%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ008-1 : 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 05:23:08 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 39
% Syntax : Number of formulae : 88 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 286 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 368 ( 176 ~; 164 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 334 ( 313 !; 0 ?; 334 :)
% Comments :
%------------------------------------------------------------------------------
tff(achievable_type,type,
achievable: ( $i * $i * $i ) > $o ).
tff(east_type,type,
east: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i > $i ).
tff(s_type,type,
s: $i > $i ).
tff(n0_type,type,
n0: $i ).
tff(m_type,type,
m: $i > $i ).
tff(boatoneast_type,type,
boatoneast: $i ).
tff(west_type,type,
west: ( $i * $i ) > $i ).
tff(boatonwest_type,type,
boatonwest: $i ).
tff(1,plain,
( achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0)))
<=> achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',start_on_west_bank) ).
tff(3,plain,
achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
<=> ( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',missionary_and_cannibal_west_to_east) ).
tff(8,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0)))
| achievable(west(m(s(s(n0))),c(s(s(n0)))),boatoneast,east(m(s(n0)),c(s(n0)))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0)))
| achievable(west(m(s(s(n0))),c(s(s(n0)))),boatoneast,east(m(s(n0)),c(s(n0)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0)))
| achievable(west(m(s(s(n0))),c(s(s(n0)))),boatoneast,east(m(s(n0)),c(s(n0)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0)))
| achievable(west(m(s(s(n0))),c(s(s(n0)))),boatoneast,east(m(s(n0)),c(s(n0)))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
achievable(west(m(s(s(n0))),c(s(s(n0)))),boatoneast,east(m(s(n0)),c(s(n0)))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
<=> ( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cannibal_east_to_west) ).
tff(19,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatoneast,east(m(s(n0)),c(s(n0))))
| achievable(west(m(s(s(n0))),c(s(s(s(n0))))),boatonwest,east(m(s(n0)),c(n0))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatoneast,east(m(s(n0)),c(s(n0))))
| achievable(west(m(s(s(n0))),c(s(s(s(n0))))),boatonwest,east(m(s(n0)),c(n0))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatoneast,east(m(s(n0)),c(s(n0))))
| achievable(west(m(s(s(n0))),c(s(s(s(n0))))),boatonwest,east(m(s(n0)),c(n0))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatoneast,east(m(s(n0)),c(s(n0))))
| achievable(west(m(s(s(n0))),c(s(s(s(n0))))),boatonwest,east(m(s(n0)),c(n0))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
achievable(west(m(s(s(n0))),c(s(s(s(n0))))),boatonwest,east(m(s(n0)),c(n0))),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(s(n0))))),boatonwest,east(m(s(n0)),c(n0)))
| achievable(west(m(s(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0)))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(s(n0))))),boatonwest,east(m(s(n0)),c(n0)))
| achievable(west(m(s(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(s(n0))))),boatonwest,east(m(s(n0)),c(n0)))
| achievable(west(m(s(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(s(n0))))),boatonwest,east(m(s(n0)),c(n0)))
| achievable(west(m(s(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0)))) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
achievable(west(m(s(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0)))),
inference(unit_resolution,[status(thm)],[28,10,25]) ).
tff(30,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
<=> ( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',missionary_east_to_west) ).
tff(34,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0))))
| achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0)))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0))))
| achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0))))
| achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0))))
| achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0)))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0)))),
inference(unit_resolution,[status(thm)],[39,36,29]) ).
tff(41,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) )
<=> ( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_cannibals_west_to_east) ).
tff(45,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0))))
| achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0)))))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0))))
| achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0))))
| achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))) )
| ~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0))))
| achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0)))))) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0))))
| achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0)))))) ),
inference(unit_resolution,[status(thm)],[50,47]) ).
tff(52,plain,
achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0)))))),
inference(unit_resolution,[status(thm)],[51,40]) ).
tff(53,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0))))))
| achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0)))))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0))))))
| achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0))))))
| achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))
| achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0))))))
| achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0)))))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( ~ achievable(west(m(s(s(n0))),c(n0)),boatoneast,east(m(s(n0)),c(s(s(s(n0))))))
| achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0)))))) ),
inference(unit_resolution,[status(thm)],[55,36]) ).
tff(57,plain,
achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0)))))),
inference(unit_resolution,[status(thm)],[56,52]) ).
tff(58,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) )
<=> ( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_missionaries_west_to_east) ).
tff(62,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) )
| ~ achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0)))))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) )
| ~ achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) )
| ~ achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))) )
| ~ achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0)))))) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ achievable(west(m(s(s(s(n0)))),c(n0)),boatonwest,east(m(n0),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0)))))) ),
inference(unit_resolution,[status(thm)],[67,64]) ).
tff(69,plain,
achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0)))))),
inference(unit_resolution,[status(thm)],[68,57]) ).
tff(70,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
( ~ achievable(west(m(s(n0)),c(n0)),boatoneast,east(m(s(s(n0))),c(s(s(s(n0))))))
| achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(unit_resolution,[status(thm)],[72,21]) ).
tff(74,plain,
achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))),
inference(unit_resolution,[status(thm)],[73,69]) ).
tff(75,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0)))))
| achievable(west(m(n0),c(n0)),boatoneast,east(m(s(s(s(n0)))),c(s(s(s(n0)))))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0)))))
| achievable(west(m(n0),c(n0)),boatoneast,east(m(s(s(s(n0)))),c(s(s(s(n0)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0)))))
| achievable(west(m(n0),c(n0)),boatoneast,east(m(s(s(s(n0)))),c(s(s(s(n0)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))
| achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))) )
| ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0)))))
| achievable(west(m(n0),c(n0)),boatoneast,east(m(s(s(s(n0)))),c(s(s(s(n0)))))) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0)))))
| achievable(west(m(n0),c(n0)),boatoneast,east(m(s(s(s(n0)))),c(s(s(s(n0)))))) ),
inference(unit_resolution,[status(thm)],[77,10]) ).
tff(79,plain,
achievable(west(m(n0),c(n0)),boatoneast,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
inference(unit_resolution,[status(thm)],[78,74]) ).
tff(80,plain,
^ [X: $i] :
refl(( ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0))))))
<=> ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0)))))) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [X: $i] : ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0))))))
<=> ! [X: $i] : ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0)))))) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: $i] : ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0))))))
<=> ! [X: $i] : ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0)))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
! [X: $i] : ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_can_get_to_east_bank) ).
tff(84,plain,
! [X: $i] : ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [X: $i] : ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [X: $i] : ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ~ ! [X: $i] : ~ achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0))))))
| ~ achievable(west(m(n0),c(n0)),boatoneast,east(m(s(s(s(n0)))),c(s(s(s(n0)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
$false,
inference(unit_resolution,[status(thm)],[87,86,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : PUZ008-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:39:03 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------