TSTP Solution File: PUZ001+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : PUZ001+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 : Mon Jul 18 18:20:24 EDT 2022
% Result : Theorem 0.18s 0.36s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 122 ( 43 unt; 0 def)
% Number of atoms : 322 ( 127 equ)
% Maximal formula atoms : 37 ( 2 avg)
% Number of connectives : 334 ( 134 ~; 137 |; 53 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 4 usr; 2 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-2 aty)
% Number of variables : 200 ( 13 sgn 106 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(background,axiom,
? [A,B,C] :
( $true
& predicate1(B,live,A)
& modifier_pp(B,in,'DreadburyMansion')
& predicate2(C,kill,A,'AuntAgatha')
& ! [D,E] :
( ( $true
& predicate1(E,live,D)
& modifier_pp(E,in,'DreadburyMansion') )
=> ( D = 'AuntAgatha'
| D = 'Butler'
| D = 'Charles' ) )
& ! [F] :
( $true
=> ! [G,H] :
( ( $true
& predicate2(H,kill,F,G) )
=> ? [I] : predicate2(I,hate,F,G) ) )
& ! [J] :
( $true
=> ~ ? [K,L,M] :
( $true
& predicate2(L,kill,J,K)
& property2(M,rich,comp_than,K)
& J = M ) )
& ! [N,O] :
( ( $true
& predicate2(O,hate,'AuntAgatha',N) )
=> ~ ? [P] : predicate2(P,hate,'Charles',N) )
& ~ ? [Q] : predicate2(Q,hate,'AuntAgatha','Butler')
& ! [R] :
( ( $true
& R != 'Butler' )
=> ? [S] : predicate2(S,hate,'AuntAgatha',R) )
& ! [T] :
( ( $true
& ~ ? [U] :
( property2(U,rich,comp_than,'AuntAgatha')
& T = U ) )
=> ? [V] : predicate2(V,hate,'Butler',T) )
& ! [W,X] :
( ( $true
& predicate2(X,hate,'AuntAgatha',W) )
=> ? [Y0] : predicate2(Y0,hate,'Butler',W) )
& ! [Z] :
( $true
=> ~ ! [A1] :
( $true
=> ? [B1] : predicate2(B1,hate,Z,A1) ) )
& 'AuntAgatha' != 'Butler' ) ).
fof(prove,conjecture,
? [A] : predicate2(A,kill,'AuntAgatha','AuntAgatha') ).
fof(subgoal_0,plain,
? [A] : predicate2(A,kill,'AuntAgatha','AuntAgatha'),
inference(strip,[],[prove]) ).
fof(negate_0_0,plain,
~ ? [A] : predicate2(A,kill,'AuntAgatha','AuntAgatha'),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( 'AuntAgatha' != 'Butler'
& modifier_pp(B,in,'DreadburyMansion')
& predicate1(B,live,A)
& ? [C] : predicate2(C,kill,A,'AuntAgatha')
& ! [N] :
( ! [O] : ~ predicate2(O,hate,'AuntAgatha',N)
| ! [P] : ~ predicate2(P,hate,'Charles',N) )
& ! [Q] : ~ predicate2(Q,hate,'AuntAgatha','Butler')
& ! [R] :
( R = 'Butler'
| ? [S] : predicate2(S,hate,'AuntAgatha',R) )
& ! [T] :
( ? [U] :
( T = U
& property2(U,rich,comp_than,'AuntAgatha') )
| ? [V] : predicate2(V,hate,'Butler',T) )
& ! [W] :
( ? [Y0] : predicate2(Y0,hate,'Butler',W)
| ! [X] : ~ predicate2(X,hate,'AuntAgatha',W) )
& ! [Z] :
? [A1] :
! [B1] : ~ predicate2(B1,hate,Z,A1)
& ! [D,E] :
( ~ modifier_pp(E,in,'DreadburyMansion')
| ~ predicate1(E,live,D)
| D = 'AuntAgatha'
| D = 'Butler'
| D = 'Charles' )
& ! [F,G] :
( ? [I] : predicate2(I,hate,F,G)
| ! [H] : ~ predicate2(H,kill,F,G) )
& ! [J,K,L,M] :
( J != M
| ~ predicate2(L,kill,J,K)
| ~ property2(M,rich,comp_than,K) ) ),
inference(canonicalize,[],[background]) ).
fof(normalize_0_1,plain,
( 'AuntAgatha' != 'Butler'
& modifier_pp(skolemFOFtoCNF_B,in,'DreadburyMansion')
& predicate1(skolemFOFtoCNF_B,live,skolemFOFtoCNF_A)
& ? [C] : predicate2(C,kill,skolemFOFtoCNF_A,'AuntAgatha')
& ! [N] :
( ! [O] : ~ predicate2(O,hate,'AuntAgatha',N)
| ! [P] : ~ predicate2(P,hate,'Charles',N) )
& ! [Q] : ~ predicate2(Q,hate,'AuntAgatha','Butler')
& ! [R] :
( R = 'Butler'
| ? [S] : predicate2(S,hate,'AuntAgatha',R) )
& ! [T] :
( ? [U] :
( T = U
& property2(U,rich,comp_than,'AuntAgatha') )
| ? [V] : predicate2(V,hate,'Butler',T) )
& ! [W] :
( ? [Y0] : predicate2(Y0,hate,'Butler',W)
| ! [X] : ~ predicate2(X,hate,'AuntAgatha',W) )
& ! [Z] :
? [A1] :
! [B1] : ~ predicate2(B1,hate,Z,A1)
& ! [D,E] :
( ~ modifier_pp(E,in,'DreadburyMansion')
| ~ predicate1(E,live,D)
| D = 'AuntAgatha'
| D = 'Butler'
| D = 'Charles' )
& ! [F,G] :
( ? [I] : predicate2(I,hate,F,G)
| ! [H] : ~ predicate2(H,kill,F,G) )
& ! [J,K,L,M] :
( J != M
| ~ predicate2(L,kill,J,K)
| ~ property2(M,rich,comp_than,K) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [R] :
( R = 'Butler'
| ? [S] : predicate2(S,hate,'AuntAgatha',R) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [R] :
( R = 'Butler'
| ? [S] : predicate2(S,hate,'AuntAgatha',R) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [R] :
( R = 'Butler'
| predicate2(skolemFOFtoCNF_S(R),hate,'AuntAgatha',R) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [N] :
( ! [O] : ~ predicate2(O,hate,'AuntAgatha',N)
| ! [P] : ~ predicate2(P,hate,'Charles',N) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [N] :
( ! [O] : ~ predicate2(O,hate,'AuntAgatha',N)
| ! [P] : ~ predicate2(P,hate,'Charles',N) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [N,O,P] :
( ~ predicate2(O,hate,'AuntAgatha',N)
| ~ predicate2(P,hate,'Charles',N) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [C] : predicate2(C,kill,skolemFOFtoCNF_A,'AuntAgatha'),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha'),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [F,G] :
( ? [I] : predicate2(I,hate,F,G)
| ! [H] : ~ predicate2(H,kill,F,G) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
! [F,G] :
( ? [I] : predicate2(I,hate,F,G)
| ! [H] : ~ predicate2(H,kill,F,G) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [F,G,H] :
( ~ predicate2(H,kill,F,G)
| predicate2(skolemFOFtoCNF_I(F,G),hate,F,G) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
predicate1(skolemFOFtoCNF_B,live,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_14,plain,
! [D,E] :
( ~ modifier_pp(E,in,'DreadburyMansion')
| ~ predicate1(E,live,D)
| D = 'AuntAgatha'
| D = 'Butler'
| D = 'Charles' ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_15,plain,
! [D,E] :
( ~ modifier_pp(E,in,'DreadburyMansion')
| ~ predicate1(E,live,D)
| D = 'AuntAgatha'
| D = 'Butler'
| D = 'Charles' ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
modifier_pp(skolemFOFtoCNF_B,in,'DreadburyMansion'),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_17,plain,
! [A] : ~ predicate2(A,kill,'AuntAgatha','AuntAgatha'),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_18,plain,
! [A] : ~ predicate2(A,kill,'AuntAgatha','AuntAgatha'),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [Z] :
? [A1] :
! [B1] : ~ predicate2(B1,hate,Z,A1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_20,plain,
! [Z] :
? [A1] :
! [B1] : ~ predicate2(B1,hate,Z,A1),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [Z,B1] : ~ predicate2(B1,hate,Z,skolemFOFtoCNF_A1(Z)),
inference(skolemize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B1,Z] : ~ predicate2(B1,hate,Z,skolemFOFtoCNF_A1(Z)),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [T] :
( ? [U] :
( T = U
& property2(U,rich,comp_than,'AuntAgatha') )
| ? [V] : predicate2(V,hate,'Butler',T) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_24,plain,
! [T] :
( ? [U] :
( T = U
& property2(U,rich,comp_than,'AuntAgatha') )
| ? [V] : predicate2(V,hate,'Butler',T) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [T] :
( ( T = skolemFOFtoCNF_U(T)
| predicate2(skolemFOFtoCNF_V(T),hate,'Butler',T) )
& ( predicate2(skolemFOFtoCNF_V(T),hate,'Butler',T)
| property2(skolemFOFtoCNF_U(T),rich,comp_than,'AuntAgatha') ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [T] :
( predicate2(skolemFOFtoCNF_V(T),hate,'Butler',T)
| property2(skolemFOFtoCNF_U(T),rich,comp_than,'AuntAgatha') ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [T] :
( T = skolemFOFtoCNF_U(T)
| predicate2(skolemFOFtoCNF_V(T),hate,'Butler',T) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_28,plain,
! [W] :
( ? [Y0] : predicate2(Y0,hate,'Butler',W)
| ! [X] : ~ predicate2(X,hate,'AuntAgatha',W) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_29,plain,
! [W] :
( ? [Y0] : predicate2(Y0,hate,'Butler',W)
| ! [X] : ~ predicate2(X,hate,'AuntAgatha',W) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [W,X] :
( ~ predicate2(X,hate,'AuntAgatha',W)
| predicate2(skolemFOFtoCNF_Y(W),hate,'Butler',W) ),
inference(clausify,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [J,K,L,M] :
( J != M
| ~ predicate2(L,kill,J,K)
| ~ property2(M,rich,comp_than,K) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_32,plain,
! [J,K,L,M] :
( J != M
| ~ predicate2(L,kill,J,K)
| ~ property2(M,rich,comp_than,K) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
'AuntAgatha' != 'Butler',
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
( R = 'Butler'
| predicate2(skolemFOFtoCNF_S(R),hate,'AuntAgatha',R) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( X_14 = 'Butler'
| predicate2(skolemFOFtoCNF_S(X_14),hate,'AuntAgatha',X_14) ),
inference(subst,[],[refute_0_0:[bind(R,$fot(X_14))]]) ).
cnf(refute_0_2,plain,
( ~ predicate2(O,hate,'AuntAgatha',N)
| ~ predicate2(P,hate,'Charles',N) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ predicate2(X_16,hate,'Charles',X_14)
| ~ predicate2(skolemFOFtoCNF_S(X_14),hate,'AuntAgatha',X_14) ),
inference(subst,[],[refute_0_2:[bind(N,$fot(X_14)),bind(O,$fot(skolemFOFtoCNF_S(X_14))),bind(P,$fot(X_16))]]) ).
cnf(refute_0_4,plain,
( ~ predicate2(X_16,hate,'Charles',X_14)
| X_14 = 'Butler' ),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_S(X_14),hate,'AuntAgatha',X_14) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,'Charles','AuntAgatha')
| 'AuntAgatha' = 'Butler' ),
inference(subst,[],[refute_0_4:[bind(X_14,$fot('AuntAgatha')),bind(X_16,$fot(skolemFOFtoCNF_I('Charles','AuntAgatha')))]]) ).
cnf(refute_0_6,plain,
predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha'),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ predicate2(H,kill,F,G)
| predicate2(skolemFOFtoCNF_I(F,G),hate,F,G) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
( ~ predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha')
| predicate2(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha') ),
inference(subst,[],[refute_0_7:[bind(F,$fot(skolemFOFtoCNF_A)),bind(G,$fot('AuntAgatha')),bind(H,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_9,plain,
predicate2(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha'),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha') )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
predicate1(skolemFOFtoCNF_B,live,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ modifier_pp(E,in,'DreadburyMansion')
| ~ predicate1(E,live,D)
| D = 'AuntAgatha'
| D = 'Butler'
| D = 'Charles' ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ modifier_pp(skolemFOFtoCNF_B,in,'DreadburyMansion')
| ~ predicate1(skolemFOFtoCNF_B,live,skolemFOFtoCNF_A)
| skolemFOFtoCNF_A = 'AuntAgatha'
| skolemFOFtoCNF_A = 'Butler'
| skolemFOFtoCNF_A = 'Charles' ),
inference(subst,[],[refute_0_11:[bind(D,$fot(skolemFOFtoCNF_A)),bind(E,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_13,plain,
( ~ modifier_pp(skolemFOFtoCNF_B,in,'DreadburyMansion')
| skolemFOFtoCNF_A = 'AuntAgatha'
| skolemFOFtoCNF_A = 'Butler'
| skolemFOFtoCNF_A = 'Charles' ),
inference(resolve,[$cnf( predicate1(skolemFOFtoCNF_B,live,skolemFOFtoCNF_A) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
modifier_pp(skolemFOFtoCNF_B,in,'DreadburyMansion'),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_A = 'AuntAgatha'
| skolemFOFtoCNF_A = 'Butler'
| skolemFOFtoCNF_A = 'Charles' ),
inference(resolve,[$cnf( modifier_pp(skolemFOFtoCNF_B,in,'DreadburyMansion') )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_A != 'AuntAgatha'
| ~ predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha')
| predicate2(skolemFOFtoCNF_C,kill,'AuntAgatha','AuntAgatha') ),
introduced(tautology,[equality,[$cnf( predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha') ),[2],$fot('AuntAgatha')]]) ).
cnf(refute_0_17,plain,
( ~ predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha')
| skolemFOFtoCNF_A = 'Butler'
| skolemFOFtoCNF_A = 'Charles'
| predicate2(skolemFOFtoCNF_C,kill,'AuntAgatha','AuntAgatha') ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A,'AuntAgatha') )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_A = 'Butler'
| skolemFOFtoCNF_A = 'Charles'
| predicate2(skolemFOFtoCNF_C,kill,'AuntAgatha','AuntAgatha') ),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha') )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
~ predicate2(A,kill,'AuntAgatha','AuntAgatha'),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_20,plain,
~ predicate2(skolemFOFtoCNF_C,kill,'AuntAgatha','AuntAgatha'),
inference(subst,[],[refute_0_19:[bind(A,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_A = 'Butler'
| skolemFOFtoCNF_A = 'Charles' ),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_C,kill,'AuntAgatha','AuntAgatha') )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
( skolemFOFtoCNF_A != 'Butler'
| ~ predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha')
| predicate2(skolemFOFtoCNF_C,kill,'Butler','AuntAgatha') ),
introduced(tautology,[equality,[$cnf( predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha') ),[2],$fot('Butler')]]) ).
cnf(refute_0_23,plain,
( ~ predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha')
| skolemFOFtoCNF_A = 'Charles'
| predicate2(skolemFOFtoCNF_C,kill,'Butler','AuntAgatha') ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A,'Butler') )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_A = 'Charles'
| predicate2(skolemFOFtoCNF_C,kill,'Butler','AuntAgatha') ),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_C,kill,skolemFOFtoCNF_A,'AuntAgatha') )],[refute_0_6,refute_0_23]) ).
cnf(refute_0_25,plain,
~ predicate2(B1,hate,Z,skolemFOFtoCNF_A1(Z)),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_26,plain,
~ predicate2(skolemFOFtoCNF_V(skolemFOFtoCNF_A1('Butler')),hate,'Butler',skolemFOFtoCNF_A1('Butler')),
inference(subst,[],[refute_0_25:[bind(B1,$fot(skolemFOFtoCNF_V(skolemFOFtoCNF_A1('Butler')))),bind(Z,$fot('Butler'))]]) ).
cnf(refute_0_27,plain,
( predicate2(skolemFOFtoCNF_V(T),hate,'Butler',T)
| property2(skolemFOFtoCNF_U(T),rich,comp_than,'AuntAgatha') ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_28,plain,
( predicate2(skolemFOFtoCNF_V(skolemFOFtoCNF_A1('Butler')),hate,'Butler',skolemFOFtoCNF_A1('Butler'))
| property2(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),rich,comp_than,'AuntAgatha') ),
inference(subst,[],[refute_0_27:[bind(T,$fot(skolemFOFtoCNF_A1('Butler')))]]) ).
cnf(refute_0_29,plain,
property2(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),rich,comp_than,'AuntAgatha'),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_V(skolemFOFtoCNF_A1('Butler')),hate,'Butler',skolemFOFtoCNF_A1('Butler')) )],[refute_0_28,refute_0_26]) ).
cnf(refute_0_30,plain,
( T = skolemFOFtoCNF_U(T)
| predicate2(skolemFOFtoCNF_V(T),hate,'Butler',T) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_A1('Butler') = skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))
| predicate2(skolemFOFtoCNF_V(skolemFOFtoCNF_A1('Butler')),hate,'Butler',skolemFOFtoCNF_A1('Butler')) ),
inference(subst,[],[refute_0_30:[bind(T,$fot(skolemFOFtoCNF_A1('Butler')))]]) ).
cnf(refute_0_32,plain,
skolemFOFtoCNF_A1('Butler') = skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_V(skolemFOFtoCNF_A1('Butler')),hate,'Butler',skolemFOFtoCNF_A1('Butler')) )],[refute_0_31,refute_0_26]) ).
cnf(refute_0_33,plain,
~ predicate2(skolemFOFtoCNF_Y(skolemFOFtoCNF_A1('Butler')),hate,'Butler',skolemFOFtoCNF_A1('Butler')),
inference(subst,[],[refute_0_25:[bind(B1,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_A1('Butler')))),bind(Z,$fot('Butler'))]]) ).
cnf(refute_0_34,plain,
( X_6 = 'Butler'
| predicate2(skolemFOFtoCNF_S(X_6),hate,'AuntAgatha',X_6) ),
inference(subst,[],[refute_0_0:[bind(R,$fot(X_6))]]) ).
cnf(refute_0_35,plain,
( ~ predicate2(X,hate,'AuntAgatha',W)
| predicate2(skolemFOFtoCNF_Y(W),hate,'Butler',W) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_36,plain,
( ~ predicate2(skolemFOFtoCNF_S(X_6),hate,'AuntAgatha',X_6)
| predicate2(skolemFOFtoCNF_Y(X_6),hate,'Butler',X_6) ),
inference(subst,[],[refute_0_35:[bind(W,$fot(X_6)),bind(X,$fot(skolemFOFtoCNF_S(X_6)))]]) ).
cnf(refute_0_37,plain,
( X_6 = 'Butler'
| predicate2(skolemFOFtoCNF_Y(X_6),hate,'Butler',X_6) ),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_S(X_6),hate,'AuntAgatha',X_6) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( skolemFOFtoCNF_A1('Butler') = 'Butler'
| predicate2(skolemFOFtoCNF_Y(skolemFOFtoCNF_A1('Butler')),hate,'Butler',skolemFOFtoCNF_A1('Butler')) ),
inference(subst,[],[refute_0_37:[bind(X_6,$fot(skolemFOFtoCNF_A1('Butler')))]]) ).
cnf(refute_0_39,plain,
skolemFOFtoCNF_A1('Butler') = 'Butler',
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_Y(skolemFOFtoCNF_A1('Butler')),hate,'Butler',skolemFOFtoCNF_A1('Butler')) )],[refute_0_38,refute_0_33]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_A1('Butler') != 'Butler'
| skolemFOFtoCNF_A1('Butler') != skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))
| 'Butler' = skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_A1('Butler'),skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))) ),[0],$fot('Butler')]]) ).
cnf(refute_0_41,plain,
( skolemFOFtoCNF_A1('Butler') != skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))
| 'Butler' = skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A1('Butler'),'Butler') )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) = skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')))]]) ).
cnf(refute_0_43,plain,
( skolemFOFtoCNF_A1('Butler') != 'Butler'
| skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) != skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))
| skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) = skolemFOFtoCNF_U('Butler') ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))) ),[1,0],$fot('Butler')]]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_A1('Butler') != 'Butler'
| skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) = skolemFOFtoCNF_U('Butler') ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) = skolemFOFtoCNF_U('Butler'),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A1('Butler'),'Butler') )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
( 'Butler' != skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))
| skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) != skolemFOFtoCNF_U('Butler')
| 'Butler' = skolemFOFtoCNF_U('Butler') ),
introduced(tautology,[equality,[$cnf( ~ $equal('Butler',skolemFOFtoCNF_U('Butler')) ),[0],$fot(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')))]]) ).
cnf(refute_0_47,plain,
( 'Butler' != skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))
| 'Butler' = skolemFOFtoCNF_U('Butler') ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),skolemFOFtoCNF_U('Butler')) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( skolemFOFtoCNF_A1('Butler') != skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))
| 'Butler' = skolemFOFtoCNF_U('Butler') ),
inference(resolve,[$cnf( $equal('Butler',skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
'Butler' = skolemFOFtoCNF_U('Butler'),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A1('Butler'),skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler'))) )],[refute_0_32,refute_0_48]) ).
cnf(refute_0_50,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_51,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_52,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( 'Butler' != skolemFOFtoCNF_U('Butler')
| skolemFOFtoCNF_U('Butler') = 'Butler' ),
inference(subst,[],[refute_0_52:[bind(X0,$fot('Butler')),bind(Y,$fot(skolemFOFtoCNF_U('Butler')))]]) ).
cnf(refute_0_54,plain,
skolemFOFtoCNF_U('Butler') = 'Butler',
inference(resolve,[$cnf( $equal('Butler',skolemFOFtoCNF_U('Butler')) )],[refute_0_49,refute_0_53]) ).
cnf(refute_0_55,plain,
( Y != X0
| Y != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_56,plain,
( X0 != Y
| Y != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
( skolemFOFtoCNF_U('Butler') != 'Butler'
| skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) != skolemFOFtoCNF_U('Butler')
| skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) = 'Butler' ),
inference(subst,[],[refute_0_56:[bind(X0,$fot(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')))),bind(Y,$fot(skolemFOFtoCNF_U('Butler'))),bind(Z0,$fot('Butler'))]]) ).
cnf(refute_0_58,plain,
( skolemFOFtoCNF_U('Butler') != 'Butler'
| skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) = 'Butler' ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),skolemFOFtoCNF_U('Butler')) )],[refute_0_45,refute_0_57]) ).
cnf(refute_0_59,plain,
skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) = 'Butler',
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U('Butler'),'Butler') )],[refute_0_54,refute_0_58]) ).
cnf(refute_0_60,plain,
( skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')) != 'Butler'
| ~ property2(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),rich,comp_than,'AuntAgatha')
| property2('Butler',rich,comp_than,'AuntAgatha') ),
introduced(tautology,[equality,[$cnf( property2(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),rich,comp_than,'AuntAgatha') ),[0],$fot('Butler')]]) ).
cnf(refute_0_61,plain,
( ~ property2(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),rich,comp_than,'AuntAgatha')
| property2('Butler',rich,comp_than,'AuntAgatha') ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),'Butler') )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
property2('Butler',rich,comp_than,'AuntAgatha'),
inference(resolve,[$cnf( property2(skolemFOFtoCNF_U(skolemFOFtoCNF_A1('Butler')),rich,comp_than,'AuntAgatha') )],[refute_0_29,refute_0_61]) ).
cnf(refute_0_63,plain,
( J != M
| ~ predicate2(L,kill,J,K)
| ~ property2(M,rich,comp_than,K) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_64,plain,
( M != M
| ~ predicate2(L,kill,M,K)
| ~ property2(M,rich,comp_than,K) ),
inference(subst,[],[refute_0_63:[bind(J,$fot(M))]]) ).
cnf(refute_0_65,plain,
M = M,
introduced(tautology,[refl,[$fot(M)]]) ).
cnf(refute_0_66,plain,
( ~ predicate2(L,kill,M,K)
| ~ property2(M,rich,comp_than,K) ),
inference(resolve,[$cnf( $equal(M,M) )],[refute_0_65,refute_0_64]) ).
cnf(refute_0_67,plain,
( ~ predicate2(X_20,kill,'Butler','AuntAgatha')
| ~ property2('Butler',rich,comp_than,'AuntAgatha') ),
inference(subst,[],[refute_0_66:[bind(K,$fot('AuntAgatha')),bind(L,$fot(X_20)),bind(M,$fot('Butler'))]]) ).
cnf(refute_0_68,plain,
~ predicate2(X_20,kill,'Butler','AuntAgatha'),
inference(resolve,[$cnf( property2('Butler',rich,comp_than,'AuntAgatha') )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
~ predicate2(skolemFOFtoCNF_C,kill,'Butler','AuntAgatha'),
inference(subst,[],[refute_0_68:[bind(X_20,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_70,plain,
skolemFOFtoCNF_A = 'Charles',
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_C,kill,'Butler','AuntAgatha') )],[refute_0_24,refute_0_69]) ).
cnf(refute_0_71,plain,
skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha') = skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'))]]) ).
cnf(refute_0_72,plain,
( skolemFOFtoCNF_A != 'Charles'
| skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha') != skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha')
| skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha') = skolemFOFtoCNF_I('Charles','AuntAgatha') ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha')) ),[1,0],$fot('Charles')]]) ).
cnf(refute_0_73,plain,
( skolemFOFtoCNF_A != 'Charles'
| skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha') = skolemFOFtoCNF_I('Charles','AuntAgatha') ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha')) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha') = skolemFOFtoCNF_I('Charles','AuntAgatha'),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A,'Charles') )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
( skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha') != skolemFOFtoCNF_I('Charles','AuntAgatha')
| ~ predicate2(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha')
| predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha') ),
introduced(tautology,[equality,[$cnf( predicate2(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha') ),[0],$fot(skolemFOFtoCNF_I('Charles','AuntAgatha'))]]) ).
cnf(refute_0_76,plain,
( ~ predicate2(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha')
| predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha') ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),skolemFOFtoCNF_I('Charles','AuntAgatha')) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( skolemFOFtoCNF_A != 'Charles'
| ~ predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha')
| predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,'Charles','AuntAgatha') ),
introduced(tautology,[equality,[$cnf( predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha') ),[2],$fot('Charles')]]) ).
cnf(refute_0_78,plain,
( ~ predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha')
| predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,'Charles','AuntAgatha') ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A,'Charles') )],[refute_0_70,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ predicate2(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha')
| predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,'Charles','AuntAgatha') ),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha') )],[refute_0_76,refute_0_78]) ).
cnf(refute_0_80,plain,
predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,'Charles','AuntAgatha'),
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_I(skolemFOFtoCNF_A,'AuntAgatha'),hate,skolemFOFtoCNF_A,'AuntAgatha') )],[refute_0_9,refute_0_79]) ).
cnf(refute_0_81,plain,
'AuntAgatha' = 'Butler',
inference(resolve,[$cnf( predicate2(skolemFOFtoCNF_I('Charles','AuntAgatha'),hate,'Charles','AuntAgatha') )],[refute_0_80,refute_0_5]) ).
cnf(refute_0_82,plain,
'AuntAgatha' != 'Butler',
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_83,plain,
$false,
inference(resolve,[$cnf( $equal('AuntAgatha','Butler') )],[refute_0_81,refute_0_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ001+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.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 May 29 00:59:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.36
% 0.18/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.37
%------------------------------------------------------------------------------