%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP222_4 : TPTP v9.3.1. Bugfixed v9.3.0.
% 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 : n011.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 07:36:54 AM UTC 2026
% Result : Theorem 21.21s 7.54s
% Output : Refutation 21.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 54
% Syntax : Number of formulae : 110 ( 91 unt; 0 typ; 0 def)
% Number of atoms : 199 ( 122 equ; 0 cnn)
% Maximal formula atoms : 24 ( 1 avg)
% Number of connectives : 400 ( 50 ~; 0 |; 13 &; 241 @)
% ( 8 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 2 con; 0-2 aty)
% Number of variables : 88 ( 0 ^; 65 !; 23 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(complex_type,type,
complex: $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(a_type,type,
a: $tType ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(dvd_decl,type,
dvd:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(plus_decl,type,
plus:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_0_decl,type,
semiring_0:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(order_bot_decl,type,
order_bot:
!>[TA: $tType] : $o ).
thf(order_top_decl,type,
order_top:
!>[TA: $tType] : $o ).
thf(wellorder_decl,type,
wellorder:
!>[TA: $tType] : $o ).
thf(comm_semiring_decl,type,
comm_semiring:
!>[TA: $tType] : $o ).
thf(zero_less_one_decl,type,
zero_less_one:
!>[TA: $tType] : $o ).
thf(semigroup_add_decl,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(semiring_numeral_decl,type,
semiring_numeral:
!>[TA: $tType] : $o ).
thf(complete_Inf_decl,type,
complete_Inf:
!>[TA: $tType] : $o ).
thf(complete_Sup_decl,type,
complete_Sup:
!>[TA: $tType] : $o ).
thf(semigroup_mult_decl,type,
semigroup_mult:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_decl,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(ordered_semiring_decl,type,
ordered_semiring:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(ordere2520102378445227354miring_decl,type,
ordere2520102378445227354miring:
!>[TA: $tType] : $o ).
thf(ordere6658533253407199908up_add_decl,type,
ordere6658533253407199908up_add:
!>[TA: $tType] : $o ).
thf(semiri3467727345109120633visors_decl,type,
semiri3467727345109120633visors:
!>[TA: $tType] : $o ).
thf(comple5582772986160207858norder_decl,type,
comple5582772986160207858norder:
!>[TA: $tType] : $o ).
thf(bounde4346867609351753570nf_top_decl,type,
bounde4346867609351753570nf_top:
!>[TA: $tType] : $o ).
thf(bounde4967611905675639751up_bot_decl,type,
bounde4967611905675639751up_bot:
!>[TA: $tType] : $o ).
thf(canoni5634975068530333245id_add_decl,type,
canoni5634975068530333245id_add:
!>[TA: $tType] : $o ).
thf(strict7427464778891057005id_add_decl,type,
strict7427464778891057005id_add:
!>[TA: $tType] : $o ).
thf(strict9044650504122735259up_add_decl,type,
strict9044650504122735259up_add:
!>[TA: $tType] : $o ).
thf(counta3822494911875563373attice_decl,type,
counta3822494911875563373attice:
!>[TA: $tType] : $o ).
thf(extended_enat2_decl,type,
extended_enat2: nat > extended_enat ).
thf(extend4730790105801354508finity_decl,type,
extend4730790105801354508finity:
!>[TA: $tType] : TA ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(vEBT_Leaf_decl,type,
vEBT_Leaf: $o > $o > vEBT_VEBT ).
thf(vEBT_VEBT_elim_dead_decl,type,
vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
thf(summarya_decl,type,
summarya: vEBT_VEBT ).
thf(35,axiom,
extended_enat @ comm_semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__0_470) ).
thf(247,plain,
extended_enat @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(41,axiom,
! [A: $o,B: $o,C: extended_enat] :
( ( C @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_VEBT_elim_dead ) )
= ( B @ ( A @ vEBT_Leaf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_VEBT__internal_Oelim__dead_Osimps_I1_J) ).
thf(257,plain,
! [A: $o,B: $o,C: extended_enat] :
( ( C @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_VEBT_elim_dead ) )
= ( B @ ( A @ vEBT_Leaf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( ( A @ extended_enat2 )
= ( B @ extended_enat2 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_enat_Oinject) ).
thf(125,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ extended_enat2 )
= ( B @ extended_enat2 ) ) )
& ( ( ( A @ extended_enat2 )
= ( B @ extended_enat2 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,axiom,
extended_enat @ order_bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder__bot_480) ).
thf(297,plain,
extended_enat @ order_bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(24,axiom,
extended_enat @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Power_Opower_494) ).
thf(229,plain,
extended_enat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,axiom,
extended_enat @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Omonoid__add_486) ).
thf(141,plain,
extended_enat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(40,axiom,
extended_enat @ complete_Sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_OSup_472) ).
thf(256,plain,
extended_enat @ complete_Sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(25,axiom,
extended_enat @ ab_semigroup_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_464) ).
thf(230,plain,
extended_enat @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(16,axiom,
extended_enat @ semiring_numeral,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_474) ).
thf(145,plain,
extended_enat @ semiring_numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
extended_enat @ counta3822494911875563373attice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Countable__Complete__Lattices_Ocountable__complete__lattice_449) ).
thf(143,plain,
extended_enat @ counta3822494911875563373attice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
extended_enat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ozero__neq__one_482) ).
thf(146,plain,
extended_enat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $o,B: $o,C: $o,D: $o] :
( ( ( B @ ( A @ vEBT_Leaf ) )
= ( D @ ( C @ vEBT_Leaf ) ) )
<=> ( ( B
<=> D )
& ( A
<=> C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_VEBT_Oinject_I2_J) ).
thf(69,plain,
! [A: $o,B: $o,C: $o,D: $o] :
( ( ( ( D
=> B )
& ( B
=> D )
& ( C
=> A )
& ( A
=> C ) )
=> ( ( B @ ( A @ vEBT_Leaf ) )
= ( D @ ( C @ vEBT_Leaf ) ) ) )
& ( ( ( B @ ( A @ vEBT_Leaf ) )
= ( D @ ( C @ vEBT_Leaf ) ) )
=> ( ( D
=> B )
& ( B
=> D )
& ( C
=> A )
& ( A
=> C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,axiom,
extended_enat @ bounde4346867609351753570nf_top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__inf__top_455) ).
thf(249,plain,
extended_enat @ bounde4346867609351753570nf_top,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1,conjecture,
( ( extended_enat @ extend4730790105801354508finity @ ( summarya @ vEBT_VEBT_elim_dead ) )
= summarya ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( extended_enat @ extend4730790105801354508finity @ ( summarya @ vEBT_VEBT_elim_dead ) )
!= summarya ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(56,plain,
( ( extended_enat @ extend4730790105801354508finity @ ( summarya @ vEBT_VEBT_elim_dead ) )
!= summarya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
extended_enat @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_466) ).
thf(142,plain,
extended_enat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: extended_enat,B: extended_enat,C: extended_enat] :
( ( ? [D: nat] :
( A
= ( D @ extended_enat2 ) )
=> ( ? [D: nat] :
( B
= ( D @ extended_enat2 ) )
=> ! [D: nat] :
( C
!= ( D @ extended_enat2 ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( D @ extended_enat2 ) )
=> ( ? [D: nat] :
( B
= ( D @ extended_enat2 ) )
=> ( C
!= ( extended_enat @ extend4730790105801354508finity ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( D @ extended_enat2 ) )
=> ( ( B
= ( extended_enat @ extend4730790105801354508finity ) )
=> ! [D: nat] :
( C
!= ( D @ extended_enat2 ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( D @ extended_enat2 ) )
=> ( ( B
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( C
!= ( extended_enat @ extend4730790105801354508finity ) ) ) )
=> ( ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( ? [D: nat] :
( B
= ( D @ extended_enat2 ) )
=> ! [D: nat] :
( C
!= ( D @ extended_enat2 ) ) ) )
=> ( ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( ? [D: nat] :
( B
= ( D @ extended_enat2 ) )
=> ( C
!= ( extended_enat @ extend4730790105801354508finity ) ) ) )
=> ( ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( ( B
= ( extended_enat @ extend4730790105801354508finity ) )
=> ! [D: nat] :
( C
!= ( D @ extended_enat2 ) ) ) )
=> ~ ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( ( B
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( C
!= ( extended_enat @ extend4730790105801354508finity ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_enat3__cases) ).
thf(147,plain,
! [A: extended_enat,B: extended_enat,C: extended_enat] :
( ( ? [D: nat] :
( A
= ( D @ extended_enat2 ) )
=> ( ? [D: nat] :
( B
= ( D @ extended_enat2 ) )
=> ! [D: nat] :
( C
!= ( D @ extended_enat2 ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( D @ extended_enat2 ) )
=> ( ? [D: nat] :
( B
= ( D @ extended_enat2 ) )
=> ( C
!= ( extended_enat @ extend4730790105801354508finity ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( D @ extended_enat2 ) )
=> ( ( B
= ( extended_enat @ extend4730790105801354508finity ) )
=> ! [D: nat] :
( C
!= ( D @ extended_enat2 ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( D @ extended_enat2 ) )
=> ( ( B
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( C
!= ( extended_enat @ extend4730790105801354508finity ) ) ) )
=> ( ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( ? [D: nat] :
( B
= ( D @ extended_enat2 ) )
=> ! [D: nat] :
( C
!= ( D @ extended_enat2 ) ) ) )
=> ( ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( ? [D: nat] :
( B
= ( D @ extended_enat2 ) )
=> ( C
!= ( extended_enat @ extend4730790105801354508finity ) ) ) )
=> ( ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( ( B
= ( extended_enat @ extend4730790105801354508finity ) )
=> ! [D: nat] :
( C
!= ( D @ extended_enat2 ) ) ) )
=> ~ ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( ( B
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( C
!= ( extended_enat @ extend4730790105801354508finity ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
extended_enat @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Omult__zero_490) ).
thf(280,plain,
extended_enat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_zero__reorient) ).
thf(61,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(51,axiom,
extended_enat @ semiri3467727345109120633visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring__no__zero__divisors_458) ).
thf(293,plain,
extended_enat @ semiri3467727345109120633visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(33,axiom,
extended_enat @ ordered_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Oordered__semiring_467) ).
thf(243,plain,
extended_enat @ ordered_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(21,axiom,
extended_enat @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring_492) ).
thf(206,plain,
extended_enat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(50,axiom,
extended_enat @ canoni5634975068530333245id_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_453) ).
thf(292,plain,
extended_enat @ canoni5634975068530333245id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(28,axiom,
( ( extended_enat @ extend4730790105801354508finity )
!= ( extended_enat @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_infinity__ne__i1) ).
thf(233,plain,
( ( extended_enat @ extend4730790105801354508finity )
!= ( extended_enat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(36,axiom,
extended_enat @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring__0_488) ).
thf(248,plain,
extended_enat @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
! [A: extended_enat] :
( ! [B: nat] :
( A
!= ( B @ extended_enat2 ) )
<=> ( A
= ( extended_enat @ extend4730790105801354508finity ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_not__enat__eq) ).
thf(270,plain,
! [A: extended_enat] :
( ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ! [B: nat] :
( A
!= ( B @ extended_enat2 ) ) )
& ( ! [B: nat] :
( A
!= ( B @ extended_enat2 ) )
=> ( A
= ( extended_enat @ extend4730790105801354508finity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(34,axiom,
( ( extended_enat @ extend4730790105801354508finity )
!= ( extended_enat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_infinity__ne__i0) ).
thf(244,plain,
( ( extended_enat @ extend4730790105801354508finity )
!= ( extended_enat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(20,axiom,
extended_enat @ complete_Inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_OInf_473) ).
thf(205,plain,
extended_enat @ complete_Inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(44,axiom,
extended_enat @ plus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oplus_497) ).
thf(279,plain,
extended_enat @ plus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(54,axiom,
extended_enat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_496) ).
thf(296,plain,
extended_enat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(49,axiom,
extended_enat @ semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_475) ).
thf(291,plain,
extended_enat @ semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(46,axiom,
extended_enat @ strict9044650504122735259up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_451) ).
thf(281,plain,
extended_enat @ strict9044650504122735259up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(19,axiom,
extended_enat @ bounded_lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Obounded__lattice_1) ).
thf(204,plain,
extended_enat @ bounded_lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
extended_enat @ dvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Odvd_499) ).
thf(144,plain,
extended_enat @ dvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [A: extended_enat] :
( ! [B: nat] :
( A
!= ( B @ extended_enat2 ) )
=> ( A
= ( extended_enat @ extend4730790105801354508finity ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_enat_Oexhaust) ).
thf(236,plain,
! [A: extended_enat] :
( ! [B: nat] :
( A
!= ( B @ extended_enat2 ) )
=> ( A
= ( extended_enat @ extend4730790105801354508finity ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(11,axiom,
extended_enat @ bounde4967611905675639751up_bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__sup__bot_454) ).
thf(140,plain,
extended_enat @ bounde4967611905675639751up_bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,axiom,
extended_enat @ ordere2520102378445227354miring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Oordered__comm__semiring_461) ).
thf(240,plain,
extended_enat @ ordere2520102378445227354miring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(43,axiom,
extended_enat @ order_top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder__top_479) ).
thf(278,plain,
extended_enat @ order_top,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(9,axiom,
! [A: nat] :
( ( extended_enat @ extend4730790105801354508finity )
!= ( A @ extended_enat2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_enat_Odistinct_I2_J) ).
thf(135,plain,
! [A: nat] :
( ( extended_enat @ extend4730790105801354508finity )
!= ( A @ extended_enat2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,axiom,
extended_enat @ wellorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Owellorder_478) ).
thf(241,plain,
extended_enat @ wellorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(53,axiom,
extended_enat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oone_498) ).
thf(295,plain,
extended_enat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(47,axiom,
! [A: extended_enat] :
( ( A
!= ( extended_enat @ extend4730790105801354508finity ) )
<=> ? [B: nat] :
( A
= ( B @ extended_enat2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_not__infinity__eq) ).
thf(282,plain,
! [A: extended_enat] :
( ( ? [B: nat] :
( A
= ( B @ extended_enat2 ) )
=> ( A
!= ( extended_enat @ extend4730790105801354508finity ) ) )
& ( ( A
!= ( extended_enat @ extend4730790105801354508finity ) )
=> ? [B: nat] :
( A
= ( B @ extended_enat2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [A: nat] :
( ( A @ extended_enat2 )
!= ( extended_enat @ extend4730790105801354508finity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_enat_Odistinct_I1_J) ).
thf(250,plain,
! [A: nat] :
( ( A @ extended_enat2 )
!= ( extended_enat @ extend4730790105801354508finity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(26,axiom,
extended_enat @ strict7427464778891057005id_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__comm__monoid__add_452) ).
thf(231,plain,
extended_enat @ strict7427464778891057005id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_one__reorient) ).
thf(114,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
extended_enat @ comm_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring_477) ).
thf(139,plain,
extended_enat @ comm_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ? [C: nat] :
( A
= ( C @ extended_enat2 ) )
=> ! [C: nat] :
( B
!= ( C @ extended_enat2 ) ) )
=> ( ( ? [C: nat] :
( A
= ( C @ extended_enat2 ) )
=> ( B
!= ( extended_enat @ extend4730790105801354508finity ) ) )
=> ( ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ! [C: nat] :
( B
!= ( C @ extended_enat2 ) ) )
=> ~ ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( B
!= ( extended_enat @ extend4730790105801354508finity ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_enat2__cases) ).
thf(207,plain,
! [A: extended_enat,B: extended_enat] :
( ( ? [C: nat] :
( A
= ( C @ extended_enat2 ) )
=> ! [C: nat] :
( B
!= ( C @ extended_enat2 ) ) )
=> ( ( ? [C: nat] :
( A
= ( C @ extended_enat2 ) )
=> ( B
!= ( extended_enat @ extend4730790105801354508finity ) ) )
=> ( ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ! [C: nat] :
( B
!= ( C @ extended_enat2 ) ) )
=> ~ ( ( A
= ( extended_enat @ extend4730790105801354508finity ) )
=> ( B
!= ( extended_enat @ extend4730790105801354508finity ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(48,axiom,
extended_enat @ semigroup_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_471) ).
thf(290,plain,
extended_enat @ semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(3,axiom,
( ( extended_enat @ zero_zero )
!= ( extended_enat @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_zero__one__enat__neq_I1_J) ).
thf(58,plain,
( ( extended_enat @ zero_zero )
!= ( extended_enat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
extended_enat @ comple5582772986160207858norder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__linorder) ).
thf(242,plain,
extended_enat @ comple5582772986160207858norder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(52,axiom,
extended_enat @ ordere6658533253407199908up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_459) ).
thf(294,plain,
extended_enat @ ordere6658533253407199908up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_zero__neq__one) ).
thf(122,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,axiom,
extended_enat @ zero_less_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ozero__less__one_476) ).
thf(232,plain,
extended_enat @ zero_less_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(39,axiom,
( ( extended_enat @ extend4730790105801354508finity @ ( summarya @ vEBT_VEBT_elim_dead ) )
= summarya ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C2_OIH_C_I2_J) ).
thf(254,plain,
( ( extended_enat @ extend4730790105801354508finity @ ( summarya @ vEBT_VEBT_elim_dead ) )
= summarya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(23,axiom,
( ( extended_enat @ top_top )
= ( extended_enat @ extend4730790105801354508finity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6249_top__enat__def) ).
thf(227,plain,
( ( extended_enat @ top_top )
= ( extended_enat @ extend4730790105801354508finity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(306,plain,
$false,
inference(e,[status(thm)],[247,257,125,297,229,141,256,230,145,143,146,69,249,56,142,147,280,61,293,243,206,292,233,248,270,244,205,279,296,291,281,204,144,236,140,240,278,135,241,295,282,250,231,114,139,207,290,58,242,294,122,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP222_4 : TPTP v9.3.1. Bugfixed v9.3.0.
% 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
% 0.15/0.46 % Computer : n011.cluster.edu
% 0.15/0.46 % Model : x86_64 x86_64
% 0.15/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.46 % Memory : 8046.5625MB
% 0.15/0.46 % OS : Linux 6.8.0-71-generic
% 0.15/0.46 % CPULimit : 300
% 0.15/0.46 % WCLimit : 300
% 0.15/0.46 % DateTime : Fri Sep 25 18:15:44 UTC 2026
% 0.07/0.46 % CPUTime :
% 0.07/0.46 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
% 1.01/1.06 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 8.76/3.25 % [INFO] Parsing done (2187ms).
% 8.76/3.27 % [INFO] Running in sequential loop mode.
% 9.54/3.64 % [INFO] eprover registered as external prover.
% 9.54/3.65 % [INFO] Scanning for conjecture ...
% 14.50/5.14 % [INFO] Found a conjecture (or negated_conjecture) and 10317 axioms. Running axiom selection ...
% 16.04/6.00 % [INFO] Axiom selection finished. Selected 53 axioms (removed 10264 axioms).
% 16.30/6.05 % [INFO] Problem is typed first-order (TPTP TFF).
% 16.30/6.06 % [INFO] Type checking passed.
% 16.30/6.07 % [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 ...
% 21.21/7.54 % External prover 'e' found a proof!
% 21.21/7.54 % [INFO] Killing All external provers ...
% 21.21/7.54 % Time passed: 6932ms (effective reasoning time: 4261ms)
% 21.21/7.54 % 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)>
% 21.21/7.54 % Axioms used in derivation (53): fact_652_zero__reorient, tcon_Extended__Nat_Oenat___Rings_Oordered__comm__semiring_461, tcon_Extended__Nat_Oenat___Countable__Complete__Lattices_Ocountable__complete__lattice_449, fact_12_enat2__cases, tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_453, tcon_Extended__Nat_Oenat___Groups_Oone_498, tcon_Extended__Nat_Oenat___Rings_Odvd_499, tcon_Extended__Nat_Oenat___Complete__Lattices_OInf_473, fact_15_enat_Oinject, tcon_Extended__Nat_Oenat___Rings_Ozero__neq__one_482, tcon_Extended__Nat_Oenat___Rings_Omult__zero_490, tcon_Extended__Nat_Oenat___Complete__Lattices_OSup_472, tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__sup__bot_454, tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring_477, tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_474, fact_9_enat_Odistinct_I2_J, tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__linorder, fact_151_VEBT_Oinject_I2_J, tcon_Extended__Nat_Oenat___Rings_Osemiring_492, fact_11_enat_Oexhaust, fact_326_one__reorient, fact_10_enat_Odistinct_I1_J, tcon_Extended__Nat_Oenat___Orderings_Oorder__bot_480, tcon_Extended__Nat_Oenat___Power_Opower_494, tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__0_470, fact_6249_top__enat__def, tcon_Extended__Nat_Oenat___Rings_Osemiring__0_488, fact_651_zero__one__enat__neq_I1_J, tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__comm__monoid__add_452, fact_742_zero__neq__one, tcon_Extended__Nat_Oenat___Rings_Ozero__less__one_476, fact_403_infinity__ne__i1, tcon_Extended__Nat_Oenat___Rings_Oordered__semiring_467, tcon_Extended__Nat_Oenat___Groups_Oplus_497, fact_13_enat3__cases, tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__inf__top_455, tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_466, fact_4_not__enat__eq, tcon_Extended__Nat_Oenat___Orderings_Oorder__top_479, tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_475, fact_768_infinity__ne__i0, tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_451, fact_1__C2_OIH_C_I2_J, tcon_Extended__Nat_Oenat___Orderings_Owellorder_478, fact_5_not__infinity__eq, tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_471, tcon_Extended__Nat_Oenat___Groups_Ozero_496, fact_217_VEBT__internal_Oelim__dead_Osimps_I1_J, tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_464, tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_459, tcon_Extended__Nat_Oenat___Groups_Omonoid__add_486, tcon_Extended__Nat_Oenat___Rings_Osemiring__no__zero__divisors_458, tcon_Extended__Nat_Oenat___Lattices_Obounded__lattice_1
% 21.21/7.54 % No. of inferences in proof: 110
% 21.21/7.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6932 ms resp. 4261 ms w/o parsing
% 21.93/7.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.93/7.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------