%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ011-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:23:08 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 244 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 421 ( 223 ~; 178 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(ocean_type,type,
ocean: $i > $o ).
tff(borders_type,type,
borders: ( $i * $i ) > $o ).
tff(african_type,type,
african: $i > $o ).
tff(asian_type,type,
asian: $i > $o ).
tff(india_type,type,
india: $i ).
tff(somalia_type,type,
somalia: $i ).
tff(indian_type,type,
indian: $i ).
tff(1,plain,
^ [African: $i,Ocean: $i,Asian: $i] :
refl(( ( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
<=> ( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
<=> ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
<=> ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [African: $i,Ocean: $i,Asian: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ocean(Ocean)
| ~ borders(Ocean,African)
| ~ african(African) )
<=> ( ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ) )),
( ( ~ ocean(Ocean)
| ~ borders(Ocean,African)
| ~ african(African)
| ~ borders(Ocean,Asian) )
<=> ( ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean)
| ~ borders(Ocean,Asian) ) )),
rewrite(( ( ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean)
| ~ borders(Ocean,Asian) )
<=> ( ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ) )),
( ( ~ ocean(Ocean)
| ~ borders(Ocean,African)
| ~ african(African)
| ~ borders(Ocean,Asian) )
<=> ( ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ) )),
( ( ~ ocean(Ocean)
| ~ borders(Ocean,African)
| ~ african(African)
| ~ borders(Ocean,Asian)
| ~ asian(Asian) )
<=> ( ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean)
| ~ asian(Asian) ) )),
rewrite(( ( ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean)
| ~ asian(Asian) )
<=> ( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ) )),
( ( ~ ocean(Ocean)
| ~ borders(Ocean,African)
| ~ african(African)
| ~ borders(Ocean,Asian)
| ~ asian(Asian) )
<=> ( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [African: $i,Ocean: $i,Asian: $i] :
( ~ ocean(Ocean)
| ~ borders(Ocean,African)
| ~ african(African)
| ~ borders(Ocean,Asian)
| ~ asian(Asian) )
<=> ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [African: $i,Ocean: $i,Asian: $i] :
( ~ ocean(Ocean)
| ~ borders(Ocean,African)
| ~ african(African)
| ~ borders(Ocean,Asian)
| ~ asian(Asian) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_common_ocean) ).
tff(7,plain,
! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( asian(india)
<=> asian(india) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
asian(india),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',india) ).
tff(13,plain,
asian(india),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( african(somalia)
<=> african(somalia) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
african(somalia),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',somalia) ).
tff(16,plain,
african(somalia),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( borders(indian,somalia)
<=> borders(indian,somalia) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
borders(indian,somalia),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indian_somalia) ).
tff(19,plain,
borders(indian,somalia),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( borders(indian,india)
<=> borders(indian,india) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
borders(indian,india),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indian_india) ).
tff(22,plain,
borders(indian,india),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ocean(indian)
<=> ocean(indian) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
ocean(indian),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indian) ).
tff(25,plain,
ocean(indian),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
| ~ asian(india)
| ~ borders(indian,india)
| ~ ocean(indian)
| ~ african(somalia)
| ~ borders(indian,somalia) )
<=> ( ~ ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
| ~ asian(india)
| ~ borders(indian,india)
| ~ ocean(indian)
| ~ african(somalia)
| ~ borders(indian,somalia) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( ~ asian(india)
| ~ borders(indian,india)
| ~ african(somalia)
| ~ borders(indian,somalia)
| ~ ocean(indian) )
<=> ( ~ asian(india)
| ~ borders(indian,india)
| ~ ocean(indian)
| ~ african(somalia)
| ~ borders(indian,somalia) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
| ~ asian(india)
| ~ borders(indian,india)
| ~ african(somalia)
| ~ borders(indian,somalia)
| ~ ocean(indian) )
<=> ( ~ ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
| ~ asian(india)
| ~ borders(indian,india)
| ~ ocean(indian)
| ~ african(somalia)
| ~ borders(indian,somalia) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
| ~ asian(india)
| ~ borders(indian,india)
| ~ african(somalia)
| ~ borders(indian,somalia)
| ~ ocean(indian) )
<=> ( ~ ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
| ~ asian(india)
| ~ borders(indian,india)
| ~ ocean(indian)
| ~ african(somalia)
| ~ borders(indian,somalia) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
| ~ asian(india)
| ~ borders(indian,india)
| ~ african(somalia)
| ~ borders(indian,somalia)
| ~ ocean(indian) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [African: $i,Ocean: $i,Asian: $i] :
( ~ asian(Asian)
| ~ borders(Ocean,Asian)
| ~ african(African)
| ~ borders(Ocean,African)
| ~ ocean(Ocean) )
| ~ asian(india)
| ~ borders(indian,india)
| ~ ocean(indian)
| ~ african(somalia)
| ~ borders(indian,somalia) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,25,22,19,16,13,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ011-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 02:38:40 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39 % SZS output start Proof
% See solution above
% 0.14/0.39 % E exiting
%------------------------------------------------------------------------------