%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : 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 08:38:17 AM UTC 2026
% Result : Theorem 5.12s 3.18s
% Output : Refutation 5.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 0 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 114 ( 2 ~; 0 |; 21 &; 75 @)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 0 ^; 21 !; 2 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(well_ordering_decl,type,
well_ordering: $i > $o ).
thf(inclusion_relation_decl,type,
inclusion_relation: $i > $i ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(reflexive_decl,type,
reflexive: $i > $o ).
thf(transitive_decl,type,
transitive: $i > $o ).
thf(antisymmetric_decl,type,
antisymmetric: $i > $o ).
thf(connected_decl,type,
connected: $i > $o ).
thf(well_founded_relation_decl,type,
well_founded_relation: $i > $o ).
thf(10,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ connected ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
thf(42,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ connected ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ well_founded_relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_wellord2) ).
thf(46,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ well_founded_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ well_ordering ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_wellord2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ well_ordering ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i] :
( ( A @ ordinal )
=> ( A @ inclusion_relation @ well_ordering ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(17,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i] : ( A @ inclusion_relation @ antisymmetric ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).
thf(44,plain,
! [A: $i] : ( A @ inclusion_relation @ antisymmetric ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i] : ( A @ inclusion_relation @ relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(31,plain,
! [A: $i] : ( A @ inclusion_relation @ relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i] : ( A @ inclusion_relation @ reflexive ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
thf(38,plain,
! [A: $i] : ( A @ inclusion_relation @ reflexive ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(21,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(33,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] : ( A @ inclusion_relation @ transitive ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).
thf(40,plain,
! [A: $i] : ( A @ inclusion_relation @ transitive ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_ordering )
<=> ( ( A @ well_founded_relation )
& ( A @ connected )
& ( A @ antisymmetric )
& ( A @ transitive )
& ( A @ reflexive ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
thf(23,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ well_founded_relation )
& ( A @ connected )
& ( A @ antisymmetric )
& ( A @ transitive )
& ( A @ reflexive ) )
=> ( A @ well_ordering ) )
& ( ( A @ well_ordering )
=> ( ( A @ well_founded_relation )
& ( A @ connected )
& ( A @ antisymmetric )
& ( A @ transitive )
& ( A @ reflexive ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,plain,
$false,
inference(e,[status(thm)],[42,46,13,17,44,31,38,21,33,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.23/0.49 % Computer : n016.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 09:07:30 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 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
% 1.43/1.37 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.95/1.65 % [INFO] Parsing done (282ms).
% 1.95/1.68 % [INFO] Running in sequential loop mode.
% 2.91/2.28 % [INFO] eprover registered as external prover.
% 2.91/2.29 % [INFO] Scanning for conjecture ...
% 3.10/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 3.29/2.41 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 3.29/2.43 % [INFO] Problem is first-order (TPTP FOF).
% 3.29/2.44 % [INFO] Type checking passed.
% 3.29/2.45 % [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 ...
% 5.12/3.17 % External prover 'e' found a proof!
% 5.12/3.17 % [INFO] Killing All external provers ...
% 5.12/3.17 % Time passed: 2462ms (effective reasoning time: 1489ms)
% 5.12/3.17 % 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)>
% 5.12/3.18 % Axioms used in derivation (10): t4_wellord2, cc2_ordinal1, cc1_ordinal1, dt_k1_wellord2, t2_wellord2, rc1_ordinal1, d4_wellord1, t6_wellord2, t5_wellord2, t3_wellord2
% 5.12/3.18 % No. of inferences in proof: 24
% 5.12/3.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2462 ms resp. 1489 ms w/o parsing
% 5.23/3.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.23/3.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------