%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU261+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 : n015.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 08:38:14 AM UTC 2026
% Result : Theorem 4.04s 2.40s
% Output : Refutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 0 equ; 0 cnn)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 153 ( 2 ~; 0 |; 31 &; 85 @)
% ( 1 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% Number of variables : 19 ( 0 ^; 17 !; 2 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(well_ordering_decl,type,
well_ordering: $i > $o ).
thf(relation_isomorphism_decl,type,
relation_isomorphism: $i > $i > $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(1,conjecture,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
& ( A @ well_ordering ) )
=> ( B @ well_ordering ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_wellord1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
& ( A @ well_ordering ) )
=> ( B @ well_ordering ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
& ( A @ well_ordering ) )
=> ( B @ well_ordering ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,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(15,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)],[3]) ).
thf(4,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(23,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( ( ( A @ well_founded_relation )
=> ( B @ well_founded_relation ) )
& ( ( A @ antisymmetric )
=> ( B @ antisymmetric ) )
& ( ( A @ connected )
=> ( B @ connected ) )
& ( ( A @ transitive )
=> ( B @ transitive ) )
& ( ( A @ reflexive )
=> ( B @ reflexive ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_wellord1) ).
thf(27,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( ( ( A @ well_founded_relation )
=> ( B @ well_founded_relation ) )
& ( ( A @ antisymmetric )
=> ( B @ antisymmetric ) )
& ( ( A @ connected )
=> ( B @ connected ) )
& ( ( A @ transitive )
=> ( B @ transitive ) )
& ( ( A @ reflexive )
=> ( B @ reflexive ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,plain,
$false,
inference(e,[status(thm)],[6,15,23,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU261+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.17/0.41 % Computer : n015.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Sat Sep 26 09:03:59 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 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
% 0.90/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.19 % [INFO] Parsing done (184ms).
% 1.43/1.20 % [INFO] Running in sequential loop mode.
% 2.05/1.60 % [INFO] eprover registered as external prover.
% 2.05/1.61 % [INFO] Scanning for conjecture ...
% 2.25/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.25/1.74 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.25/1.76 % [INFO] Problem is first-order (TPTP FOF).
% 2.25/1.77 % [INFO] Type checking passed.
% 2.25/1.77 % [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 ...
% 3.69/2.39 % External prover 'e' found a proof!
% 3.69/2.40 % [INFO] Killing All external provers ...
% 3.69/2.40 % Time passed: 1828ms (effective reasoning time: 1188ms)
% 3.69/2.40 % 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)>
% 4.04/2.40 % Axioms used in derivation (3): d4_wellord1, rc1_funct_1, t53_wellord1
% 4.04/2.40 % No. of inferences in proof: 10
% 4.04/2.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1828 ms resp. 1188 ms w/o parsing
% 4.04/2.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.04/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------