%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ008-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n013.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 08:21:04 AM UTC 2026
% Result : Unsatisfiable 4.26s 8.13s
% Output : Refutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 842 ( 66 ~; 64 |; 0 &; 712 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 94 ( 0 ^; 94 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(achievable_decl,type,
achievable: $i > $i > $i > $o ).
thf(west_decl,type,
west: $i > $i > $i ).
thf(m_decl,type,
m: $i > $i ).
thf(n0_decl,type,
n0: $i ).
thf(c_decl,type,
c: $i > $i ).
thf(east_decl,type,
east: $i > $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(safe_decl,type,
safe: $i > $i > $o ).
thf(boatoneast_decl,type,
boatoneast: $i ).
thf(boatonwest_decl,type,
boatonwest: $i ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ s @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ s @ s @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ c @ ( A @ s @ s @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_missionaries_west_to_east) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ s @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ s @ s @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ c @ ( A @ s @ s @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ s @ ( A @ safe ) )
| ~ ( D @ s @ c @ ( C @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cannibal_east_to_west) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ s @ ( A @ safe ) )
| ~ ( D @ s @ c @ ( C @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ s @ c @ ( C @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ s @ ( C @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cannibal_west_to_east) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ s @ c @ ( C @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ s @ ( C @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ s @ c @ ( C @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ s @ ( C @ s @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ c @ ( A @ s @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',missionary_and_cannibal_west_to_east) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ s @ c @ ( C @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ s @ ( C @ s @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ c @ ( A @ s @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: $i] : ( n0 @ ( A @ greater_or_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',great_eq_base) ).
thf(43,plain,
! [A: $i] : ( n0 @ ( A @ greater_or_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ s @ s @ c @ ( C @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ s @ s @ ( C @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ s @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_cannibals_west_to_east) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ s @ s @ c @ ( C @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ s @ s @ ( C @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ s @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ c @ ( A @ s @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ s @ ( A @ s @ safe ) )
| ~ ( D @ s @ c @ ( C @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',missionary_and_cannibal_east_to_west) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ c @ ( A @ s @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ s @ ( A @ s @ safe ) )
| ~ ( D @ s @ c @ ( C @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ s @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ s @ s @ ( A @ safe ) )
| ~ ( D @ s @ s @ c @ ( C @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_cannibals_east_to_west) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ s @ s @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ s @ s @ ( A @ safe ) )
| ~ ( D @ s @ s @ c @ ( C @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ c @ ( A @ s @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ ( A @ s @ safe ) )
| ~ ( D @ c @ ( C @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',missionary_east_to_west) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ c @ ( A @ s @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ ( A @ s @ safe ) )
| ~ ( D @ c @ ( C @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater_or_equal ) )
| ( B @ s @ ( A @ s @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',great_eq_recursive) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater_or_equal ) )
| ( B @ s @ ( A @ s @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
n0 @ c @ ( n0 @ m @ east ) @ ( boatonwest @ ( n0 @ s @ s @ s @ c @ ( n0 @ s @ s @ s @ m @ west ) @ achievable ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_on_west_bank) ).
thf(32,plain,
n0 @ c @ ( n0 @ m @ east ) @ ( boatonwest @ ( n0 @ s @ s @ s @ c @ ( n0 @ s @ s @ s @ m @ west ) @ achievable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( n0 @ s @ s @ s @ c @ ( n0 @ s @ s @ s @ m @ east ) @ ( A @ ( n0 @ c @ ( n0 @ m @ west ) @ achievable ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_can_get_to_east_bank) ).
thf(17,plain,
! [A: $i] :
~ ( n0 @ s @ s @ s @ c @ ( n0 @ s @ s @ s @ m @ east ) @ ( A @ ( n0 @ c @ ( n0 @ m @ west ) @ achievable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ s @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ c @ ( A @ s @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',missionary_west_to_east) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ s @ safe ) )
| ~ ( B @ ( A @ safe ) )
| ~ ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ c @ ( A @ s @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] : ( A @ ( n0 @ safe ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_missionaries_is_safe) ).
thf(23,plain,
! [A: $i] : ( A @ ( n0 @ safe ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ c @ ( A @ s @ s @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ ( A @ s @ s @ safe ) )
| ~ ( D @ c @ ( C @ s @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_missionaries_east_to_west) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ c @ ( C @ m @ east ) @ ( boatonwest @ ( B @ c @ ( A @ s @ s @ m @ west ) @ achievable ) ) )
| ~ ( D @ ( C @ safe ) )
| ~ ( B @ ( A @ s @ s @ safe ) )
| ~ ( D @ c @ ( C @ s @ s @ m @ east ) @ ( boatoneast @ ( B @ c @ ( A @ m @ west ) @ achievable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ safe ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',same_or_more_missionaries_is_safe) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ safe ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,plain,
$false,
inference(e,[status(thm)],[41,44,39,35,43,24,37,28,21,33,32,17,26,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ008-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/5.99 % Computer : n013.cluster.edu
% 0.12/5.99 % Model : x86_64 x86_64
% 0.12/5.99 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.99 % Memory : 8046.5625MB
% 0.12/5.99 % OS : Linux 6.8.0-71-generic
% 0.12/5.99 % CPULimit : 300
% 0.12/5.99 % WCLimit : 300
% 0.12/5.99 % DateTime : Sat Sep 26 05:02:42 UTC 2026
% 0.12/6.00 % CPUTime :
% 0.12/6.00 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/6.57 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/6.78 % [INFO] Parsing done (202ms).
% 1.18/6.79 % [INFO] Running in sequential loop mode.
% 1.92/7.20 % [INFO] eprover registered as external prover.
% 2.05/7.20 % [INFO] Scanning for conjecture ...
% 2.23/7.31 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.23/7.39 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.40/7.44 % [INFO] Problem is propositional (TPTP CNF).
% 2.40/7.45 % [INFO] Type checking passed.
% 2.40/7.45 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.93/8.12 % External prover 'e' found a proof!
% 3.93/8.12 % [INFO] Killing All external provers ...
% 3.93/8.12 % Time passed: 1986ms (effective reasoning time: 1323ms)
% 3.93/8.13 % Axioms used in derivation (15): no_missionaries_is_safe, cannibal_west_to_east, two_cannibals_west_to_east, cannibal_east_to_west, missionary_and_cannibal_east_to_west, missionary_east_to_west, missionary_west_to_east, two_cannibals_east_to_west, two_missionaries_east_to_west, great_eq_recursive, same_or_more_missionaries_is_safe, start_on_west_bank, missionary_and_cannibal_west_to_east, two_missionaries_west_to_east, great_eq_base
% 3.93/8.13 % No. of inferences in proof: 33
% 4.26/8.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1986 ms resp. 1323 ms w/o parsing
% 4.43/8.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.43/8.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------