%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PLA003-1 : 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 05:22:49 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 42
% Syntax : Number of formulae : 96 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 321 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 397 ( 184 ~; 172 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 363 ( 324 !; 0 ?; 363 :)
% Comments :
%------------------------------------------------------------------------------
tff(can_type,type,
can: ( $i * $i * $i ) > $o ).
tff(bananas_type,type,
bananas: ( $i * $i ) > $i ).
tff(ceiling_type,type,
ceiling: $i ).
tff(l2_type,type,
l2: $i ).
tff(ladder_type,type,
ladder: ( $i * $i ) > $i ).
tff(floor_type,type,
floor: $i ).
tff(monkey_type,type,
monkey: ( $i * $i * $i ) > $i ).
tff(the_bananas_type,type,
the_bananas: $i ).
tff(nothing_type,type,
nothing: $i ).
tff(the_ladder_type,type,
the_ladder: $i ).
tff(l1_type,type,
l1: $i ).
tff(l0_type,type,
l0: $i ).
tff(1,plain,
( can(monkey(l0,floor,nothing),ladder(l1,floor),bananas(l2,ceiling))
<=> can(monkey(l0,floor,nothing),ladder(l1,floor),bananas(l2,ceiling)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
can(monkey(l0,floor,nothing),ladder(l1,floor),bananas(l2,ceiling)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_situation) ).
tff(3,plain,
can(monkey(l0,floor,nothing),ladder(l1,floor),bananas(l2,ceiling)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
refl(( ( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) )
<=> ( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) )
<=> ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) )
<=> ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
rewrite(( ( can(monkey(Location2,floor,nothing),Ladder,Bananas)
| ~ can(monkey(Location1,floor,nothing),Ladder,Bananas) )
<=> ( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( can(monkey(Location2,floor,nothing),Ladder,Bananas)
| ~ can(monkey(Location1,floor,nothing),Ladder,Bananas) )
<=> ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( can(monkey(Location2,floor,nothing),Ladder,Bananas)
| ~ can(monkey(Location1,floor,nothing),Ladder,Bananas) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',go_holding_nothing) ).
tff(10,plain,
! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) )
| ~ can(monkey(l0,floor,nothing),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l1,floor,nothing),ladder(l1,floor),bananas(l2,ceiling)) )
<=> ( ~ ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) )
| ~ can(monkey(l0,floor,nothing),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l1,floor,nothing),ladder(l1,floor),bananas(l2,ceiling)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) )
| ~ can(monkey(l0,floor,nothing),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l1,floor,nothing),ladder(l1,floor),bananas(l2,ceiling)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [Location2: $i,Location1: $i,Ladder: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),Ladder,Bananas)
| can(monkey(Location2,floor,nothing),Ladder,Bananas) )
| ~ can(monkey(l0,floor,nothing),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l1,floor,nothing),ladder(l1,floor),bananas(l2,ceiling)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
can(monkey(l1,floor,nothing),ladder(l1,floor),bananas(l2,ceiling)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [Location: $i,Bananas: $i,Height: $i] :
refl(( ( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) )
<=> ( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) )
<=> ! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) )
<=> ! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [Location: $i,Bananas: $i,Height: $i] :
rewrite(( ( can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas)
| ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas) )
<=> ( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Location: $i,Bananas: $i,Height: $i] :
( can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas)
| ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas) )
<=> ! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [Location: $i,Bananas: $i,Height: $i] :
( can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas)
| ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',grab_ladder) ).
tff(24,plain,
! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) )
| ~ can(monkey(l1,floor,nothing),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l1,floor,the_ladder),ladder(l1,floor),bananas(l2,ceiling)) )
<=> ( ~ ! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) )
| ~ can(monkey(l1,floor,nothing),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l1,floor,the_ladder),ladder(l1,floor),bananas(l2,ceiling)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) )
| ~ can(monkey(l1,floor,nothing),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l1,floor,the_ladder),ladder(l1,floor),bananas(l2,ceiling)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [Location: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,nothing),ladder(Location,Height),Bananas)
| can(monkey(Location,Height,the_ladder),ladder(Location,Height),Bananas) )
| ~ can(monkey(l1,floor,nothing),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l1,floor,the_ladder),ladder(l1,floor),bananas(l2,ceiling)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
can(monkey(l1,floor,the_ladder),ladder(l1,floor),bananas(l2,ceiling)),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
^ [Location2: $i,Location1: $i,Bananas: $i] :
refl(( ( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) )
<=> ( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) )
<=> ! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) )
<=> ! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [Location2: $i,Location1: $i,Bananas: $i] :
rewrite(( ( can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas)
| ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas) )
<=> ( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Location2: $i,Location1: $i,Bananas: $i] :
( can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas)
| ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas) )
<=> ! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [Location2: $i,Location1: $i,Bananas: $i] :
( can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas)
| ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',go_holding_ladder) ).
tff(38,plain,
! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) )
| ~ can(monkey(l1,floor,the_ladder),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l2,floor,the_ladder),ladder(l2,floor),bananas(l2,ceiling)) )
<=> ( ~ ! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) )
| ~ can(monkey(l1,floor,the_ladder),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l2,floor,the_ladder),ladder(l2,floor),bananas(l2,ceiling)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) )
| ~ can(monkey(l1,floor,the_ladder),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l2,floor,the_ladder),ladder(l2,floor),bananas(l2,ceiling)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Location2: $i,Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,the_ladder),ladder(Location1,floor),Bananas)
| can(monkey(Location2,floor,the_ladder),ladder(Location2,floor),Bananas) )
| ~ can(monkey(l1,floor,the_ladder),ladder(l1,floor),bananas(l2,ceiling))
| can(monkey(l2,floor,the_ladder),ladder(l2,floor),bananas(l2,ceiling)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
can(monkey(l2,floor,the_ladder),ladder(l2,floor),bananas(l2,ceiling)),
inference(unit_resolution,[status(thm)],[44,41,31]) ).
tff(46,plain,
^ [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
refl(( ( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) )
<=> ( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) )
<=> ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) )
<=> ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
rewrite(( ( can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas)
| ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas) )
<=> ( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas)
| ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas) )
<=> ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas)
| ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',drop_ladder) ).
tff(52,plain,
! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) )
| ~ can(monkey(l2,floor,the_ladder),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,floor,nothing),ladder(l2,floor),bananas(l2,ceiling)) )
<=> ( ~ ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) )
| ~ can(monkey(l2,floor,the_ladder),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,floor,nothing),ladder(l2,floor),bananas(l2,ceiling)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) )
| ~ can(monkey(l2,floor,the_ladder),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,floor,nothing),ladder(l2,floor),bananas(l2,ceiling)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [Location: $i,Any_height: $i,Bananas: $i,Height: $i] :
( ~ can(monkey(Location,Height,the_ladder),ladder(Location,Any_height),Bananas)
| can(monkey(Location,Height,nothing),ladder(Location,floor),Bananas) )
| ~ can(monkey(l2,floor,the_ladder),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,floor,nothing),ladder(l2,floor),bananas(l2,ceiling)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
can(monkey(l2,floor,nothing),ladder(l2,floor),bananas(l2,ceiling)),
inference(unit_resolution,[status(thm)],[58,55,45]) ).
tff(60,plain,
^ [Location1: $i,Bananas: $i] :
refl(( ( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) )
<=> ( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) )
<=> ! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) )
<=> ! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
^ [Location1: $i,Bananas: $i] :
rewrite(( ( can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas)
| ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas) )
<=> ( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [Location1: $i,Bananas: $i] :
( can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas)
| ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas) )
<=> ! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [Location1: $i,Bananas: $i] :
( can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas)
| ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',climb_up) ).
tff(66,plain,
! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( ~ ! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) )
| ~ can(monkey(l2,floor,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling)) )
<=> ( ~ ! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) )
| ~ can(monkey(l2,floor,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) )
| ~ can(monkey(l2,floor,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [Location1: $i,Bananas: $i] :
( ~ can(monkey(Location1,floor,nothing),ladder(Location1,floor),Bananas)
| can(monkey(Location1,ceiling,nothing),ladder(Location1,floor),Bananas) )
| ~ can(monkey(l2,floor,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling)),
inference(unit_resolution,[status(thm)],[72,69,59]) ).
tff(74,plain,
^ [Location: $i,Ladder: $i,Height: $i] :
refl(( ( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
<=> ( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
<=> ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
<=> ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',grab_bananas) ).
tff(78,plain,
! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ( ~ ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
| ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling)) )
<=> ( ~ ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
| ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling))
| ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling)) )
<=> ( ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
| can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling))
| ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling)) )
<=> ( ~ ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
| ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling)) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
| can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling))
| ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling)) )
<=> ( ~ ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
| ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling)) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
| can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling))
| ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [Location: $i,Ladder: $i,Height: $i] :
( can(monkey(Location,Height,the_bananas),Ladder,bananas(Location,Height))
| ~ can(monkey(Location,Height,nothing),Ladder,bananas(Location,Height)) )
| ~ can(monkey(l2,ceiling,nothing),ladder(l2,floor),bananas(l2,ceiling))
| can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling)) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling)),
inference(unit_resolution,[status(thm)],[86,80,73]) ).
tff(88,plain,
^ [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] :
refl(( ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What)
<=> ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] : ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What)
<=> ! [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] : ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] : ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What)
<=> ! [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] : ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
! [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] : ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_the_monkey_can_get_the_bananas) ).
tff(92,plain,
! [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] : ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] : ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] : ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [Somewhere: $i,Ladder: $i,What: $i,Some_height: $i] : ~ can(monkey(Somewhere,Some_height,the_bananas),Ladder,What)
| ~ can(monkey(l2,ceiling,the_bananas),ladder(l2,floor),bananas(l2,ceiling)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
$false,
inference(unit_resolution,[status(thm)],[95,94,87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PLA003-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:18:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% See solution above
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------