%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n014.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 08:38:34 AM UTC 2026
% Result : Theorem 6.67s 3.21s
% Output : Refutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 48 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 160 ( 4 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 435 ( 23 ~; 2 |; 49 &; 300 @)
% ( 4 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 2 con; 0-3 aty)
% Number of variables : 85 ( 0 ^; 62 !; 23 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(antisymmetric_relstr_decl,type,
antisymmetric_relstr: $i > $o ).
thf(lower_bounded_relstr_decl,type,
lower_bounded_relstr: $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(ex_sup_of_relstr_set_decl,type,
ex_sup_of_relstr_set: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(ex_inf_of_relstr_set_decl,type,
ex_inf_of_relstr_set: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(finite_decl,type,
finite: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(relstr_set_smaller_decl,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(relstr_element_smaller_decl,type,
relstr_element_smaller: $i > $i > $i > $o ).
thf(related_decl,type,
related: $i > $i > $i > $o ).
thf(17,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ lower_bounded_relstr )
<=> ? [B: $i] :
( ( B @ ( A @ the_carrier @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_yellow_0) ).
thf(69,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ? [B: $i] :
( ( B @ ( A @ the_carrier @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( B @ element ) ) )
=> ( A @ lower_bounded_relstr ) )
& ( ( A @ lower_bounded_relstr )
=> ? [B: $i] :
( ( B @ ( A @ the_carrier @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(56,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ ex_inf_of_relstr_set ) )
& ( empty_set @ ( A @ ex_sup_of_relstr_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ ex_inf_of_relstr_set ) )
& ( empty_set @ ( A @ ex_sup_of_relstr_set ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ ! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ ex_inf_of_relstr_set ) )
& ( empty_set @ ( A @ ex_sup_of_relstr_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ in ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).
thf(74,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ in ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
=> ( C @ ( B @ ( A @ relstr_element_smaller ) ) ) )
& ( ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ in ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( B @ ( A @ ex_inf_of_relstr_set ) )
<=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_yellow_0) ).
thf(97,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) )
=> ( B @ ( A @ ex_inf_of_relstr_set ) ) )
& ( ( B @ ( A @ ex_inf_of_relstr_set ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_element_smaller ) ) )
=> ( C @ ( D @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_element_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(24,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(109,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(20,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(81,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(80,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( empty_set @ ( A @ relstr_element_smaller ) ) )
& ( B @ ( empty_set @ ( A @ relstr_set_smaller ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
thf(63,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( empty_set @ ( A @ relstr_element_smaller ) ) )
& ( B @ ( empty_set @ ( A @ relstr_set_smaller ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(67,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(40,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(58,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(36,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(83,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(60,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( B @ ( A @ ex_sup_of_relstr_set ) )
<=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow_0) ).
thf(85,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) )
=> ( B @ ( A @ ex_sup_of_relstr_set ) ) )
& ( ( B @ ( A @ ex_sup_of_relstr_set ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( D @ ( B @ ( A @ relstr_set_smaller ) ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) )
& ( C @ ( B @ ( A @ relstr_set_smaller ) ) )
& ( A @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(32,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(45,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(54,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(49,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(344,plain,
$false,
inference(e,[status(thm)],[69,56,25,52,74,38,97,109,81,80,63,67,43,40,58,36,83,60,85,32,45,54,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.13/0.40 % Computer : n014.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 09:18:47 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.84/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.19 % [INFO] Parsing done (211ms).
% 1.38/1.21 % [INFO] Running in sequential loop mode.
% 2.04/1.63 % [INFO] eprover registered as external prover.
% 2.04/1.63 % [INFO] Scanning for conjecture ...
% 2.22/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ...
% 2.39/1.81 % [INFO] Axiom selection finished. Selected 22 axioms (removed 4 axioms).
% 2.39/1.85 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.86 % [INFO] Type checking passed.
% 2.39/1.87 % [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 ...
% 6.67/3.21 % External prover 'e' found a proof!
% 6.67/3.21 % [INFO] Killing All external provers ...
% 6.67/3.21 % Time passed: 2666ms (effective reasoning time: 1993ms)
% 6.67/3.21 % 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)>
% 6.67/3.21 % Axioms used in derivation (22): t6_boole, t16_yellow_0, t6_yellow_0, dt_l1_orders_2, fc1_struct_0, existence_l1_struct_0, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, t1_subset, t7_boole, existence_l1_orders_2, rc3_struct_0, t15_yellow_0, existence_m1_subset_1, d4_yellow_0, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, t2_subset, d8_lattice3
% 6.67/3.21 % No. of inferences in proof: 48
% 6.67/3.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2666 ms resp. 1993 ms w/o parsing
% 6.67/3.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.67/3.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------