%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ032-1 : 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 : n018.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 08:21:10 AM UTC 2026
% Result : Unsatisfiable 3.68s 2.34s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 136 ( 22 ~; 20 |; 0 &; 94 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_truth_decl,type,
a_truth: $i > $o ).
thf(truthteller_decl,type,
truthteller: $i > $i ).
thf(c_decl,type,
c: $i ).
thf(liar_decl,type,
liar: $i > $i ).
thf(says_decl,type,
says: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(mumble_decl,type,
mumble: $i ).
thf(b_decl,type,
b: $i ).
thf(8,axiom,
mumble @ ( a @ says ) @ a_truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_mumbles) ).
thf(25,plain,
mumble @ ( a @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ truthteller @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ~ ( A @ a_truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truths_are_told_by_truthtellers) ).
thf(21,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)],[6]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ liar @ a_truth )
| ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truthteller_or_liar) ).
thf(13,plain,
! [A: $i] :
( ( A @ liar @ a_truth )
| ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ a_truth )
| ~ ( B @ ( A @ says ) @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truthtellers_tell_truth) ).
thf(17,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)],[4]) ).
thf(10,axiom,
b @ liar @ ( c @ says ) @ a_truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_says_b_is_a_liar) ).
thf(27,plain,
b @ liar @ ( c @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,negated_conjecture,
~ ( c @ truthteller @ a_truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_a_truthteller) ).
thf(11,plain,
~ ( c @ truthteller @ a_truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( B @ a_truth )
| ~ ( B @ ( A @ says ) @ a_truth )
| ~ ( A @ liar @ a_truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',liars_lie) ).
thf(19,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(3,axiom,
! [A: $i] :
( ~ ( A @ liar @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_both) ).
thf(15,plain,
! [A: $i] :
( ~ ( A @ liar @ a_truth )
| ~ ( A @ truthteller @ a_truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
a @ liar @ ( a @ says ) @ ( b @ says ) @ a_truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_says_a_says_hes_a_liar) ).
thf(26,plain,
a @ liar @ ( a @ says ) @ ( b @ says ) @ a_truth,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ liar @ a_truth )
| ~ ( A @ ( B @ says ) @ a_truth )
| ( A @ a_truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',liars_are_told_by_liars) ).
thf(23,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)],[7]) ).
thf(31,plain,
$false,
inference(e,[status(thm)],[25,21,13,17,27,11,19,15,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ032-1 : 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
% 0.12/0.40 % Computer : n018.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 05:08:36 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.18 % [INFO] Parsing done (184ms).
% 1.25/1.19 % [INFO] Running in sequential loop mode.
% 2.10/1.62 % [INFO] eprover registered as external prover.
% 2.10/1.63 % [INFO] Scanning for conjecture ...
% 2.31/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 2.31/1.75 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.31/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.31/1.77 % [INFO] Type checking passed.
% 2.31/1.78 % [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 ...
% 3.68/2.34 % External prover 'e' found a proof!
% 3.68/2.34 % [INFO] Killing All external provers ...
% 3.68/2.34 % Time passed: 1787ms (effective reasoning time: 1137ms)
% 3.68/2.34 % Axioms used in derivation (9): c_says_b_is_a_liar, a_mumbles, truthteller_or_liar, b_says_a_says_hes_a_liar, liars_lie, truthtellers_tell_truth, not_both, truths_are_told_by_truthtellers, liars_are_told_by_liars
% 3.68/2.34 % No. of inferences in proof: 21
% 3.68/2.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1787 ms resp. 1137 ms w/o parsing
% 3.68/2.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.68/2.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------