TSTP Solution File: DAT144^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT144^1 : TPTP v8.1.2. Released v7.0.0.
% 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 07:39:35 EDT 2024
% Result : Theorem 32.16s 22.05s
% Output : Refutation 32.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 111
% Syntax : Number of formulae : 205 ( 85 unt; 19 typ; 0 def)
% Number of atoms : 514 ( 144 equ; 16 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1819 ( 22 ~; 0 |; 42 &;1536 @)
% ( 0 <=>; 219 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 505 ( 505 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 6 con; 0-6 aty)
% Number of variables : 862 ( 66 ^ 762 !; 18 ?; 862 :)
% ( 16 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(real_type,type,
real: $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(bNF_pred_DEADID_type,type,
bNF_pred_DEADID:
!>[TA: $tType] : ( TA > $o ) ).
thf(bNF_Grp_type,type,
bNF_Grp:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > TB > TA > $o ) ).
thf(bNF_eq_onp_type,type,
bNF_eq_onp:
!>[TA: $tType] : ( ( TA > $o ) > TA > TA > $o ) ).
thf(neg_type,type,
neg:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > ( TB > TA > $o ) > $o ) ).
thf(pos_type,type,
pos:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > ( TB > TA > $o ) > $o ) ).
thf(quotient_type,type,
quotient:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TB > TA ) > ( TA > TB ) > ( TB > TA > $o ) > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(domainp_type,type,
domainp:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > TB > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: a > $o ).
thf(x_type,type,
x: a ).
thf(86,axiom,
p @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(340,plain,
p @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TA > $o,F: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( ! [G: TB] :
( ( A @ G @ G )
=> ( E @ ( B @ G ) ) )
=> ( E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Quotient__abs__induct) ).
thf(157,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TA > $o,F: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( ! [G: TB] :
( ( A @ G @ G )
=> ( E @ ( B @ G ) ) )
=> ( E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( neg @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA > TB > $o] : ( pos @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_NEG__POS) ).
thf(129,plain,
! [TA: $tType,TB: $tType] :
( ( neg @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA > TB > $o] : ( pos @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(17,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_subset__refl) ).
thf(134,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(37,axiom,
! [TA: $tType,A: TA] :
( ( bNF_pred_DEADID @ TA @ A )
=> ( bNF_pred_DEADID @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_DEADID_Opred__mono__strong) ).
thf(194,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(77,axiom,
! [TA: $tType,A: TA > TA > $o] :
( ! [B: TA] : ( A @ B @ B )
=> ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_refl__ge__eq) ).
thf(314,plain,
! [TA: $tType,A: TA > TA > $o] :
( ! [B: TA] : ( A @ B @ B )
=> ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(5,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_subset__trans) ).
thf(101,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(89,axiom,
! [TA: $tType] :
( ( (=) @ TA )
= ( bNF_eq_onp @ TA @ ( bNF_pred_DEADID @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_DEADID_Orel__eq__onp) ).
thf(347,plain,
! [TA: $tType] :
( ( (=) @ TA )
= ( bNF_eq_onp @ TA @ ( bNF_pred_DEADID @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A = B )
=> ( ( bNF_pred_DEADID @ TA @ A )
= ( bNF_pred_DEADID @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_DEADID_Opred__cong__simp) ).
thf(217,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A = B )
=> ( ( bNF_pred_DEADID @ TA @ A )
= ( bNF_pred_DEADID @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( TA > TB > $o ) @ ( bNF_Grp @ TA @ TB @ A @ C ) @ ( bNF_Grp @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Grp__mono) ).
thf(120,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( TA > TB > $o ) @ ( bNF_Grp @ TA @ TB @ A @ C ) @ ( bNF_Grp @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TB] :
( ( ( A @ B )
= C )
=> ( ( member @ TB @ B @ D )
=> ( bNF_Grp @ TB @ TA @ D @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_GrpI) ).
thf(269,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TB] :
( ( ( A @ B )
= C )
=> ( ( member @ TB @ B @ D )
=> ( bNF_Grp @ TB @ TA @ D @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(39,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] :
( ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A )
=> ( A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ge__eq__refl) ).
thf(202,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] :
( ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A )
=> ( A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(29,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_top__conj_I2_J) ).
thf(174,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TA,F: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( ( A @ ( C @ E ) @ ( C @ F ) )
= ( E = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Quotient__rel__rep) ).
thf(320,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TA,F: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( ( A @ ( C @ E ) @ ( C @ F ) )
= ( E = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TA > $o] :
( ( domainp @ TA @ TB @ A @ B )
=> ( ! [D: TA,E: TB] :
( ( A @ D @ E )
=> ( C @ D ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Domainp_Oinducts) ).
thf(284,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TA > $o] :
( ( domainp @ TA @ TB @ A @ B )
=> ( ! [D: TA,E: TB] :
( ( A @ D @ E )
=> ( C @ D ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( ( B @ ( C @ E ) )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Quotient__abs__rep) ).
thf(228,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( ( B @ ( C @ E ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(31,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_contra__subsetD) ).
thf(179,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,axiom,
! [TA: $tType] :
( ( bNF_pred_DEADID @ TA )
= ( ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_DEADID_Opred__True) ).
thf(253,plain,
! [TA: $tType] :
( ( bNF_pred_DEADID @ TA )
= ( ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(7,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_set__eq__subset) ).
thf(106,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( ( B @ E )
= ( B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Quotient__rel__abs) ).
thf(221,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( ( B @ E )
= ( B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o,C: TA > TB > $o] :
( ( pos @ TA @ TB @ A @ B )
=> ( ( pos @ TA @ TB @ B @ C )
=> ( pos @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_POS__trans) ).
thf(132,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o,C: TA > TB > $o] :
( ( pos @ TA @ TB @ A @ B )
=> ( ( pos @ TA @ TB @ B @ C )
=> ( pos @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(57,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_top1I) ).
thf(265,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( domainp @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Domainp_ODomainI) ).
thf(312,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( domainp @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(10,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_equalityD2) ).
thf(116,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_predicate2D) ).
thf(243,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB] :
( ( domainp @ TB @ TA @ A @ B )
=> ~ ! [C: TA] :
~ ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Domainp_Ocases) ).
thf(307,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB] :
( ( domainp @ TB @ TA @ A @ B )
=> ~ ! [C: TA] :
~ ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType] :
( ( quotient @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ! [E: TA,F: TB] :
( ( D @ E @ F )
=> ( ( B @ E )
= F ) )
& ! [E: TB] : ( D @ ( C @ E ) @ E )
& ! [E: TA,F: TA] :
( ( A @ E @ F )
= ( ? [G: TB] :
( ( D @ E @ G )
& ( D @ F @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Quotient__alt__def3) ).
thf(292,plain,
! [TA: $tType,TB: $tType] :
( ( quotient @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ! [E: TA,F: TB] :
( ( D @ E @ F )
=> ( ( B @ E )
= F ) )
& ! [E: TB] : ( D @ ( C @ E ) @ E )
& ! [E: TA,F: TA] :
( ( A @ E @ F )
= ( ? [G: TB] :
( ( D @ E @ G )
& ( D @ F @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(52,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_UNIV__witness) ).
thf(248,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType] :
( ( quotient @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ! [E: TA,F: TB] :
( ( D @ E @ F )
=> ( ( B @ E )
= F ) )
& ! [E: TB] : ( D @ ( C @ E ) @ E )
& ! [E: TA,F: TA] :
( ( A @ E @ F )
= ( ( D @ E @ ( B @ F ) )
& ( D @ F @ ( B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Quotient__alt__def2) ).
thf(302,plain,
! [TA: $tType,TB: $tType] :
( ( quotient @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ! [E: TA,F: TB] :
( ( D @ E @ F )
=> ( ( B @ E )
= F ) )
& ! [E: TB] : ( D @ ( C @ E ) @ E )
& ! [E: TA,F: TA] :
( ( A @ E @ F )
= ( ( D @ E @ ( B @ F ) )
& ( D @ F @ ( B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( A @ ( C @ ( B @ E ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Quotient__rep__abs) ).
thf(260,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( A @ ( C @ ( B @ E ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TB,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ ( C @ E ) @ F )
=> ( E
= ( B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Quotient__rel__abs2) ).
thf(160,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TB,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ ( C @ E ) @ F )
=> ( E
= ( B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61,axiom,
! [TA: $tType] :
( ( bNF_pred_DEADID @ TA )
= ( ^ [A: TA] : ( A = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_DEADID_Opred__rel) ).
thf(275,plain,
! [TA: $tType] :
( ( bNF_pred_DEADID @ TA )
= ( ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o] :
( ( quotient @ TB @ TA @ ( bNF_eq_onp @ TB @ A ) @ B @ C @ D )
=> ( A @ ( C @ ( undefined @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_type__definition__Quotient__not__empty__witness) ).
thf(361,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o] :
( ( quotient @ TB @ TA @ ( bNF_eq_onp @ TB @ A ) @ B @ C @ D )
=> ( A @ ( C @ ( undefined @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ( quotient @ TA @ TB @ ( bNF_eq_onp @ TA @ A ) @ B @ C @ D )
=> ( ( domainp @ TA @ TB @ D )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_eq__onp__to__Domainp) ).
thf(329,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ( quotient @ TA @ TB @ ( bNF_eq_onp @ TA @ A ) @ B @ C @ D )
=> ( ( domainp @ TA @ TB @ D )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(45,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_subset__UNIV) ).
thf(224,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType] :
( ( neg @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA > TB > $o] : ( ord_less_eq @ ( TA > TB > $o ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_NEG__def) ).
thf(188,plain,
! [TA: $tType,TB: $tType] :
( ( neg @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA > TB > $o] : ( ord_less_eq @ ( TA > TB > $o ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( A @ ( C @ E ) @ ( C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Quotient__rep__reflp) ).
thf(169,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( A @ ( C @ E ) @ ( C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(124,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)],[13]) ).
thf(8,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_equalityD1) ).
thf(109,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA,D: TB] :
( ( bNF_Grp @ TA @ TB @ A @ B @ C @ D )
=> ~ ( ( ( B @ C )
= D )
=> ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_GrpE) ).
thf(256,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA,D: TB] :
( ( bNF_Grp @ TA @ TB @ A @ B @ C @ D )
=> ~ ( ( ( B @ C )
= D )
=> ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(70,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_iso__tuple__UNIV__I) ).
thf(298,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_subset__iff) ).
thf(166,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(63,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_UNIV__I) ).
thf(279,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( ( ord_less_eq @ ( TA > TA > $o ) @ A @ ( (=) @ TA ) )
=> ( ( C @ ( B @ E ) )
= E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Quotient__rep__abs__eq) ).
thf(149,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( ( ord_less_eq @ ( TA > TA > $o ) @ A @ ( (=) @ TA ) )
=> ( ( C @ ( B @ E ) )
= E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(36,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(191,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(64,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_subsetI) ).
thf(281,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: $o,D: TB,E: TA] :
( ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
& C )
=> ( C
& ( ( A @ D @ E )
=> ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_predicate2D__conj) ).
thf(204,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: $o,D: TB,E: TA] :
( ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
& C )
=> ( C
& ( ( A @ D @ E )
=> ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(84,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( bNF_eq_onp @ TA @ A @ B @ B )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_eq__onp__same__args) ).
thf(335,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( bNF_eq_onp @ TA @ A @ B @ B )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB] :
( ( domainp @ TB @ TA @ A @ B )
=> ~ ! [C: TA] :
~ ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_DomainpE) ).
thf(181,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB] :
( ( domainp @ TB @ TA @ A @ B )
=> ~ ! [C: TA] :
~ ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(90,axiom,
! [TA: $tType,A: $o,B: $o,C: TA > $o,D: TA] :
( ( A = B )
=> ( ( ( bNF_eq_onp @ TA @ C @ D @ D )
& A )
= ( ( C @ D )
& B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_eq__onp__live__step) ).
thf(350,plain,
! [TA: $tType,A: $o,B: $o,C: TA > $o,D: TA] :
( ( A = B )
=> ( ( ( bNF_eq_onp @ TA @ C @ D @ D )
& A )
= ( ( C @ D )
& B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(9,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_top__set__def) ).
thf(113,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_predicate2I) ).
thf(245,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Collect__mono__iff) ).
thf(98,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ( quotient @ TA @ TB @ ( bNF_eq_onp @ TA @ A ) @ B @ C @ D )
=> ? [E: TA] : ( A @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_type__definition__Quotient__not__empty) ).
thf(345,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ( quotient @ TA @ TB @ ( bNF_eq_onp @ TA @ A ) @ B @ C @ D )
=> ? [E: TA] : ( A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(6,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_subset__antisym) ).
thf(103,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA] :
? [C: TB] : ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Domainp__iff) ).
thf(323,plain,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA] :
? [C: TB] : ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA] :
? [C: TA,D: TB] :
( ( B = C )
& ( A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Domainp_Osimps) ).
thf(240,plain,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA] :
? [C: TA,D: TB] :
( ( B = C )
& ( A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( A @ F @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Quotient__refl2) ).
thf(155,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( A @ F @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( domainp @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Domainp__refl) ).
thf(278,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rev__predicate2D) ).
thf(226,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( A @ E @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Quotient__refl1) ).
thf(267,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( A @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(69,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(295,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Collect__mono) ).
thf(95,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_rev__subsetD) ).
thf(177,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o,C: TA > TB > $o] :
( ( neg @ TA @ TB @ A @ B )
=> ( ( neg @ TA @ TB @ B @ C )
=> ( neg @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_NEG__trans) ).
thf(127,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o,C: TA > TB > $o] :
( ( neg @ TA @ TB @ A @ B )
=> ( ( neg @ TA @ TB @ B @ C )
=> ( neg @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(85,axiom,
! [TA: $tType,A: TA > $o] : ( ord_less_eq @ ( TA > TA > $o ) @ ( bNF_eq_onp @ TA @ A ) @ ( (=) @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_eq__onp__le__eq) ).
thf(338,plain,
! [TA: $tType,A: TA > $o] : ( ord_less_eq @ ( TA > TA > $o ) @ ( bNF_eq_onp @ TA @ A ) @ ( (=) @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( domainp @ TA @ TB @ D )
= ( ^ [E: TA] : ( A @ E @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Quotient__to__Domainp) ).
thf(250,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( domainp @ TA @ TB @ D )
= ( ^ [E: TA] : ( A @ E @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(48,axiom,
! [A: set @ real] :
( ? [B: real] : ( member @ real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member @ real @ C @ A )
=> ( ord_less_eq @ real @ C @ B ) )
=> ? [B: real] :
( ! [C: real] :
( ( member @ real @ C @ A )
=> ( ord_less_eq @ real @ C @ B ) )
& ! [C: real] :
( ! [D: real] :
( ( member @ real @ D @ A )
=> ( ord_less_eq @ real @ D @ C ) )
=> ( ord_less_eq @ real @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_complete__real) ).
thf(231,plain,
! [A: set @ real] :
( ? [B: real] : ( member @ real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member @ real @ C @ A )
=> ( ord_less_eq @ real @ C @ B ) )
=> ? [B: real] :
( ! [C: real] :
( ( member @ real @ C @ A )
=> ( ord_less_eq @ real @ C @ B ) )
& ! [C: real] :
( ! [D: real] :
( ( member @ real @ D @ A )
=> ( ord_less_eq @ real @ D @ C ) )
=> ( ord_less_eq @ real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TA,F: TB] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( ( E
= ( B @ F ) )
=> ( ( C @ E )
= ( C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Quotient__Rep__eq) ).
thf(319,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(34,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_subsetD) ).
thf(186,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(28,axiom,
! [TA: $tType] :
( ( domainp @ TA @ TA @ ( (=) @ TA ) )
= ( top_top @ ( TA > $o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Domain__eq__top) ).
thf(171,plain,
! [TA: $tType] :
( ( domainp @ TA @ TA @ ( (=) @ TA ) )
= ( top_top @ ( TA > $o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_equalityE) ).
thf(139,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(67,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_subsetCE) ).
thf(290,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TB,F: TA,G: TB > TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( E
= ( B @ F ) )
=> ( ( A @ F @ F )
=> ( ( ( C @ E )
= ( G @ E ) )
=> ( A @ ( G @ E ) @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Quotient__rep__abs__fold__unmap) ).
thf(207,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TB,F: TA,G: TB > TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( E
= ( B @ F ) )
=> ( ( A @ F @ F )
=> ( ( ( C @ E )
= ( G @ E ) )
=> ( A @ ( G @ E ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(42,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_top__empty__eq) ).
thf(214,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType] :
( ( pos @ TA @ TB )
= ( ord_less_eq @ ( TA > TB > $o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_POS__def) ).
thf(287,plain,
! [TA: $tType,TB: $tType] :
( ( pos @ TA @ TB )
= ( ord_less_eq @ ( TA > TB > $o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(71,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_set__rev__mp) ).
thf(300,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( quotient @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ! [E: TA,F: TB] :
( ( D @ E @ F )
=> ( ( B @ E )
= F ) )
& ! [E: TB] : ( D @ ( C @ E ) @ E )
& ! [E: TA,F: TA] :
( ( A @ E @ F )
= ( ( D @ E @ ( B @ E ) )
& ( D @ F @ ( B @ F ) )
& ( ( B @ E )
= ( B @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Quotient__alt__def) ).
thf(146,plain,
! [TA: $tType,TB: $tType] :
( ( quotient @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o] :
( ! [E: TA,F: TB] :
( ( D @ E @ F )
=> ( ( B @ E )
= F ) )
& ! [E: TB] : ( D @ ( C @ E ) @ E )
& ! [E: TA,F: TA] :
( ( A @ E @ F )
= ( ( D @ E @ ( B @ E ) )
& ( D @ F @ ( B @ F ) )
& ( ( B @ E )
= ( B @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(33,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_subset__eq) ).
thf(183,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(60,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_set__mp) ).
thf(273,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(73,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_in__mono) ).
thf(305,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(81,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_UNIV__eq__I) ).
thf(326,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( pos @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA > TB > $o] : ( neg @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_POS__NEG) ).
thf(136,plain,
! [TA: $tType,TB: $tType] :
( ( pos @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA > TB > $o] : ( neg @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(87,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( bNF_eq_onp @ TA @ B @ D @ E )
=> ( bNF_eq_onp @ TA @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_eq__onp__mono0) ).
thf(341,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( bNF_eq_onp @ TA @ B @ D @ E )
=> ( bNF_eq_onp @ TA @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(92,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( bNF_eq_onp @ TA @ A @ B @ C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_eq__onp__to__eq) ).
thf(358,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( bNF_eq_onp @ TA @ A @ B @ C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TB,F: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( ( F
= ( B @ E ) )
=> ( D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Quotient__to__transfer) ).
thf(195,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TB > TA > $o,E: TB,F: TA] :
( ( quotient @ TB @ TA @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( ( F
= ( B @ E ) )
=> ( D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1,conjecture,
bNF_eq_onp @ a @ p @ x @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( bNF_eq_onp @ a @ p @ x @ x ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(94,plain,
~ ( bNF_eq_onp @ a @ p @ x @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(83,axiom,
! [TA: $tType] :
( ( bNF_eq_onp @ TA @ ( top_top @ ( TA > $o ) ) )
= ( (=) @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_eq__onp__top__eq__eq) ).
thf(332,plain,
! [TA: $tType] :
( ( bNF_eq_onp @ TA @ ( top_top @ ( TA > $o ) ) )
= ( (=) @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(25,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_top__conj_I1_J) ).
thf(163,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( pos @ TB @ TA @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_POS__apply) ).
thf(122,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( pos @ TB @ TA @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(91,axiom,
! [TA: $tType,A: TA > $o,B: TA > TA > $o,C: TA] :
( ( ( bNF_eq_onp @ TA @ A )
= B )
=> ( ( A @ C )
= ( B @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_eq__onp__eqD) ).
thf(354,plain,
! [TA: $tType,A: TA > $o,B: TA > TA > $o,C: TA] :
( ( ( bNF_eq_onp @ TA @ A )
= B )
=> ( ( A @ C )
= ( B @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( ( A @ E @ E )
& ( A @ F @ F )
& ( ( B @ E )
= ( B @ F ) ) )
= ( A @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Quotient__rel) ).
thf(309,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA > TB > $o,E: TA,F: TA] :
( ( quotient @ TA @ TB @ A @ B @ C @ D )
=> ( ( ( A @ E @ E )
& ( A @ F @ F )
& ( ( B @ E )
= ( B @ F ) ) )
= ( A @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(365,plain,
$false,
inference(e,[status(thm)],[340,157,129,134,194,314,101,347,217,120,269,202,174,320,284,228,179,253,106,221,132,265,312,116,243,307,292,248,302,260,160,275,361,329,224,188,169,124,109,256,298,166,279,149,191,281,204,335,181,350,113,245,98,345,103,323,240,155,278,226,267,295,95,177,127,338,250,231,319,186,171,139,290,207,214,287,300,146,183,273,305,326,136,341,358,195,94,332,163,122,354,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT144^1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 6 11:34:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.90/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.89/1.11 % [INFO] Parsing done (253ms).
% 1.89/1.11 % [INFO] Running in sequential loop mode.
% 2.63/1.32 % [INFO] eprover registered as external prover.
% 2.63/1.32 % [INFO] cvc4 registered as external prover.
% 2.63/1.33 % [INFO] Scanning for conjecture ...
% 2.68/1.41 % [INFO] Found a conjecture and 318 axioms. Running axiom selection ...
% 3.10/1.49 % [INFO] Axiom selection finished. Selected 91 axioms (removed 227 axioms).
% 3.41/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 3.51/1.62 % [INFO] Type checking passed.
% 3.51/1.62 % [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 ...
% 32.16/22.05 % External prover 'e' found a proof!
% 32.16/22.05 % [INFO] Killing All external provers ...
% 32.16/22.05 % Time passed: 21522ms (effective reasoning time: 20929ms)
% 32.16/22.05 % 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)>
% 32.16/22.05 % Axioms used in derivation (91): fact_115_Quotient__to__Domainp, fact_83_UNIV__witness, fact_73_top__set__def, fact_22_Quotient__alt__def2, fact_109_DomainpE, conj_0, fact_90_subsetI, fact_92_set__mp, fact_104_Collect__mono, fact_5_DEADID_Orel__eq__onp, fact_23_Quotient__alt__def3, fact_29_DEADID_Opred__rel, fact_98_equalityD1, fact_28_Quotient__to__transfer, fact_1_eq__onp__mono0, fact_31_predicate2D__conj, fact_24_Quotient__rel__abs2, fact_103_subset__refl, fact_127_POS__def, fact_4_eq__onp__live__step, fact_71_predicate2D, fact_37_predicate2I, fact_128_POS__NEG, fact_12_refl__ge__eq, fact_34_DEADID_Opred__mono__strong, fact_99_equalityD2, fact_125_POS__trans, fact_33_DEADID_Opred__cong__simp, fact_19_Quotient__rel__abs, fact_8_eq__onp__top__eq__eq, fact_46_Collect__mem__eq, fact_18_Quotient__alt__def, fact_11_ge__eq__refl, fact_88_NEG__def, fact_112_Domainp_ODomainI, fact_80_UNIV__I, fact_95_subsetCE, fact_147_GrpI, fact_111_Domainp_Osimps, fact_126_POS__apply, fact_6_eq__onp__le__eq, fact_86_eq__onp__to__Domainp, fact_87_type__definition__Quotient__not__empty__witness, fact_113_Domainp_Oinducts, fact_17_Quotient__abs__rep, fact_27_Quotient__rep__abs__eq, fact_3_eq__onp__same__args, fact_108_Collect__mono__iff, fact_102_rev__subsetD, fact_106_set__eq__subset, fact_26_Quotient__abs__induct, fact_100_set__rev__mp, fact_45_mem__Collect__eq, fact_101_subset__iff, fact_96_equalityE, fact_94_subsetD, fact_105_subset__trans, fact_72_top__empty__eq, fact_9_top__conj_I2_J, fact_110_Domainp_Ocases, fact_119_Domain__eq__top, fact_84_iso__tuple__UNIV__I, fact_47_Collect__cong, fact_230_complete__real, fact_14_Quotient__refl1, fact_146_GrpE, fact_20_Quotient__rel__rep, fact_121_Domainp__iff, fact_114_NEG__trans, fact_124_NEG__POS, fact_7_type__definition__Quotient__not__empty, fact_32_Quotient__rep__abs__fold__unmap, fact_15_Quotient__refl2, fact_144_Grp__mono, fact_21_Quotient__rep__abs, fact_107_contra__subsetD, fact_10_top__conj_I1_J, fact_93_in__mono, fact_30_DEADID_Opred__True, fact_97_subset__eq, fact_25_Quotient__rep__reflp, fact_2_eq__onp__to__eq, fact_36_top1I, fact_13_Quotient__rel, fact_120_Domainp__refl, fact_0_eq__onp__eqD, fact_16_Quotient__Rep__eq, fact_91_subset__antisym, fact_81_UNIV__eq__I, fact_70_rev__predicate2D, fact_82_subset__UNIV
% 32.16/22.05 % No. of inferences in proof: 186
% 32.16/22.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21522 ms resp. 20929 ms w/o parsing
% 32.62/22.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.62/22.13 % [INFO] Killing All external provers ...
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