%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.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 08:08:44 AM UTC 2026
% Result : Theorem 3.95s 2.44s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 210 ( 4 ~; 5 |; 19 &; 149 @)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 56 !; 4 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(inclusion_comparable_decl,type,
inclusion_comparable: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(ordinal_subset_decl,type,
ordinal_subset: $i > $i > $o ).
thf(13,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(53,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( A @ ( A @ inclusion_comparable ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_xboole_0) ).
thf(41,plain,
! [A: $i] : ( A @ ( A @ inclusion_comparable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( A @ ( A @ ordinal_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( A @ ( A @ ordinal_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(39,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( B @ ( A @ inclusion_comparable ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_ordinal1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( B @ ( A @ inclusion_comparable ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( B @ ( A @ inclusion_comparable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ inclusion_comparable ) )
<=> ( ( A @ ( B @ subset ) )
| ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_xboole_0) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
| ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ inclusion_comparable ) ) )
& ( ( B @ ( A @ inclusion_comparable ) )
=> ( ( A @ ( B @ subset ) )
| ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( A @ ( B @ ordinal_subset ) )
| ( B @ ( A @ ordinal_subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( A @ ( B @ ordinal_subset ) )
| ( B @ ( A @ ordinal_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ inclusion_comparable ) )
=> ( A @ ( B @ inclusion_comparable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r3_xboole_0) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ inclusion_comparable ) )
=> ( A @ ( B @ inclusion_comparable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(37,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(57,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(29,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( B @ ( A @ ordinal_subset ) )
<=> ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( ( B @ ( A @ subset ) )
=> ( B @ ( A @ ordinal_subset ) ) )
& ( ( B @ ( A @ ordinal_subset ) )
=> ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(71,plain,
$false,
inference(e,[status(thm)],[53,41,64,27,39,18,43,23,51,62,37,25,57,29,67,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 02:38:54 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.20 % [INFO] Parsing done (213ms).
% 1.47/1.21 % [INFO] Running in sequential loop mode.
% 2.19/1.62 % [INFO] eprover registered as external prover.
% 2.19/1.63 % [INFO] Scanning for conjecture ...
% 2.37/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 36 axioms. Running axiom selection ...
% 2.37/1.79 % [INFO] Axiom selection finished. Selected 15 axioms (removed 21 axioms).
% 2.53/1.82 % [INFO] Problem is first-order (TPTP FOF).
% 2.53/1.83 % [INFO] Type checking passed.
% 2.53/1.83 % [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 ...
% 3.95/2.43 % External prover 'e' found a proof!
% 3.95/2.43 % [INFO] Killing All external provers ...
% 3.95/2.43 % Time passed: 1894ms (effective reasoning time: 1213ms)
% 3.95/2.43 % 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)>
% 3.95/2.43 % Axioms used in derivation (15): redefinition_r1_ordinal1, t1_subset, d9_xboole_0, reflexivity_r3_xboole_0, cc2_ordinal1, t4_subset, cc1_ordinal1, symmetry_r3_xboole_0, connectedness_r1_ordinal1, reflexivity_r1_tarski, reflexivity_r1_ordinal1, antisymmetry_r2_hidden, t3_subset, existence_m1_subset_1, rc1_ordinal1
% 3.95/2.43 % No. of inferences in proof: 34
% 3.95/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1894 ms resp. 1213 ms w/o parsing
% 3.95/2.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.95/2.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------