%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP227^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% 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 : n002.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 : Wed Sep 30 08:07:17 AM UTC 2026
% Result : Theorem 12.53s 3.77s
% Output : Refutation 13.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 32
% Syntax : Number of formulae : 66 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 48 equ; 6 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 459 ( 38 ~; 10 |; 13 &; 302 @)
% ( 0 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 71 ( 70 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 148 ( 12 ^; 134 !; 2 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc3368934014287244435at_num_type,type,
produc3368934014287244435at_num: $tType ).
thf(produc4471711990508489141at_nat_type,type,
produc4471711990508489141at_nat: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(produc2963631642982155120at_num_type,type,
produc2963631642982155120at_num: $tType ).
thf(produc7248412053542808358at_nat_type,type,
produc7248412053542808358at_nat: $tType ).
thf(list_P7037539587688870467BT_nat_type,type,
list_P7037539587688870467BT_nat: $tType ).
thf(list_P4547456442757143711BT_int_type,type,
list_P4547456442757143711BT_int: $tType ).
thf(list_P5647936690300460905T_VEBT_type,type,
list_P5647936690300460905T_VEBT: $tType ).
thf(produc8243902056947475879T_VEBT_type,type,
produc8243902056947475879T_VEBT: $tType ).
thf(produc8923325533196201883nteger_type,type,
produc8923325533196201883nteger: $tType ).
thf(list_P3126845725202233233VEBT_o_type,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(list_P7495141550334521929T_VEBT_type,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(list_P8526636022914148096eger_o_type,type,
list_P8526636022914148096eger_o: $tType ).
thf(option4927543243414619207at_nat_type,type,
option4927543243414619207at_nat: $tType ).
thf(list_P3744719386663036955um_num_type,type,
list_P3744719386663036955um_num: $tType ).
thf(list_P6011104703257516679at_nat_type,type,
list_P6011104703257516679at_nat: $tType ).
thf(produc9072475918466114483BT_nat_type,type,
produc9072475918466114483BT_nat: $tType ).
thf(produc4894624898956917775BT_int_type,type,
produc4894624898956917775BT_int: $tType ).
thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $tType ).
thf(list_P7333126701944960589_nat_o_type,type,
list_P7333126701944960589_nat_o: $tType ).
thf(list_P6285523579766656935_o_nat_type,type,
list_P6285523579766656935_o_nat: $tType ).
thf(list_P3795440434834930179_o_int_type,type,
list_P3795440434834930179_o_int: $tType ).
thf(produc334124729049499915VEBT_o_type,type,
produc334124729049499915VEBT_o: $tType ).
thf(produc2504756804600209347T_VEBT_type,type,
produc2504756804600209347T_VEBT: $tType ).
thf(produc6271795597528267376eger_o_type,type,
produc6271795597528267376eger_o: $tType ).
thf(product_prod_num_num_type,type,
product_prod_num_num: $tType ).
thf(product_prod_nat_num_type,type,
product_prod_nat_num: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(list_P4002435161011370285od_o_o_type,type,
list_P4002435161011370285od_o_o: $tType ).
thf(list_VEBT_VEBT_type,type,
list_VEBT_VEBT: $tType ).
thf(set_list_nat_type,type,
set_list_nat: $tType ).
thf(product_prod_o_nat_type,type,
product_prod_o_nat: $tType ).
thf(product_prod_o_int_type,type,
product_prod_o_int: $tType ).
thf(list_Code_integer_type,type,
list_Code_integer: $tType ).
thf(set_VEBT_VEBT_type,type,
set_VEBT_VEBT: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_set_int_type,type,
set_set_int: $tType ).
thf(set_Code_integer_type,type,
set_Code_integer: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $tType ).
thf(set_Extended_enat_type,type,
set_Extended_enat: $tType ).
thf(list_complex_type,type,
list_complex: $tType ).
thf(product_prod_o_o_type,type,
product_prod_o_o: $tType ).
thf(set_complex_type,type,
set_complex: $tType ).
thf(filter_real_type,type,
filter_real: $tType ).
thf(option_num_type,type,
option_num: $tType ).
thf(filter_nat_type,type,
filter_nat: $tType ).
thf(set_char_type,type,
set_char: $tType ).
thf(list_real_type,type,
list_real: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(list_num_type,type,
list_num: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(list_int_type,type,
list_int: $tType ).
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $tType ).
thf(set_rat_type,type,
set_rat: $tType ).
thf(set_num_type,type,
set_num: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(set_int_type,type,
set_int: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(list_o_type,type,
list_o: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(set_o_type,type,
set_o: $tType ).
thf(char_type,type,
char: $tType ).
thf(real_type,type,
real: $tType ).
thf(rat_type,type,
rat: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ma_decl,type,
ma: nat ).
thf(mi_decl,type,
mi: nat ).
thf(xa_decl,type,
xa: nat ).
thf(13,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_le__antisym) ).
thf(101,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5343_linorder__linear) ).
thf(152,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1937_verit__comp__simplify1_I2_J) ).
thf(121,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(26,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_le__refl) ).
thf(141,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5260_order__class_Oorder__eq__iff) ).
thf(108,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5314_Orderings_Oorder__eq__iff) ).
thf(123,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5372_order__antisym__conv) ).
thf(67,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5108_dual__order_Orefl) ).
thf(119,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_Nat_Oex__has__greatest__nat) ).
thf(51,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5265_ord__eq__le__trans) ).
thf(136,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5275_order__antisym) ).
thf(42,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_nat__le__linear) ).
thf(37,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5285_order__trans) ).
thf(110,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5270_ord__le__eq__trans) ).
thf(125,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5299_dual__order_Oantisym) ).
thf(157,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_eq__imp__le) ).
thf(132,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(18,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_le__trans) ).
thf(116,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
~ ( ( xa = mi )
| ( xa = ma ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False) ).
thf(160,plain,
~ ( ( xa = mi )
| ( xa = ma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5367_linorder__le__cases) ).
thf(70,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
( ( xa != mi )
& ( xa != ma ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( xa != mi )
& ( xa != ma ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(34,plain,
~ ( ( xa != mi )
& ( xa != ma ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5304_dual__order_Otrans) ).
thf(45,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1932_verit__la__disequality) ).
thf(113,plain,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5280_order_Otrans) ).
thf(39,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5294_dual__order_Oeq__iff) ).
thf(130,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
ord_less_eq_nat @ mi @ ma,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__C5_Ohyps_C_I7_J) ).
thf(167,plain,
ord_less_eq_nat @ mi @ ma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5309_antisym) ).
thf(48,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5103_order__refl) ).
thf(150,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ( ord_less_eq_nat @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5251_nle__le) ).
thf(154,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ( ord_less_eq_nat @ B @ A )
& ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(11,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5255_le__cases3) ).
thf(72,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5289_linorder__wlog) ).
thf(143,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(12,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_bounded__Max__nat) ).
thf(87,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5339_order__eq__refl) ).
thf(104,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(168,plain,
$false,
inference(e,[status(thm)],[101,152,121,141,108,123,67,119,51,136,42,37,110,125,157,132,116,160,70,34,45,113,39,130,167,48,150,154,72,143,87,104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP227^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% 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
% 0.09/0.21 % Computer : n002.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 20:24:07 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.84/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 5.85/2.14 % [INFO] Parsing done (1346ms).
% 6.22/2.15 % [INFO] Running in sequential loop mode.
% 6.61/2.32 % [INFO] eprover registered as external prover.
% 6.61/2.33 % [INFO] Scanning for conjecture ...
% 8.22/2.79 % [INFO] Found a conjecture (or negated_conjecture) and 10254 axioms. Running axiom selection ...
% 8.97/2.99 % [INFO] Axiom selection finished. Selected 31 axioms (removed 10223 axioms).
% 9.53/3.03 % [INFO] Problem is higher-order (TPTP THF).
% 9.53/3.04 % [INFO] Type checking passed.
% 9.53/3.04 % [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 ...
% 12.53/3.76 % External prover 'e' found a proof!
% 12.53/3.76 % [INFO] Killing All external provers ...
% 12.53/3.76 % Time passed: 3409ms (effective reasoning time: 1614ms)
% 12.53/3.77 % 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)>
% 12.53/3.77 % Axioms used in derivation (31): fact_5294_dual__order_Oeq__iff, fact_5255_le__cases3, fact_5367_linorder__le__cases, fact_5251_nle__le, fact_5265_ord__eq__le__trans, fact_5299_dual__order_Oantisym, fact_1932_verit__la__disequality, fact_437_le__refl, fact_5275_order__antisym, fact_5260_order__class_Oorder__eq__iff, fact_5280_order_Otrans, fact_5343_linorder__linear, fact_5285_order__trans, fact_1937_verit__comp__simplify1_I2_J, fact_5372_order__antisym__conv, fact_5304_dual__order_Otrans, fact_5108_dual__order_Orefl, fact_442_Nat_Oex__has__greatest__nat, fact_1__C5_Ohyps_C_I7_J, fact_978_bounded__Max__nat, fact_5103_order__refl, fact_440_le__antisym, fact_441_nat__le__linear, fact_438_le__trans, fact_5270_ord__le__eq__trans, fact_5339_order__eq__refl, fact_5289_linorder__wlog, fact_5314_Orderings_Oorder__eq__iff, fact_439_eq__imp__le, fact_0_False, fact_5309_antisym
% 12.53/3.77 % No. of inferences in proof: 66
% 12.53/3.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3409 ms resp. 1614 ms w/o parsing
% 13.05/3.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.05/3.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------