TSTP Solution File: PUZ008-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Sun Sep 18 14:10:48 EDT 2022
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 42
% Syntax : Number of formulae : 78 ( 20 unt; 9 typ; 0 def)
% Number of atoms : 234 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 312 ( 151 ~; 139 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 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 : 262 ( 249 !; 0 ?; 262 :)
% 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] :
( ~ 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(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0))))
| achievable(west(m(s(n0)),c(s(s(s(n0))))),boatonwest,east(m(s(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(n0)),c(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0))))
| achievable(west(m(s(n0)),c(s(s(s(n0))))),boatonwest,east(m(s(s(n0))),c(n0))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,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(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0))))
| achievable(west(m(s(n0)),c(s(s(s(n0))))),boatonwest,east(m(s(s(n0))),c(n0))) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,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(s(s(n0)))),boatoneast,east(m(s(s(n0))),c(s(n0))))
| achievable(west(m(s(n0)),c(s(s(s(n0))))),boatonwest,east(m(s(s(n0))),c(n0))) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
achievable(west(m(s(n0)),c(s(s(s(n0))))),boatonwest,east(m(s(s(n0))),c(n0))),
inference(unit_resolution,[status(thm)],[32,21,29]) ).
tff(34,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(s(s(n0))))),boatonwest,east(m(s(s(n0))),c(n0)))
| achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(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(n0)),c(s(s(s(n0))))),boatonwest,east(m(s(s(n0))),c(n0)))
| achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,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(s(s(n0))))),boatonwest,east(m(s(s(n0))),c(n0)))
| achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,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(s(s(n0))))),boatonwest,east(m(s(s(n0))),c(n0)))
| achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0)))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0)))),
inference(unit_resolution,[status(thm)],[36,10,33]) ).
tff(38,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(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0))))
| achievable(west(m(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(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(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0))))
| achievable(west(m(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,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(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0))))
| achievable(west(m(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0))) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,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(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0))))
| achievable(west(m(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0))) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
achievable(west(m(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0))),
inference(unit_resolution,[status(thm)],[40,21,37]) ).
tff(42,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(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(quant_intro,[status(thm)],[42]) ).
tff(44,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(45,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(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(modus_ponens,[status(thm)],[45,44]) ).
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(skolemize,[status(sab)],[46]) ).
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))))) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
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(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0)))
| achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(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(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0)))
| achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0))))) ) ),
inference(rewrite,[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(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0)))
| achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,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(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0)))
| achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0))))) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0))))),
inference(unit_resolution,[status(thm)],[51,48,41]) ).
tff(53,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(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0)))))
| achievable(west(m(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(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(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0)))))
| achievable(west(m(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(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(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0)))))
| achievable(west(m(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(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(Z),c(s(W))))
| achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))) )
| ~ achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0)))))
| achievable(west(m(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(s(n0)))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
achievable(west(m(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(s(n0)))),
inference(unit_resolution,[status(thm)],[55,21,52]) ).
tff(57,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(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(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(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(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(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(58,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(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(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(59,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(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(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)],[58,57]) ).
tff(60,plain,
achievable(west(m(n0),c(n0)),boatoneast,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
inference(unit_resolution,[status(thm)],[59,48,56]) ).
tff(61,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(62,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)],[61]) ).
tff(63,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(64,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(65,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)],[64,63]) ).
tff(66,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)],[65]) ).
tff(67,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)],[66,62]) ).
tff(68,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(69,plain,
$false,
inference(unit_resolution,[status(thm)],[68,67,60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 18:38:36 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------