%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU299+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 : n004.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 08:38:22 AM UTC 2026
% Result : Theorem 8.68s 3.76s
% Output : Refutation 10.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 86 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 398 ( 42 equ; 0 cnn)
% Maximal formula atoms : 46 ( 4 avg)
% Number of connectives : 882 ( 65 ~; 0 |; 227 &; 505 @)
% ( 3 <=>; 82 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 3 con; 0-2 aty)
% Number of variables : 153 ( 0 ^; 98 !; 55 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(succ_decl,type,
succ: $i > $i ).
thf(omega_decl,type,
omega: $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(finite_decl,type,
finite: $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(natural_decl,type,
natural: $i > $o ).
thf(15,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(120,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(78,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(179,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(5,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(85,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [A: $i] :
( ( ( A @ ordinal )
& ( A @ empty ) )
=> ( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_arytm_3) ).
thf(165,plain,
! [A: $i] :
( ( ( A @ ordinal )
& ( A @ empty ) )
=> ( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(32,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(197,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(22,axiom,
! [A: $i] :
~ ( A @ succ @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(156,plain,
! [A: $i] :
~ ( A @ succ @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(17,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(129,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
thf(159,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(35,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(208,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ! [B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( D = E )
& ( E @ ordinal ) )
& ( B = D )
& ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( B = C ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( D = C )
& ( A @ succ @ ( D @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e18_27__finset_1__1) ).
thf(213,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ! [B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( D = E )
& ( E @ ordinal ) )
& ( B = D )
& ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( B = C ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( ? [D: $i] :
( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( D = C )
& ( A @ succ @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( ( omega @ ( E @ in ) )
=> ! [F: $i] :
( ( E @ powerset @ powerset @ ( F @ element ) )
=> ~ ( ! [G: $i] :
~ ( ! [H: $i] :
( ( ( H @ ( G @ subset ) )
& ( F @ ( H @ in ) ) )
=> ( H = G ) )
& ( F @ ( G @ in ) ) )
& ( F != empty_set ) ) ) )
& ( C = E )
& ( E @ ordinal ) )
& ( D = C )
& ( A @ succ @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(145,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(39,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(282,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(177,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(43,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(314,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(203,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(277,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(6,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(90,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i] :
( ( ( A @ natural )
& ( A @ ordinal ) )
=> ( ( A @ succ @ natural )
& ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_arytm_3) ).
thf(138,plain,
! [A: $i] :
( ( ( A @ natural )
& ( A @ ordinal ) )
=> ( ( A @ succ @ natural )
& ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(101,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,axiom,
? [A: $i] :
( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
thf(184,plain,
? [A: $i] :
( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(16,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(125,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(147,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(133,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(109,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(193,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(8,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(96,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(105,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(34,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(205,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(41,axiom,
( ~ ( omega @ empty )
& ( omega @ ordinal )
& ( omega @ epsilon_connected )
& ( omega @ epsilon_transitive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal2) ).
thf(298,plain,
( ~ ( omega @ empty )
& ( omega @ ordinal )
& ( omega @ epsilon_connected )
& ( omega @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(180,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(191,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ordinal )
=> ? [B: $i] :
! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( ? [D: $i] :
( ( ( omega @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ powerset @ powerset @ ( E @ element ) )
=> ~ ( ! [F: $i] :
~ ( ! [G: $i] :
( ( ( G @ ( F @ subset ) )
& ( E @ ( G @ in ) ) )
=> ( G = F ) )
& ( E @ ( F @ in ) ) )
& ( E != empty_set ) ) ) )
& ( C = D )
& ( D @ ordinal ) )
& ( A @ succ @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e18_27__finset_1__1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ordinal )
=> ? [B: $i] :
! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( ? [D: $i] :
( ( ( omega @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ powerset @ powerset @ ( E @ element ) )
=> ~ ( ! [F: $i] :
~ ( ! [G: $i] :
( ( ( G @ ( F @ subset ) )
& ( E @ ( G @ in ) ) )
=> ( G = F ) )
& ( E @ ( F @ in ) ) )
& ( E != empty_set ) ) ) )
& ( C = D )
& ( D @ ordinal ) )
& ( A @ succ @ ( C @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ ! [A: $i] :
( ( A @ ordinal )
=> ? [B: $i] :
! [C: $i] :
( ( ( ? [D: $i] :
( ( ( omega @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ powerset @ powerset @ ( E @ element ) )
=> ~ ( ! [F: $i] :
~ ( ! [G: $i] :
( ( ( G @ ( F @ subset ) )
& ( E @ ( G @ in ) ) )
=> ( G = F ) )
& ( E @ ( F @ in ) ) )
& ( E != empty_set ) ) ) )
& ( C = D )
& ( D @ ordinal ) )
& ( A @ succ @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( ? [D: $i] :
( ( ( omega @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ powerset @ powerset @ ( E @ element ) )
=> ~ ( ! [F: $i] :
~ ( ! [G: $i] :
( ( ( G @ ( F @ subset ) )
& ( E @ ( G @ in ) ) )
=> ( G = F ) )
& ( E @ ( F @ in ) ) )
& ( E != empty_set ) ) ) )
& ( C = D )
& ( D @ ordinal ) )
& ( A @ succ @ ( C @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(118,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(42,axiom,
( ( empty_set @ ordinal )
& ( empty_set @ epsilon_connected )
& ( empty_set @ epsilon_transitive )
& ( empty_set @ empty )
& ( empty_set @ one_to_one )
& ( empty_set @ function )
& ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(304,plain,
( ( empty_set @ ordinal )
& ( empty_set @ epsilon_connected )
& ( empty_set @ epsilon_transitive )
& ( empty_set @ empty )
& ( empty_set @ one_to_one )
& ( empty_set @ function )
& ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(13,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(114,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [A: $i] :
( ( omega @ ( A @ element ) )
=> ( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_arytm_3) ).
thf(171,plain,
! [A: $i] :
( ( omega @ ( A @ element ) )
=> ( ( A @ natural )
& ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_arytm_3) ).
thf(272,plain,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(82,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(107,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(294,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(94,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1006,plain,
$false,
inference(e,[status(thm)],[120,78,179,85,165,197,156,129,159,208,213,145,282,177,314,203,277,90,138,101,184,125,147,133,109,193,96,105,205,298,180,191,44,118,304,114,171,272,82,107,294,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU299+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.07/0.38 % Computer : n004.cluster.edu
% 0.07/0.38 % Model : x86_64 x86_64
% 0.07/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.38 % Memory : 8046.5625MB
% 0.07/0.38 % OS : Linux 6.8.0-71-generic
% 0.07/0.38 % CPULimit : 300
% 0.07/0.38 % WCLimit : 300
% 0.07/0.38 % DateTime : Sat Sep 26 09:07:51 UTC 2026
% 0.07/0.39 % CPUTime :
% 0.07/0.39 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
% 0.79/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/1.21 % [INFO] Parsing done (220ms).
% 1.15/1.22 % [INFO] Running in sequential loop mode.
% 2.02/1.61 % [INFO] eprover registered as external prover.
% 2.02/1.61 % [INFO] Scanning for conjecture ...
% 2.20/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 46 axioms. Running axiom selection ...
% 2.43/1.85 % [INFO] Axiom selection finished. Selected 41 axioms (removed 5 axioms).
% 2.68/1.91 % [INFO] Problem is first-order (TPTP FOF).
% 2.68/1.93 % [INFO] Type checking passed.
% 2.68/1.93 % [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 ...
% 8.68/3.76 % External prover 'e' found a proof!
% 8.68/3.76 % [INFO] Killing All external provers ...
% 8.68/3.76 % Time passed: 3233ms (effective reasoning time: 2529ms)
% 8.68/3.76 % 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)>
% 8.68/3.76 % Axioms used in derivation (41): cc2_finset_1, fc1_ordinal2, rc3_funct_1, cc1_relat_1, rc1_funct_1, cc2_ordinal1, cc1_arytm_3, rc4_funct_1, rc1_arytm_3, cc1_ordinal1, rc3_ordinal1, rc2_relat_1, s1_tarski__e18_27__finset_1__1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, cc2_arytm_3, fc4_relat_1, rc3_relat_1, rc2_subset_1, cc1_funct_1, fc1_subset_1, fc3_ordinal1, rc2_funct_1, rc1_subset_1, cc3_ordinal1, cc2_funct_1, rc1_ordinal1, rc1_relat_1, rc2_finset_1, reflexivity_r1_tarski, rc2_ordinal1, rc3_finset_1, rc1_finset_1, cc1_finset_1, fc2_arytm_3, rc1_xboole_0, fc12_relat_1, fc1_ordinal1, fc2_ordinal1, cc3_arytm_3
% 8.68/3.76 % No. of inferences in proof: 86
% 8.68/3.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3233 ms resp. 2529 ms w/o parsing
% 10.32/3.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.32/3.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------