%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP226^4 : TPTP v9.3.1. Bugfixed v9.2.1.
% 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 : n010.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 14.63s 5.47s
% Output : Refutation 15.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 52
% Syntax : Number of formulae : 106 ( 94 unt; 0 typ; 0 def)
% Number of atoms : 142 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 222 ( 6 ~; 0 |; 0 &; 200 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 5 con; 0-3 aty)
% Number of variables : 56 ( 10 ^; 44 !; 2 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $tType ).
thf(code_natural_type,type,
code_natural: $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(literal_type,type,
literal: $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(size_decl,type,
size:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(semidom_decl,type,
semidom:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(no_top_decl,type,
no_top:
!>[TA: $tType] : $o ).
thf(semiring_0_decl,type,
semiring_0:
!>[TA: $tType] : $o ).
thf(order_bot_decl,type,
order_bot:
!>[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(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(comm_monoid_diff_decl,type,
comm_monoid_diff:
!>[TA: $tType] : $o ).
thf(semiring_1_cancel_decl,type,
semiring_1_cancel:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(ordered_semiring_0_decl,type,
ordered_semiring_0:
!>[TA: $tType] : $o ).
thf(linordered_semiring_decl,type,
linordered_semiring:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(ordere2520102378445227354miring_decl,type,
ordere2520102378445227354miring:
!>[TA: $tType] : $o ).
thf(topolo6943815403480290642id_add_decl,type,
topolo6943815403480290642id_add:
!>[TA: $tType] : $o ).
thf(cancel2418104881723323429up_add_decl,type,
cancel2418104881723323429up_add:
!>[TA: $tType] : $o ).
thf(topolo1898628316856586783d_mult_decl,type,
topolo1898628316856586783d_mult:
!>[TA: $tType] : $o ).
thf(semiri6843258321239162965malize_decl,type,
semiri6843258321239162965malize:
!>[TA: $tType] : $o ).
thf(semido2269285787275462019factor_decl,type,
semido2269285787275462019factor:
!>[TA: $tType] : $o ).
thf(topolo4211221413907600880p_mult_decl,type,
topolo4211221413907600880p_mult:
!>[TA: $tType] : $o ).
thf(semiri2026040879449505780visors_decl,type,
semiri2026040879449505780visors:
!>[TA: $tType] : $o ).
thf(topolo5987344860129210374id_add_decl,type,
topolo5987344860129210374id_add:
!>[TA: $tType] : $o ).
thf(topolo4987421752381908075d_mult_decl,type,
topolo4987421752381908075d_mult:
!>[TA: $tType] : $o ).
thf(ordere8940638589300402666id_add_decl,type,
ordere8940638589300402666id_add:
!>[TA: $tType] : $o ).
thf(strict7427464778891057005id_add_decl,type,
strict7427464778891057005id_add:
!>[TA: $tType] : $o ).
thf(linord2810124833399127020strict_decl,type,
linord2810124833399127020strict:
!>[TA: $tType] : $o ).
thf(ordere1170586879665033532d_diff_decl,type,
ordere1170586879665033532d_diff:
!>[TA: $tType] : $o ).
thf(strict9044650504122735259up_add_decl,type,
strict9044650504122735259up_add:
!>[TA: $tType] : $o ).
thf(semiri6575147826004484403cancel_decl,type,
semiri6575147826004484403cancel:
!>[TA: $tType] : $o ).
thf(normal6328177297339901930cative_decl,type,
normal6328177297339901930cative:
!>[TA: $tType] : $o ).
thf(semiri1453513574482234551roduct_decl,type,
semiri1453513574482234551roduct:
!>[TA: $tType] : $o ).
thf(condit1219197933456340205attice_decl,type,
condit1219197933456340205attice:
!>[TA: $tType] : $o ).
thf(ball_decl,type,
ball:
!>[TA: $tType] : ( ( set @ TA ) > ( TA > $o ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(vEBT_V8194947554948674370ptions_decl,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(vEBT_set_vebt_decl,type,
vEBT_set_vebt: vEBT_VEBT > ( set @ nat ) ).
thf(vEBT_VEBT_minNull_decl,type,
vEBT_VEBT_minNull: vEBT_VEBT > $o ).
thf(vEBT_VEBT_set_vebt_decl,type,
vEBT_VEBT_set_vebt: vEBT_VEBT > ( set @ nat ) ).
thf(vEBT_vebt_member_decl,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: vEBT_VEBT ).
thf(x_decl,type,
x: nat ).
thf(3,axiom,
! [A: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ A )
=> ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_not__min__Null__member) ).
thf(56,plain,
! [A: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ A )
=> ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,axiom,
ordered_semiring_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__semiring__0_60) ).
thf(93,plain,
ordered_semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
=> ( vEBT_vebt_member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_valid__member__both__member__options) ).
thf(70,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
=> ( vEBT_vebt_member @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(46,axiom,
topolo6943815403480290642id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Limits_Otopological__monoid__add_51) ).
thf(118,plain,
topolo6943815403480290642id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(12,axiom,
semiri6843258321239162965malize @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___GCD_Osemiring__gcd__mult__normalize_47) ).
thf(80,plain,
semiri6843258321239162965malize @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,axiom,
comm_monoid_diff @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(114,plain,
comm_monoid_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(24,axiom,
semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_80) ).
thf(94,plain,
semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(30,axiom,
normal6328177297339901930cative @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Onormalization__semidom__multiplicative_24) ).
thf(101,plain,
normal6328177297339901930cative @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(20,axiom,
semiri1453513574482234551roduct @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_19) ).
thf(88,plain,
semiri1453513574482234551roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(43,axiom,
ordere8940638589300402666id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_33) ).
thf(115,plain,
ordere8940638589300402666id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,axiom,
strict7427464778891057005id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_32) ).
thf(120,plain,
strict7427464778891057005id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(38,axiom,
semido2269285787275462019factor @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__divide__unit__factor_43) ).
thf(110,plain,
semido2269285787275462019factor @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(53,axiom,
zero_less_one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__less__one_81) ).
thf(125,plain,
zero_less_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(35,axiom,
( vEBT_set_vebt
= ( ^ [A: vEBT_VEBT] : ( collect @ nat @ ( vEBT_V8194947554948674370ptions @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3669_set__vebt__def) ).
thf(106,plain,
( vEBT_set_vebt
= ( ^ [A: vEBT_VEBT] : ( collect @ nat @ ( vEBT_V8194947554948674370ptions @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(49,axiom,
no_top @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top_92) ).
thf(121,plain,
no_top @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(16,axiom,
semiring_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__0_91) ).
thf(84,plain,
semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(61,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( vEBT_VEBT_minNull @ A )
=> ~ ( vEBT_vebt_member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_min__Null__member) ).
thf(89,plain,
! [A: vEBT_VEBT,B: nat] :
( ( vEBT_VEBT_minNull @ A )
=> ~ ( vEBT_vebt_member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(44,axiom,
cancel2418104881723323429up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_50) ).
thf(116,plain,
cancel2418104881723323429up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(45,axiom,
order_bot @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder__bot_83) ).
thf(117,plain,
order_bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(17,axiom,
semiri6575147826004484403cancel @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel_26) ).
thf(85,plain,
semiri6575147826004484403cancel @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(31,axiom,
linordered_semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semiring_59) ).
thf(102,plain,
linordered_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_69) ).
thf(92,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,axiom,
semiring_1_cancel @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1__cancel_66) ).
thf(97,plain,
semiring_1_cancel @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(37,axiom,
topolo5987344860129210374id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Limits_Otopological__comm__monoid__add_38) ).
thf(109,plain,
topolo5987344860129210374id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(52,axiom,
strict9044650504122735259up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_27) ).
thf(124,plain,
strict9044650504122735259up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(11,axiom,
! [TA: $tType] :
( ( ball @ TA )
= ( ^ [A: set @ TA,B: TA > $o] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5570_Ball__def__raw) ).
thf(77,plain,
! [TA: $tType] :
( ( ball @ TA )
= ( ^ [A: set @ TA,B: TA > $o] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(26,axiom,
topolo1898628316856586783d_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Limits_Otopological__monoid__mult_48) ).
thf(96,plain,
topolo1898628316856586783d_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(9,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_mem__Collect__eq) ).
thf(73,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
topolo4987421752381908075d_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Limits_Otopological__comm__monoid__mult_37) ).
thf(105,plain,
topolo4987421752381908075d_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1,conjecture,
( ( vEBT_vebt_member @ t @ x )
= ( member @ nat @ x @ ( vEBT_set_vebt @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
( ( vEBT_vebt_member @ t @ x )
!= ( member @ nat @ x @ ( vEBT_set_vebt @ t ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(54,plain,
( ( vEBT_vebt_member @ t @ x )
!= ( member @ nat @ x @ ( vEBT_set_vebt @ t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone_106) ).
thf(86,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(41,axiom,
vEBT_invar_vebt @ t @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(113,plain,
vEBT_invar_vebt @ t @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(13,axiom,
comm_semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring_82) ).
thf(81,plain,
comm_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
ordere2520102378445227354miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__comm__semiring_56) ).
thf(76,plain,
ordere2520102378445227354miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,axiom,
( vEBT_VEBT_set_vebt
= ( ^ [A: vEBT_VEBT] : ( collect @ nat @ ( vEBT_vebt_member @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3614_set__vebt_H__def) ).
thf(98,plain,
( vEBT_VEBT_set_vebt
= ( ^ [A: vEBT_VEBT] : ( collect @ nat @ ( vEBT_vebt_member @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(32,axiom,
semidom @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom_99) ).
thf(103,plain,
semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(7,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
= ( vEBT_vebt_member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_both__member__options__equiv__member) ).
thf(66,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
= ( vEBT_vebt_member @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
topolo4211221413907600880p_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Limits_Otopological__semigroup__mult_42) ).
thf(108,plain,
topolo4211221413907600880p_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(40,axiom,
ordere1170586879665033532d_diff @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff) ).
thf(112,plain,
ordere1170586879665033532d_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(51,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Omult__zero_96) ).
thf(123,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Collect__mem__eq) ).
thf(63,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
linord2810124833399127020strict @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict_31) ).
thf(95,plain,
linord2810124833399127020strict @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(19,axiom,
comm_semiring_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__0_75) ).
thf(87,plain,
comm_semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(33,axiom,
condit1219197933456340205attice @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_17) ).
thf(104,plain,
condit1219197933456340205attice @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(14,axiom,
size @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(82,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(47,axiom,
semigroup_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult_76) ).
thf(119,plain,
semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__cong) ).
thf(58,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(39,axiom,
ab_semigroup_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult_65) ).
thf(111,plain,
ab_semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(50,axiom,
semiri2026040879449505780visors @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_40) ).
thf(122,plain,
semiri2026040879449505780visors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(15,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_58) ).
thf(83,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
ordered_semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__semiring_70) ).
thf(100,plain,
ordered_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(126,plain,
$false,
inference(e,[status(thm)],[56,93,70,118,80,114,94,101,88,115,120,110,125,106,121,84,61,89,116,117,85,102,92,97,109,124,77,96,73,105,54,86,113,81,76,98,103,66,108,112,123,63,95,87,104,82,119,58,111,122,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP226^4 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.09 % 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
% 0.11/0.21 % Computer : n010.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 20:22:04 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 7.74/3.08 % [INFO] Parsing done (2288ms).
% 7.74/3.11 % [INFO] Running in sequential loop mode.
% 8.60/3.50 % [INFO] eprover registered as external prover.
% 8.60/3.51 % [INFO] Scanning for conjecture ...
% 10.81/4.20 % [INFO] Found a conjecture (or negated_conjecture) and 9010 axioms. Running axiom selection ...
% 11.89/4.56 % [INFO] Axiom selection finished. Selected 51 axioms (removed 8959 axioms).
% 11.89/4.59 % [INFO] Problem is higher-order (TPTP THF).
% 12.16/4.60 % [INFO] Type checking passed.
% 12.16/4.61 % [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 ...
% 14.63/5.47 % External prover 'e' found a proof!
% 14.63/5.47 % [INFO] Killing All external provers ...
% 14.63/5.47 % Time passed: 5122ms (effective reasoning time: 2354ms)
% 14.63/5.47 % 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)>
% 14.63/5.47 % Axioms used in derivation (51): tcon_Nat_Onat___Rings_Olinordered__semiring_59, tcon_Nat_Onat___Rings_Onormalization__semidom__multiplicative_24, tcon_Nat_Onat___Limits_Otopological__monoid__add_51, tcon_Nat_Onat___Groups_Osemigroup__add_80, tcon_Nat_Onat___Groups_Ocancel__semigroup__add_58, fact_12_not__min__Null__member, fact_5_valid__member__both__member__options, tcon_Nat_Onat___Groups_Oab__semigroup__add_69, tcon_Nat_Onat___Rings_Ocomm__semiring_82, tcon_Nat_Onat___Rings_Ocomm__semiring__0_75, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, tcon_Nat_Onat___Nat_Osize, fact_44_Collect__mem__eq, fact_3669_set__vebt__def, fact_0_min__Null__member, tcon_Nat_Onat___Rings_Osemiring__0_91, tcon_Nat_Onat___Rings_Oordered__comm__semiring_56, tcon_Nat_Onat___Rings_Osemiring__1__cancel_66, tcon_Nat_Onat___Limits_Otopological__monoid__mult_48, tcon_Nat_Onat___Limits_Otopological__semigroup__mult_42, fact_4_both__member__options__equiv__member, fact_43_mem__Collect__eq, tcon_Nat_Onat___Groups_Oab__semigroup__mult_65, fact_5570_Ball__def__raw, tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff, tcon_Nat_Onat___Rings_Oordered__semiring__0_60, tcon_Nat_Onat___Groups_Osemigroup__mult_76, tcon_Nat_Onat___Rings_Osemidom_99, tcon_Nat_Onat___Rings_Ozero__less__one_81, tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_19, tcon_Nat_Onat___Rings_Oordered__semiring_70, tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict_31, tcon_Nat_Onat___Rings_Osemidom__divide__unit__factor_43, tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_17, tcon_Nat_Onat___Rings_Omult__zero_96, tcon_fun___Orderings_Oorder__bot, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel_26, tcon_Nat_Onat___Limits_Otopological__comm__monoid__add_38, tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_33, tcon_Nat_Onat___Limits_Otopological__comm__monoid__mult_37, tcon_Nat_Onat___GCD_Osemiring__gcd__mult__normalize_47, tcon_Nat_Onat___Groups_Oone_106, tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_32, tcon_Nat_Onat___Orderings_Ono__top_92, tcon_Nat_Onat___Orderings_Oorder__bot_83, fact_45_Collect__cong, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_50, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_27, tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_40, conj_0, fact_3614_set__vebt_H__def
% 14.63/5.47 % No. of inferences in proof: 106
% 14.63/5.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5122 ms resp. 2354 ms w/o parsing
% 15.02/5.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.02/5.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------