%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PUZ001+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:59:48 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 44 ( 23 unt; 0 def)
% Number of atoms : 236 ( 61 equ)
% Maximal formula atoms : 37 ( 5 avg)
% Number of connectives : 268 ( 76 ~; 100 |; 82 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 2 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-2 aty)
% Number of variables : 215 ( 172 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [A,B,C] :
( 'AuntAgatha' != 'Butler'
& ! [Z] :
( $true
=> ~ ! [A1] :
( $true
=> ? [B1] : predicate2(B1,hate,Z,A1) ) )
& ! [W,X] :
( ( predicate2(X,hate,'AuntAgatha',W)
& $true )
=> ? [Y] : predicate2(Y,hate,'Butler',W) )
& ! [T] :
( ( ~ ? [U] :
( T = U
& property2(U,rich,comp_than,'AuntAgatha') )
& $true )
=> ? [V] : predicate2(V,hate,'Butler',T) )
& ! [R] :
( ( R != 'Butler'
& $true )
=> ? [S] : predicate2(S,hate,'AuntAgatha',R) )
& ~ ? [Q] : predicate2(Q,hate,'AuntAgatha','Butler')
& ! [N,O] :
( ( predicate2(O,hate,'AuntAgatha',N)
& $true )
=> ~ ? [P] : predicate2(P,hate,'Charles',N) )
& ! [J] :
( $true
=> ~ ? [K,L,M] :
( J = M
& property2(M,rich,comp_than,K)
& predicate2(L,kill,J,K)
& $true ) )
& ! [F] :
( $true
=> ! [G,H] :
( ( predicate2(H,kill,F,G)
& $true )
=> ? [I] : predicate2(I,hate,F,G) ) )
& ! [D,E] :
( ( modifier_pp(E,in,'DreadburyMansion')
& predicate1(E,live,D)
& $true )
=> ( D = 'Charles'
| D = 'Butler'
| D = 'AuntAgatha' ) )
& predicate2(C,kill,A,'AuntAgatha')
& modifier_pp(B,in,'DreadburyMansion')
& predicate1(B,live,A)
& $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,conjecture,
? [A] : predicate2(A,kill,'AuntAgatha','AuntAgatha'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ ? [A] : predicate2(A,kill,'AuntAgatha','AuntAgatha'),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
? [A,B,C] :
( 'AuntAgatha' != 'Butler'
& ! [Z] :
( ? [A1] :
( ! [B1] : ~ predicate2(B1,hate,Z,A1)
& $true )
| $false )
& ! [W,X] :
( ? [Y] : predicate2(Y,hate,'Butler',W)
| ~ predicate2(X,hate,'AuntAgatha',W)
| $false )
& ! [T] :
( ? [V] : predicate2(V,hate,'Butler',T)
| ? [U] :
( T = U
& property2(U,rich,comp_than,'AuntAgatha') )
| $false )
& ! [R] :
( ? [S] : predicate2(S,hate,'AuntAgatha',R)
| R = 'Butler'
| $false )
& ! [Q] : ~ predicate2(Q,hate,'AuntAgatha','Butler')
& ! [N,O] :
( ! [P] : ~ predicate2(P,hate,'Charles',N)
| ~ predicate2(O,hate,'AuntAgatha',N)
| $false )
& ! [J] :
( ! [K,L,M] :
( J != M
| ~ property2(M,rich,comp_than,K)
| ~ predicate2(L,kill,J,K)
| $false )
| $false )
& ! [F] :
( ! [G,H] :
( ? [I] : predicate2(I,hate,F,G)
| ~ predicate2(H,kill,F,G)
| $false )
| $false )
& ! [D,E] :
( D = 'Charles'
| D = 'Butler'
| D = 'AuntAgatha'
| ~ modifier_pp(E,in,'DreadburyMansion')
| ~ predicate1(E,live,D)
| $false )
& predicate2(C,kill,A,'AuntAgatha')
& modifier_pp(B,in,'DreadburyMansion')
& predicate1(B,live,A)
& $true ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
( 'AuntAgatha' != 'Butler'
& ( ( ! [Z] :
? [A1] :
! [B1] : ~ predicate2(B1,hate,Z,A1)
& $true )
| $false )
& ! [W] :
( ? [Y] : predicate2(Y,hate,'Butler',W)
| ! [X] : ~ predicate2(X,hate,'AuntAgatha',W)
| $false )
& ! [T] :
( ? [V] : predicate2(V,hate,'Butler',T)
| ? [U] :
( T = U
& property2(U,rich,comp_than,'AuntAgatha') )
| $false )
& ! [R] :
( ? [S] : predicate2(S,hate,'AuntAgatha',R)
| R = 'Butler'
| $false )
& ! [Q] : ~ predicate2(Q,hate,'AuntAgatha','Butler')
& ! [N] :
( ! [P] : ~ predicate2(P,hate,'Charles',N)
| ! [O] : ~ predicate2(O,hate,'AuntAgatha',N)
| $false )
& ( ! [J,M] :
( J != M
| ! [K] :
( ~ property2(M,rich,comp_than,K)
| ! [L] : ~ predicate2(L,kill,J,K)
| $false ) )
| $false )
& ( ! [F,G] :
( ? [I] : predicate2(I,hate,F,G)
| ! [H] : ~ predicate2(H,kill,F,G)
| $false )
| $false )
& ! [D] :
( D = 'Charles'
| D = 'Butler'
| D = 'AuntAgatha'
| ! [E] :
( ~ modifier_pp(E,in,'DreadburyMansion')
| ~ predicate1(E,live,D)
| $false ) )
& ? [A] :
( ? [C] : predicate2(C,kill,A,'AuntAgatha')
& ? [B] :
( modifier_pp(B,in,'DreadburyMansion')
& predicate1(B,live,A)
& $true ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( 'AuntAgatha' != 'Butler'
& ( ( ! [Z,B1] : ~ predicate2(B1,hate,Z,sK8_skl(Z))
& $true )
| $false )
& ! [W] :
( predicate2(sK7_skl(W),hate,'Butler',W)
| ! [X] : ~ predicate2(X,hate,'AuntAgatha',W)
| $false )
& ! [T] :
( predicate2(sK6_skl(T),hate,'Butler',T)
| ( T = sK5_skl(T)
& property2(sK5_skl(T),rich,comp_than,'AuntAgatha') )
| $false )
& ! [R] :
( predicate2(sK4_skl(R),hate,'AuntAgatha',R)
| R = 'Butler'
| $false )
& ! [Q] : ~ predicate2(Q,hate,'AuntAgatha','Butler')
& ! [N] :
( ! [P] : ~ predicate2(P,hate,'Charles',N)
| ! [O] : ~ predicate2(O,hate,'AuntAgatha',N)
| $false )
& ( ! [J,M] :
( J != M
| ! [K] :
( ~ property2(M,rich,comp_than,K)
| ! [L] : ~ predicate2(L,kill,J,K)
| $false ) )
| $false )
& ( ! [F,G] :
( predicate2(sK3_skl(G,F),hate,F,G)
| ! [H] : ~ predicate2(H,kill,F,G)
| $false )
| $false )
& ! [D] :
( D = 'Charles'
| D = 'Butler'
| D = 'AuntAgatha'
| ! [E] :
( ~ modifier_pp(E,in,'DreadburyMansion')
| ~ predicate1(E,live,D)
| $false ) )
& predicate2(sK2_skl,kill,sK0_skl,'AuntAgatha')
& modifier_pp(sK1_skl,in,'DreadburyMansion')
& predicate1(sK1_skl,live,sK0_skl)
& $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(I,sK3_skl(G,F)),skolemize(S,sK4_skl(R)),skolemize(U,sK5_skl(T)),skolemize(V,sK6_skl(T)),skolemize(Y,sK7_skl(W)),skolemize(A1,sK8_skl(Z))],[f5]) ).
fof(f7,plain,
( 'AuntAgatha' != 'Butler'
& ! [Z] :
? [A1] :
! [B1] : ~ predicate2(B1,hate,Z,sK8_skl(Z))
& ! [W] :
( ? [Y] : predicate2(sK7_skl(W),hate,'Butler',W)
| ! [X] : ~ predicate2(X,hate,'AuntAgatha',W) )
& ! [T] :
( ? [V] : predicate2(sK6_skl(T),hate,'Butler',T)
| ? [U] :
( T = sK5_skl(T)
& property2(sK5_skl(T),rich,comp_than,'AuntAgatha') ) )
& ! [R] :
( ? [S] : predicate2(sK4_skl(R),hate,'AuntAgatha',R)
| R = 'Butler' )
& ! [Q] : ~ predicate2(Q,hate,'AuntAgatha','Butler')
& ! [N] :
( ! [P] : ~ predicate2(P,hate,'Charles',N)
| ! [O] : ~ predicate2(O,hate,'AuntAgatha',N) )
& ! [J,M] :
( J != M
| ! [K] :
( ~ property2(M,rich,comp_than,K)
| ! [L] : ~ predicate2(L,kill,J,K) ) )
& ! [F,G] :
( ? [I] : predicate2(sK3_skl(G,F),hate,F,G)
| ! [H] : ~ predicate2(H,kill,F,G) )
& ! [D] :
( D = 'Charles'
| D = 'Butler'
| D = 'AuntAgatha'
| ! [E] :
( ~ modifier_pp(E,in,'DreadburyMansion')
| ~ predicate1(E,live,D) ) )
& ? [A] :
( ? [C] : predicate2(sK2_skl,kill,sK0_skl,'AuntAgatha')
& ? [B] :
( modifier_pp(sK1_skl,in,'DreadburyMansion')
& predicate1(sK1_skl,live,sK0_skl) ) ) ),
inference(true_and_false_simplification,[status(thm)],[f6]) ).
fof(f8,plain,
predicate1(sK1_skl,live,sK0_skl),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [DreadburyMansion] : modifier_pp(sK1_skl,in,'DreadburyMansion'),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [AuntAgatha] : predicate2(sK2_skl,kill,sK0_skl,'AuntAgatha'),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0,X1,DreadburyMansion,AuntAgatha,Butler,Charles] :
( X1 = 'Charles'
| X1 = 'Butler'
| X1 = 'AuntAgatha'
| ~ modifier_pp(X0,in,'DreadburyMansion')
| ~ predicate1(X0,live,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f12,plain,
! [X0,X1,X2] :
( predicate2(sK3_skl(X2,X1),hate,X1,X2)
| ~ predicate2(X0,kill,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( X1 != X3
| ~ property2(X3,rich,comp_than,X2)
| ~ predicate2(X0,kill,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f14,plain,
! [X0,AuntAgatha,X1,X2,Charles] :
( ~ predicate2(X2,hate,'Charles',X1)
| ~ predicate2(X0,hate,'AuntAgatha',X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
! [X0,Butler,AuntAgatha] :
( predicate2(sK4_skl(X0),hate,'AuntAgatha',X0)
| X0 = 'Butler' ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [X0,AuntAgatha,Butler] :
( predicate2(sK6_skl(X0),hate,'Butler',X0)
| property2(sK5_skl(X0),rich,comp_than,'AuntAgatha') ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [X0,Butler] :
( predicate2(sK6_skl(X0),hate,'Butler',X0)
| X0 = sK5_skl(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,AuntAgatha,X1,Butler] :
( predicate2(sK7_skl(X1),hate,'Butler',X1)
| ~ predicate2(X0,hate,'AuntAgatha',X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0,X1] : ~ predicate2(X0,hate,X1,sK8_skl(X1)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
! [AuntAgatha,Butler] : 'AuntAgatha' != 'Butler',
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [A] : ~ predicate2(A,kill,'AuntAgatha','AuntAgatha'),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,AuntAgatha] : ~ predicate2(X0,kill,'AuntAgatha','AuntAgatha'),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ property2(X1,rich,comp_than,X2)
| ~ predicate2(X0,kill,X1,X2) ),
inference(destructive_equality_resolution,[status(thm)],[f13]) ).
fof(f28,plain,
! [Butler] : sK8_skl('Butler') = sK5_skl(sK8_skl('Butler')),
inference(resolution,[status(thm)],[f18,f20]) ).
fof(f29,plain,
! [AuntAgatha] : ~ property2(sK0_skl,rich,comp_than,'AuntAgatha'),
inference(resolution,[status(thm)],[f24,f10]) ).
fof(f30,plain,
! [X0,Charles,X1,Butler] :
( X1 = 'Butler'
| ~ predicate2(X0,hate,'Charles',X1) ),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f31,plain,
! [AuntAgatha] : predicate2(sK3_skl('AuntAgatha',sK0_skl),hate,sK0_skl,'AuntAgatha'),
inference(resolution,[status(thm)],[f12,f10]) ).
fof(f32,plain,
! [X0,Butler] :
( X0 = 'Butler'
| predicate2(sK7_skl(X0),hate,'Butler',X0) ),
inference(resolution,[status(thm)],[f19,f16]) ).
fof(f33,plain,
! [Butler] : sK8_skl('Butler') = 'Butler',
inference(resolution,[status(thm)],[f32,f20]) ).
fof(f34,plain,
! [DreadburyMansion,AuntAgatha,Butler,Charles] :
( sK0_skl = 'Charles'
| sK0_skl = 'Butler'
| sK0_skl = 'AuntAgatha'
| ~ modifier_pp(sK1_skl,in,'DreadburyMansion') ),
inference(resolution,[status(thm)],[f11,f8]) ).
fof(f35,plain,
! [AuntAgatha,Butler,Charles] :
( sK0_skl = 'Charles'
| sK0_skl = 'Butler'
| sK0_skl = 'AuntAgatha' ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f9]) ).
fof(f38,plain,
! [Butler] : sK8_skl('Butler') = sK5_skl('Butler'),
inference(backward_demodulation,[status(thm)],[f33,f28]) ).
fof(f39,plain,
! [X0,Butler] : ~ predicate2(X0,hate,'Butler','Butler'),
inference(paramodulation,[status(thm)],[f33,f20]) ).
fof(f40,plain,
! [Butler] : 'Butler' = sK5_skl('Butler'),
inference(forward_demodulation,[status(thm)],[f33,f38]) ).
fof(f42,plain,
! [Butler,AuntAgatha] : property2(sK5_skl('Butler'),rich,comp_than,'AuntAgatha'),
inference(resolution,[status(thm)],[f39,f17]) ).
fof(f44,plain,
! [Butler,AuntAgatha] : property2('Butler',rich,comp_than,'AuntAgatha'),
inference(forward_demodulation,[status(thm)],[f40,f42]) ).
fof(f48,plain,
! [AuntAgatha,Butler,Charles] :
( sK0_skl = 'Charles'
| sK0_skl = 'Butler'
| predicate2(sK2_skl,kill,'AuntAgatha','AuntAgatha') ),
inference(paramodulation,[status(thm)],[f35,f10]) ).
fof(f52,plain,
! [Butler,Charles] :
( sK0_skl = 'Charles'
| sK0_skl = 'Butler' ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f23]) ).
fof(f55,plain,
! [Butler,AuntAgatha,Charles] :
( sK0_skl = 'Charles'
| ~ property2('Butler',rich,comp_than,'AuntAgatha') ),
inference(paramodulation,[status(thm)],[f52,f29]) ).
fof(f59,plain,
! [Charles] : sK0_skl = 'Charles',
inference(forward_subsumption_resolution,[status(thm)],[f55,f44]) ).
fof(f61,plain,
! [AuntAgatha,Charles] : predicate2(sK3_skl('AuntAgatha',sK0_skl),hate,'Charles','AuntAgatha'),
inference(backward_demodulation,[status(thm)],[f59,f31]) ).
fof(f65,plain,
! [AuntAgatha,Charles] : predicate2(sK3_skl('AuntAgatha','Charles'),hate,'Charles','AuntAgatha'),
inference(forward_demodulation,[status(thm)],[f59,f61]) ).
fof(f71,plain,
! [AuntAgatha,Butler] : 'AuntAgatha' = 'Butler',
inference(resolution,[status(thm)],[f65,f30]) ).
fof(f72,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f71,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ001+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 03:44:12 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.042950 seconds
% 0.12/0.42 % CPU time: 0.137646 seconds
% 0.12/0.42 % Total memory used: 80.716 MB
% 0.12/0.42 % Net memory used: 80.227 MB
%------------------------------------------------------------------------------