TSTP Solution File: ITP222_2 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP222_2 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:49:03 EDT 2024
% Result : Theorem 14.33s 5.15s
% Output : Refutation 14.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 108
% Syntax : Number of formulae : 163 ( 90 unt; 55 typ; 0 def)
% Number of atoms : 196 ( 119 equ; 0 cnn)
% Maximal formula atoms : 24 ( 1 avg)
% Number of connectives : 367 ( 50 ~; 0 |; 5 &; 229 @)
% ( 5 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 2 con; 0-2 aty)
% Number of variables : 119 ( 0 ^ 57 !; 23 ?; 119 :)
% ( 39 !>; 0 ?*; 0 @-; 0 @+)
% 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(bool_type,type,
bool: $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(bounded_lattice_type,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(dvd_type,type,
dvd:
!>[TA: $tType] : $o ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(plus_type,type,
plus:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(power_type,type,
power:
!>[TA: $tType] : $o ).
thf(semiring_type,type,
semiring:
!>[TA: $tType] : $o ).
thf(mult_zero_type,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_0_type,type,
semiring_0:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(order_bot_type,type,
order_bot:
!>[TA: $tType] : $o ).
thf(order_top_type,type,
order_top:
!>[TA: $tType] : $o ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : $o ).
thf(comm_semiring_type,type,
comm_semiring:
!>[TA: $tType] : $o ).
thf(zero_less_one_type,type,
zero_less_one:
!>[TA: $tType] : $o ).
thf(semigroup_add_type,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(semiring_numeral_type,type,
semiring_numeral:
!>[TA: $tType] : $o ).
thf(complete_Inf_type,type,
complete_Inf:
!>[TA: $tType] : $o ).
thf(complete_Sup_type,type,
complete_Sup:
!>[TA: $tType] : $o ).
thf(semigroup_mult_type,type,
semigroup_mult:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_type,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(ordered_semiring_type,type,
ordered_semiring:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(ordere2520102378445227354miring_type,type,
ordere2520102378445227354miring:
!>[TA: $tType] : $o ).
thf(ordere6658533253407199908up_add_type,type,
ordere6658533253407199908up_add:
!>[TA: $tType] : $o ).
thf(semiri3467727345109120633visors_type,type,
semiri3467727345109120633visors:
!>[TA: $tType] : $o ).
thf(comple5582772986160207858norder_type,type,
comple5582772986160207858norder:
!>[TA: $tType] : $o ).
thf(bounde4346867609351753570nf_top_type,type,
bounde4346867609351753570nf_top:
!>[TA: $tType] : $o ).
thf(bounde4967611905675639751up_bot_type,type,
bounde4967611905675639751up_bot:
!>[TA: $tType] : $o ).
thf(canoni5634975068530333245id_add_type,type,
canoni5634975068530333245id_add:
!>[TA: $tType] : $o ).
thf(strict7427464778891057005id_add_type,type,
strict7427464778891057005id_add:
!>[TA: $tType] : $o ).
thf(strict9044650504122735259up_add_type,type,
strict9044650504122735259up_add:
!>[TA: $tType] : $o ).
thf(counta3822494911875563373attice_type,type,
counta3822494911875563373attice:
!>[TA: $tType] : $o ).
thf(extended_enat2_type,type,
extended_enat2: nat > extended_enat ).
thf(extend4730790105801354508finity_type,type,
extend4730790105801354508finity:
!>[TA: $tType] : TA ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(vEBT_Leaf_type,type,
vEBT_Leaf: bool > bool > vEBT_VEBT ).
thf(vEBT_VEBT_elim_dead_type,type,
vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
thf(summarya_type,type,
summarya: vEBT_VEBT ).
thf(44,axiom,
strict9044650504122735259up_add @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_451) ).
thf(217,plain,
strict9044650504122735259up_add @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(43,axiom,
mult_zero @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Omult__zero_490) ).
thf(216,plain,
mult_zero @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(31,axiom,
wellorder @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Owellorder_478) ).
thf(192,plain,
wellorder @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
bounded_lattice @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Obounded__lattice_1) ).
thf(156,plain,
bounded_lattice @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(39,axiom,
( ( vEBT_VEBT_elim_dead @ summarya @ ( extend4730790105801354508finity @ extended_enat ) )
= summarya ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C2_OIH_C_I2_J) ).
thf(205,plain,
( ( vEBT_VEBT_elim_dead @ summarya @ ( extend4730790105801354508finity @ extended_enat ) )
= summarya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(24,axiom,
power @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Power_Opower_494) ).
thf(180,plain,
power @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(30,axiom,
ordere2520102378445227354miring @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Oordered__comm__semiring_461) ).
thf(191,plain,
ordere2520102378445227354miring @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(47,axiom,
semigroup_add @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_475) ).
thf(226,plain,
semigroup_add @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(33,axiom,
ordered_semiring @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Oordered__semiring_467) ).
thf(194,plain,
ordered_semiring @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
semiring_numeral @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_474) ).
thf(95,plain,
semiring_numeral @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(27,axiom,
zero_less_one @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ozero__less__one_476) ).
thf(183,plain,
zero_less_one @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(28,axiom,
( ( extend4730790105801354508finity @ extended_enat )
!= ( one_one @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_infinity__ne__i1) ).
thf(184,plain,
( ( extend4730790105801354508finity @ extended_enat )
!= ( one_one @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
complete_Inf @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_OInf_473) ).
thf(157,plain,
complete_Inf @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
counta3822494911875563373attice @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Countable__Complete__Lattices_Ocountable__complete__lattice_449) ).
thf(93,plain,
counta3822494911875563373attice @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(49,axiom,
semiri3467727345109120633visors @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring__no__zero__divisors_458) ).
thf(228,plain,
semiri3467727345109120633visors @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(3,axiom,
( ( zero_zero @ extended_enat )
!= ( one_one @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_zero__one__enat__neq_I1_J) ).
thf(57,plain,
( ( zero_zero @ extended_enat )
!= ( one_one @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
comm_semiring @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring_477) ).
thf(89,plain,
comm_semiring @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_zero__neq__one) ).
thf(74,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(54,axiom,
order_bot @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder__bot_480) ).
thf(233,plain,
order_bot @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(4,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_zero__reorient) ).
thf(60,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: nat] :
( ( extend4730790105801354508finity @ extended_enat )
!= ( extended_enat2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_enat_Odistinct_I2_J) ).
thf(85,plain,
! [A: nat] :
( ( extend4730790105801354508finity @ extended_enat )
!= ( extended_enat2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,axiom,
! [A: nat] :
( ( extended_enat2 @ A )
!= ( extend4730790105801354508finity @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_enat_Odistinct_I1_J) ).
thf(201,plain,
! [A: nat] :
( ( extended_enat2 @ A )
!= ( extend4730790105801354508finity @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(12,axiom,
ab_semigroup_add @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_466) ).
thf(92,plain,
ab_semigroup_add @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(50,axiom,
ordere6658533253407199908up_add @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_459) ).
thf(229,plain,
ordere6658533253407199908up_add @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(17,axiom,
! [A: bool,B: bool,C: extended_enat] :
( ( vEBT_VEBT_elim_dead @ ( vEBT_Leaf @ A @ B ) @ C )
= ( vEBT_Leaf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_VEBT__internal_Oelim__dead_Osimps_I1_J) ).
thf(97,plain,
! [A: bool,B: bool,C: extended_enat] :
( ( vEBT_VEBT_elim_dead @ ( vEBT_Leaf @ A @ B ) @ C )
= ( vEBT_Leaf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(46,axiom,
semigroup_mult @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_471) ).
thf(225,plain,
semigroup_mult @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_enat_Oinject) ).
thf(77,plain,
! [A: nat,B: nat] :
( ( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,axiom,
comple5582772986160207858norder @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__linorder) ).
thf(193,plain,
comple5582772986160207858norder @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(16,axiom,
zero_neq_one @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ozero__neq__one_482) ).
thf(96,plain,
zero_neq_one @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,axiom,
ab_semigroup_mult @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_464) ).
thf(181,plain,
ab_semigroup_mult @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(22,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ? [C: nat] :
( A
= ( extended_enat2 @ C ) )
=> ! [C: nat] :
( B
!= ( extended_enat2 @ C ) ) )
=> ( ( ? [C: nat] :
( A
= ( extended_enat2 @ C ) )
=> ( B
!= ( extend4730790105801354508finity @ extended_enat ) ) )
=> ( ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ! [C: nat] :
( B
!= ( extended_enat2 @ C ) ) )
=> ~ ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( B
!= ( extend4730790105801354508finity @ extended_enat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_enat2__cases) ).
thf(159,plain,
! [A: extended_enat,B: extended_enat] :
( ( ? [C: nat] :
( A
= ( extended_enat2 @ C ) )
=> ! [C: nat] :
( B
!= ( extended_enat2 @ C ) ) )
=> ( ( ? [C: nat] :
( A
= ( extended_enat2 @ C ) )
=> ( B
!= ( extend4730790105801354508finity @ extended_enat ) ) )
=> ( ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ! [C: nat] :
( B
!= ( extended_enat2 @ C ) ) )
=> ~ ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( B
!= ( extend4730790105801354508finity @ extended_enat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(29,axiom,
! [A: extended_enat] :
( ! [B: nat] :
( A
!= ( extended_enat2 @ B ) )
=> ( A
= ( extend4730790105801354508finity @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_enat_Oexhaust) ).
thf(187,plain,
! [A: extended_enat] :
( ! [B: nat] :
( A
!= ( extended_enat2 @ B ) )
=> ( A
= ( extend4730790105801354508finity @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(51,axiom,
one @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oone_498) ).
thf(230,plain,
one @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(11,axiom,
monoid_add @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Omonoid__add_486) ).
thf(91,plain,
monoid_add @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,axiom,
comm_semiring_0 @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__0_470) ).
thf(198,plain,
comm_semiring_0 @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(5,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_one__reorient) ).
thf(67,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,axiom,
semiring_0 @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring__0_488) ).
thf(199,plain,
semiring_0 @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(26,axiom,
strict7427464778891057005id_add @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__comm__monoid__add_452) ).
thf(182,plain,
strict7427464778891057005id_add @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(52,axiom,
zero @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_496) ).
thf(231,plain,
zero @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(45,axiom,
! [A: extended_enat] :
( ( A
!= ( extend4730790105801354508finity @ extended_enat ) )
<=> ? [B: nat] :
( A
= ( extended_enat2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_not__infinity__eq) ).
thf(218,plain,
! [A: extended_enat] :
( ( ( A
!= ( extend4730790105801354508finity @ extended_enat ) )
=> ? [B: nat] :
( A
= ( extended_enat2 @ B ) ) )
& ( ? [B: nat] :
( A
= ( extended_enat2 @ B ) )
=> ( A
!= ( extend4730790105801354508finity @ extended_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(21,axiom,
semiring @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring_492) ).
thf(158,plain,
semiring @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1,conjecture,
( ( vEBT_VEBT_elim_dead @ summarya @ ( extend4730790105801354508finity @ extended_enat ) )
= summarya ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( vEBT_VEBT_elim_dead @ summarya @ ( extend4730790105801354508finity @ extended_enat ) )
!= summarya ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(55,plain,
( ( vEBT_VEBT_elim_dead @ summarya @ ( extend4730790105801354508finity @ extended_enat ) )
!= summarya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(40,axiom,
! [A: extended_enat] :
( ! [B: nat] :
( A
!= ( extended_enat2 @ B ) )
<=> ( A
= ( extend4730790105801354508finity @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_not__enat__eq) ).
thf(207,plain,
! [A: extended_enat] :
( ( ! [B: nat] :
( A
!= ( extended_enat2 @ B ) )
=> ( A
= ( extend4730790105801354508finity @ extended_enat ) ) )
& ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ! [B: nat] :
( A
!= ( extended_enat2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(41,axiom,
order_top @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder__top_479) ).
thf(214,plain,
order_top @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(34,axiom,
( ( extend4730790105801354508finity @ extended_enat )
!= ( zero_zero @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_infinity__ne__i0) ).
thf(195,plain,
( ( extend4730790105801354508finity @ extended_enat )
!= ( zero_zero @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(14,axiom,
dvd @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Odvd_499) ).
thf(94,plain,
dvd @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(37,axiom,
bounde4346867609351753570nf_top @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__inf__top_455) ).
thf(200,plain,
bounde4346867609351753570nf_top @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(23,axiom,
( ( top_top @ extended_enat )
= ( extend4730790105801354508finity @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6249_top__enat__def) ).
thf(178,plain,
( ( top_top @ extended_enat )
= ( extend4730790105801354508finity @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
bounde4967611905675639751up_bot @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Obounded__semilattice__sup__bot_454) ).
thf(90,plain,
bounde4967611905675639751up_bot @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,axiom,
canoni5634975068530333245id_add @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_453) ).
thf(227,plain,
canoni5634975068530333245id_add @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(42,axiom,
plus @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oplus_497) ).
thf(215,plain,
plus @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(53,axiom,
complete_Sup @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Complete__Lattices_OSup_472) ).
thf(232,plain,
complete_Sup @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(18,axiom,
! [A: extended_enat,B: extended_enat,C: extended_enat] :
( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ( C
!= ( extend4730790105801354508finity @ extended_enat ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ( B
= ( extend4730790105801354508finity @ extended_enat ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ( B
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( C
!= ( extend4730790105801354508finity @ extended_enat ) ) ) )
=> ( ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ( C
!= ( extend4730790105801354508finity @ extended_enat ) ) ) )
=> ( ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( ( B
= ( extend4730790105801354508finity @ extended_enat ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ~ ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( ( B
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( C
!= ( extend4730790105801354508finity @ extended_enat ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_enat3__cases) ).
thf(100,plain,
! [A: extended_enat,B: extended_enat,C: extended_enat] :
( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ( C
!= ( extend4730790105801354508finity @ extended_enat ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ( B
= ( extend4730790105801354508finity @ extended_enat ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ? [D: nat] :
( A
= ( extended_enat2 @ D ) )
=> ( ( B
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( C
!= ( extend4730790105801354508finity @ extended_enat ) ) ) )
=> ( ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ( ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( ? [D: nat] :
( B
= ( extended_enat2 @ D ) )
=> ( C
!= ( extend4730790105801354508finity @ extended_enat ) ) ) )
=> ( ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( ( B
= ( extend4730790105801354508finity @ extended_enat ) )
=> ! [D: nat] :
( C
!= ( extended_enat2 @ D ) ) ) )
=> ~ ( ( A
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( ( B
= ( extend4730790105801354508finity @ extended_enat ) )
=> ( C
!= ( extend4730790105801354508finity @ extended_enat ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(234,plain,
$false,
inference(cvc4,[status(thm)],[217,216,192,156,205,180,191,226,194,95,183,184,157,93,228,57,89,74,233,60,85,201,92,229,97,225,77,193,96,181,159,187,230,91,198,67,199,182,231,218,158,55,207,214,195,94,200,178,90,227,215,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ITP222_2 : TPTP v8.1.2. Released v8.0.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n004.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 14:26:09 EDT 2024
% 0.17/0.37 % CPUTime :
% 1.04/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 5.38/2.51 % [INFO] Parsing done (1484ms).
% 5.38/2.52 % [INFO] Running in sequential loop mode.
% 5.98/2.82 % [INFO] eprover registered as external prover.
% 5.98/2.82 % [INFO] cvc4 registered as external prover.
% 5.98/2.82 % [INFO] Scanning for conjecture ...
% 9.32/3.81 % [INFO] Found a conjecture and 10361 axioms. Running axiom selection ...
% 10.52/4.25 % [INFO] Axiom selection finished. Selected 52 axioms (removed 10309 axioms).
% 10.52/4.28 % [INFO] Problem is typed first-order (TPTP TFF).
% 10.52/4.29 % [INFO] Type checking passed.
% 10.52/4.29 % [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 ...
% 14.33/5.15 % External prover 'cvc4' found a proof!
% 14.33/5.15 % [INFO] Killing All external provers ...
% 14.33/5.15 % Time passed: 4600ms (effective reasoning time: 2618ms)
% 14.33/5.15 % 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)>
% 14.33/5.15 % Axioms used in derivation (52): tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__linorder, 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___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
% 14.33/5.15 % No. of inferences in proof: 108
% 14.33/5.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4600 ms resp. 2618 ms w/o parsing
% 14.33/5.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.33/5.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------