%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ020-1 : 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 : 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 08:21:07 AM UTC 2026
% Result : Unsatisfiable 3.62s 2.35s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 198 ( 50 ~; 44 |; 0 &; 104 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(knight_decl,type,
knight: $i > $o ).
thf(husband_decl,type,
husband: $i ).
thf(says_decl,type,
says: $i > $i > $o ).
thf(person_decl,type,
person: $i > $o ).
thf(statement_by_decl,type,
statement_by: $i > $i ).
thf(knave_decl,type,
knave: $i > $o ).
thf(a_truth_decl,type,
a_truth: $i > $o ).
thf(wife_decl,type,
wife: $i ).
thf(15,axiom,
! [A: $i] :
( ( A @ knight )
| ~ ( A @ statement_by @ a_truth )
| ~ ( A @ person ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_make_true_statements) ).
thf(52,plain,
! [A: $i] :
( ( A @ knight )
| ~ ( A @ statement_by @ a_truth )
| ~ ( A @ person ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
( ~ ( husband @ knight )
| ( husband @ statement_by @ a_truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knight_husband_makes_true_statements) ).
thf(43,plain,
( ~ ( husband @ knight )
| ( husband @ statement_by @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( A @ knave )
| ~ ( A @ knight )
| ~ ( A @ person ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_both_a_knight_and_knave) ).
thf(47,plain,
! [A: $i] :
( ~ ( A @ knave )
| ~ ( A @ knight )
| ~ ( A @ person ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
~ ( husband @ knight ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_knight_husband) ).
thf(20,plain,
~ ( husband @ knight ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( B @ a_truth )
| ~ ( B @ ( A @ says ) )
| ~ ( A @ knight ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_say_the_truth) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ a_truth )
| ~ ( B @ ( A @ says ) )
| ~ ( A @ knight ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( B @ a_truth )
| ( B @ a_truth )
| ~ ( B @ ( A @ says ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',statements_are_true_or_false) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( B @ a_truth )
| ( B @ a_truth )
| ~ ( B @ ( A @ says ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ statement_by ) )
| ~ ( B @ ( A @ says ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',peoples_statements) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ statement_by ) )
| ~ ( B @ ( A @ says ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
wife @ person,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wife) ).
thf(32,plain,
wife @ person,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
( ( husband @ statement_by @ a_truth )
| ~ ( wife @ knight ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knight_wife_means_truthful_husband) ).
thf(45,plain,
( ( husband @ statement_by @ a_truth )
| ~ ( wife @ knight ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ says ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',people_do_not_equal_their_statements1) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ says ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ knave )
| ( A @ knight )
| ~ ( A @ person ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',everyone_a_knight_or_knave) ).
thf(59,plain,
! [A: $i] :
( ( A @ knave )
| ( A @ knight )
| ~ ( A @ person ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
husband @ person,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',husband) ).
thf(54,plain,
husband @ person,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
( ( wife @ knight )
| ~ ( husband @ knight )
| ~ ( husband @ statement_by @ a_truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truthful_knight_husband_means_knight_wife) ).
thf(49,plain,
( ( wife @ knight )
| ~ ( husband @ knight )
| ~ ( husband @ statement_by @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
husband != wife,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',husband_not_wife) ).
thf(40,plain,
husband != wife,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A
!= ( B @ statement_by ) )
| ~ ( A @ person ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',people_do_not_equal_their_statement2) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ statement_by ) )
| ~ ( A @ person ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
( ( wife @ knight )
| ( husband @ statement_by @ a_truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knight_wife_or_truthful_husband) ).
thf(55,plain,
( ( wife @ knight )
| ( husband @ statement_by @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ knave )
| ( A @ statement_by @ a_truth )
| ~ ( A @ person ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_make_false_statements) ).
thf(36,plain,
! [A: $i] :
( ( A @ knave )
| ( A @ statement_by @ a_truth )
| ~ ( A @ person ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( B @ a_truth )
| ~ ( B @ ( A @ says ) )
| ~ ( A @ knave ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_do_not_say_the_truth) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( B @ a_truth )
| ~ ( B @ ( A @ says ) )
| ~ ( A @ knave ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
husband @ statement_by @ ( husband @ says ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',husband_makes_statements) ).
thf(51,plain,
husband @ statement_by @ ( husband @ says ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(61,plain,
$false,
inference(e,[status(thm)],[52,43,47,20,57,38,33,32,45,22,59,54,49,40,26,55,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ020-1 : 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
% 0.14/0.40 % Computer : n013.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 05:04:51 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.17 % [INFO] Parsing done (184ms).
% 1.28/1.18 % [INFO] Running in sequential loop mode.
% 1.91/1.58 % [INFO] eprover registered as external prover.
% 1.91/1.59 % [INFO] Scanning for conjecture ...
% 2.11/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.28/1.73 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.28/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.28/1.76 % [INFO] Type checking passed.
% 2.28/1.77 % [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 ...
% 3.62/2.35 % External prover 'e' found a proof!
% 3.62/2.35 % [INFO] Killing All external provers ...
% 3.62/2.35 % Time passed: 1805ms (effective reasoning time: 1160ms)
% 3.62/2.35 % Axioms used in derivation (18): knight_husband_makes_true_statements, knaves_make_false_statements, people_do_not_equal_their_statement2, husband, wife, not_both_a_knight_and_knave, husband_not_wife, knaves_do_not_say_the_truth, truthful_knight_husband_means_knight_wife, everyone_a_knight_or_knave, husband_makes_statements, knight_wife_or_truthful_husband, knight_wife_means_truthful_husband, statements_are_true_or_false, knights_make_true_statements, knights_say_the_truth, peoples_statements, people_do_not_equal_their_statements1
% 3.62/2.35 % No. of inferences in proof: 39
% 3.62/2.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1805 ms resp. 1160 ms w/o parsing
% 3.93/2.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.93/2.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------