%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ001-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 : 300s
% DateTime : Sat Jun 21 05:23:06 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 42
% Syntax : Number of formulae : 90 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 336 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 477 ( 239 ~; 205 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 116 ( 106 !; 0 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
tff(richer_type,type,
richer: ( $i * $i ) > $o ).
tff(agatha_type,type,
agatha: $i ).
tff(butler_type,type,
butler: $i ).
tff(hates_type,type,
hates: ( $i * $i ) > $o ).
tff(charles_type,type,
charles: $i ).
tff(lives_type,type,
lives: $i > $o ).
tff(killed_type,type,
killed: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
refl(( ( ~ hates(agatha,X)
| hates(butler,X) )
<=> ( ~ hates(agatha,X)
| hates(butler,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
<=> ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
<=> ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',same_hates) ).
tff(5,plain,
! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( hates(agatha,charles)
<=> hates(agatha,charles) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
hates(agatha,charles),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',agatha_hates_charles) ).
tff(10,plain,
hates(agatha,charles),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
| ~ hates(agatha,charles)
| hates(butler,charles) )
<=> ( ~ ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
| ~ hates(agatha,charles)
| hates(butler,charles) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
| ~ hates(agatha,charles)
| hates(butler,charles) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
| ~ hates(agatha,charles)
| hates(butler,charles) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
hates(butler,charles),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
( hates(agatha,agatha)
<=> hates(agatha,agatha) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
hates(agatha,agatha),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',agatha_hates_agatha) ).
tff(17,plain,
hates(agatha,agatha),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
| ~ hates(agatha,agatha)
| hates(butler,agatha) )
<=> ( ~ ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
| ~ hates(agatha,agatha)
| hates(butler,agatha) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
| ~ hates(agatha,agatha)
| hates(butler,agatha) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [X: $i] :
( ~ hates(agatha,X)
| hates(butler,X) )
| ~ hates(agatha,agatha)
| hates(butler,agatha) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
hates(butler,agatha),
inference(unit_resolution,[status(thm)],[20,17,7]) ).
tff(22,plain,
^ [X: $i] :
refl(( ( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) )
<=> ( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) )
<=> ! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) )
<=> ! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [X: $i] :
rewrite(( ( ~ hates(X,agatha)
| ~ hates(X,butler)
| ~ hates(X,charles) )
<=> ( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [X: $i] :
( ~ hates(X,agatha)
| ~ hates(X,butler)
| ~ hates(X,charles) )
<=> ! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [X: $i] :
( ~ hates(X,agatha)
| ~ hates(X,butler)
| ~ hates(X,charles) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_one_hates_everyone) ).
tff(28,plain,
! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) )
| ~ hates(butler,charles)
| ~ hates(butler,butler)
| ~ hates(butler,agatha) )
<=> ( ~ ! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) )
| ~ hates(butler,charles)
| ~ hates(butler,butler)
| ~ hates(butler,agatha) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) )
| ~ hates(butler,charles)
| ~ hates(butler,butler)
| ~ hates(butler,agatha) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [X: $i] :
( ~ hates(X,charles)
| ~ hates(X,butler)
| ~ hates(X,agatha) )
| ~ hates(butler,charles)
| ~ hates(butler,butler)
| ~ hates(butler,agatha) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ hates(butler,butler),
inference(unit_resolution,[status(thm)],[34,31,21,14]) ).
tff(36,plain,
^ [X: $i] :
refl(( ( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) )
<=> ( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) )
<=> ! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) )
<=> ! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [X: $i] :
rewrite(( ( ~ lives(X)
| richer(X,agatha)
| hates(butler,X) )
<=> ( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [X: $i] :
( ~ lives(X)
| richer(X,agatha)
| hates(butler,X) )
<=> ! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X: $i] :
( ~ lives(X)
| richer(X,agatha)
| hates(butler,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',butler_hates_poor) ).
tff(42,plain,
! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( lives(butler)
<=> lives(butler) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
lives(butler),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',butler) ).
tff(48,plain,
lives(butler),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ( ~ ! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) )
| hates(butler,butler)
| richer(butler,agatha)
| ~ lives(butler) )
<=> ( ~ ! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) )
| hates(butler,butler)
| richer(butler,agatha)
| ~ lives(butler) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) )
| hates(butler,butler)
| richer(butler,agatha)
| ~ lives(butler) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [X: $i] :
( hates(butler,X)
| richer(X,agatha)
| ~ lives(X) )
| hates(butler,butler)
| richer(butler,agatha)
| ~ lives(butler) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( hates(butler,butler)
| richer(butler,agatha) ),
inference(unit_resolution,[status(thm)],[51,48,45]) ).
tff(53,plain,
richer(butler,agatha),
inference(unit_resolution,[status(thm)],[52,35]) ).
tff(54,plain,
^ [X: $i] :
refl(( ( ~ hates(agatha,X)
| ~ hates(charles,X) )
<=> ( ~ hates(agatha,X)
| ~ hates(charles,X) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) )
<=> ! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) )
<=> ! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_hates) ).
tff(58,plain,
! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ( ~ ! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) )
| ~ hates(agatha,agatha)
| ~ hates(charles,agatha) )
<=> ( ~ ! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) )
| ~ hates(agatha,agatha)
| ~ hates(charles,agatha) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) )
| ~ hates(agatha,agatha)
| ~ hates(charles,agatha) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [X: $i] :
( ~ hates(agatha,X)
| ~ hates(charles,X) )
| ~ hates(agatha,agatha)
| ~ hates(charles,agatha) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
~ hates(charles,agatha),
inference(unit_resolution,[status(thm)],[63,60,17]) ).
tff(65,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ killed(X,Y)
| hates(X,Y) )
<=> ( ~ killed(X,Y)
| hates(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',killer_hates_victim) ).
tff(69,plain,
! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) )
| ~ killed(charles,agatha)
| hates(charles,agatha) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) )
| ~ killed(charles,agatha)
| hates(charles,agatha) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) )
| ~ killed(charles,agatha)
| hates(charles,agatha) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| hates(X,Y) )
| ~ killed(charles,agatha)
| hates(charles,agatha) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
~ killed(charles,agatha),
inference(unit_resolution,[status(thm)],[74,71,64]) ).
tff(76,plain,
( ( killed(butler,agatha)
| killed(charles,agatha) )
<=> ( killed(butler,agatha)
| killed(charles,agatha) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
( killed(butler,agatha)
| killed(charles,agatha) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_neither_charles_nor_butler_did_it) ).
tff(78,plain,
( killed(butler,agatha)
| killed(charles,agatha) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
killed(butler,agatha),
inference(unit_resolution,[status(thm)],[78,75]) ).
tff(80,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ killed(X,Y)
| ~ richer(X,Y) )
<=> ( ~ killed(X,Y)
| ~ richer(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',poorer_killer) ).
tff(84,plain,
! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) )
| ~ killed(butler,agatha)
| ~ richer(butler,agatha) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) )
| ~ killed(butler,agatha)
| ~ richer(butler,agatha) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) )
| ~ killed(butler,agatha)
| ~ richer(butler,agatha) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] :
( ~ killed(X,Y)
| ~ richer(X,Y) )
| ~ killed(butler,agatha)
| ~ richer(butler,agatha) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
$false,
inference(unit_resolution,[status(thm)],[89,86,79,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ001-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:38:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------