%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ024-1 : 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 : n012.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 1.81s 1.28s
% Output : Refutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 412 ( 74 ~; 80 |; 0 &; 258 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_truth_decl,type,
a_truth: $i > $o ).
thf(truthteller_decl,type,
truthteller: $i > $i ).
thf(people_decl,type,
people: $i > $i > $i > $o ).
thf(c_decl,type,
c: $i ).
thf(b_decl,type,
b: $i ).
thf(a_decl,type,
a: $i ).
thf(says_decl,type,
says: $i > $i > $i ).
thf(all_are_liars_decl,type,
all_are_liars: $i ).
thf(one_truthteller_decl,type,
one_truthteller: $i ).
thf(liar_decl,type,
liar: $i > $i ).
thf(19,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(52,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)],[19]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ liar @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( one_truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_truthteller_two_liars) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ liar @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( one_truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
one_truthteller @ ( b @ says ) @ a_truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_says_one_truthteller) ).
thf(45,plain,
one_truthteller @ ( b @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ liar @ a_truth )
| ~ ( B @ liar @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ( one_truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',three_liars) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ liar @ a_truth )
| ~ ( B @ liar @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ( one_truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ liar @ a_truth )
| ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthteller_or_liar) ).
thf(54,plain,
! [A: $i] :
( ( A @ liar @ a_truth )
| ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,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(39,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)],[12]) ).
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(35,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(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ( one_truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_truthtellers) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ( one_truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ( all_are_liars @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_truthtellers) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ( all_are_liars @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
a @ ( c @ ( b @ people ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_c_a_people) ).
thf(24,plain,
a @ ( c @ ( b @ people ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( all_are_liars @ ( A @ says ) @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',speaker_is_lying) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( all_are_liars @ ( A @ says ) @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
b @ ( c @ ( a @ people ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_c_b_people) ).
thf(25,plain,
b @ ( c @ ( a @ people ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( one_truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_is_not_the_truthteller) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( one_truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( one_truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_is_the_truth_teller) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ truthteller @ a_truth )
| ( B @ truthteller @ a_truth )
| ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( one_truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( A @ truthteller @ a_truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_truthteller) ).
thf(21,plain,
! [A: $i] :
~ ( A @ truthteller @ a_truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,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(33,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)],[9]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( one_truthteller @ ( A @ says ) @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_says_one_truthteller) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ truthteller @ a_truth )
| ~ ( B @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) )
| ~ ( one_truthteller @ ( A @ says ) @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ liar @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_both) ).
thf(31,plain,
! [A: $i] :
( ~ ( A @ liar @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
all_are_liars @ ( a @ says ) @ a_truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_says_all_are_liars) ).
thf(26,plain,
all_are_liars @ ( a @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
a @ ( b @ ( c @ people ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_b_a_people) ).
thf(23,plain,
a @ ( b @ ( c @ people ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[52,41,45,27,54,39,35,48,43,24,37,25,46,29,21,33,50,31,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PUZ024-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % 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
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sat Sep 26 05:04:50 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 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
% 0.39/0.61 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.70 % [INFO] Parsing done (94ms).
% 0.69/0.71 % [INFO] Running in sequential loop mode.
% 0.89/0.89 % [INFO] eprover registered as external prover.
% 1.06/0.90 % [INFO] Scanning for conjecture ...
% 1.06/0.94 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 1.06/0.97 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 1.06/0.99 % [INFO] Problem is propositional (TPTP CNF).
% 1.06/0.99 % [INFO] Type checking passed.
% 1.06/0.99 % [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 ...
% 1.81/1.28 % External prover 'e' found a proof!
% 1.81/1.28 % [INFO] Killing All external provers ...
% 1.81/1.28 % Time passed: 882ms (effective reasoning time: 565ms)
% 1.81/1.28 % Axioms used in derivation (19): one_says_one_truthteller, a_c_b_people, truthteller_or_liar, one_truthteller_two_liars, c_b_a_people, b_c_a_people, two_truthtellers, liars_lie, truthtellers_tell_truth, not_both, one_is_the_truth_teller, truths_are_told_by_truthtellers, three_liars, b_says_one_truthteller, all_truthtellers, one_is_not_the_truthteller, a_says_all_are_liars, speaker_is_lying, liars_are_told_by_liars
% 1.81/1.28 % No. of inferences in proof: 41
% 1.81/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 882 ms resp. 565 ms w/o parsing
% 2.08/1.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.08/1.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------