%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI012+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 : n007.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 3.16s 2.50s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 5 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 121 ( 5 ~; 4 |; 21 &; 75 @)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 9 !; 9 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(object_decl,type,
object: $i > $o ).
thf(exemplifies_property_decl,type,
exemplifies_property: $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(1,conjecture,
( ? [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(2,negated_conjecture,
~ ( ? [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(neg_conjecture,[status(cth)],[1]) ).
thf(5,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)],[2]) ).
thf(3,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(13,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)],[3]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',connectedness_of_greater_than) ).
thf(20,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)],[4]) ).
thf(23,plain,
$false,
inference(e,[status(thm)],[5,13,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI012+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
% 0.12/0.41 % Computer : n007.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sat Sep 26 04:37:39 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 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
% 0.93/1.29 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.55 % [INFO] Parsing done (255ms).
% 1.22/1.57 % [INFO] Running in sequential loop mode.
% 1.78/2.05 % [INFO] eprover registered as external prover.
% 1.78/2.06 % [INFO] Scanning for conjecture ...
% 1.78/2.11 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.78/2.12 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.78/2.13 % [INFO] Problem is first-order (TPTP FOF).
% 1.78/2.14 % [INFO] Type checking passed.
% 1.78/2.14 % [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 ...
% 2.84/2.50 % External prover 'e' found a proof!
% 3.16/2.50 % [INFO] Killing All external provers ...
% 3.16/2.50 % Time passed: 1840ms (effective reasoning time: 919ms)
% 3.16/2.50 % 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)>
% 3.16/2.50 % Axioms used in derivation (2): definition_none_greater, connectedness_of_greater_than
% 3.16/2.50 % No. of inferences in proof: 8
% 3.16/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1840 ms resp. 919 ms w/o parsing
% 3.16/2.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.16/2.54 % [INFO] Killing All external provers ...
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