%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ008-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:22:44 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 25 unt; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 165 ( 89 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 8 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(no_missionaries_is_safe,axiom,
! [VAR_0] : safe(n0,VAR_0),
file('theBenchmark.p',no_missionaries_is_safe) ).
cnf(c_1,plain,
safe(n0,A),
inference(clausify,[status(thm)],[no_missionaries_is_safe]) ).
fof(same_or_more_missionaries_is_safe,axiom,
! [VAR_0,VAR_1] :
( safe(VAR_0,VAR_1)
| ~ greater_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',same_or_more_missionaries_is_safe) ).
cnf(c_2,plain,
( safe(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[same_or_more_missionaries_is_safe]) ).
fof(great_eq_base,axiom,
! [VAR_0] : greater_or_equal(VAR_0,n0),
file('theBenchmark.p',great_eq_base) ).
cnf(c_3,plain,
greater_or_equal(A,n0),
inference(clausify,[status(thm)],[great_eq_base]) ).
fof(great_eq_recursive,axiom,
! [VAR_0,VAR_1] :
( ~ greater_or_equal(VAR_0,VAR_1)
| greater_or_equal(s(VAR_0),s(VAR_1)) ),
file('theBenchmark.p',great_eq_recursive) ).
cnf(c_4,plain,
( ~ greater_or_equal(A,B)
| greater_or_equal(s(A),s(B)) ),
inference(clausify,[status(thm)],[great_eq_recursive]) ).
fof(cannibal_east_to_west,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( achievable(west(m(VAR_0),c(s(VAR_1))),boatonwest,east(m(VAR_2),c(VAR_3)))
| ~ safe(VAR_2,VAR_3)
| ~ safe(VAR_0,s(VAR_1))
| ~ achievable(west(m(VAR_0),c(VAR_1)),boatoneast,east(m(VAR_2),c(s(VAR_3)))) ),
file('theBenchmark.p',cannibal_east_to_west) ).
cnf(c_6,plain,
( achievable(west(m(A),c(s(B))),boatonwest,east(m(C),c(D)))
| ~ safe(C,D)
| ~ safe(A,s(B))
| ~ achievable(west(m(A),c(B)),boatoneast,east(m(C),c(s(D)))) ),
inference(clausify,[status(thm)],[cannibal_east_to_west]) ).
fof(two_cannibals_west_to_east,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( achievable(west(m(VAR_0),c(VAR_1)),boatoneast,east(m(VAR_2),c(s(s(VAR_3)))))
| ~ safe(VAR_2,s(s(VAR_3)))
| ~ safe(VAR_0,VAR_1)
| ~ achievable(west(m(VAR_0),c(s(s(VAR_1)))),boatonwest,east(m(VAR_2),c(VAR_3))) ),
file('theBenchmark.p',two_cannibals_west_to_east) ).
cnf(c_7,plain,
( achievable(west(m(A),c(B)),boatoneast,east(m(C),c(s(s(D)))))
| ~ safe(C,s(s(D)))
| ~ safe(A,B)
| ~ achievable(west(m(A),c(s(s(B)))),boatonwest,east(m(C),c(D))) ),
inference(clausify,[status(thm)],[two_cannibals_west_to_east]) ).
fof(missionary_east_to_west,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( achievable(west(m(s(VAR_0)),c(VAR_1)),boatonwest,east(m(VAR_2),c(VAR_3)))
| ~ safe(VAR_2,VAR_3)
| ~ safe(s(VAR_0),VAR_1)
| ~ achievable(west(m(VAR_0),c(VAR_1)),boatoneast,east(m(s(VAR_2)),c(VAR_3))) ),
file('theBenchmark.p',missionary_east_to_west) ).
cnf(c_10,plain,
( achievable(west(m(s(A)),c(B)),boatonwest,east(m(C),c(D)))
| ~ safe(C,D)
| ~ safe(s(A),B)
| ~ achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(D))) ),
inference(clausify,[status(thm)],[missionary_east_to_west]) ).
fof(two_missionaries_west_to_east,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( achievable(west(m(VAR_0),c(VAR_1)),boatoneast,east(m(s(s(VAR_2))),c(VAR_3)))
| ~ safe(s(s(VAR_2)),VAR_3)
| ~ safe(VAR_0,VAR_1)
| ~ achievable(west(m(s(s(VAR_0))),c(VAR_1)),boatonwest,east(m(VAR_2),c(VAR_3))) ),
file('theBenchmark.p',two_missionaries_west_to_east) ).
cnf(c_11,plain,
( achievable(west(m(A),c(B)),boatoneast,east(m(s(s(C))),c(D)))
| ~ safe(s(s(C)),D)
| ~ safe(A,B)
| ~ achievable(west(m(s(s(A))),c(B)),boatonwest,east(m(C),c(D))) ),
inference(clausify,[status(thm)],[two_missionaries_west_to_east]) ).
fof(missionary_and_cannibal_west_to_east,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( achievable(west(m(VAR_0),c(VAR_1)),boatoneast,east(m(s(VAR_2)),c(s(VAR_3))))
| ~ safe(s(VAR_2),s(VAR_3))
| ~ safe(VAR_0,VAR_1)
| ~ achievable(west(m(s(VAR_0)),c(s(VAR_1))),boatonwest,east(m(VAR_2),c(VAR_3))) ),
file('theBenchmark.p',missionary_and_cannibal_west_to_east) ).
cnf(c_13,plain,
( achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(s(D))))
| ~ safe(s(C),s(D))
| ~ safe(A,B)
| ~ achievable(west(m(s(A)),c(s(B))),boatonwest,east(m(C),c(D))) ),
inference(clausify,[status(thm)],[missionary_and_cannibal_west_to_east]) ).
fof(missionary_and_cannibal_east_to_west,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( achievable(west(m(s(VAR_0)),c(s(VAR_1))),boatonwest,east(m(VAR_2),c(VAR_3)))
| ~ safe(VAR_2,VAR_3)
| ~ safe(s(VAR_0),s(VAR_1))
| ~ achievable(west(m(VAR_0),c(VAR_1)),boatoneast,east(m(s(VAR_2)),c(s(VAR_3)))) ),
file('theBenchmark.p',missionary_and_cannibal_east_to_west) ).
cnf(c_14,plain,
( achievable(west(m(s(A)),c(s(B))),boatonwest,east(m(C),c(D)))
| ~ safe(C,D)
| ~ safe(s(A),s(B))
| ~ achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(s(D)))) ),
inference(clausify,[status(thm)],[missionary_and_cannibal_east_to_west]) ).
fof(start_on_west_bank,axiom,
achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))),
file('theBenchmark.p',start_on_west_bank) ).
cnf(c_15,plain,
achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))),
inference(clausify,[status(thm)],[start_on_west_bank]) ).
fof(prove_can_get_to_east_bank,axiom,
! [VAR_0] : ~ achievable(west(m(n0),c(n0)),VAR_0,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
file('theBenchmark.p',prove_can_get_to_east_bank) ).
cnf(c_16,plain,
~ achievable(west(m(n0),c(n0)),A,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
inference(clausify,[status(thm)],[prove_can_get_to_east_bank]) ).
cnf(c_17,plain,
safe(A,n0),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_18,plain,
greater_or_equal(s(A),s(n0)),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_19,plain,
( ~ safe(s(s(s(n0))),s(s(s(n0))))
| ~ safe(n0,n0)
| ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(resolve,[status(thm)],[c_16,c_13]) ).
cnf(c_24,plain,
greater_or_equal(s(s(A)),s(s(n0))),
inference(resolve,[status(thm)],[c_4,c_18]) ).
cnf(c_25,plain,
safe(s(A),s(n0)),
inference(resolve,[status(thm)],[c_2,c_18]) ).
cnf(c_26,plain,
( ~ safe(s(s(s(n0))),s(s(s(n0))))
| ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_28,plain,
( ~ greater_or_equal(s(s(s(n0))),s(s(s(n0))))
| ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(resolve,[status(thm)],[c_26,c_2]) ).
cnf(c_29,plain,
( ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_30,plain,
( ~ greater_or_equal(s(n0),s(n0))
| ~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(resolve,[status(thm)],[c_29,c_4]) ).
cnf(c_33,plain,
~ achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))),
inference(resolve,[status(thm)],[c_30,c_18]) ).
cnf(c_79,plain,
( achievable(west(m(s(s(s(n0)))),c(s(n0))),boatoneast,east(m(n0),c(s(s(n0)))))
| ~ safe(n0,s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(resolve,[status(thm)],[c_7,c_15]) ).
cnf(c_80,plain,
( achievable(west(m(s(s(s(n0)))),c(s(n0))),boatoneast,east(m(n0),c(s(s(n0)))))
| ~ safe(n0,s(s(n0))) ),
inference(resolve,[status(thm)],[c_79,c_25]) ).
cnf(c_34,plain,
achievable(west(m(s(s(s(n0)))),c(s(n0))),boatoneast,east(m(n0),c(s(s(n0))))),
inference(resolve,[status(thm)],[c_80,c_1]) ).
cnf(c_36,plain,
safe(s(s(A)),s(s(n0))),
inference(resolve,[status(thm)],[c_2,c_24]) ).
cnf(c_81,plain,
( achievable(west(m(s(A)),c(s(n0))),boatonwest,east(m(B),c(C)))
| ~ safe(B,C)
| ~ achievable(west(m(A),c(s(n0))),boatoneast,east(m(s(B)),c(C))) ),
inference(resolve,[status(thm)],[c_10,c_25]) ).
cnf(c_82,plain,
( achievable(west(m(s(A)),c(s(n0))),boatonwest,east(m(s(s(B))),c(s(s(n0)))))
| ~ achievable(west(m(A),c(s(n0))),boatoneast,east(m(s(s(s(B)))),c(s(s(n0))))) ),
inference(resolve,[status(thm)],[c_81,c_36]) ).
cnf(c_47,plain,
~ achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0))))),
inference(resolve,[status(thm)],[c_82,c_33]) ).
cnf(c_83,plain,
( achievable(west(m(s(s(s(n0)))),c(s(s(n0)))),boatonwest,east(m(n0),c(s(n0))))
| ~ safe(n0,s(n0))
| ~ safe(s(s(s(n0))),s(s(n0))) ),
inference(resolve,[status(thm)],[c_6,c_34]) ).
cnf(c_84,plain,
( achievable(west(m(s(s(s(n0)))),c(s(s(n0)))),boatonwest,east(m(n0),c(s(n0))))
| ~ safe(n0,s(n0)) ),
inference(resolve,[status(thm)],[c_83,c_36]) ).
cnf(c_49,plain,
achievable(west(m(s(s(s(n0)))),c(s(s(n0)))),boatonwest,east(m(n0),c(s(n0)))),
inference(resolve,[status(thm)],[c_84,c_1]) ).
cnf(c_85,plain,
( achievable(west(m(s(s(s(n0)))),c(n0)),boatoneast,east(m(n0),c(s(s(s(n0))))))
| ~ safe(n0,s(s(s(n0))))
| ~ safe(s(s(s(n0))),n0) ),
inference(resolve,[status(thm)],[c_7,c_49]) ).
cnf(c_86,plain,
( achievable(west(m(s(s(s(n0)))),c(n0)),boatoneast,east(m(n0),c(s(s(s(n0))))))
| ~ safe(n0,s(s(s(n0)))) ),
inference(resolve,[status(thm)],[c_85,c_17]) ).
cnf(c_50,plain,
achievable(west(m(s(s(s(n0)))),c(n0)),boatoneast,east(m(n0),c(s(s(s(n0)))))),
inference(resolve,[status(thm)],[c_86,c_1]) ).
cnf(c_87,plain,
( achievable(west(m(s(s(s(n0)))),c(s(n0))),boatonwest,east(m(n0),c(s(s(n0)))))
| ~ safe(n0,s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(resolve,[status(thm)],[c_6,c_50]) ).
cnf(c_88,plain,
( achievable(west(m(s(s(s(n0)))),c(s(n0))),boatonwest,east(m(n0),c(s(s(n0)))))
| ~ safe(n0,s(s(n0))) ),
inference(resolve,[status(thm)],[c_87,c_25]) ).
cnf(c_53,plain,
achievable(west(m(s(s(s(n0)))),c(s(n0))),boatonwest,east(m(n0),c(s(s(n0))))),
inference(resolve,[status(thm)],[c_88,c_1]) ).
cnf(c_89,plain,
( achievable(west(m(n0),c(A)),boatoneast,east(m(B),c(s(s(C)))))
| ~ safe(B,s(s(C)))
| ~ achievable(west(m(n0),c(s(s(A)))),boatonwest,east(m(B),c(C))) ),
inference(resolve,[status(thm)],[c_7,c_1]) ).
cnf(c_90,plain,
( achievable(west(m(n0),c(A)),boatoneast,east(m(s(s(B))),c(s(s(n0)))))
| ~ achievable(west(m(n0),c(s(s(A)))),boatonwest,east(m(s(s(B))),c(n0))) ),
inference(resolve,[status(thm)],[c_89,c_36]) ).
cnf(c_59,plain,
~ achievable(west(m(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0))),
inference(resolve,[status(thm)],[c_90,c_47]) ).
cnf(c_91,plain,
( achievable(west(m(s(n0)),c(s(n0))),boatoneast,east(m(s(s(n0))),c(s(s(n0)))))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0)) ),
inference(resolve,[status(thm)],[c_11,c_53]) ).
cnf(c_92,plain,
( achievable(west(m(s(n0)),c(s(n0))),boatoneast,east(m(s(s(n0))),c(s(s(n0)))))
| ~ safe(s(s(n0)),s(s(n0))) ),
inference(resolve,[status(thm)],[c_91,c_25]) ).
cnf(c_65,plain,
achievable(west(m(s(n0)),c(s(n0))),boatoneast,east(m(s(s(n0))),c(s(s(n0))))),
inference(resolve,[status(thm)],[c_92,c_36]) ).
cnf(c_93,plain,
( achievable(west(m(n0),c(s(A))),boatonwest,east(m(B),c(C)))
| ~ safe(B,C)
| ~ achievable(west(m(n0),c(A)),boatoneast,east(m(B),c(s(C)))) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_94,plain,
( achievable(west(m(n0),c(s(A))),boatonwest,east(m(B),c(n0)))
| ~ achievable(west(m(n0),c(A)),boatoneast,east(m(B),c(s(n0)))) ),
inference(resolve,[status(thm)],[c_93,c_17]) ).
cnf(c_68,plain,
~ achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0)))),
inference(resolve,[status(thm)],[c_94,c_59]) ).
cnf(c_95,plain,
( achievable(west(m(n0),c(A)),boatoneast,east(m(s(s(B))),c(C)))
| ~ safe(s(s(B)),C)
| ~ achievable(west(m(s(s(n0))),c(A)),boatonwest,east(m(B),c(C))) ),
inference(resolve,[status(thm)],[c_11,c_1]) ).
cnf(c_96,plain,
( achievable(west(m(n0),c(A)),boatoneast,east(m(s(s(B))),c(s(n0))))
| ~ achievable(west(m(s(s(n0))),c(A)),boatonwest,east(m(B),c(s(n0)))) ),
inference(resolve,[status(thm)],[c_95,c_25]) ).
cnf(c_72,plain,
~ achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0)))),
inference(resolve,[status(thm)],[c_96,c_68]) ).
cnf(c_97,plain,
( achievable(west(m(s(s(A))),c(s(s(n0)))),boatonwest,east(m(B),c(C)))
| ~ safe(B,C)
| ~ achievable(west(m(s(A)),c(s(n0))),boatoneast,east(m(s(B)),c(s(C)))) ),
inference(resolve,[status(thm)],[c_14,c_36]) ).
cnf(c_98,plain,
( achievable(west(m(s(s(A))),c(s(s(n0)))),boatonwest,east(m(s(B)),c(s(n0))))
| ~ achievable(west(m(s(A)),c(s(n0))),boatoneast,east(m(s(s(B))),c(s(s(n0))))) ),
inference(resolve,[status(thm)],[c_97,c_25]) ).
cnf(c_77,plain,
~ achievable(west(m(s(n0)),c(s(n0))),boatoneast,east(m(s(s(n0))),c(s(s(n0))))),
inference(resolve,[status(thm)],[c_98,c_72]) ).
cnf(c_78,plain,
$false,
inference(resolve,[status(thm)],[c_77,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ008-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 05:08:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 964174 was started by sandbox on n001,
% 0.09/0.37 % Sat Sep 26 05:08:56 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 34.
% 0.09/0.40 % Level of proof is 12.
% 0.09/0.40 % Maximum clause weight is 85.000.
% 0.09/0.40 % Given clauses 49.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------