%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NLP267^5 : TPTP v9.3.1. Released v8.1.0.
% 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 : n013.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 : Wed Sep 30 08:16:19 AM UTC 2026
% Result : Theorem 3.61s 2.11s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 25 ( 8 unt; 0 typ; 5 def)
% Number of atoms : 78 ( 5 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 134 ( 5 ~; 0 |; 7 &; 109 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 27 ( 11 ^; 16 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_decl,type,
mrel: mworld > mworld > $o ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mnot_decl,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mand_decl,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_decl,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mbox_decl,type,
mbox: ( mworld > $o ) > mworld > $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: $i > mworld > $o ).
thf(dest_decl,type,
dest: $i > mworld > $o ).
thf(class_decl,type,
class: $i > mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(8,axiom,
mlocal @ ( mbox @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law4) ).
thf(25,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ( ( price @ ninetyfive @ A )
& ( price @ seventy @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
mlocal @ ( mbox @ ( class @ second ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',belief2) ).
thf(29,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( class @ second @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law2) ).
thf(21,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ( ( dest @ paris @ A )
& ( class @ second @ A ) )
=> ( price @ seventy @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ C )
& ( mrel @ A @ B ) )
=> ( mrel @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(17,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ C )
& ( mrel @ A @ B ) )
=> ( mrel @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
mlocal @ ( mbox @ ( dest @ paris ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',belief1) ).
thf(27,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( dest @ paris @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
mlocal @ ( mbox @ ( price @ seventy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( price @ seventy @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
mlocal @ ( mbox @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law3) ).
thf(23,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ( ( class @ first @ A )
& ( class @ second @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law1) ).
thf(19,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ( ( dest @ paris @ A )
& ( class @ first @ A ) )
=> ( price @ ninetyfive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(15,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[25,29,21,17,27,11,23,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP267^5 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % 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
% 0.10/0.22 % Computer : n013.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 11:50:36 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.83/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/1.00 % [INFO] Parsing done (206ms).
% 1.15/1.02 % [INFO] Running in sequential loop mode.
% 2.02/1.42 % [INFO] eprover registered as external prover.
% 2.02/1.43 % [INFO] Scanning for conjecture ...
% 2.23/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.23/1.57 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.23/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.59 % [INFO] Type checking passed.
% 2.23/1.60 % [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 ...
% 3.61/2.11 % External prover 'e' found a proof!
% 3.61/2.11 % [INFO] Killing All external provers ...
% 3.61/2.11 % Time passed: 1751ms (effective reasoning time: 1083ms)
% 3.61/2.11 % 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)>
% 3.61/2.11 % Axioms used in derivation (8): law1, mrel_euclidean, law3, belief1, law4, law2, mrel_reflexive, belief2
% 3.61/2.11 % No. of inferences in proof: 20
% 3.61/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1751 ms resp. 1083 ms w/o parsing
% 3.61/2.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.61/2.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------