%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ023-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n003.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 5.20s 8.08s
% Output : Refutation 5.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 22
% Syntax : Number of formulae : 45 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 131 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 428 ( 78 ~; 86 |; 0 &; 264 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 64 ( 0 ^; 64 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(an_answer_decl,type,
an_answer: $i > $o ).
thf(a_truth_decl,type,
a_truth: $i > $o ).
thf(says_decl,type,
says: $i > $i > $i ).
thf(liar_decl,type,
liar: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(garbage_decl,type,
garbage: $i ).
thf(people_decl,type,
people: $i > $i > $i > $o ).
thf(truthteller_decl,type,
truthteller: $i > $i ).
thf(one_truthteller_decl,type,
one_truthteller: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(b_liar_and_c_truthteller_decl,type,
b_liar_and_c_truthteller: $i ).
thf(b_and_c_truthtellers_decl,type,
b_and_c_truthtellers: $i ).
thf(b_truthteller_and_c_liar_decl,type,
b_truthteller_and_c_liar: $i ).
thf(b_and_c_liars_decl,type,
b_and_c_liars: $i ).
thf(17,axiom,
! [A: $i] :
( ( A @ liar @ a_truth )
| ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthteller_or_liar) ).
thf(52,plain,
! [A: $i] :
( ( A @ liar @ a_truth )
| ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(22,axiom,
( ( b_and_c_liars @ an_answer )
| ~ ( c @ liar @ a_truth )
| ~ ( b @ liar @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_and_c_liars) ).
thf(61,plain,
( ( b_and_c_liars @ an_answer )
| ~ ( c @ liar @ a_truth )
| ~ ( b @ liar @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
one_truthteller @ ( a @ says ) @ ( b @ says ) @ a_truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_says_a_says_one_truthteller) ).
thf(48,plain,
one_truthteller @ ( a @ says ) @ ( b @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( A @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ( one_truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identify_one_truthteller2) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( A @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ( one_truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ liar @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ( A @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_are_told_by_liars) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ liar @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ( A @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( one_truthteller @ a_truth )
| ~ ( C @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_truthtellers3) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( one_truthteller @ a_truth )
| ~ ( C @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
( ( b_and_c_truthtellers @ an_answer )
| ~ ( c @ truthteller @ a_truth )
| ~ ( b @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_and_c_truthtellers) ).
thf(57,plain,
( ( b_and_c_truthtellers @ an_answer )
| ~ ( c @ truthteller @ a_truth )
| ~ ( b @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( one_truthteller @ a_truth )
| ~ ( C @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_truthtellers2) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( one_truthteller @ a_truth )
| ~ ( C @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ( A @ truthteller @ a_truth )
| ~ ( one_truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_is_the_truthteller) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ( A @ truthteller @ a_truth )
| ~ ( one_truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ( one_truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identify_one_truthteller1) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ( one_truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ~ ( C @ truthteller @ a_truth )
| ( one_truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identify_one_truthteller3) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ~ ( C @ truthteller @ a_truth )
| ( one_truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( one_truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_truthtellers1) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( one_truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
( ( b_truthteller_and_c_liar @ an_answer )
| ~ ( c @ liar @ a_truth )
| ~ ( b @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_truthteller_and_c_liar) ).
thf(59,plain,
( ( b_truthteller_and_c_liar @ an_answer )
| ~ ( c @ liar @ a_truth )
| ~ ( b @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,axiom,
garbage @ ( a @ says ) @ a_truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_says_garbage) ).
thf(27,plain,
garbage @ ( a @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
b @ liar @ ( c @ says ) @ a_truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_says_b_lies) ).
thf(54,plain,
b @ liar @ ( c @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( A @ liar @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_both) ).
thf(49,plain,
! [A: $i] :
( ~ ( A @ liar @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ a_truth )
| ~ ( B @ ( A @ says ) @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthtellers_tell_truth) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ a_truth )
| ~ ( B @ ( A @ says ) @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
( ( b_liar_and_c_truthteller @ an_answer )
| ~ ( c @ truthteller @ a_truth )
| ~ ( b @ liar @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_liar_and_c_truthteller) ).
thf(55,plain,
( ( b_liar_and_c_truthteller @ an_answer )
| ~ ( c @ truthteller @ a_truth )
| ~ ( b @ liar @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( A @ an_answer ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_an_answer) ).
thf(23,plain,
! [A: $i] :
~ ( A @ an_answer ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ truthteller @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ~ ( A @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truths_are_told_by_truthtellers) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ truthteller @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ~ ( A @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( B @ a_truth )
| ~ ( B @ ( A @ says ) @ a_truth )
| ~ ( A @ liar @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_lie) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( B @ a_truth )
| ~ ( B @ ( A @ says ) @ a_truth )
| ~ ( A @ liar @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
c @ ( b @ ( a @ people ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_b_and_c_are_people) ).
thf(51,plain,
c @ ( b @ ( a @ people ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(63,plain,
$false,
inference(e,[status(thm)],[52,61,48,42,25,46,57,28,38,32,34,44,59,27,54,49,40,55,23,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.16/5.41 % Computer : n003.cluster.edu
% 0.16/5.41 % Model : x86_64 x86_64
% 0.16/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.41 % Memory : 8046.5625MB
% 0.16/5.41 % OS : Linux 6.8.0-71-generic
% 0.16/5.41 % CPULimit : 300
% 0.16/5.41 % WCLimit : 300
% 0.16/5.41 % DateTime : Sat Sep 26 05:06:59 UTC 2026
% 0.16/5.41 % CPUTime :
% 0.16/5.41 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
% 1.21/6.15 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.50/6.35 % [INFO] Parsing done (193ms).
% 1.50/6.37 % [INFO] Running in sequential loop mode.
% 2.62/6.95 % [INFO] eprover registered as external prover.
% 2.62/6.96 % [INFO] Scanning for conjecture ...
% 2.87/7.09 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 3.03/7.17 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 3.13/7.23 % [INFO] Problem is propositional (TPTP CNF).
% 3.13/7.24 % [INFO] Type checking passed.
% 3.13/7.24 % [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 ...
% 5.20/8.07 % External prover 'e' found a proof!
% 5.20/8.07 % [INFO] Killing All external provers ...
% 5.20/8.08 % Time passed: 2454ms (effective reasoning time: 1695ms)
% 5.20/8.08 % Axioms used in derivation (21): b_says_a_says_one_truthteller, identify_one_truthteller3, truthteller_or_liar, b_truthteller_and_c_liar, two_truthtellers3, liars_lie, truthtellers_tell_truth, not_both, identify_one_truthteller2, one_is_the_truthteller, two_truthtellers1, b_liar_and_c_truthteller, two_truthtellers2, b_and_c_truthtellers, a_b_and_c_are_people, a_says_garbage, c_says_b_lies, truths_are_told_by_truthtellers, identify_one_truthteller1, liars_are_told_by_liars, b_and_c_liars
% 5.20/8.08 % No. of inferences in proof: 45
% 5.20/8.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2454 ms resp. 1695 ms w/o parsing
% 5.49/8.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.49/8.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------