%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ026-1 : 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 : n020.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 3.00s
% Output : Refutation 4.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 47 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 382 ( 74 ~; 62 |; 0 &; 246 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_truth_decl,type,
a_truth: $i > $o ).
thf(liar_decl,type,
liar: $i > $i ).
thf(normal_decl,type,
normal: $i > $i ).
thf(truthteller_decl,type,
truthteller: $i > $i ).
thf(people_decl,type,
people: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(says_decl,type,
says: $i > $i > $i ).
thf(not_normal_decl,type,
not_normal: $i > $i ).
thf(22,axiom,
! [A: $i] :
( ( A @ normal @ a_truth )
| ( A @ not_normal @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normal_or_not_normal) ).
thf(60,plain,
! [A: $i] :
( ( A @ normal @ a_truth )
| ( A @ not_normal @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ normal @ a_truth )
| ~ ( A @ normal @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_normal2) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ normal @ a_truth )
| ~ ( A @ normal @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( A @ liar @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_truthteller_and_liar) ).
thf(49,plain,
! [A: $i] :
( ~ ( A @ liar @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_truthtellers1) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ truthteller @ a_truth )
| ~ ( B @ normal @ a_truth )
| ~ ( A @ liar @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_one_of_each) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ truthteller @ a_truth )
| ~ ( B @ normal @ a_truth )
| ~ ( A @ liar @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
c @ not_normal @ ( c @ says ) @ a_truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_says_c_not_normal) ).
thf(46,plain,
c @ not_normal @ ( c @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [A: $i] :
( ~ ( A @ normal @ a_truth )
| ~ ( A @ not_normal @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_normal_and_not_normal) ).
thf(57,plain,
! [A: $i] :
( ~ ( A @ normal @ a_truth )
| ~ ( A @ not_normal @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
a @ normal @ ( a @ says ) @ a_truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_says_a_normal) ).
thf(29,plain,
a @ normal @ ( a @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
a @ ( c @ ( b @ people ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_c_a_are_people) ).
thf(28,plain,
a @ ( c @ ( b @ people ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( A @ normal @ a_truth )
| ~ ( A @ liar @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_liar_and_normal) ).
thf(38,plain,
! [A: $i] :
( ~ ( A @ normal @ a_truth )
| ~ ( A @ liar @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ normal @ a_truth )
| ( B @ truthteller @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ~ ( A @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthtellers_and_normal_tell_truth) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ normal @ a_truth )
| ( B @ truthteller @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ~ ( A @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ normal @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_truthteller_and_normal) ).
thf(34,plain,
! [A: $i] :
( ~ ( A @ normal @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ liar @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_liars1) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ liar @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
a @ normal @ ( b @ says ) @ a_truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_says_a_normal) ).
thf(59,plain,
a @ normal @ ( b @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,axiom,
a @ ( b @ ( c @ people ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_b_a_are_people) ).
thf(27,plain,
a @ ( b @ ( c @ people ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_truthtellers2) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ truthteller @ a_truth )
| ~ ( A @ truthteller @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
c @ ( b @ ( a @ people ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_b_c_are_people) ).
thf(26,plain,
c @ ( b @ ( a @ people ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,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(55,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)],[19]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ normal @ a_truth )
| ~ ( A @ normal @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_normal1) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ normal @ a_truth )
| ~ ( A @ normal @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ normal @ a_truth )
| ( A @ liar @ a_truth )
| ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',person_is_one_type) ).
thf(30,plain,
! [A: $i] :
( ( A @ normal @ a_truth )
| ( A @ liar @ a_truth )
| ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,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(51,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)],[17]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ liar @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_liars2) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ liar @ a_truth )
| ~ ( A @ liar @ a_truth )
| ~ ( C @ ( B @ ( A @ people ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ normal @ a_truth )
| ( B @ liar @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ( A @ a_truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_and_normal_lie) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( B @ normal @ a_truth )
| ( B @ liar @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ( A @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(64,plain,
$false,
inference(e,[status(thm)],[60,53,49,42,24,46,57,29,28,38,32,34,44,59,27,40,26,55,36,30,51,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ026-1 : 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
% 0.15/0.53 % Computer : n020.cluster.edu
% 0.15/0.53 % Model : x86_64 x86_64
% 0.15/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.53 % Memory : 8046.5625MB
% 0.15/0.53 % OS : Linux 6.8.0-71-generic
% 0.15/0.53 % CPULimit : 300
% 0.15/0.53 % WCLimit : 300
% 0.15/0.53 % DateTime : Sat Sep 26 05:05:50 UTC 2026
% 0.15/0.53 % CPUTime :
% 0.15/0.53 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
% 0.95/1.33 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.58 % [INFO] Parsing done (240ms).
% 1.24/1.60 % [INFO] Running in sequential loop mode.
% 1.99/2.14 % [INFO] eprover registered as external prover.
% 1.99/2.15 % [INFO] Scanning for conjecture ...
% 2.22/2.27 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 2.38/2.35 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.38/2.38 % [INFO] Problem is propositional (TPTP CNF).
% 2.38/2.38 % [INFO] Type checking passed.
% 2.38/2.39 % [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 ...
% 3.86/2.99 % External prover 'e' found a proof!
% 3.86/2.99 % [INFO] Killing All external provers ...
% 3.86/2.99 % Time passed: 2248ms (effective reasoning time: 1387ms)
% 3.86/3.00 % Axioms used in derivation (22): b_c_a_are_people, normal_or_not_normal, not_truthteller_and_normal, not_two_liars2, b_says_a_normal, not_two_truthtellers2, not_two_normal1, c_b_a_are_people, not_liar_and_normal, not_two_truthtellers1, liars_and_normal_lie, not_two_liars1, liars_lie, a_b_c_are_people, person_is_one_type, not_normal_and_not_normal, truthtellers_and_normal_tell_truth, c_says_c_not_normal, truthtellers_tell_truth, not_truthteller_and_liar, not_two_normal2, a_says_a_normal
% 3.86/3.00 % No. of inferences in proof: 47
% 3.86/3.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2248 ms resp. 1387 ms w/o parsing
% 4.20/3.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.20/3.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------