%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI022+1 : TPTP v9.3.1. Released v7.4.0.
% 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 08:19:33 AM UTC 2026
% Result : Theorem 4.26s 7.60s
% Output : Refutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 5 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 213 ( 11 ~; 6 |; 37 &; 123 @)
% ( 6 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 1 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 37 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(substance_decl,type,
substance: $i > $o ).
thf(exists_decl,type,
exists: $i > $o ).
thf(conceivedThru_decl,type,
conceivedThru: $i > $i > $o ).
thf(canBeConceivedAsNonExisting_decl,type,
canBeConceivedAsNonExisting: $i > $o ).
thf(essenceInvExistence_decl,type,
essenceInvExistence: $i > $o ).
thf(god_decl,type,
god: $i > $o ).
thf(being_decl,type,
being: $i > $o ).
thf(absolutelyInfinite_decl,type,
absolutelyInfinite: $i > $o ).
thf(selfCaused_decl,type,
selfCaused: $i > $o ).
thf(natureConcOnlyByExistence_decl,type,
natureConcOnlyByExistence: $i > $o ).
thf(inItself_decl,type,
inItself: $i > $o ).
thf(hasEssence_decl,type,
hasEssence: $i > $o ).
thf(mode_decl,type,
mode: $i > $o ).
thf(modification_decl,type,
modification: $i > $i > $o ).
thf(existsIn_decl,type,
existsIn: $i > $i > $o ).
thf(constInInfAttributes_decl,type,
constInInfAttributes: $i > $o ).
thf(attributeOf_decl,type,
attributeOf: $i > $i > $o ).
thf(expressesEternalEssentiality_decl,type,
expressesEternalEssentiality: $i > $o ).
thf(expressesInfiniteEssentiality_decl,type,
expressesInfiniteEssentiality: $i > $o ).
thf(conceivedThruItself_decl,type,
conceivedThruItself: $i > $o ).
thf(7,axiom,
! [A: $i] :
( ( A @ inItself )
=> ( A @ selfCaused ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',is_in_itself_is_self_caused) ).
thf(42,plain,
! [A: $i] :
( ( A @ inItself )
=> ( A @ selfCaused ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ exists )
<=> ( ( ( A != B )
& ( B @ ( A @ existsIn ) ) )
| ( A @ ( A @ existsIn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( ( ( ( A != B )
& ( B @ ( A @ existsIn ) ) )
| ( A @ ( A @ existsIn ) ) )
=> ( A @ exists ) )
& ( ( A @ exists )
=> ( ( ( A != B )
& ( B @ ( A @ existsIn ) ) )
| ( A @ ( A @ existsIn ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ god )
<=> ( ( A @ absolutelyInfinite )
& ( A @ being ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',god) ).
thf(28,plain,
! [A: $i] :
( ( ( ( A @ absolutelyInfinite )
& ( A @ being ) )
=> ( A @ god ) )
& ( ( A @ god )
=> ( ( A @ absolutelyInfinite )
& ( A @ being ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i] :
( ( ( A @ hasEssence )
& ( A @ essenceInvExistence ) )
=> ( A @ exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',essence_involves_existence_exists) ).
thf(73,plain,
! [A: $i] :
( ( ( A @ hasEssence )
& ( A @ essenceInvExistence ) )
=> ( A @ exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ being )
=> ( A @ hasEssence ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',being_has_essense) ).
thf(44,plain,
! [A: $i] :
( ( A @ being )
=> ( A @ hasEssence ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ substance )
<=> ( ( A @ conceivedThruItself )
& ( A @ inItself ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substance) ).
thf(86,plain,
! [A: $i] :
( ( ( ( A @ conceivedThruItself )
& ( A @ inItself ) )
=> ( A @ substance ) )
& ( ( A @ substance )
=> ( ( A @ conceivedThruItself )
& ( A @ inItself ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ selfCaused )
<=> ( ( A @ natureConcOnlyByExistence )
& ( A @ essenceInvExistence ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_caused) ).
thf(35,plain,
! [A: $i] :
( ( ( ( A @ natureConcOnlyByExistence )
& ( A @ essenceInvExistence ) )
=> ( A @ selfCaused ) )
& ( ( A @ selfCaused )
=> ( ( A @ natureConcOnlyByExistence )
& ( A @ essenceInvExistence ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ canBeConceivedAsNonExisting )
=> ~ ( A @ essenceInvExistence ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',can_be_conceived_as_non_existing) ).
thf(26,plain,
! [A: $i] :
( ( A @ canBeConceivedAsNonExisting )
=> ~ ( A @ essenceInvExistence ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ absolutelyInfinite )
<=> ( ( ( A @ ( B @ attributeOf ) )
=> ( ( B @ expressesInfiniteEssentiality )
& ( B @ expressesEternalEssentiality ) ) )
& ( A @ constInInfAttributes )
& ( A @ substance ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absolutely_infinite) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( ( ( ( A @ ( B @ attributeOf ) )
=> ( ( B @ expressesInfiniteEssentiality )
& ( B @ expressesEternalEssentiality ) ) )
& ( A @ constInInfAttributes )
& ( A @ substance ) )
=> ( A @ absolutelyInfinite ) )
& ( ( A @ absolutelyInfinite )
=> ( ( ( A @ ( B @ attributeOf ) )
=> ( ( B @ expressesInfiniteEssentiality )
& ( B @ expressesEternalEssentiality ) ) )
& ( A @ constInInfAttributes )
& ( A @ substance ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( A @ conceivedThru ) )
=> ( ( A != B )
& ( B @ ( A @ conceivedThru ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conceived_through) ).
thf(19,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( A @ conceivedThru ) )
=> ( ( A != B )
& ( B @ ( A @ conceivedThru ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ substance )
=> ( A @ exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',has_substance_exists) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ substance )
=> ( A @ exists ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i] :
( ( A @ substance )
=> ( A @ exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ mode )
<=> ( ( ( C @ ( A @ conceivedThru ) )
& ( C @ ( A @ existsIn ) ) )
| ( ( B @ substance )
& ( B @ ( A @ modification ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mode) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C @ ( A @ conceivedThru ) )
& ( C @ ( A @ existsIn ) ) )
| ( ( B @ substance )
& ( B @ ( A @ modification ) ) ) )
=> ( A @ mode ) )
& ( ( A @ mode )
=> ( ( ( C @ ( A @ conceivedThru ) )
& ( C @ ( A @ existsIn ) ) )
| ( ( B @ substance )
& ( B @ ( A @ modification ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ substance )
=> ( A @ being ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',has_substance_being) ).
thf(93,plain,
! [A: $i] :
( ( A @ substance )
=> ( A @ being ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(95,plain,
$false,
inference(e,[status(thm)],[42,61,28,73,44,86,35,26,75,19,15,46,93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI022+1 : TPTP v9.3.1. Released v7.4.0.
% 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
% 0.15/5.41 % Computer : n014.cluster.edu
% 0.15/5.41 % Model : x86_64 x86_64
% 0.15/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.41 % Memory : 8046.5625MB
% 0.15/5.41 % OS : Linux 6.8.0-71-generic
% 0.15/5.41 % CPULimit : 300
% 0.15/5.41 % WCLimit : 300
% 0.15/5.41 % DateTime : Sat Sep 26 04:40:09 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.42 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
% 0.18/6.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/6.22 % [INFO] Parsing done (222ms).
% 1.32/6.24 % [INFO] Running in sequential loop mode.
% 1.97/6.64 % [INFO] eprover registered as external prover.
% 1.97/6.65 % [INFO] Scanning for conjecture ...
% 2.17/6.74 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 2.32/6.80 % [INFO] Axiom selection finished. Selected 12 axioms (removed 9 axioms).
% 2.32/6.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.32/6.84 % [INFO] Type checking passed.
% 2.32/6.84 % [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 ...
% 3.99/7.59 % External prover 'e' found a proof!
% 3.99/7.59 % [INFO] Killing All external provers ...
% 3.99/7.60 % Time passed: 2034ms (effective reasoning time: 1349ms)
% 3.99/7.60 % 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)>
% 4.26/7.60 % Axioms used in derivation (12): substance, god, being_has_essense, conceived_through, can_be_conceived_as_non_existing, essence_involves_existence_exists, self_caused, exists, is_in_itself_is_self_caused, has_substance_being, absolutely_infinite, mode
% 4.26/7.60 % No. of inferences in proof: 28
% 4.26/7.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2034 ms resp. 1349 ms w/o parsing
% 4.26/7.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.26/7.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------