0] :
( ~ neq(Y0,nil)
| ~ segmentP(W,Y0)
| ~ segmentP(X0,Y0)
| ~ ssList(Y0) ) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_2
& nil = W
& nil = X0
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( ~ neq(Y0,nil)
| ~ segmentP(W,Y0)
| ~ segmentP(X0,Y0)
| ~ ssList(Y0) ) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_2
& nil = W
& nil = X0
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( ~ neq(Y0,nil)
| ~ segmentP(W,Y0)
| ~ segmentP(X0,Y0)
| ~ ssList(Y0) ) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( nil != skolemFOFtoCNF_U_2
& nil = X0
& nil = skolemFOFtoCNF_V_13
& nil = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( ~ neq(Y0,nil)
| ~ segmentP(X0,Y0)
| ~ segmentP(skolemFOFtoCNF_W_13,Y0)
| ~ ssList(Y0) ) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X0] :
( nil != skolemFOFtoCNF_U_2
& nil = X0
& nil = skolemFOFtoCNF_V_13
& nil = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0)
& ! [Y0] :
( ~ neq(Y0,nil)
| ~ segmentP(X0,Y0)
| ~ segmentP(skolemFOFtoCNF_W_13,Y0)
| ~ ssList(Y0) ) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( nil != skolemFOFtoCNF_U_2
& nil = skolemFOFtoCNF_V_13
& 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] :
( ~ neq(Y0,nil)
| ~ segmentP(skolemFOFtoCNF_W_13,Y0)
| ~ segmentP(skolemFOFtoCNF_X_10,Y0)
| ~ ssList(Y0) ) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
nil != 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]) ).
cnf(refute_1_0,plain,
nil != 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( $equal(skolemFOFtoCNF_U_2,skolemFOFtoCNF_W_13) )],[refute_1_1,refute_1_9]) ).
cnf(refute_1_11,plain,
( nil != nil
| skolemFOFtoCNF_U_2 != nil
| nil = skolemFOFtoCNF_U_2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_U_2) ),[1],$fot(nil)]]) ).
cnf(refute_1_12,plain,
( nil != nil
| nil = skolemFOFtoCNF_U_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,nil) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
nil != nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_2) )],[refute_1_12,refute_1_0]) ).
cnf(refute_1_14,plain,
nil = nil,
introduced(tautology,[refl,[$fot(nil)]]) ).
cnf(refute_1_15,plain,
$false,
inference(resolve,[$cnf( $equal(nil,nil) )],[refute_1_14,refute_1_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC037+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 11 21:13:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.43/3.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.43/3.66
% 3.43/3.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.43/3.67
%------------------------------------------------------------------------------