%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NLP267_2 : TPTP v9.3.1. Released v8.2.0.
% 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 : n001.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 08:05:19 AM UTC 2026
% Result : Theorem 3.10s 2.05s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 121 ( 6 ~; 0 |; 8 &; 88 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf('$ki_world_type',type,
'$ki_world': $tType ).
thf('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
thf('$ki_accessible_decl',type,
'$ki_accessible': '$ki_world' > '$ki_world' > $o ).
thf(seventy_decl,type,
seventy: $i ).
thf(ninetyfive_decl,type,
ninetyfive: $i ).
thf(second_decl,type,
second: $i ).
thf(paris_decl,type,
paris: $i ).
thf(first_decl,type,
first: $i ).
thf(price_decl,type,
price: '$ki_world' > $i > $o ).
thf(dest_decl,type,
dest: '$ki_world' > $i > $o ).
thf(class_decl,type,
class: '$ki_world' > $i > $o ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( seventy @ ( A @ price ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( seventy @ ( A @ price ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( seventy @ ( A @ price ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( paris @ ( A @ dest ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',belief1) ).
thf(24,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( paris @ ( A @ dest ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(14,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ( ( second @ ( A @ class ) )
& ( first @ ( A @ class ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',law3) ).
thf(20,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ( ( second @ ( A @ class ) )
& ( first @ ( A @ class ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ( ( seventy @ ( A @ price ) )
& ( ninetyfive @ ( A @ price ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',law4) ).
thf(22,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ( ( seventy @ ( A @ price ) )
& ( ninetyfive @ ( A @ price ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ( ( second @ ( A @ class ) )
& ( paris @ ( A @ dest ) ) )
=> ( seventy @ ( A @ price ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',law2) ).
thf(18,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ( ( second @ ( A @ class ) )
& ( paris @ ( A @ dest ) ) )
=> ( seventy @ ( A @ price ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ( ( first @ ( A @ class ) )
& ( paris @ ( A @ dest ) ) )
=> ( ninetyfive @ ( A @ price ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',law1) ).
thf(16,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ( ( first @ ( A @ class ) )
& ( paris @ ( A @ dest ) ) )
=> ( ninetyfive @ ( A @ price ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( second @ ( A @ class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',belief2) ).
thf(26,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( second @ ( A @ class ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,plain,
$false,
inference(e,[status(thm)],[10,24,14,20,22,18,16,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP267_2 : TPTP v9.3.1. Released v8.2.0.
% 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
% 0.14/0.62 % Computer : n001.cluster.edu
% 0.14/0.62 % Model : x86_64 x86_64
% 0.14/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.62 % Memory : 8046.5625MB
% 0.14/0.62 % OS : Linux 6.8.0-71-generic
% 0.14/0.62 % CPULimit : 300
% 0.14/0.62 % WCLimit : 300
% 0.14/0.62 % DateTime : Sat Sep 26 01:57:13 UTC 2026
% 0.19/0.63 % CPUTime :
% 0.19/0.63 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
% 0.19/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.96/1.06 % [INFO] Parsing done (109ms).
% 0.96/1.06 % [INFO] Running in sequential loop mode.
% 1.47/1.35 % [INFO] eprover registered as external prover.
% 1.47/1.36 % [INFO] Scanning for conjecture ...
% 1.70/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 1.89/1.50 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.89/1.52 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.89/1.53 % [INFO] Type checking passed.
% 1.89/1.53 % [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 ...
% 3.10/2.04 % External prover 'e' found a proof!
% 3.10/2.04 % [INFO] Killing All external provers ...
% 3.10/2.04 % Time passed: 1322ms (effective reasoning time: 977ms)
% 3.10/2.04 % 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)>
% 3.10/2.05 % Axioms used in derivation (7): law1, law3, belief1, law4, law2, mrel_reflexive, belief2
% 3.10/2.05 % No. of inferences in proof: 18
% 3.10/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1322 ms resp. 977 ms w/o parsing
% 3.10/2.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.10/2.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------