TSTP Solution File: SWC047+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC047+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 21:26:17 EDT 2022
% Result : Theorem 1.69s 1.91s
% Output : CNFRefutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 38 unt; 0 def)
% Number of atoms : 354 ( 192 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 411 ( 155 ~; 95 |; 140 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 83 ( 0 sgn 33 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( V != X0
| U != W
| X0 != W
| ( ( nil != V
| nil = U )
& ( ~ neq(V,nil)
| ? [Y] :
( ssList(Y)
& neq(Y,nil)
& rearsegP(V,Y)
& rearsegP(U,Y) ) ) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ( X0 != W )
& ~ ( nil != V ) )
=> nil = U ) ) ) ),
inference(strip,[],[co1]) ).
fof(subgoal_1,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ( X0 != W )
& ( nil != V
| nil = U )
& ~ ~ neq(V,nil) )
=> ? [Y] :
( ssList(Y)
& neq(Y,nil)
& rearsegP(V,Y)
& rearsegP(U,Y) ) ) ) ) ),
inference(strip,[],[co1]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ( X0 != W )
& ~ ( nil != V ) )
=> nil = U ) ) ) ),
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
& X0 = W
& nil = V
& ssList(X0) ) ) ) ),
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
& X0 = W
& nil = V
& skolemFOFtoCNF_U_1 = W
& ssList(X0) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& V = X0
& X0 = W
& nil = V
& skolemFOFtoCNF_U_1 = W
& ssList(X0) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ssList(skolemFOFtoCNF_V_12)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& X0 = W
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& X0 = W
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ssList(skolemFOFtoCNF_W_12)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& X0 = skolemFOFtoCNF_W_12
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X0] :
( nil != skolemFOFtoCNF_U_1
& X0 = skolemFOFtoCNF_W_12
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0) ),
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
& skolemFOFtoCNF_X_9 = skolemFOFtoCNF_W_12
& ssList(skolemFOFtoCNF_X_9) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
nil != skolemFOFtoCNF_U_1,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
skolemFOFtoCNF_X_9 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_11,plain,
nil = skolemFOFtoCNF_V_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
nil != skolemFOFtoCNF_U_1,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_X_9 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_3,plain,
nil = skolemFOFtoCNF_V_12,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y0
| Y0 = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X != Y0
| Y0 = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( nil != skolemFOFtoCNF_V_12
| skolemFOFtoCNF_V_12 = nil ),
inference(subst,[],[refute_0_6:[bind(X,$fot(nil)),bind(Y0,$fot(skolemFOFtoCNF_V_12))]]) ).
cnf(refute_0_8,plain,
skolemFOFtoCNF_V_12 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_12) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_V_12 != nil
| skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) ),[0],$fot(nil)]]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,nil) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
nil = skolemFOFtoCNF_X_9,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( nil != skolemFOFtoCNF_X_9
| skolemFOFtoCNF_X_9 = nil ),
inference(subst,[],[refute_0_6:[bind(X,$fot(nil)),bind(Y0,$fot(skolemFOFtoCNF_X_9))]]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_X_9 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_9) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_X_9 != nil
| skolemFOFtoCNF_X_9 != skolemFOFtoCNF_W_12
| nil = skolemFOFtoCNF_W_12 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12) ),[0],$fot(nil)]]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_X_9 != skolemFOFtoCNF_W_12
| nil = skolemFOFtoCNF_W_12 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,nil) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_17,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y0,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_18,plain,
skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
inference(resolve,[$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( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_X_9 != skolemFOFtoCNF_W_12
| nil = skolemFOFtoCNF_U_1 ),
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_12) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
nil = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12) )],[refute_0_1,refute_0_21]) ).
cnf(refute_0_23,plain,
( nil != skolemFOFtoCNF_U_1
| skolemFOFtoCNF_U_1 = nil ),
inference(subst,[],[refute_0_6:[bind(X,$fot(nil)),bind(Y0,$fot(skolemFOFtoCNF_U_1))]]) ).
cnf(refute_0_24,plain,
skolemFOFtoCNF_U_1 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_1) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( nil != nil
| skolemFOFtoCNF_U_1 != nil
| nil = skolemFOFtoCNF_U_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_U_1) ),[1],$fot(nil)]]) ).
cnf(refute_0_26,plain,
( nil != nil
| nil = skolemFOFtoCNF_U_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,nil) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
nil != nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_1) )],[refute_0_26,refute_0_0]) ).
cnf(refute_0_28,plain,
nil = nil,
introduced(tautology,[refl,[$fot(nil)]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( $equal(nil,nil) )],[refute_0_28,refute_0_27]) ).
fof(negate_1_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ( X0 != W )
& ( nil != V
| nil = U )
& ~ ~ neq(V,nil) )
=> ? [Y] :
( ssList(Y)
& neq(Y,nil)
& rearsegP(V,Y)
& rearsegP(U,Y) ) ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( U = W
& V = X0
& X0 = W
& neq(V,nil)
& ssList(X0)
& ( nil != V
| nil = U )
& ! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ ssList(Y) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ssList(skolemFOFtoCNF_U_2)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( V = X0
& X0 = W
& skolemFOFtoCNF_U_2 = W
& neq(V,nil)
& ssList(X0)
& ( nil != V
| nil = skolemFOFtoCNF_U_2 )
& ! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(V,Y)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ ssList(Y) ) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
ssList(skolemFOFtoCNF_U_2),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [U] :
( ~ ssList(U)
| rearsegP(U,U) ),
inference(canonicalize,[],[ax49]) ).
fof(normalize_1_4,plain,
! [U] :
( ~ ssList(U)
| rearsegP(U,U) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( V = X0
& X0 = W
& skolemFOFtoCNF_U_2 = W
& neq(V,nil)
& ssList(X0)
& ( nil != V
| nil = skolemFOFtoCNF_U_2 )
& ! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(V,Y)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ ssList(Y) ) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_6,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( X0 = W
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ rearsegP(skolemFOFtoCNF_V_13,Y)
| ~ ssList(Y) ) ) ) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
? [W] :
( ssList(W)
& ? [X0] :
( X0 = W
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ rearsegP(skolemFOFtoCNF_V_13,Y)
| ~ ssList(Y) ) ) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( X0 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ rearsegP(skolemFOFtoCNF_V_13,Y)
| ~ ssList(Y) ) ) ),
inference(skolemize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
? [X0] :
( X0 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ rearsegP(skolemFOFtoCNF_V_13,Y)
| ~ ssList(Y) ) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
( skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10
& skolemFOFtoCNF_X_10 = skolemFOFtoCNF_W_13
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(skolemFOFtoCNF_X_10)
& ( nil != skolemFOFtoCNF_V_13
| nil = skolemFOFtoCNF_U_2 )
& ! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ rearsegP(skolemFOFtoCNF_V_13,Y)
| ~ ssList(Y) ) ),
inference(skolemize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ rearsegP(skolemFOFtoCNF_V_13,Y)
| ~ ssList(Y) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [Y] :
( ~ neq(Y,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ rearsegP(skolemFOFtoCNF_V_13,Y)
| ~ ssList(Y) ),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
skolemFOFtoCNF_X_10 = skolemFOFtoCNF_W_13,
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_14,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_15,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_16,plain,
neq(skolemFOFtoCNF_V_13,nil),
inference(conjunct,[],[normalize_1_10]) ).
cnf(refute_1_0,plain,
ssList(skolemFOFtoCNF_U_2),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ ssList(U)
| rearsegP(U,U) ),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
( ~ ssList(skolemFOFtoCNF_U_2)
| rearsegP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_U_2) ),
inference(subst,[],[refute_1_1:[bind(U,$fot(skolemFOFtoCNF_U_2))]]) ).
cnf(refute_1_3,plain,
rearsegP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_U_2),
inference(resolve,[$cnf( ssList(skolemFOFtoCNF_U_2) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
( ~ neq(Y,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ rearsegP(skolemFOFtoCNF_V_13,Y)
| ~ ssList(Y) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_5,plain,
skolemFOFtoCNF_X_10 = skolemFOFtoCNF_W_13,
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_6,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_7,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_8,plain,
( X != X
| X != Y0
| Y0 = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).
cnf(refute_1_9,plain,
( X != Y0
| Y0 = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13 ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_V_13)),bind(Y0,$fot(skolemFOFtoCNF_X_10))]]) ).
cnf(refute_1_11,plain,
skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) )],[refute_1_6,refute_1_10]) ).
cnf(refute_1_12,plain,
( skolemFOFtoCNF_X_10 != skolemFOFtoCNF_V_13
| skolemFOFtoCNF_X_10 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_V_13 = skolemFOFtoCNF_W_13 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_10,skolemFOFtoCNF_W_13) ),[0],$fot(skolemFOFtoCNF_V_13)]]) ).
cnf(refute_1_13,plain,
( skolemFOFtoCNF_X_10 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_V_13 = skolemFOFtoCNF_W_13 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_10,skolemFOFtoCNF_V_13) )],[refute_1_11,refute_1_12]) ).
cnf(refute_1_14,plain,
skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_15,plain,
( skolemFOFtoCNF_U_2 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 = skolemFOFtoCNF_U_2 ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_U_2)),bind(Y0,$fot(skolemFOFtoCNF_W_13))]]) ).
cnf(refute_1_16,plain,
skolemFOFtoCNF_W_13 = skolemFOFtoCNF_U_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,skolemFOFtoCNF_W_13) )],[refute_1_14,refute_1_15]) ).
cnf(refute_1_17,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_W_13 != skolemFOFtoCNF_U_2
| skolemFOFtoCNF_V_13 = skolemFOFtoCNF_U_2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_U_2) ),[0],$fot(skolemFOFtoCNF_W_13)]]) ).
cnf(refute_1_18,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_V_13 = skolemFOFtoCNF_U_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_13,skolemFOFtoCNF_U_2) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
( skolemFOFtoCNF_X_10 != skolemFOFtoCNF_W_13
| skolemFOFtoCNF_V_13 = skolemFOFtoCNF_U_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_W_13) )],[refute_1_13,refute_1_18]) ).
cnf(refute_1_20,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_U_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_10,skolemFOFtoCNF_W_13) )],[refute_1_5,refute_1_19]) ).
cnf(refute_1_21,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_U_2
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| rearsegP(skolemFOFtoCNF_V_13,Y) ),
introduced(tautology,[equality,[$cnf( ~ rearsegP(skolemFOFtoCNF_V_13,Y) ),[0],$fot(skolemFOFtoCNF_U_2)]]) ).
cnf(refute_1_22,plain,
( ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| rearsegP(skolemFOFtoCNF_V_13,Y) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_U_2) )],[refute_1_20,refute_1_21]) ).
cnf(refute_1_23,plain,
( ~ neq(Y,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,Y)
| ~ ssList(Y) ),
inference(resolve,[$cnf( rearsegP(skolemFOFtoCNF_V_13,Y) )],[refute_1_22,refute_1_4]) ).
cnf(refute_1_24,plain,
( ~ neq(skolemFOFtoCNF_U_2,nil)
| ~ rearsegP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_U_2)
| ~ ssList(skolemFOFtoCNF_U_2) ),
inference(subst,[],[refute_1_23:[bind(Y,$fot(skolemFOFtoCNF_U_2))]]) ).
cnf(refute_1_25,plain,
( ~ neq(skolemFOFtoCNF_U_2,nil)
| ~ ssList(skolemFOFtoCNF_U_2) ),
inference(resolve,[$cnf( rearsegP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_U_2) )],[refute_1_3,refute_1_24]) ).
cnf(refute_1_26,plain,
neq(skolemFOFtoCNF_V_13,nil),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_27,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_U_2
| ~ neq(skolemFOFtoCNF_V_13,nil)
| neq(skolemFOFtoCNF_U_2,nil) ),
introduced(tautology,[equality,[$cnf( neq(skolemFOFtoCNF_V_13,nil) ),[0],$fot(skolemFOFtoCNF_U_2)]]) ).
cnf(refute_1_28,plain,
( ~ neq(skolemFOFtoCNF_V_13,nil)
| neq(skolemFOFtoCNF_U_2,nil) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_U_2) )],[refute_1_20,refute_1_27]) ).
cnf(refute_1_29,plain,
neq(skolemFOFtoCNF_U_2,nil),
inference(resolve,[$cnf( neq(skolemFOFtoCNF_V_13,nil) )],[refute_1_26,refute_1_28]) ).
cnf(refute_1_30,plain,
~ ssList(skolemFOFtoCNF_U_2),
inference(resolve,[$cnf( neq(skolemFOFtoCNF_U_2,nil) )],[refute_1_29,refute_1_25]) ).
cnf(refute_1_31,plain,
$false,
inference(resolve,[$cnf( ssList(skolemFOFtoCNF_U_2) )],[refute_1_0,refute_1_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC047+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.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 22:55:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.69/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.69/1.91
% 1.69/1.91 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.69/1.91
%------------------------------------------------------------------------------