## TPTP Problem File: PUZ008-2.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : PUZ008-2 : TPTP v8.1.0. Released v1.0.0.
% Domain   : Puzzles
% Problem  : Missionaries and Cannibals
% Version  : Especial.
%            Theorem formulation : Procedural.
% English  : There are 3 missionaries, 3 cannibals, and a boat on the west
%            bank of a river. All wish to cross, but the boat holds
%            at most 2 people. If the cannibals ever outnumber the
%            missionaries on either bank of the river the outnumbered
%            missionaries will be eaten. Can they all safely cross the
%            river?  If so, how? (The boat cannot cross empty.)

% Refs     :
% Source   : [ANL]
% Names    : mission.ver2.in [ANL]

% Status   : Unsatisfiable
% Rating   : 0.33 v8.1.0, 0.00 v7.3.0, 0.20 v7.2.0, 0.22 v7.1.0, 0.14 v6.4.0, 0.00 v6.2.0, 0.12 v6.0.0, 0.00 v3.3.0, 0.33 v3.2.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :   32 (   2 unt;   0 nHn;  32 RR)
%            Number of literals    :   62 (   0 equ;  31 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 3-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)
% SPC      : CNF_UNS_EPR_NEQ_HRN

%--------------------------------------------------------------------------
%----Moving cannibals only, west to east
cnf(bccc_mmm_to_cc_bmmmc,axiom,
( ~ banks(west(m(n0),c(n3)),east(m(n3),c(n0)),boatonwest)
| banks(west(m(n0),c(n2)),east(m(n3),c(n1)),boatoneast) ) ).

cnf(bmmmcc_c_to_mmmc_cc,axiom,
( ~ banks(west(m(n3),c(n2)),east(m(n0),c(n1)),boatonwest)
| banks(west(m(n3),c(n1)),east(m(n0),c(n2)),boatoneast) ) ).

cnf(bcc_mmmc_to_c_mmmcc,axiom,
( ~ banks(west(m(n0),c(n2)),east(m(n3),c(n1)),boatonwest)
| banks(west(m(n0),c(n1)),east(m(n3),c(n2)),boatoneast) ) ).

cnf(bmmmc_cc_to_mmm_ccc,axiom,
( ~ banks(west(m(n3),c(n1)),east(m(n0),c(n2)),boatonwest)
| banks(west(m(n3),c(n0)),east(m(n0),c(n3)),boatoneast) ) ).

cnf(bc_mmmcc_to_x_bmmmccc,axiom,
( ~ banks(west(m(n0),c(n1)),east(m(n3),c(n2)),boatonwest)
| banks(west(m(n0),c(n0)),east(m(n3),c(n3)),boatoneast) ) ).

cnf(bmmmccc_x_to_mmmc_bcc,axiom,
( ~ banks(west(m(n3),c(n3)),east(m(n0),c(n0)),boatonwest)
| banks(west(m(n3),c(n1)),east(m(n0),c(n2)),boatoneast) ) ).

cnf(bccc_mmm_to_c_bmmmcc,axiom,
( ~ banks(west(m(n0),c(n3)),east(m(n3),c(n0)),boatonwest)
| banks(west(m(n0),c(n1)),east(m(n3),c(n2)),boatoneast) ) ).

cnf(bmmmcc_c_to_mmm_bccc,axiom,
( ~ banks(west(m(n3),c(n2)),east(m(n0),c(n1)),boatonwest)
| banks(west(m(n3),c(n0)),east(m(n0),c(n3)),boatoneast) ) ).

cnf(bcc_mmmc_to_x_bmmmccc,axiom,
( ~ banks(west(m(n0),c(n2)),east(m(n3),c(n1)),boatonwest)
| banks(west(m(n0),c(n0)),east(m(n3),c(n3)),boatoneast) ) ).

%----Moving cannibals only, east to west
cnf(cc_bmmmc_to_bccc_mmm,axiom,
( ~ banks(west(m(n0),c(n2)),east(m(n3),c(n1)),boatoneast)
| banks(west(m(n0),c(n3)),east(m(n3),c(n0)),boatonwest) ) ).

cnf(c_bmmmcc_to_bcc_mmmc,axiom,
( ~ banks(west(m(n0),c(n1)),east(m(n3),c(n2)),boatoneast)
| banks(west(m(n0),c(n2)),east(m(n3),c(n1)),boatonwest) ) ).

cnf(mmm_bccc_to_bmmmc_cc,axiom,
( ~ banks(west(m(n3),c(n0)),east(m(n0),c(n3)),boatoneast)
| banks(west(m(n3),c(n1)),east(m(n0),c(n2)),boatonwest) ) ).

cnf(mmmcc_bc_to_bmmmccc_x,axiom,
( ~ banks(west(m(n3),c(n2)),east(m(n0),c(n1)),boatoneast)
| banks(west(m(n3),c(n3)),east(m(n0),c(n0)),boatonwest) ) ).

cnf(mmmc_bcc_to_bmmmcc_c,axiom,
( ~ banks(west(m(n3),c(n1)),east(m(n0),c(n2)),boatoneast)
| banks(west(m(n3),c(n2)),east(m(n0),c(n1)),boatonwest) ) ).

cnf(c_bmmmcc_to_bccc_mmm,axiom,
( ~ banks(west(m(n0),c(n1)),east(m(n3),c(n2)),boatoneast)
| banks(west(m(n0),c(n3)),east(m(n3),c(n0)),boatonwest) ) ).

cnf(mmmc_bcc_to_bmmmccc_x,axiom,
( ~ banks(west(m(n3),c(n1)),east(m(n0),c(n2)),boatoneast)
| banks(west(m(n3),c(n3)),east(m(n0),c(n0)),boatonwest) ) ).

cnf(mmm_bccc_to_bmmmcc_c,axiom,
( ~ banks(west(m(n3),c(n0)),east(m(n0),c(n3)),boatoneast)
| banks(west(m(n3),c(n2)),east(m(n0),c(n1)),boatonwest) ) ).

%----Moving missionaries only, west to east
cnf(bmmmcc_c_to_mmcc_bmc,axiom,
( ~ banks(west(m(n3),c(n2)),east(m(n0),c(n1)),boatonwest)
| banks(west(m(n2),c(n2)),east(m(n1),c(n1)),boatoneast) ) ).

cnf(bmc_mmcc_to_c_bmmmcc,axiom,
( ~ banks(west(m(n1),c(n1)),east(m(n2),c(n2)),boatonwest)
| banks(west(m(n0),c(n1)),east(m(n3),c(n2)),boatoneast) ) ).

cnf(bmmmc_cc_to_mc_bmmcc,axiom,
( ~ banks(west(m(n3),c(n1)),east(m(n0),c(n2)),boatonwest)
| banks(west(m(n1),c(n1)),east(m(n2),c(n2)),boatoneast) ) ).

cnf(bmmcc_mc_to_cc_bmmmc,axiom,
( ~ banks(west(m(n2),c(n2)),east(m(n1),c(n1)),boatonwest)
| banks(west(m(n0),c(n2)),east(m(n3),c(n1)),boatoneast) ) ).

%----Moving missionaries only, east to west
cnf(c_bmmmcc_to_bmc_mmcc,axiom,
( ~ banks(west(m(n0),c(n1)),east(m(n3),c(n2)),boatoneast)
| banks(west(m(n1),c(n1)),east(m(n2),c(n2)),boatonwest) ) ).

cnf(mmcc_bmc_to_bmmmcc_c,axiom,
( ~ banks(west(m(n2),c(n2)),east(m(n1),c(n1)),boatoneast)
| banks(west(m(n3),c(n2)),east(m(n0),c(n1)),boatonwest) ) ).

cnf(cc_bmmmc_to_bmmcc_mc,axiom,
( ~ banks(west(m(n0),c(n2)),east(m(n3),c(n1)),boatoneast)
| banks(west(m(n2),c(n2)),east(m(n1),c(n1)),boatonwest) ) ).

cnf(mc_bmmcc_to_bmmmc_cc,axiom,
( ~ banks(west(m(n1),c(n1)),east(m(n2),c(n2)),boatoneast)
| banks(west(m(n3),c(n1)),east(m(n0),c(n2)),boatonwest) ) ).

%----Moving a missionary and a cannibal, west to east
cnf(bmmmccc_x_to_mmcc_bmc,axiom,
( ~ banks(west(m(n3),c(n3)),east(m(n0),c(n0)),boatonwest)
| banks(west(m(n2),c(n2)),east(m(n1),c(n1)),boatoneast) ) ).

cnf(bmmcc_mc_to_mc_bmmcc,axiom,
( ~ banks(west(m(n2),c(n2)),east(m(n1),c(n1)),boatonwest)
| banks(west(m(n1),c(n1)),east(m(n2),c(n2)),boatoneast) ) ).

cnf(bmc_mmcc_to_x_bmmmccc,axiom,
( ~ banks(west(m(n1),c(n1)),east(m(n2),c(n2)),boatonwest)
| banks(west(m(n0),c(n0)),east(m(n3),c(n3)),boatoneast) ) ).

%----Moving a missionary and a cannibal, east to west
cnf(mc_bmmcc_to_bmmcc_mc,axiom,
( ~ banks(west(m(n1),c(n1)),east(m(n2),c(n2)),boatoneast)
| banks(west(m(n2),c(n2)),east(m(n1),c(n1)),boatonwest) ) ).

cnf(mmcc_bmc_to_bmmmccc_x,axiom,
( ~ banks(west(m(n2),c(n2)),east(m(n1),c(n1)),boatoneast)
| banks(west(m(n3),c(n3)),east(m(n0),c(n0)),boatonwest) ) ).

%----The problem to be solved
cnf(starting_configuration,hypothesis,
banks(west(m(n3),c(n3)),east(m(n0),c(n0)),boatonwest) ).

cnf(prove_can_get_across,negated_conjecture,
~ banks(west(m(n0),c(n0)),east(m(n3),c(n3)),boatoneast) ).

%--------------------------------------------------------------------------
```