%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI015+1 : TPTP v9.3.1. Released v7.2.0.
% 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 : n016.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 08:19:32 AM UTC 2026
% Result : Theorem 4.12s 17.65s
% Output : Refutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 14 equ; 0 cnn)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 288 ( 9 ~; 4 |; 58 &; 178 @)
% ( 3 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 49 ( 0 ^; 36 !; 13 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(exemplifies_property_decl,type,
exemplifies_property: $i > $i > $o ).
thf(existence_decl,type,
existence: $i ).
thf(god_decl,type,
god: $i ).
thf(object_decl,type,
object: $i > $o ).
thf(property_decl,type,
property: $i > $o ).
thf(is_the_decl,type,
is_the: $i > $i > $o ).
thf(exemplifies_relation_decl,type,
exemplifies_relation: $i > $i > $i > $o ).
thf(greater_than_decl,type,
greater_than: $i ).
thf(none_greater_decl,type,
none_greater: $i ).
thf(conceivable_decl,type,
conceivable: $i ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ object )
& ( B @ property )
& ( A @ property ) )
=> ( ( ( C @ ( B @ exemplifies_property ) )
& ( A @ ( C @ is_the ) ) )
<=> ? [D: $i] :
( ( D @ ( B @ exemplifies_property ) )
& ! [E: $i] :
( ( E @ object )
=> ( ( E @ ( A @ exemplifies_property ) )
=> ( E = D ) ) )
& ( D @ ( A @ exemplifies_property ) )
& ( D @ object ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',description_axiom_schema_instance) ).
thf(24,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ object )
& ( B @ property )
& ( A @ property ) )
=> ( ( ? [D: $i] :
( ( D @ ( B @ exemplifies_property ) )
& ! [E: $i] :
( ( E @ object )
=> ( ( E @ ( A @ exemplifies_property ) )
=> ( E = D ) ) )
& ( D @ ( A @ exemplifies_property ) )
& ( D @ object ) )
=> ( ( C @ ( B @ exemplifies_property ) )
& ( A @ ( C @ is_the ) ) ) )
& ( ( ( C @ ( B @ exemplifies_property ) )
& ( A @ ( C @ is_the ) ) )
=> ? [D: $i] :
( ( D @ ( B @ exemplifies_property ) )
& ! [E: $i] :
( ( E @ object )
=> ( ( E @ ( A @ exemplifies_property ) )
=> ( E = D ) ) )
& ( D @ ( A @ exemplifies_property ) )
& ( D @ object ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ object )
=> ~ ( A @ property ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',objects_are_not_properties) ).
thf(14,plain,
! [A: $i] :
( ( A @ object )
=> ~ ( A @ property ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ is_the ) )
=> ( ( A @ object )
& ( B @ property ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',description_is_property_and_described_is_object) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ is_the ) )
=> ( ( A @ object )
& ( B @ property ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
god @ ( existence @ exemplifies_property ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',god_exists) ).
thf(2,negated_conjecture,
~ ( god @ ( existence @ exemplifies_property ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ( god @ ( existence @ exemplifies_property ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ object )
& ( B @ object )
& ( A @ property ) )
=> ( ( ( B = C )
& ( A @ ( B @ is_the ) ) )
<=> ? [D: $i] :
( ( D = C )
& ! [E: $i] :
( ( E @ object )
=> ( ( E @ ( A @ exemplifies_property ) )
=> ( E = D ) ) )
& ( D @ ( A @ exemplifies_property ) )
& ( D @ object ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',description_axiom_identity_instance) ).
thf(45,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ object )
& ( B @ object )
& ( A @ property ) )
=> ( ( ? [D: $i] :
( ( D = C )
& ! [E: $i] :
( ( E @ object )
=> ( ( E @ ( A @ exemplifies_property ) )
=> ( E = D ) ) )
& ( D @ ( A @ exemplifies_property ) )
& ( D @ object ) )
=> ( ( B = C )
& ( A @ ( B @ is_the ) ) ) )
& ( ( ( B = C )
& ( A @ ( B @ is_the ) ) )
=> ? [D: $i] :
( ( D = C )
& ! [E: $i] :
( ( E @ object )
=> ( ( E @ ( A @ exemplifies_property ) )
=> ( E = D ) ) )
& ( D @ ( A @ exemplifies_property ) )
& ( D @ object ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ object )
=> ( ( ~ ( A @ ( existence @ exemplifies_property ) )
& ( none_greater @ ( A @ is_the ) ) )
=> ? [B: $i] :
( ( B @ ( conceivable @ exemplifies_property ) )
& ( A @ ( B @ ( greater_than @ exemplifies_relation ) ) )
& ( B @ object ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_2) ).
thf(91,plain,
! [A: $i] :
( ( A @ object )
=> ( ( ~ ( A @ ( existence @ exemplifies_property ) )
& ( none_greater @ ( A @ is_the ) ) )
=> ? [B: $i] :
( ( B @ ( conceivable @ exemplifies_property ) )
& ( A @ ( B @ ( greater_than @ exemplifies_relation ) ) )
& ( B @ object ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ object )
=> ( ( A @ ( none_greater @ exemplifies_property ) )
<=> ( ~ ? [B: $i] :
( ( B @ ( conceivable @ exemplifies_property ) )
& ( A @ ( B @ ( greater_than @ exemplifies_relation ) ) )
& ( B @ object ) )
& ( A @ ( conceivable @ exemplifies_property ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_none_greater) ).
thf(80,plain,
! [A: $i] :
( ( A @ object )
=> ( ( ( ~ ? [B: $i] :
( ( B @ ( conceivable @ exemplifies_property ) )
& ( A @ ( B @ ( greater_than @ exemplifies_relation ) ) )
& ( B @ object ) )
& ( A @ ( conceivable @ exemplifies_property ) ) )
=> ( A @ ( none_greater @ exemplifies_property ) ) )
& ( ( A @ ( none_greater @ exemplifies_property ) )
=> ( ~ ? [B: $i] :
( ( B @ ( conceivable @ exemplifies_property ) )
& ( A @ ( B @ ( greater_than @ exemplifies_relation ) ) )
& ( B @ object ) )
& ( A @ ( conceivable @ exemplifies_property ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ exemplifies_property ) )
=> ( ( A @ object )
& ( B @ property ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplifier_is_object_and_exemplified_is_property) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ exemplifies_property ) )
=> ( ( A @ object )
& ( B @ property ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
? [A: $i] :
( ( A @ ( none_greater @ exemplifies_property ) )
& ( A @ object ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_1) ).
thf(87,plain,
? [A: $i] :
( ( A @ ( none_greater @ exemplifies_property ) )
& ( A @ object ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( B @ object )
& ( A @ object ) )
=> ( ( A = B )
| ( A @ ( B @ ( greater_than @ exemplifies_relation ) ) )
| ( B @ ( A @ ( greater_than @ exemplifies_relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_of_greater_than) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( ( B @ object )
& ( A @ object ) )
=> ( ( A = B )
| ( A @ ( B @ ( greater_than @ exemplifies_relation ) ) )
| ( B @ ( A @ ( greater_than @ exemplifies_relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
none_greater @ ( god @ is_the ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_god) ).
thf(96,plain,
none_greater @ ( god @ is_the ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(100,plain,
$false,
inference(e,[status(thm)],[24,14,20,13,45,91,80,16,87,77,96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI015+1 : TPTP v9.3.1. Released v7.2.0.
% 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
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.13/15.47 % CPULimit : 300
% 0.13/15.47 % WCLimit : 300
% 0.13/15.47 % DateTime : Sat Sep 26 04:44:45 UTC 2026
% 0.13/15.47 % CPUTime :
% 0.13/15.47 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
% 1.18/16.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/16.25 % [INFO] Parsing done (200ms).
% 1.44/16.27 % [INFO] Running in sequential loop mode.
% 2.04/16.66 % [INFO] eprover registered as external prover.
% 2.04/16.67 % [INFO] Scanning for conjecture ...
% 2.23/16.75 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.23/16.78 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.38/16.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/16.83 % [INFO] Type checking passed.
% 2.38/16.84 % [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 ...
% 4.12/17.64 % External prover 'e' found a proof!
% 4.12/17.64 % [INFO] Killing All external provers ...
% 4.12/17.64 % Time passed: 2034ms (effective reasoning time: 1371ms)
% 4.12/17.64 % 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)>
% 4.12/17.65 % Axioms used in derivation (10): premise_2, exemplifier_is_object_and_exemplified_is_property, connectedness_of_greater_than, definition_god, definition_none_greater, objects_are_not_properties, premise_1, description_is_property_and_described_is_object, description_axiom_identity_instance, description_axiom_schema_instance
% 4.12/17.65 % No. of inferences in proof: 24
% 4.12/17.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2034 ms resp. 1371 ms w/o parsing
% 4.45/17.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.45/17.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------