%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ001_4 : TPTP v9.3.1. Released v9.3.0.
% 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 : n014.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 08:21:02 AM UTC 2026
% Result : Theorem 3.92s 2.34s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 158 ( 18 ~; 4 |; 2 &; 117 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 58 ( 0 ^; 54 !; 4 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(person_type,type,
person: $tType ).
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf(agatha_decl,type,
agatha: person ).
thf(butler_decl,type,
butler: person ).
thf(charles_decl,type,
charles: person ).
thf(lives_decl,type,
lives: '$world' > person > $o ).
thf(killed_decl,type,
killed: '$world' > person > person > $o ).
thf(hates_decl,type,
hates: '$world' > person > person > $o ).
thf(richer_decl,type,
richer: '$world' > person > person > $o ).
thf(14,axiom,
! [A: '$world',B: person] :
( ( B != butler )
=> ( B @ ( agatha @ ( A @ hates ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_7) ).
thf(52,plain,
! [A: '$world',B: person] :
( ( B != butler )
=> ( B @ ( agatha @ ( A @ hates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: '$world',B: '$world'] : ( B @ ( A @ '$accessible_world' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
thf(57,plain,
! [A: '$world',B: '$world'] : ( B @ ( A @ '$accessible_world' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [A: '$world',B: person] :
( ~ ( agatha @ ( B @ ( A @ richer ) ) )
=> ( B @ ( butler @ ( A @ hates ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_8) ).
thf(61,plain,
! [A: '$world',B: person] :
( ~ ( agatha @ ( B @ ( A @ richer ) ) )
=> ( B @ ( butler @ ( A @ hates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: '$world'] : ( agatha @ ( A @ lives ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_2_1) ).
thf(41,plain,
! [A: '$world'] : ( agatha @ ( A @ lives ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [A: '$world',B: person] :
( ( B @ ( agatha @ ( A @ hates ) ) )
=> ( B @ ( butler @ ( A @ hates ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_9) ).
thf(59,plain,
! [A: '$world',B: person] :
( ( B @ ( agatha @ ( A @ hates ) ) )
=> ( B @ ( butler @ ( A @ hates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: '$world'] : ( agatha != butler ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_11a) ).
thf(49,plain,
agatha != butler,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [A: '$world',B: person] :
( ( B @ ( agatha @ ( A @ hates ) ) )
=> ~ ( B @ ( charles @ ( A @ hates ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_6) ).
thf(39,plain,
! [A: '$world',B: person] :
( ( B @ ( agatha @ ( A @ hates ) ) )
=> ~ ( B @ ( charles @ ( A @ hates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: '$world'] :
? [B: person] :
( ( agatha @ ( B @ ( A @ killed ) ) )
& ( B @ ( A @ lives ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_1) ).
thf(43,plain,
! [A: '$world'] :
? [B: person] :
( ( agatha @ ( B @ ( A @ killed ) ) )
& ( B @ ( A @ lives ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: '$world',B: person,C: person] :
( ( C @ ( B @ ( A @ killed ) ) )
=> ~ ( C @ ( B @ ( A @ richer ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_5) ).
thf(47,plain,
! [A: '$world',B: person,C: person] :
( ( C @ ( B @ ( A @ killed ) ) )
=> ~ ( C @ ( B @ ( A @ richer ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: '$world'] : ( charles @ ( A @ lives ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_2_3) ).
thf(28,plain,
! [A: '$world'] : ( charles @ ( A @ lives ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: '$world',B: person] :
( ( B @ ( A @ lives ) )
=> ( ( B = charles )
| ( B = butler )
| ( B = agatha ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_3) ).
thf(33,plain,
! [A: '$world',B: person] :
( ( B @ ( A @ lives ) )
=> ( ( B = charles )
| ( B = butler )
| ( B = agatha ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: '$world'] : ( butler @ ( A @ lives ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_2_2) ).
thf(26,plain,
! [A: '$world'] : ( butler @ ( A @ lives ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [A: '$world',B: person,C: person] :
( ( C @ ( B @ ( A @ killed ) ) )
=> ( C @ ( B @ ( A @ hates ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_4) ).
thf(55,plain,
! [A: '$world',B: person,C: person] :
( ( C @ ( B @ ( A @ killed ) ) )
=> ( C @ ( B @ ( A @ hates ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: '$world',B: person] :
? [C: person] :
~ ( C @ ( B @ ( A @ hates ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_10) ).
thf(23,plain,
! [A: '$world',B: person] :
? [C: person] :
~ ( C @ ( B @ ( A @ hates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: '$world'] : ( charles != agatha ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_11c) ).
thf(36,plain,
charles != agatha,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: '$world'] : ( butler != charles ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55_11b) ).
thf(30,plain,
butler != charles,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( agatha @ ( agatha @ ( A @ killed ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55) ).
thf(2,negated_conjecture,
~ ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( agatha @ ( agatha @ ( A @ killed ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( agatha @ ( agatha @ ( A @ killed ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(63,plain,
$false,
inference(e,[status(thm)],[52,57,61,41,59,49,39,43,47,28,33,26,55,23,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ001_4 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % 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
% 0.11/0.39 % Computer : n014.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 05:02:17 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 0.85/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.17 % [INFO] Parsing done (197ms).
% 1.26/1.20 % [INFO] Input problem is non-classical (logic $alethic_modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.46/1.21 %%% First-order logic specification detected, trying modal-logic-to-TXF embedding (redirected from embedding '$$modal' to embedding '$$fomlModel' version 1.3.7) ... Use flag -p FORCE_HIGHERORDER if you want to have THF output instead.
% 1.62/1.33 % [INFO] Running in sequential loop mode.
% 2.30/1.62 % [INFO] eprover registered as external prover.
% 2.30/1.63 % [INFO] Scanning for conjecture ...
% 2.30/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.58/1.70 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.58/1.73 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.58/1.74 % [INFO] Type checking passed.
% 2.58/1.74 % [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 ...
% 3.92/2.33 % External prover 'e' found a proof!
% 3.92/2.33 % [INFO] Killing All external provers ...
% 3.92/2.33 % Time passed: 1795ms (effective reasoning time: 997ms)
% 3.92/2.33 % Solved by 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)>
% 3.92/2.34 % Axioms used in derivation (16): pel55_1, pel55_11a, pel55_6, pel55_9, pel55_11c, pel55_2_3, pel55_11b, pel55_7, pel55_2_1, pel55_5, pel55_4, mrel_universal, pel55_10, pel55_8, pel55_3, pel55_2_2
% 3.92/2.34 % No. of inferences in proof: 36
% 3.92/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1795 ms resp. 997 ms w/o parsing
% 3.92/2.39 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.92/2.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------