%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ022-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:23:11 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 26
% Syntax : Number of formulae : 50 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 373 ( 0 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 626 ( 324 ~; 273 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 97 ( 89 !; 0 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
tff(borders_type,type,
borders: ( $i * $i ) > $o ).
tff(indian_type,type,
indian: $i ).
tff(northern_territory_type,type,
northern_territory: $i ).
tff(western_australia_type,type,
western_australia: $i ).
tff(state_type,type,
state: $i > $o ).
tff(ocean_type,type,
ocean: $i > $o ).
tff(1,plain,
( borders(indian,northern_territory)
<=> borders(indian,northern_territory) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
borders(indian,northern_territory),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indian_nt) ).
tff(3,plain,
borders(indian,northern_territory),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ borders(Y,X)
| borders(X,Y) )
<=> ( ~ borders(Y,X)
| borders(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_borders) ).
tff(8,plain,
! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
| ~ borders(indian,northern_territory)
| borders(northern_territory,indian) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
| ~ borders(indian,northern_territory)
| borders(northern_territory,indian) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
| ~ borders(indian,northern_territory)
| borders(northern_territory,indian) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
| ~ borders(indian,northern_territory)
| borders(northern_territory,indian) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
borders(northern_territory,indian),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( borders(indian,western_australia)
<=> borders(indian,western_australia) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
borders(indian,western_australia),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indian_wa) ).
tff(17,plain,
borders(indian,western_australia),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
| ~ borders(indian,western_australia)
| borders(western_australia,indian) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
| ~ borders(indian,western_australia)
| borders(western_australia,indian) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
| ~ borders(indian,western_australia)
| borders(western_australia,indian) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] :
( ~ borders(Y,X)
| borders(X,Y) )
| ~ borders(indian,western_australia)
| borders(western_australia,indian) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
borders(western_australia,indian),
inference(unit_resolution,[status(thm)],[20,10,17]) ).
tff(22,plain,
^ [State2: $i,Ocean: $i,State1: $i] :
refl(( ( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
<=> ( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
<=> ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
<=> ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [State2: $i,Ocean: $i,State1: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ state(State1)
| ~ state(State2)
| ~ borders(State1,State2) )
<=> ( ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) )),
( ( ~ state(State1)
| ~ state(State2)
| ~ borders(State1,State2)
| ~ borders(State1,Ocean) )
<=> ( ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1)
| ~ borders(State1,Ocean) ) )),
rewrite(( ( ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1)
| ~ borders(State1,Ocean) )
<=> ( ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) )),
( ( ~ state(State1)
| ~ state(State2)
| ~ borders(State1,State2)
| ~ borders(State1,Ocean) )
<=> ( ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) )),
( ( ~ state(State1)
| ~ state(State2)
| ~ borders(State1,State2)
| ~ borders(State1,Ocean)
| ~ borders(State2,Ocean) )
<=> ( ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1)
| ~ borders(State2,Ocean) ) )),
rewrite(( ( ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1)
| ~ borders(State2,Ocean) )
<=> ( ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) )),
( ( ~ state(State1)
| ~ state(State2)
| ~ borders(State1,State2)
| ~ borders(State1,Ocean)
| ~ borders(State2,Ocean) )
<=> ( ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) )),
( ( ~ state(State1)
| ~ state(State2)
| ~ borders(State1,State2)
| ~ borders(State1,Ocean)
| ~ borders(State2,Ocean)
| ~ ocean(Ocean) )
<=> ( ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1)
| ~ ocean(Ocean) ) )),
rewrite(( ( ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1)
| ~ ocean(Ocean) )
<=> ( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) )),
( ( ~ state(State1)
| ~ state(State2)
| ~ borders(State1,State2)
| ~ borders(State1,Ocean)
| ~ borders(State2,Ocean)
| ~ ocean(Ocean) )
<=> ( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [State2: $i,Ocean: $i,State1: $i] :
( ~ state(State1)
| ~ state(State2)
| ~ borders(State1,State2)
| ~ borders(State1,Ocean)
| ~ borders(State2,Ocean)
| ~ ocean(Ocean) )
<=> ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [State2: $i,Ocean: $i,State1: $i] :
( ~ state(State1)
| ~ state(State2)
| ~ borders(State1,State2)
| ~ borders(State1,Ocean)
| ~ borders(State2,Ocean)
| ~ ocean(Ocean) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_borders) ).
tff(28,plain,
! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( borders(western_australia,northern_territory)
<=> borders(western_australia,northern_territory) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
borders(western_australia,northern_territory),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wa_nt) ).
tff(34,plain,
borders(western_australia,northern_territory),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( state(northern_territory)
<=> state(northern_territory) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
state(northern_territory),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',northern_territory) ).
tff(37,plain,
state(northern_territory),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( state(western_australia)
<=> state(western_australia) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
state(western_australia),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',western_australia) ).
tff(40,plain,
state(western_australia),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ocean(indian)
<=> ocean(indian) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
ocean(indian),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indian) ).
tff(43,plain,
ocean(indian),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
| ~ borders(western_australia,northern_territory)
| ~ state(western_australia)
| ~ state(northern_territory)
| ~ borders(northern_territory,indian)
| ~ ocean(indian)
| ~ borders(western_australia,indian) )
<=> ( ~ ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
| ~ borders(western_australia,northern_territory)
| ~ state(western_australia)
| ~ state(northern_territory)
| ~ borders(northern_territory,indian)
| ~ ocean(indian)
| ~ borders(western_australia,indian) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ ocean(indian)
| ~ borders(northern_territory,indian)
| ~ borders(western_australia,indian)
| ~ borders(western_australia,northern_territory)
| ~ state(northern_territory)
| ~ state(western_australia) )
<=> ( ~ borders(western_australia,northern_territory)
| ~ state(western_australia)
| ~ state(northern_territory)
| ~ borders(northern_territory,indian)
| ~ ocean(indian)
| ~ borders(western_australia,indian) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
| ~ ocean(indian)
| ~ borders(northern_territory,indian)
| ~ borders(western_australia,indian)
| ~ borders(western_australia,northern_territory)
| ~ state(northern_territory)
| ~ state(western_australia) )
<=> ( ~ ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
| ~ borders(western_australia,northern_territory)
| ~ state(western_australia)
| ~ state(northern_territory)
| ~ borders(northern_territory,indian)
| ~ ocean(indian)
| ~ borders(western_australia,indian) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
| ~ ocean(indian)
| ~ borders(northern_territory,indian)
| ~ borders(western_australia,indian)
| ~ borders(western_australia,northern_territory)
| ~ state(northern_territory)
| ~ state(western_australia) )
<=> ( ~ ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
| ~ borders(western_australia,northern_territory)
| ~ state(western_australia)
| ~ state(northern_territory)
| ~ borders(northern_territory,indian)
| ~ ocean(indian)
| ~ borders(western_australia,indian) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
| ~ ocean(indian)
| ~ borders(northern_territory,indian)
| ~ borders(western_australia,indian)
| ~ borders(western_australia,northern_territory)
| ~ state(northern_territory)
| ~ state(western_australia) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [State2: $i,Ocean: $i,State1: $i] :
( ~ ocean(Ocean)
| ~ borders(State2,Ocean)
| ~ borders(State1,Ocean)
| ~ borders(State1,State2)
| ~ state(State2)
| ~ state(State1) )
| ~ borders(western_australia,northern_territory)
| ~ state(western_australia)
| ~ state(northern_territory)
| ~ borders(northern_territory,indian)
| ~ ocean(indian)
| ~ borders(western_australia,indian) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,43,40,37,34,31,21,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ022-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.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 : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:41:46 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------