%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ021-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 08:21:07 AM UTC 2026
% Result : Unsatisfiable 3.86s 2.41s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 248 ( 36 ~; 36 |; 0 &; 176 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(says_decl,type,
says: $i > $i > $o ).
thf(me_decl,type,
me: $i ).
thf(a_truth_decl,type,
a_truth: $i > $i > $o ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(knave_decl,type,
knave: $i > $i ).
thf(rich_decl,type,
rich: $i > $i ).
thf(knight_decl,type,
knight: $i > $i ).
thf(poor_decl,type,
poor: $i > $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ poor @ a_truth ) )
| ( B @ ( A @ rich @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rich_or_poor) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ poor @ a_truth ) )
| ( B @ ( A @ rich @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( A @ ( me @ rich @ ( me @ knave @ and ) @ a_truth ) )
| ~ ( A @ ( me @ says ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_statement_exists1) ).
thf(14,plain,
! [A: $i] :
( ~ ( A @ ( me @ rich @ ( me @ knave @ and ) @ a_truth ) )
| ~ ( A @ ( me @ says ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ knave @ a_truth ) )
| ( B @ ( A @ knight @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knight_or_knave) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ knave @ a_truth ) )
| ( B @ ( A @ knight @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ poor @ a_truth ) )
| ~ ( B @ ( A @ rich @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_rich_and_poor) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ poor @ a_truth ) )
| ~ ( B @ ( A @ rich @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ knave @ a_truth ) )
| ~ ( B @ ( A @ knight @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_knight_and_knave) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ knave @ a_truth ) )
| ~ ( B @ ( A @ knight @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ a_truth ) )
| ~ ( C @ ( A @ says ) )
| ~ ( B @ ( A @ knight @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_tell_truth1) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ a_truth ) )
| ~ ( C @ ( A @ says ) )
| ~ ( B @ ( A @ knight @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ( A @ ( me @ rich @ ( me @ knave @ and ) @ a_truth ) )
| ( A @ ( me @ says ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_statement_exists2) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( me @ rich @ ( me @ knave @ and ) @ a_truth ) )
| ( A @ ( me @ says ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ a_truth ) )
| ( C @ ( A @ says ) )
| ~ ( B @ ( A @ knight @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_tell_truth2) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ a_truth ) )
| ( C @ ( A @ says ) )
| ~ ( B @ ( A @ knight @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ a_truth ) )
| ~ ( C @ ( A @ a_truth ) )
| ( C @ ( B @ ( A @ and ) @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjunction3) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ a_truth ) )
| ~ ( C @ ( A @ a_truth ) )
| ( C @ ( B @ ( A @ and ) @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ a_truth ) )
| ( C @ ( A @ says ) )
| ~ ( B @ ( A @ knave @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_lie2) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ a_truth ) )
| ( C @ ( A @ says ) )
| ~ ( B @ ( A @ knave @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ a_truth ) )
| ~ ( C @ ( B @ ( A @ and ) @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjunction1) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ a_truth ) )
| ~ ( C @ ( B @ ( A @ and ) @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ a_truth ) )
| ~ ( C @ ( B @ ( A @ and ) @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjunction2) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ a_truth ) )
| ~ ( C @ ( B @ ( A @ and ) @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ a_truth ) )
| ~ ( C @ ( A @ says ) )
| ~ ( B @ ( A @ knave @ a_truth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_lie1) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ a_truth ) )
| ~ ( C @ ( A @ says ) )
| ~ ( B @ ( A @ knave @ a_truth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(55,plain,
$false,
inference(e,[status(thm)],[24,14,20,22,18,26,15,28,38,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n017.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 05:00:33 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.18 % [INFO] Parsing done (178ms).
% 1.19/1.19 % [INFO] Running in sequential loop mode.
% 1.78/1.60 % [INFO] eprover registered as external prover.
% 1.96/1.60 % [INFO] Scanning for conjecture ...
% 2.12/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.12/1.74 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.12/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.12/1.76 % [INFO] Type checking passed.
% 2.12/1.76 % [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 ...
% 3.86/2.41 % External prover 'e' found a proof!
% 3.86/2.41 % [INFO] Killing All external provers ...
% 3.86/2.41 % Time passed: 1860ms (effective reasoning time: 1213ms)
% 3.86/2.41 % Axioms used in derivation (11): not_rich_and_poor, conjunction3, knaves_lie2, knaves_lie1, rich_or_poor, knights_tell_truth1, conjunction1, knights_tell_truth2, conjunction2, not_knight_and_knave, knight_or_knave
% 3.86/2.41 % No. of inferences in proof: 27
% 3.86/2.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1860 ms resp. 1213 ms w/o parsing
% 3.86/2.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.86/2.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------