%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI013+1 : TPTP v9.3.1. Released v7.2.0.
% 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 : n010.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 3.77s 13.23s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 4 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 208 ( 7 ~; 0 |; 34 &; 134 @)
% ( 1 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 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 : 35 ( 0 ^; 18 !; 17 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(exemplifies_property_decl,type,
exemplifies_property: $i > $i > $o ).
thf(existence_decl,type,
existence: $i ).
thf(god_decl,type,
god: $i ).
thf(property_decl,type,
property: $i > $o ).
thf(object_decl,type,
object: $i > $o ).
thf(is_the_decl,type,
is_the: $i > $i > $o ).
thf(none_greater_decl,type,
none_greater: $i ).
thf(conceivable_decl,type,
conceivable: $i ).
thf(exemplifies_relation_decl,type,
exemplifies_relation: $i > $i > $i > $o ).
thf(greater_than_decl,type,
greater_than: $i ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ is_the ) )
=> ( ( A @ object )
& ( B @ property ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',description_is_property_and_described_is_object) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ is_the ) )
=> ( ( A @ object )
& ( B @ property ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',definition_none_greater) ).
thf(28,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)],[6]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',premise_2) ).
thf(45,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)],[9]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ property )
=> ( ? [B: $i] :
( ( A @ ( B @ is_the ) )
& ( B @ object ) )
=> ! [B: $i] :
( ( B @ object )
=> ( ( A @ ( B @ is_the ) )
=> ( B @ ( A @ exemplifies_property ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',description_theorem_2) ).
thf(22,plain,
! [A: $i] :
( ( A @ property )
=> ( ? [B: $i] :
( ( A @ ( B @ is_the ) )
& ( B @ object ) )
=> ! [B: $i] :
( ( B @ object )
=> ( ( A @ ( B @ is_the ) )
=> ( B @ ( A @ exemplifies_property ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ property )
=> ( ? [B: $i] :
( ! [C: $i] :
( ( C @ object )
=> ( ( C @ ( A @ exemplifies_property ) )
=> ( C = B ) ) )
& ( B @ ( A @ exemplifies_property ) )
& ( B @ object ) )
=> ? [B: $i] :
( ( A @ ( B @ is_the ) )
& ( B @ object ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',description_theorem_1) ).
thf(12,plain,
! [A: $i] :
( ( A @ property )
=> ( ? [B: $i] :
( ! [C: $i] :
( ( C @ object )
=> ( ( C @ ( A @ exemplifies_property ) )
=> ( C = B ) ) )
& ( B @ ( A @ exemplifies_property ) )
& ( B @ object ) )
=> ? [B: $i] :
( ( A @ ( B @ is_the ) )
& ( B @ object ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
( ? [A: $i] :
( ( A @ ( none_greater @ exemplifies_property ) )
& ( A @ object ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( B @ object )
=> ( ( B @ ( none_greater @ exemplifies_property ) )
=> ( B = A ) ) )
& ( A @ ( none_greater @ exemplifies_property ) )
& ( A @ object ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_2) ).
thf(39,plain,
( ? [A: $i] :
( ( A @ ( none_greater @ exemplifies_property ) )
& ( A @ object ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( B @ object )
=> ( ( B @ ( none_greater @ exemplifies_property ) )
=> ( B = A ) ) )
& ( A @ ( none_greater @ exemplifies_property ) )
& ( A @ object ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
? [A: $i] :
( ( A @ ( none_greater @ exemplifies_property ) )
& ( A @ object ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_1) ).
thf(35,plain,
? [A: $i] :
( ( A @ ( none_greater @ exemplifies_property ) )
& ( A @ object ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
none_greater @ ( god @ is_the ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_god) ).
thf(50,plain,
none_greater @ ( god @ is_the ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
god @ ( existence @ exemplifies_property ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',god_exists) ).
thf(2,negated_conjecture,
~ ( god @ ( existence @ exemplifies_property ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ( god @ ( existence @ exemplifies_property ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(51,plain,
$false,
inference(e,[status(thm)],[24,28,45,22,12,39,35,50,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI013+1 : TPTP v9.3.1. Released v7.2.0.
% 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
% 0.13/10.93 % Computer : n010.cluster.edu
% 0.13/10.93 % Model : x86_64 x86_64
% 0.13/10.93 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.93 % Memory : 8046.5625MB
% 0.13/10.93 % OS : Linux 6.8.0-71-generic
% 0.13/10.93 % CPULimit : 300
% 0.13/10.93 % WCLimit : 300
% 0.13/10.93 % DateTime : Sat Sep 26 04:40:13 UTC 2026
% 0.13/10.94 % CPUTime :
% 0.13/10.94 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
% 0.93/11.52 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/11.72 % [INFO] Parsing done (198ms).
% 1.28/11.73 % [INFO] Running in sequential loop mode.
% 1.87/12.16 % [INFO] eprover registered as external prover.
% 1.87/12.17 % [INFO] Scanning for conjecture ...
% 2.07/12.28 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.17/12.33 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.17/12.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.17/12.39 % [INFO] Type checking passed.
% 2.17/12.40 % [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 ...
% 3.77/13.22 % External prover 'e' found a proof!
% 3.77/13.22 % [INFO] Killing All external provers ...
% 3.77/13.22 % Time passed: 2147ms (effective reasoning time: 1485ms)
% 3.77/13.22 % 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)>
% 3.77/13.22 % Axioms used in derivation (8): premise_2, description_theorem_2, definition_none_greater, premise_1, description_theorem_1, description_is_property_and_described_is_object, lemma_2, definition_god
% 3.77/13.22 % No. of inferences in proof: 20
% 3.77/13.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2147 ms resp. 1485 ms w/o parsing
% 3.94/13.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.94/13.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------