%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NLP267^17 : TPTP v9.3.1. Released v8.1.0.
% 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 : 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 : Wed Sep 30 08:16:18 AM UTC 2026
% Result : Theorem 4.61s 2.58s
% Output : Refutation 4.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 31 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 102 ( 5 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 218 ( 7 ~; 0 |; 12 &; 183 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 37 ( 12 ^; 25 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mindex_type,type,
mindex: $tType ).
thf(mrel_decl,type,
mrel: mindex > mworld > mworld > $o ).
thf('#b_u_decl',type,
'#b_u': mindex ).
thf('#b_s_decl',type,
'#b_s': mindex ).
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: mindex > ( 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: mindex,B: mworld > $o,C: mworld] :
! [D: mworld] :
( ( mrel @ A @ C @ D )
=> ( B @ D ) ) ) ) ).
thf(6,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#b_s' @ A @ C )
& ( mrel @ '#b_s' @ A @ B ) )
=> ( mrel @ '#b_s' @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#b_s_euclidean') ).
thf(24,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#b_s' @ A @ C )
& ( mrel @ '#b_s' @ A @ B ) )
=> ( mrel @ '#b_s' @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: mworld] :
( ( mrel @ '#b_s' @ mactual @ A )
=> ( price @ seventy @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#b_u' @ A @ C )
& ( mrel @ '#b_u' @ A @ B ) )
=> ( mrel @ '#b_u' @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#b_u_euclidean') ).
thf(20,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#b_u' @ A @ C )
& ( mrel @ '#b_u' @ A @ B ) )
=> ( mrel @ '#b_u' @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: mworld] : ( mrel @ '#b_s' @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#b_s_reflexive') ).
thf(22,plain,
! [A: mworld] : ( mrel @ '#b_s' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ '#b_u' @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#b_u_reflexive') ).
thf(18,plain,
! [A: mworld] : ( mrel @ '#b_u' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(26,plain,
! [A: mworld] :
( ( mrel @ '#b_s' @ mactual @ A )
=> ( ( ( dest @ paris @ A )
& ( class @ first @ A ) )
=> ( price @ ninetyfive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(28,plain,
! [A: mworld] :
( ( mrel @ '#b_s' @ mactual @ A )
=> ( ( ( dest @ paris @ A )
& ( class @ second @ A ) )
=> ( price @ seventy @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(38,plain,
! [A: mworld] :
( ( mrel @ '#b_s' @ mactual @ A )
=> ( ( dest @ paris @ A )
& ( class @ second @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_u) ).
thf(32,plain,
! [A: mworld] :
( ( mrel @ '#b_u' @ mactual @ A )
=> ~ ( ( class @ first @ A )
& ( class @ second @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4_s) ).
thf(34,plain,
! [A: mworld] :
( ( mrel @ '#b_s' @ mactual @ A )
=> ~ ( ( price @ seventy @ A )
& ( price @ ninetyfive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4_u) ).
thf(36,plain,
! [A: mworld] :
( ( mrel @ '#b_u' @ mactual @ A )
=> ~ ( ( price @ seventy @ A )
& ( price @ ninetyfive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_s) ).
thf(30,plain,
! [A: mworld] :
( ( mrel @ '#b_s' @ mactual @ A )
=> ~ ( ( class @ first @ A )
& ( class @ second @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[24,14,20,22,18,26,28,38,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NLP267^17 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.10/0.21 % Computer : n018.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 11:50:17 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.18/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.67/1.16 % [INFO] Parsing done (234ms).
% 1.67/1.18 % [INFO] Running in sequential loop mode.
% 2.61/1.61 % [INFO] eprover registered as external prover.
% 2.61/1.62 % [INFO] Scanning for conjecture ...
% 2.83/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.83/1.78 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 3.05/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 3.05/1.81 % [INFO] Type checking passed.
% 3.05/1.81 % [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 ...
% 4.61/2.58 % External prover 'e' found a proof!
% 4.61/2.58 % [INFO] Killing All external provers ...
% 4.61/2.58 % Time passed: 2182ms (effective reasoning time: 1395ms)
% 4.61/2.58 % 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)>
% 4.61/2.58 % Axioms used in derivation (11): axiom_3_s, mrel_#b_s_reflexive, mrel_#b_u_reflexive, axiom_2, axiom_4_u, axiom_1, axiom_4_s, mrel_#b_s_euclidean, axiom_5, mrel_#b_u_euclidean, axiom_3_u
% 4.61/2.58 % No. of inferences in proof: 26
% 4.61/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2182 ms resp. 1395 ms w/o parsing
% 4.93/2.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.93/2.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------